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COMPUTATION RULES AND LOGARITHMS 
 
•» 
 
 Jl^^m 
 
COMPUTATION RULES 
 
 AND 
 
 LOGARITHMS 
 
 WITH TABLES OF OTHER USEFUL FUNCTIONS 
 
 BY 
 
 SILAS W. HOLMAN 
 
 Peofessob op Physics at the 
 
 MASSAOHnSEITS iHSTITUTB OF TEOmfOLOST 
 
 MACMILLAN AND CO. 
 
 AND LONDON 
 
 1896 
 
 All rights reaevoed 
 
7 i 
 
 /\-%%Q>35' 
 
 Copyright, 1895, 
 By S. W. HOLMAN. 
 
 NottoDoB 33rtZ3 
 
 J. S. Gushing & Co. - Berwick & Smith 
 Norwood Maes. U.S.A. 
 
CONTENTS. 
 
 PAGE 
 
 Peefacb vii 
 
 Computation Kules xi 
 
 Proper Number of Places of Significant Figures xi 
 
 Fundamental Principles xii 
 
 Kules in Detail xiii 
 
 Rejection . . xiii 
 
 Multiplication and Division xiii 
 
 Logarithms xiii 
 
 Addition or Subtraction xiv 
 
 Nujnerical Substitution in FormulaB xiv 
 
 Notation by Powers of Ten xv 
 
 Statement of the Method xv 
 
 Symmetrical Grouping of Figures xvi 
 
 Examples i to ii xvii 
 
 Logarithms. Nature of xxiv 
 
 Tables, Description of xxv 
 
 To Find the Logarithm of a Number xxvii 
 
 Decimal Point in Logarithmic Tables xxix 
 
 Antilogarithms : Number Cokresponding xxx 
 
 Cologarithms .... xxxi 
 
 Habit in Reading off Numbers and Logarithms xxxii 
 
 PovsTERs and Roots by Logarithms xxxiv 
 
 Powers and Roots of Numbers greater than Unity xxxiv 
 
 Powers of Decimal Fractions xxxiv 
 
 Roots of Decimal Fractions xxxv 
 
 Squares and Square Roots xxxvi 
 
 Reciprocals xxxviii 
 
 Natural Sines, Cosines, Tangents, and Cotangents . . xxxviii 
 
 V 
 
VI CONTENTS. 
 
 PAGE 
 
 Logarithms of Sines, Cosines, Tangents, and Cotangents . xxxix 
 
 Slide Wire Ratios xl 
 
 Definitions and Explanations underlying the Computation 
 
 Rules xli 
 
 Significant Figures xli 
 
 Places of I'iguies xli 
 
 Places of Decimals xlii 
 
 Accuracy; Reliability xlii 
 
 Mean ; Average xlii 
 
 Deviation Measure xlii 
 
 Rules for Significant Figures xliii 
 
 Rejection Error xliii 
 
 Law and Amount of Accumulated Rejection Error xliv 
 
 TABLES. 
 
 Logarithms, Four-Place ' 2 
 
 Antilogarithms, Four-Place 4 
 
 COLOGARITHMS, FoUR-PlACE 6 
 
 Logarithms, Five-Place 9 
 
 Square Roots and Squares, Four-Place 30 
 
 Reciprocals, Four-Place 34 
 
 Slide Wire Ratios, Four-Place .36 
 
 Natural Sines and Cosines, Four-Place 38 
 
 Natural Tangents and Cotangents, Four-Place 40 
 
 Logarithms of Sines and Cosines, Four-Place 42 
 
 Logarithms of Tangents and Cotangents, Four-Place ... 44 
 
 Logarithms of Sines, Cosines, Tangents, and Cotangents, 
 
 Five-Place 47 
 
 Constants 70 
 
PREFACE. 
 
 It -would probably be within safe limits to assert that one-half of 
 the time expended in computations is wasted through the use of an 
 excessive number of places of figures, and through failure to employ 
 logarithms. . This waste might be almost wholly avoided by follow- 
 ing a few simple computation rules and practising slightly with 
 logarithm tables. 
 
 The loss from the use of superfluous figures will be appreciated 
 when it is considered that in direct or logarithmic multiplication and 
 division with four, five, and six places of figures the work is respec- 
 tively in the ratio of i : 2 : 3, or perhaps more nearly 2:3:4. Thus 
 contrary to the fallacious excuse so commonly given that it is just 
 about as easy to use six- or seven-place tables as smaller ones,' the 
 work is doubled or trebled by the use of six places instead of four. 
 Even the employment of six- or seven-place tables, and dropping 
 superfluous places when four or five are desired, causes much loss 
 of time. 
 
 The proper employment of logarithms for work of four or more 
 places effects a saving of one-quarter and upward of the time 
 required for direct multiplication or division, with a lessening of 
 fatigue and a gain of accuracy. 
 
 The following pages contain simple rules to enable one to answer 
 for himself the question, how many places of figures ought I to use 
 in this computation ? — also, an explanatioii of the use of the nota- 
 tion by powers of ten; certain instructions, more or less novel in 
 form, as to the use of the logarithm and other tables ; and a collection 
 of useful tables. This collection is designed to contain all the mathe- 
 matical tables ordinarily required, and nothing more, in practical 
 work in all branches of the engineering professions, and by students 
 of physics, chemistry, and engineering, for work of any grade not 
 exceeding about one-twentieth of one per cent in accuracy. For 
 
Vin PKEPACE. 
 
 many persons the present volume should, therefore, provide all the 
 logarithmic and trigonometric tables needed for the entire range of 
 their practice. For work of greater precision than the above limit, 
 the more bulky Vega, or some similar reliable seven-place table 
 would be reqmred. It is exceedingly rare that more than six or 
 seven places are necessary, while for most work five are sufficient, 
 although a striking chapter of absurd illustrations might be gleaned 
 from various text-books and tables where ten- and even twenty-place 
 logarithms are given, often for quantities uncertain in their fourth 
 or fifth place. Person^ doing much work with squares, cubes, square 
 roots, cube roots, or reciprocals of more than four places would natu- 
 rally make use of the Barlow Tables. 
 
 The rules for significant figures (pages xi to xv) are intended to 
 be terse, direct, and simple, so that they may be easily acquired and 
 retained. The strong type emphasizes the leading portions. The 
 ordinary and finer types give details and explanations. Tor the sake 
 of affording still greater prominence to the main working portions, 
 some explanatory matter which will be unnecessary to many per- 
 sons has been transferred from its more logical position of precedence 
 to the latter part of the text. These rules in various forms have 
 been in successful use by large classes of students, in connection 
 with the author's " Physical Laboratory Notes " (printed, but not 
 published, by the Massachusetts Institute of Technology), and his 
 " Precision of Measurements." The recognition of the need of such 
 rules amongst engineers and others whose practical work demands 
 rapid and reliable computations was the cause of their general intro- 
 duction into this laboratory instruction. It is therefore hoped that 
 they may render effective service to others besides the students for 
 whom they have been more directly designed. 
 
 In the arrangement of the tables, the effort has been exerted to 
 make them correct, legible, systematic, and convenient in use. A 
 new set of tables is, of course, liable to contain mistakes ; notices of 
 errata will therefore be thankfully received. 
 
 The special indexing of the corners of pages, the use of heavy 
 type at points to be made conspicuous, the employment of spaces 
 rather than rules for the partition of lines and columns, and the 
 style of type, and kind of paper used, are believed to conduce to 
 legibility. As to system of arrangement, there are few novelties 
 other than the insertion of the logs, cologs, and reciprocals of i .000 
 to 1. 100 at the top of the respective four-place tables, and the division 
 
PEBFACB. IX 
 
 of most of the four-place tables so that the second page begins with 
 5.0 instead of the customary 4.5. The frequent occurrence of cor 
 rection and reduction factors, ranging from i.o to i.i, renders this 
 by far the most frequently used part of the table ; while at the same 
 time, on account of the large tabular differences, interpolation is 
 here the most laborious. The insertion of logs, cologs, and recipro- 
 cals from 1.0 to I.I with increments of o.ooi and o.oooi, respec- 
 tively, in the four- and five-place tables, obviates this interpolation. 
 In tables of antilogs and square roots the addition would be of little 
 service. In the tables of logarithms and of square roots, heavier 
 type has been used at apparently scattered points throughout the 
 body of the tables. These points, in -the five-place logarithm tables, 
 for instance, are where the first two figures in the mantissa change 
 by one unit in the second place, e.g. 00, 01, 02, etc. The obvious 
 service of this is to aid the eye in finding any desired mantissa in 
 working the table backward to obtain the antilog or number corre- 
 sponding. The object is, of course, the same in the other tables. 
 
 As to the wisdom of departing from the usual custom of omitting 
 decimal points entirely from logarithm tables, the author believes 
 that the retention of the point promotes clearness of comprehension 
 of the tables by beginners, and lessens mental effort in more experi- 
 enced computers, especially when associated with the notation by 
 powers of 10, as in the explanations here given. It seems unfortu- 
 nate that this simple notation, so useful in computation and so great 
 an aid in the explanation of numerical relations, is not universally 
 incorporated into arithmetical instruction. 
 
 The rules for the employment of logarithms and of the tables 
 have not been prepared especially to meet the need of those entirely 
 unfamiliar with the principles of logarithms, although they would 
 probably be intelligible to any mature beginner. It is thought, how- 
 ever, that the explanations and instructions given may prove an aid 
 even to those who are already somewhat familiar with the subject. 
 
 RoGBBS Laboratory of Physics, 
 
 Massachusetts Institute of Technology. 
 
 Boston, August, 1895. 
 
COMPUTATIOIN^ EULES. 
 
 o»{o 
 
 PROPER NUMBER OF PLACES OF SIGNIFICANT FIGURES. 
 
 The following three pages contain the rules and their underlying 
 principles in a condensed form for ready reference. For readers to 
 whom some of the terms employed are unfamiliar, or who desire 
 fuller proofs and explanations, some additional pages of " Definitions 
 and Explanations " have been appended. 
 
 These rules should enable a computer to decide at the outset of 
 his work, or at the successive stages of it, what number of places of 
 significant figures he should retain in order to avoid waste of labor 
 on the one hand or sacrifice of accuracy on the other. They provide 
 for a sufficient number of places to assure that (barring mistakes) 
 the accumulated error arising from the rejection of further places 
 shall be always smaller, usually much smaller, than the supposed 
 uncertainty of the data or result, in computations involving not 
 more than about 20 rejections. The retention of more places is 
 worse than useless. It adds nothing to the accuracy of the result, 
 although increasing materially the labor of computing, and the lia- 
 bility to mistake. The aggregate value of the time thus wasted, 
 — obvious enough to any one who has had occasion to perform 
 extended computations, — may be appreciated from the fact that the 
 use of five places where four would suffice, nearly doubles the labor ; 
 using six places instead of four, nearly trebles it ; thus wasting 100 
 and 200 per cent respectively of the necessary amount of work, and 
 probably a greater proportion of time. Moreover, incongruities in 
 the use of places of figures arouse skepticism as to the competence 
 of the worker in other directions. 
 
Xil COMPUTATION EULBS. 
 
 FUNDAMENTAL PRINCIPLES. 
 
 Retain everywhere enough places to correspond to two unreliable 
 places in the final result ; the direct object of this is to keep the first 
 place of unreliable figures in the final result substantially free from the 
 accumulated rejection errors. 
 
 Exceptions. — A final result is seldom stated to more than one 
 uncertain place unless the uncertainty of that place is small (say 
 plus or minus four or less). 
 
 Example : i, page xvi. 
 
 Single direct measurements generally yield numbers extending to 
 only one uncertain place. This should not, however, be taken as a 
 reason for relaxing the application of the above rule to subsequent 
 steps of the computation, especially in deducing the mean or average 
 of several single observations. 
 
 Final zeros occurring in decimal fractions should be retained 
 when any other digit in the same place would be retained. This is 
 of course essential to show that this place is known. 
 
 The foregoing principles consistently carried out constitute en- 
 tirely sufficient rules. But more detailed instructions are usually 
 required at the outset. These are readily understood in view of the 
 two following propositions, which one can easily verify by algebra 
 or by numerical examples. 
 
 Proposition I. — In multiplication or division, the percentage 
 accuracy of the product or quotient cannot exceed that of the factor 
 whose percentage accuracy is least. 
 
 Proposition II. — In addition or subtraction, the result cannot 
 be accurate beyond the first decimal place which is inaccurate in any 
 component. 
 
 A more general form of statement from which these follow is : 
 If several numbers are multiplied or divided, a given percentage 
 error in any one of them will produce the same percentage error 
 in the result. If several numbers are added or subtracted, a given 
 error or change in the digit in any decimal or other place will 
 produce an. equal error or change in the digit in the same decimal 
 place in the result. 
 
COMPUTATION RULES. XUl 
 
 RULES IN DETAIL. 
 
 Eejectioi^. — In casting off places of figures, increase by i the last 
 figure retained when the first left-hand rejected figure is 5 or greater ; 
 otherwise leave it unchanged. 
 
 Example. — If the last two figures are rejected 
 
 756827.9 becomes 756830. 
 
 and 0.00 263 439 becomes 0.00 263 4. 
 
 A MEAN OK AVERAGE should always be carried to two unreliable 
 figures. 
 
 A mean is more reliable than the single observation from which 
 it is computed (in proportion to ^^/n, the square root of the number 
 of observations). Thus, as the data frequently extend to only one 
 unreliable figure, the mean will often have to be carried two places 
 further than the single observation. 
 
 Multiplication or Division. — Ascertain from the object of the 
 work the percentage accuracy desired in the final result ; or, by inspec- 
 tion of the data, find the percentage accuracy of that factor for which 
 this is least, i.e. for which the deviation-measure or the estimated 
 error, expressed as a per cent, is largest. See Example i, page xvii. 
 
 In direct multiplication or division retain in every factor, product, 
 and quotient throughout the entire process, and in final results, for an 
 accuracy of about 
 
 One per cent, or worse, four (4) places of significant figures; 
 
 One-tenth per cent, or worse, five (5) places of significant figures; 
 and so on. 
 
 In the ordinary and the shortened processes of "long multi- 
 plication," it is best to carry out the partial products one place 
 beyond that yielding the last place required in the result under the 
 above rule. 
 
 Examples: 2-5, page xvii. 
 
 Logarithms. — If the multiplication or division is performed by 
 means of logarithms, the mantissa should contain as many places as 
 are required by the foregoing rules for the direct process; i.e. for about 
 
 One per cent, or worse, use four (4) place tables; 
 
 One-tenth per cent, or worse, use five (5) place tables. 
 
 Examples : 2-5, page xvii. 
 
xiv COMPUTATION RULES. 
 
 Addition ob Subtkaction. — Ascertain from the stated object of 
 the work the percentage accuracy desired. If this is about 
 
 One per cent, or worse, carry the result to four (4) places of signifi- 
 cant figures; 
 
 One-tenth per cent, or worse, carry the result to five (5) places of 
 significant figures; and so on, and carry each component quantity to 
 that place of decimals which would correspond to this required place in 
 the result, that is, stand in the same column with that place. 
 
 Examples: 6-8, page xix. 
 
 When the desired acoukacy is not stated, inspect the data 
 to find the component whose first uncertain place is furthest to the left, 
 i.e. whose deviation measure (page xlii), in units, not percentage or 
 fractional, is greatest. Retain this component to two uncertain 
 places, and all other components to the place which would stand in the 
 same column with this second place. 
 
 Examples: 6-8, page xix. 
 
 N. B. — If the number of components approaches 20, care may 
 well be taken in refined work that an unusually large rejection error 
 does not enter through a special combination of rejected figures. 
 The rules are, however, sufficient for the worst possible case. 
 
 The computer should notice that the percentage precision of a 
 result which is the difference of two or more quantities will usually 
 be smaller, and may be much smaller, than that of any of the 
 component quantities. 
 
 Numerical Substitution in Formulae. — A large number of formulae 
 may be represented by the type 
 
 a-b ±c-d± ••• 
 x = - 
 
 p-q ±r-s ± 
 
 where a, b, c, d, etc., represent numbers to be multiplied, divided, 
 added, or subtracted, etc., as indicated. Any one or more of the 
 factors and terms may be wanting ; or, there may be several in place 
 of two ; and so on. 
 
 Obviously, in order that the result x shall be accurate to a speci- 
 fied per cent, both numerator and denominator must be at least of 
 that accuracy, and each should therefore be carried out to the num- 
 ber of places of significant figures needed in x. Then as the numer- 
 ator consists of two or more terms ab and be added or subtracted, 
 
COMPUTATION KULES. XV 
 
 inspection under the foregoing rules for addition or subtraction will 
 show to what decimal place each of these terms must be carried. 
 Further, a and 6 must each be carried to the number of significant 
 figures thus required in the product ab, and so on. 
 
 In complicated formulae this process of inspection is sometimes 
 slightly troublesome, but is essential unless the necessary precision 
 of the components has been otherwise studied ; as, for example, by 
 the simple applications of the differential calculus as in the author's 
 " Precision of Measurements." 
 
 Examples: 9-1 1, page xx. Practical examples of substitution in 
 moderately simple formulae. 
 
 NOTATION BY POWERS OF TEN. 
 
 Statement of the Method. — Eegard the decimal point as merely 
 an affix whose sole purpose is to indicate which is the units' place 
 of figures. Fix the attention firmly upon the units' place as the centre 
 of symmetry of our customary system of notation. The too universal 
 reference to the decimal point, rather than to the units' place, in 
 arithmetical rules and explanations, has resulted in masking this 
 symmetry and in thus depriving the student of its important aid. 
 In oiu: common decimal system of notation, a digit in the units' 
 place represents so many times unity, i.e. so many times 10° (=1), 
 or so many units. In the first place to the left of the units' place 
 the digit represents so many times 10+^, i.e. so many tens, and in the 
 first place to the right, so many times io~', i.e. so many tenths; in 
 the second place to the left so many times 10+^, i.e. hundreds, and to 
 the right so many times io~^, i.e. hundredths; in the sixth places, so 
 many times 10"'"° and io~^, i.e. millions and millionths, respectively; 
 and so on. The fundamental symmetry of the whole system about 
 the units' place is thus obvious, and should not be lost sight of. 
 
 In counting up places, whether to right or left, always begin with 
 the units' place as zero. 
 
 It is clear, then, that we may write numbers in this way : 
 
 for 90 
 
 write 
 
 9-10^; 
 
 for 60G0 
 
 write 
 
 6.ooo'io' or 6" 10^ as the case may require ; 
 
 for 345 
 
 write 
 
 S^S'io''; 
 
 for 0.00 005 
 
 write 
 
 5-10-'; 
 
 for 0.00 468 9 
 
 write 
 
 4.689-10-'; 
 
 for 850.72 
 
 write 
 
 8.507210^ ; and so on. That is, 
 
Xvi COMPUTATION EULES. 
 
 Separate the number into two factors, the first being the original 
 number with the decimal point changed in position so as to follow the 
 first figure; the other being lo-", where the sign is plus for a whole 
 number and minus for a fraction, and where n is the number of places 
 the decimal point has been moved. 
 
 To transform a number expressed in tMs way back into the ordi- 
 nary form, move the decimal point n places, making the number a 
 whole (or a larger) number if n is plus, and a fraction if n is minus. 
 
 Associate firmly in the mind the plus sign with whole numbers, 
 the minus sign with fractions ; thus avoiding confusion as to the 
 sign of n. 
 
 In much work, the factoring need not be written out, but may 
 merely be mental. 
 
 This notation reduces the error and work of locating the decimal point in 
 multiplication or division, especially in expressions containing several terms 
 in the numerator and denominator. It is very helpful in connection with the 
 characteristic of logarithms, and the location of the decimal point in evolution, 
 involution, and finding reciprocals. It saves space and promotes clearness in 
 expressing large numbers or small fractions, and it is the best aid in following 
 the decimal point while using the slide rule. It also enables one to dispense 
 with characteristics in certain parts of computations (see Examples, page xxi). 
 
 An abbreviated notation helpful in one's own work, but perhaps not to be 
 urged for general adoption, consists in dropping the -lo, thus, 
 
 instead of 4.507-102 write merely 4.507^ 
 instead of 5.3704-10-3 write merely 5.3704-3 
 
 The adoption of the bracket or parenthesis, e.g. (4.507)2, for either notation 
 in cases of possible doubt removes all risk of mistaking these indices for ordinary 
 exponents of powers. 
 
 Examples 9, 10, 1 1 give incidentally illustrations of the use of the notation 
 by powers of 10. 
 
 Symmetrical Grouping of Figures. — For writing numbers, adopt 
 the following system of groups and spaces : — 
 
 Write 143 258.64 796 
 
 instead of 143,258.647,96, the usual method. 
 
 A still clearer method would be to write 
 
 143 25864 796 
 
 denoting the units' place by the heavy figure, but this is impracti- 
 cable. The proposed system is symmetrical about the units' place, 
 the customary system is not. It groups together the units, tens, 
 and hundreds of thousandths, of millionths, etc., as well as of thou- 
 
COMPUTATION EULES. XVU 
 
 sands, millions, etc. It is clearer and less liable to error by the 
 substitution of spaces for the commas to mark off the groups 
 Exception is usually to be made in the case of a decimal fraction 
 containing only three or four places. Thus write 0.4612 rather 
 than 0.46 12, and 6.382 rather than 6.38 2. 
 
 EXAMPLES. 
 
 Example 1. — Suppose that a final result was stated as 298549. ± o.io per 
 cent; this would mean that its uncertainty or deviation-measure or estimated 
 measure of accuracy (see page xlii) was ± o.io per cent. To how many places 
 should it be retained? o-i per cent of the number is 0.00 1 x 300000= 300. 
 Therefore the last three places are uncertain, but as the uncertainty in the 
 first left-hand one is small (3) , two uncertain places should be retained. The 
 result, therefore, should be written 298 550. -± o.io per cent. 
 
 Suppose a result given as 47.58 243 5 ± 0-0062- This would be an incorrect 
 
 use of figures. The ± 0.0062 shows that the result is uncertain in the third and 
 
 fourth, and therefore in all subsequent decimal places.* The fifth and sixth 
 
 places of significant figures are thus unreliable, so that the seventh and eighth 
 
 places are entirely valueless, and should, therefore, be rejected. We should 
 
 be at liberty to -use our judgment as to whether the result should then be 
 
 written 
 
 47.58 24 ±0.00 62 or 47.582 ± 0.006, 
 
 since the uncertainty in the fifth place is large. The second is more common 
 practice. In this example the uncertainty is ± 0.0062/47. =± 0.00013, °^ 
 ±0.013 Psr cent. It might, therefore, have been expressed as ± 13 parts in 
 100,000, or ± 0.013 per cent instead of as ± 0.0062 units. It is always expressed 
 in the same unit as the quantity itself, e.g. ft., lbs., etc., except when directly 
 stated to be a percentage. 
 
 Example 2. — Desired with an accuracy of 2 per cent, the volume of a right 
 circular cylinder whose radius r is 6-0428 inches, and length I 12.653 inches- 
 Volume V= irrH. By the rule for multiplication, since the result is desired to 
 worse than one per cent, the data and all steps should be carried to four places 
 of significant figures- Hence, we should have 
 
 V= 3-142 X 6.0432 X 12.65 = I4SI' 
 
 By ordinary multiplication : 
 
 By shortened multiplication : 
 
 6.043 
 6.043 
 I8I29 
 24162 
 
 36258 
 
 3.142 
 36.52 
 6284 
 1 5710 
 
 18852 
 9426 
 1 14.7 
 
 "4-7 
 12.65 
 
 S73S 
 6882 
 
 2294 
 1147 
 
 145 1. 
 
 6.043 
 
 6.043 
 
 36258 
 
 240 
 
 18 
 
 3.142 
 36.52 
 9426 
 18 84 
 
 I SS 
 6 
 
 114.7 
 1265 
 
 "47 
 2294 
 690 
 
 36.52 
 
 36.52 
 
 55 
 
 
 "4-7 
 
 1451- 
 
 * This quantity ± 0.0062, or whatever may be its value, is the " average devia- 
 tion" or the "deviation-measure" of the result; that is, the average amount by 
 which several results similarly obtained would differ from their mean. A fuller 
 explanation is given at page xlii. The " probable error," which is nearly identical 
 with the average deviation, is commonly used in its stead. Either suffices. 
 
XVIU 
 
 COMPUTATION EXILES. 
 
 Observe that the partial products beyond the place standing over the fifth 
 place of the result In each multiplication are useless. Hence the obvious saving 
 of labor in the shortened process, which is also more compact. The process is 
 easily understood by inspection of the example. Multiply first by the first left- 
 hand figure of the multiplier. If the resulting partial product has one more 
 place than is desired in the result, then drop the last figure of the multiplicand 
 when multiplying by the second figure of the multiplier ; drop the last two, when 
 multiplying by the third figure ; and so on. If, however, the first partial product 
 has not the desired number, the dropping of figures must be deferred till the 
 third figure of the multiplier is used. 
 
 Xizample 3. — Desired the volume V=TrH of a right circular cylinder 
 whose dimensions are 
 
 in. in. 
 
 r = 6.0428 ± J per cent, I = 12.653 ± -f^ per cent. 
 
 The result cannot be more accurate than the least precise factor, which is 
 obviously r. Under the rule, I per cent computations call for five places of 
 significant figures. Hence we should have to find by multiplication or by five- 
 place logarithms, 
 
 V= 3.1416 X (6.0428)2 X 12.653. 
 
 Note in this connection that the error in V is proportional to twice the 
 percentage error in r, since r enters in the second power, and that in general 
 where a numberis raised to any power n the percentage error in the result is 
 increased to n times its value in the data. These rules, however, provide suflS- 
 ciently for such cases. See " Definitions and Explanations." 
 
 Example 4. — Desired the volume V = irrH of a right circular cylinder 
 whose dimensions are given as 
 
 r = 6.043 ± 0.017 inches, I = 12.653 ± 0.038 inches. 
 
 Under the general principle of retaining places to correspond to two uncer- 
 tain figures in the result in the data, r should have four places and I five places, 
 judging from their stated precision. But the weaker quantity fixes the number 
 of places in the result, so that we should use but four places : 
 
 F= 3.142 X (6.043)2 X 12.65. 
 
 Ezample 5. — Desired the ratio of the diameter to the length in each of the 
 Examples 2, 3, and 4. 
 
 The number of places of figures to be used would be respectively four, 
 five, and four, just as in the above solutions. A factor in the denominator fol- 
 lows precisely the same rule as to places of significant figures as the one in the 
 numerator. To contrast the ordinary and shortened solutions, the following are 
 given : 
 
 12.65)6.043(0.4777 
 5060 
 9830 
 8855 
 9750 
 8855 
 8950 
 8855 
 
 6.043 
 5060 
 9830 
 
 8855 
 
 975 
 889 
 
 "86 
 
 91 
 
 12.65 
 
 0.4777 
 
COMPUTATION RULES. XIX 
 
 Iizample 6. — Desired the value to 0.6 per cent of 
 
 47-34 89 + 174.32 825 - 5.62 147. 
 
 For o. 1 per cent or worse (page xiv), we must retain places in tlie compo- 
 nents to correspond to five places in the result. By inspection we see that the 
 result will be slightly more than 200. Hence its fifth place will be the second dec- 
 imal place, and we need retain no place beyond that in the components. Thus, 
 
 47-35 
 174-33 
 
 221.68 
 
 -s-62 
 
 216.06 l± an unknown amount as precision-measure]. 
 
 Example 7. — Desired the algebraic sum of 
 
 47'- 34 89 ± 0.0042, i74'.32 825 ± 0.00 089, and — 5'.62 147 ± 0.00 008. 
 
 By inspection the weaker component, that is, the one whose first uncertain 
 place is furthest to the left, is the first number. Retaining this to two uncertain 
 figures would carry it to the fourth decimal place. It will then be useless to 
 retain the other components beyond that place, and we shall have 
 
 47-3489 
 174-3283 
 
 221.67 72 
 -S-621S 
 
 216.0557 [± more than o'.oo 42]. 
 
 Example 8. — Desired the algebraic sum of 
 
 47'. 34 89 ± 0.05 per cent, 174'. 32 825 ± 0.02 per cent, — 5'.62 147 ±0.1 per cent. 
 
 0.05 per cent of 47. is 0.024 i 0-02 per cent of 174. is 0.035 > °- ' P^'^ '^^^^ °^ 
 5.6 is 0.00 56. Hence the weakest component is now the second, and this, and 
 consequently the others, should be retained to three decimal places. Thus, 
 we have 
 
 47-349 
 
 174-328 
 
 221.677 
 
 . —5.621 
 
 216.056 [± more than o'.035]. 
 
 Example 9. — The horse-power, HP, which could safely be transmitted by 
 a wrought-iron shaft of diameter d inches, running at a speed N rotations per 
 minute, the safe shearing load of wrought iron being represented by/, is given 
 by the expression 
 
 ^j,_ 2,r^yjy 
 
 16-I2-3300O 
 
XX COMPUTATION KTJLES. 
 
 [Deduced from Lanza's "Applied Mechanics," page 336. The several con- 
 stants 2, 16, 12, and 33000 would of course be combined into a single constant 
 in a working formula, but they are here left separate for purposes of better 
 illustration.] 
 
 To how many places of significant figures should the quantities, result, and 
 various steps of the computation be carried out to assure against a computation 
 error in the result, sensible as compared to one per cent ? 
 
 Solution. — In this and all similar problems, where the expression consists 
 merely of a number of factors in the numerator and denominator (either or 
 both), without additions or subtractions, the solution of the significant figure 
 problem can be made without any knowledge of the magnitude of the component 
 quantities, such as d, f, y, etc. In this example, as the result is desired to one 
 per cent, according to the rules it should be carried to four places of significant 
 figures. Hence, according to the rule, page xiii, or to Proposition II, page xii, 
 each factor of the whole expression should be carried to four places. In this 
 expression every quantity is a factor, either in the first or a higher power, viz. 2, 
 ir2, d^, /, JV, 16, 12, and 33000. Each, therefore, should he carried to four 
 figures. Hence, also, if direct multiplication be employed in the solution, each 
 product and quotient must be carried to four places. If logarithms are used 
 (they should be) four-place tables should be chosen. When a quantity enters 
 as a factor of the nth power this is equivalent to its entering n times as a simple 
 factor or as n separate factors, all with the same percentage error of the same 
 sign. See also note under example 3. 
 
 The constants 2, 16, 12, and 33000 do not require to be carried to more 
 places than they are here given because they are complete as they stand, that is, 
 all further figures are known to be zero as a matter of definition or mathematical 
 fact. If either of them had been an experimental constant , that is, determined 
 by measurement, it should have been carried out to four places even if the last 
 figure or two were zero. For instance, if experimental, the 16 should have been 
 written 16.0, 16.00, 16.000, and so on according to the number of places to which 
 it was known (see rule, page xii). Failure on the part of those who write such 
 formulse to adhere to this convention, or to indicate in some clear way the 
 degree of accuracy possessed by such constants, is a serious source of annoyance 
 and trouble to those who use them. 
 
 As elsewhere it must not be inferred if certain of the quantities, e.g. d or/, 
 in this expression cannot be carried out to this desired number of figures, that 
 consequently the result will not have the accuracy desired in the given case. 
 The outcome of such a condition would merely be that these factors would be 
 liable to introduce more than a safe computation error. For instance, if /were 
 given as loioo lbs. per square inch, we should have no certainty that it was 
 carried far enough. The presumption would be that it was cori-ect to but three 
 places, and therefore not exact enough. If, however, from a knowledge of tlie 
 subject we were aware that the best known value was loi 10, we should know 
 that the error from using loioo was only i in 1000 or o. i per cent, and hence 
 admissible. On the other hand, if we know that the best value was 10050, we 
 should know that the computation error in tlie result from using loioo was 0.5 
 per cent, and hence by no means safe in the above problem. 
 
 More complete methods for ascertaining the exact accuracy needed in each 
 component measured quantity in such formulae, are given in the author's 
 " Precision of Measurements." It is to be remembered that we are now dealing 
 
COMPUTATION KULES.- 
 
 XXI 
 
 merely with rules for computation errors, and these are not suited to the other 
 problem. They are intended to secure a safe number of places for the worst 
 case, and would, therefore, impose unduly severe requirements as to the accu- 
 racy necessary in the measurement of the components in most cases. 
 
 Numerical Substitution. — The numerical expression to he solved if written 
 out would he 
 
 2-3. 142^- 1. 3642- 10 000-300 
 
 1 6- 12- 33 000 
 2-3.1422-1. 3645- 10^-3-102 . 
 
 in the ordinary notation ; 
 
 i.6-ioi'i.2-ioi-3.3-io* 
 2(3.142)^(1.364)810^-32 
 
 in the notation by powers of 10 (page xv); 
 
 1.61-1.21-3.3* 
 
 in the abbreviated notation by powers of 10 (page xv). 
 
 The first would be worked out in the usual manner by direct multiplica- 
 tion or by logarithms, as shown below. 
 
 The second would be worked as follows : 
 Multiply together the terms other than 10" of the 
 
 numerator, i.e. 2 x 3.1422 x 1.364'^ X 3 = 150.3 
 
 Multiply together the terms other than 10" of the 
 
 denominator, i.e. 1.6 x 1.2 x 3.3 = 6.336 
 
 Divide numerator by denominator = 23.72 
 
 Add together all indices of powers of 10 in numerator, also in denom- 
 inator, and subtract the latter from the former. Or, better, add 
 (algebraically) all the indices, reversing the sign of those in the 
 denominator, thus : 4 + 2 — 1 — 1 — 4 = 0. 
 The result is therefore 23.72'io'' = 23.72 
 
 Note distinctly that all this writing out of the fraction and of the several 
 steps is merely for the purpose of this explanation. In an actual solution such 
 of these operations as are essential to the work would be conducted mentally, 
 the actual multiplication and division alone being written out. 
 
 If the solution were made by logarithms, it might assume either of the two 
 following forms. The first is the usual one, the second shows how the use of 
 the powers of 10 enables us, if we choose, to dispense with writing character- 
 istics in very many places, —a saving of just so much labor. The factor 10" 
 in the second result is, of course, obtained by summing mentally the indices of 
 the factors 10, those in the denominator being taken with reversed sign, as in 
 the preceding paragraph. These indices would not be written out, but taken 
 by direct inspection of the data as originally written. 
 
 Denorainator. 
 
 Usual 
 Method. 
 
 Dropping 
 
 Characteristics. 
 
 Numerator. 
 
 Usual 
 Method. 
 
 Dropping 
 
 Dharacterist 
 
 log 16. 
 
 = 1. 2041 
 
 .2041 
 
 log 2. 
 
 = 0.3010 
 
 .3010 
 
 log 12. 
 
 = 1.0792 
 
 .0792 
 
 2 X log 3.142 
 
 = 0-9944 
 
 -9944 
 
 log 33 000. 
 
 = 4-5185 
 
 •5185 
 
 3 X log 1.364 
 
 = 0.4044 
 
 .4044 
 
 log denom. 
 
 = 6.8018 
 
 .8018 
 
 log 10 000 
 log 300. 
 
 = 4- 
 
 = 2.4771 
 
 ■4771 
 
 
 
 
 Result, 
 
 8.1769 
 6.8018 
 
 2.1769 
 .8018 
 
 
 1-3751 
 23.72 
 
 I-3751 
 23.72-1 
 
XXH COMPUTATION RULES. 
 
 Example 10. — The crushing load of a hollow, cast-iron pillar of circular 
 section, with concentric surfaces of diameters D and d as given by Hodgkiuson 
 (Lanza, "Applied Mechanics," page 332) is 
 
 „ ,r(D2 - (22) 
 
 c = 100 801—^^ -■ 
 
 4 
 
 Desired to ten per cent the load which a pillar of external and internal diame- 
 ters 4.032 inches and 2.16 inches, respectively, would carry. How many places 
 of figures should he used in the computation ? 
 
 Ten per cent results call for three figures in all factors (page xiii). The 
 factors in this expression are 109 801, ir, {D^ — d^), and 4, each of which 
 should therefore be carried to three figures. The first two should therefore be 
 1 10 000 and 3. 14. The 4 is a complete number as it stands. D''—d^=4.d^—2.2^ 
 roughly = 16.0 — 4.8 = 11.2. To have three figures, it should therefore be car- 
 ried to the first decimal place. Then as it is made up of two quantities, one 
 subtracted from the other, each of these should be carried (page xiv) to the 
 decimal place desired in the result, i.e. to the tenths' place. This requires D^ 
 to contain three figures, 16.0, and hence D should contain three figures (since 
 D^ consists of the factors DxD), i.e. should be written 4.03 inches. The require- 
 ment of one decimal place in d^ calls for but two figures, 4.8, and hence two 
 figures, 2.2 inches, in d. The numerical expression to be solved would then be 
 
 3.14(4.032 _ 2.2^) 
 
 c= 1 10 000 -^ ^^^ ^ -, 
 
 4 
 
 which would be most easily worked by a simple slide rule, or by direct multipli- 
 cation. 
 
 Example 11. — Desired to o. i per cent the fraction of dry steam in a 
 sample of steam, using the following observations made with the "Barrus 
 Calorimeter" (Peabody's " Themodynamics of the Steam Engine," page 234), 
 the formula being 
 
 _ TF(g2 -qi)+e- w(q - qs) 
 *- wr 
 
 where 
 
 X = fraction of a mixture which is dry steam . . ... 
 
 JF = weight of cooling water 573 5 lbs. 
 
 w = weight of condensed water 29.89^3. 
 
 t = temperature of steam 
 
 (1 = initial temperature of cooling water 37°-49 ^• 
 
 f2 = final temperature of cooling water 83°.84F. 
 
 <3 = temperature of condensed water 304'^. 88 F. 
 
 qs = "heat of liquid " at t°s, from ig and tables . , . . . . 274.4 
 
 q-i = "heat of liquid" at t°2, from t^ and tables 51.91 B. T. U. 
 
 qi = " heat of liquid " at t°u from ti and tables ... . 5.53 B. T. U. 
 
 5 =" heat of liquid " at «°, from f and tables 287.6 B. T. U. 
 
 e = radiation loss during test 120. B. T. U. 
 
 r = latent heat of steam at 2°, from tables 891.2 B.T.U. 
 
 What number of places of figures should be used throughout ? 
 
 Solution. — For o. i per cent the result, and therefore all factors, should 
 have five places of figures (page xiii). The only factors of the whole expression 
 
COMPUTATION RULES. xxiii 
 
 are the whole numerator, w, and r. They should therefore be carried to five 
 places. Note, however, that w and r are not so given in the data. Whether, 
 however, they are given closely enough must he determined by other means (see 
 remark at foot of page xx). Their product must, however, be carried to five 
 places, and five-place log tables should be employed. The numerator consists of 
 three terms, whose values, roughly, are 
 
 570(52. — 6.)= 2600., 120., and 30(288. — 274.)= 420. 
 . •. numerator = 2600. + 120. — 420. = 2300., roughly. 
 
 To have five places the numerator must be carried to one place of decimals, 
 as also must each of its terms. The first term is composed of two factors, W 
 and (32 — Si), each of which must therefore be carried to five places. Then 
 36 (Z2 — <?i — 52. — 6 = 46. roughly, it must be carried to the third decimal place. 
 Hence q-^ and 51 must each be carried to the third decimal place. The third 
 term, in order to extend to the first decimal place, must contain four figures. 
 It consists of two factors, w and {q — qa), each of which must thus contain four 
 figures. To make the value oi q - qs contain four figures, its numerical value, 
 14, must he carried to the second decimal place. This would require that both 
 q and qs be carried to the second decimal place, or to five figures each. 
 
 To summarize, then, putting in an interrogation point wherever a figure is 
 wanting in the data, we have as the numerical expression to be solved 
 
 573-S ? (51-91 ? - 5-53?)+ I20-? - 29.89( 287.6? - 274.4?) ^^ 
 
 "" - 29.89 ?x 891.2? °-9^^- 
 
 Obviously, then, on inspection, although we might cany out the products 
 W(q2 — qi), io{q — qs), and lor, each to the necessary five figures, much doubt 
 is cast upon the sufficiency of the data themselves to give the desired o.i 
 per cent in the result. The problem would require a detailed study by other 
 tnethods to decide that point, — the result of which, it may be incidentally 
 asserted, would be adverse. 
 
 Note. — It may not be amiss in connection with these problems to call 
 attention to the very large amount of engineering computations in which four, 
 often three (slide rule), places of figures are abundant. In the design of 
 machines and structures, the strength and sizes of parts, such as struts and tie 
 rods, beams, pillars, shafting, etc., and the strains or stresses in them, often can- 
 not, or need not, be fixed upon within an accuracy of one or even many per 
 cent. This limit is fixed by the unreliability of materials or workmanship, or 
 by ignorance of the exact conditions to which the parts may be subjected. Like 
 uncertainties affect many of the data upon which specifications, estimates, and 
 contracts for engineering work are based, and the experimental constants in 
 sundiy formulae. More than three or four places of figures can be indulged in 
 for such work only at an extravagant waste of time. On the other hand it is 
 necessary to discriminate sharply such operations as linear, angular, surface, 
 and sometimes levelling, measurements in surveying and geodetic work where 
 the accuracy may be very high. 
 
LOaARITHMS. 
 
 oXKo 
 
 Before reading the following pages become familiar with the 
 "Notation by Powers of lo," page xv. 
 
 The common or Briggs logarithm of a given number is the expo- 
 nent of that power to which lo must be raised to produce the 
 number. Thus, 3 is the common logarithm of 1000, since 10' = 1000. 
 
 To multiply numbers together, add their logarithms. The sum is 
 the logarithm of the desired product. 
 
 Proof. — The product 10" x 10' X ••• X iC" is io''+'-+'", since 
 powers of the same number may be multiplied together by adding 
 their exponents. Therefore, if ^1=10°, iJ=io', •••, Jf = lo", 
 ^ X -B X ••• X M= io''+'+-+"'. That is, a + & H h m is the log- 
 arithm of ^4 X -B X ••• y. M. But a, b, •■•, m are respectively log^, 
 log B, •■■, log 31. Hence, log (A x B x ■■■ X M) = log J. -|- log B 
 + ■■■ +\o%M. 
 
 To divide one number by another, subtract the logarithm of the 
 latter from that of the former. The difference is the logarithm of 
 the quotient. 
 
 Proof. — Following the foregoing notation, A/B = lo'/io' = 
 10° X 10' = lo""'. Hence log A/B = a—b = log A — log B. 
 
 Logarithm of a number of several figures. — As 1 = 10" and 10 = lo'^, 
 the logarithm of i is o and of 10 is i, and the logarithm of any 
 number greater than o and less than 10, that is, of any number in 
 the units' place (whether or not followed by a decimal fraction) is 
 less than i, that is, it is a fraction. It is expressed as a decimal 
 fraction. 
 
 From the definition of a logarithm it is obvious that the logarithm 
 of any stated power of 10 is the index of the power; i.e. log 10*" 
 = ±n when ±n is any number, whole or fractional, positive or neg- 
 
LOGARITHMS. XXV 
 
 ative. Hence, taking first a specific example, the logarithm of 306.2, 
 being of course the same as the logarithm of its equal, is the same 
 as the logarithm of 3.062-10^ (see "Notation by Powers of 10," page 
 xv), -which is, log 3.062 + log 10^ = .4860 + 2., which is usually 
 written 2.4860. The .4860 is found from tables, as shown later. 
 
 Similarly, log 0.00 306 2 = log 3.062-10"^ = log 3.062 +log io~^ = 
 .4860 — 3., which is usually written either 3.4860 or 7.4860 — 10, as 
 will be further explained. 
 
 The logarithm then consists of, or may be separated into, two 
 parts, viz. first, the decimal part called the mantissa, which is the 
 logarithm of the first factor in the above separation; second, the 
 integral part, or whole number, preceding the decimal point, and 
 called the characteristic or index, which is the logarithm of the 
 second factor 10=*=", and which, therefore, is ±n. 
 
 Tables of logarithms contain the logarithms of the numbers from 
 I. to 10., by steps larger or smaller, and to as many decimal places as 
 may be requisite for the accuracy sought in the work in which they 
 are to be employed. But all numbers whatever, from o to 00, are one 
 of these numbers i. to 10. multiplied by some power of ten, i.e. by 
 ^o-". Tor example. 
 
 4 628 326 = 4.62 832 6-10^, and 0.03 986 = 3.986-10^ 
 
 2 
 
 Hence, the tables enable one, by merely prefixing to the tabular 
 value the proper " characteristic " ± w, to obtain the logarithm of 
 any number whatever, from zero to infinity. The quantity directly 
 given in the table is obviously the mantissa of the desired logarithm, 
 and is therefore always a decimal fraction. 
 
 Since any table gives the mantissa to only a specified number of 
 decimal places, it can represent only a correspondingly restricted 
 number of places of significant figures in the original number. It is 
 to be remembered that a change of one unit in the last decimal place 
 of the mantissa corresponds at all points throughout a table to a 
 constant percentage change (" Definitions and Explanations ") in the 
 number corresponding. The amount of this change is such that it 
 becomes the proper custom to use logarithm tables giving the mantissa 
 to a number of places equal to the number of significant figures re- 
 tained in the original quantities. Thus, if the numbers entering into 
 the computation are properly retained to four places- of significant 
 figures, a four-place logarithm table should be used in connection with 
 them ; if to five significant figures, a five-place table ; and so on. 
 
XXVI LOGARITHMS. 
 
 Four-place logarithm tables contain the logarithms to four decimal 
 places of all numbers of three figures from i.oo to 9.99, and enable 
 one by interpolation to obtain the four-place logarithm of any four- 
 place number from i.ooo to 9.999. By merely prefixing the proper 
 characteristic ± n, therefore, the four-place logarithm of any four- 
 place number from o to 00 is obtained, or, in other words, the four- 
 place logarithm of any number whatever from o to 00 in so far 'as 
 this is governed by the first four significant figures of the number. 
 Four-place tables should not be employed upon work of an accuracy 
 exceeding one-half of one per cent. 
 
 Five-place tables give directly the logarithms to one place further 
 than four-place tables. I.e. to five decimal places, for numbers from 
 1.000 to 9.999, and thence, by interpolation, from i.oooo to 9.9999. 
 Thus, with the proper characteristic, these tables furnish the log- 
 arithms of all five-figure numbers from o to 90, that is, of any num- 
 ber whatever in so far as this is governed by the first five significant 
 figures of the number. Five-place tables should not be employed 
 in work of an accuracy exceeding one-twentieth of one per cent. 
 
 Six-place tables are sometimes arranged with the same steps as 
 five-place, i.e. giving directly the logarithm to six decimal places 
 of numbers from i.ooo to 9.999 only. Such tables are of no prac- 
 tical service ; for it is entirely useless to employ six-place logarithms 
 in work on five-place numbers, and interpolation for six-place num- 
 bers in tables of so large steps as this, besides being less reliable, 
 is more laborious and annoying than is the use of the more bulky 
 tables of smaller steps. 
 
 If six-place tables are desired, it is usual to employ, dropping 
 the last place, tables which give directly seven-place logarithms of 
 numbers from i.oooo to 9.9999 with convenient interpolation tables 
 for the next place. Of these, the Vega tables are among the most 
 convenient, legible, and reliable, being also comparatively inexpen- 
 sive. ■ The seventh place is very rarely demanded by physical, 
 chemical, or engineering work. 
 
 The relative labor in using four, five, and six place tables lies probably 
 between the ratios 1:2:3 and 2:3:4. Assuming the first estimate to hold, 
 the labor is doubled by using a five-place instead of a four-place table, and 
 is increased one-half by using a six instead of a five place table. Hence, as 
 there is no sensible gain from using an excess of places, it is obviously very 
 important to employ a table of the smallest admissible number of places. But, 
 on the other hand, the use of too few places must be guarded against. As an 
 instance of a somewhat dangerous practice may be cited the use of four-place 
 
LOGARITHMS. 
 
 XXVII 
 
 tables in o. i per cent work. This is a not infrequent practice, most common 
 perhaps in chemical computation, and, of course, arising from the exceeding 
 convenience of cards containing four-place logarithms. It will be shown at 
 page xliv, that four places are not sufficient for o. i per cent direct computations, 
 and the error if four-place logarithms are used is sensibly the same. The com- 
 putation error may easily rise to o. 2 or o. 3 per cent with four-place tables even 
 in ordinary computations. 
 
 To Find the Logarithms of a Number. 
 
 Rule. — Regard the number Q as separated into two factors 
 q X 10*", where q begins in the units' place (see " Notation by 
 Powers of 10," page xv). Find in the tables the logarithm of q. 
 This will be the mantissa of the' desired logarithm. Prefix to this 
 the characteristic or index ± n. 
 
 A few examples will sufficiently elucidate the process. 
 
 Iizample. — Desired the logarithm to four decimal places of the number 306. 
 
 Write the number, or, better, merely consider it as if factored in the form 
 3.06-10^. In the four-place table, on the line 3.0 and in the column headed 
 6 will be found .4857, which is log 3.06. Obviously, log lo^ = 2. Therefore 
 log 306. = log 3.06 + log io2 = .4857 -f 2, which is usually written 2.4857. 
 
 Further Bsamples. Interpolation. — Desired to four decimal places the 
 logarithm of 306.2. 
 
 This will lie between the logs of 306 and 307 (and approximately 0.2 of the 
 way), and as the table is not carried out further we must interpolate. 
 
 Difference = .0014, usually written 
 14. 
 
 The desired mantissa will be 0.2 of 
 the way from .4857 to .4871. Hence 
 we must add to the former number 
 0.2-14. = 3- 
 
 The interpolation may always be made by subtracting and multi- 
 plying as in this example, but to save the labor, logarithm tables 
 are usually provided with marginal interpolation tables, by the aid 
 of which interpolations may easily be made mentally. 
 
 Thus in taking out log 3.062 we find log 3.06 = .4857- By inspection, differ- 
 ence = 14. In the interpolation table headed 14, line 2, stands 3, which is there- 
 fore the desired 0.2 of 14. Therefore log 3.062 = .4860. This operation could, 
 of course, be carried otit mentally. 
 
 The present tables are arranged so that the interpolation tables stand oppo- 
 site, or nearly so, to the logarithms to which they correspond. This not only 
 gives them a convenient location but enables the computer usually to avoid 
 even the mental subtraction of the successive logarithms to find the difference, 
 since this will, of course, be that at the bead of the nearest difference table. 
 Usually also the error introduced by using an interpolation table slightly too 
 large or too small is negligible. 
 
 For 3.07 we find .4871 
 
 For 3.06 we find -4857 
 
 Interpolation, 0:2 of 14 = 2.8 = 3 
 
 . •. log 3.062 = .4860 
 log 306.2 = log 3.062 -I- log 10^ = 2.4860 
 
xxviii LOGARITHMS. 
 
 Interpolation becomes more laborious and more liable to error, 
 if conducted mentally, in proportion as the difference is large. It 
 is therefore greatest in the first quarter of any logarithm table. But 
 it happens that in physical, chemical, and engineering computations 
 there very often enter correction or reduction factors and other 
 terms of the form (i + a) or i/(i — a), where a is a decimal frac- 
 tion rarely as large as o.i. The frequency of such terms calls for 
 a disproportionately large number of the more laborious interpola- 
 tions. To avoid this labor and increased chance of error, the excel- 
 lent practice has been adopted in some five-place tables of inserting 
 two pages giving the logarithms from i.o to i.i, by steps only one- 
 tenth as large as in the rest of the tables, thus doing away with 
 all interpolation in this most used and most troublesome portion 
 of the table, without adding seriously to its bulk. Such a table 
 has here been prefixed to the five-place table. In the four-place 
 table the same result has been accomplished here, in a manner which 
 is perhaps novel, by the insertion of ten additional lines at the head 
 of the table. The Vega seven-place tables unfortunately lack this 
 feature. 
 
 To find Logarithm of a Decimal Fraction. — The procedure is 
 precisely the same as for a whole number. Note that the log- 
 arithm of a decimal fraction is always negative, and, conversely, 
 that a negative characteristic always denotes a decimal fraction. 
 
 Example. — Desired the log of o.oo 306 2. 
 
 log 0.00 306 2 = log 3.o62TO~' 
 
 log 3.07 = .4871 
 
 3.06 = .4857 
 
 o. 2 of difference = 3 
 
 . •. log 3.062 = .4860 
 
 log 10-3 = - 3. 
 
 . •. log 0.00 306 2 = .4857 — 3. 
 
 This is written eitiier 3.4857 or 7.4857 — 10. The latter form is ohtalned by 
 adding 10 to the characteristic and appending — 10 to the whole. The num- 
 bers thus appended must in many instances, but not in all, be followed up in 
 the computation in order to correctly locate the decimal point at the ■ close. 
 This is, however, usually very little trouble. The second method is the very 
 general practice find is based on the assertion that when several logarithms are 
 to be added, it is more convenient to have all the characteristics positive. The 
 author is, however, of the opinion that this conventional method serves almost 
 no useful purpose, and that it is better and less troublesome in every way to 
 retain the negative characteristic. It is almost as easy to add a column of num- 
 bers in which some are negative, and are therefore subtracted when they are 
 
 Difference = 14. 
 
LOGAKITHMS. XXIX 
 
 reached instead of being added, as to add a column in which all are positive. 
 And if the negative characteristic is retained, all care and writing of — lo or 
 its multiples is avoided. Moreover, the logarithm is complete in itself and 
 shows at once that it is the log of a decimal fraction. These remarks apply not 
 only to the logarithms of ordinary numbers but to the logarithms of the trigono- 
 metric functions. 
 
 Example of addition where some of the characteristics are negative. Places 
 beyond the first of the mantissa are not added in this illustration. 
 
 2.4036 Beginning at the bottom of the columns we have 
 
 T.2168 5 + 3 = 8 + 2 = 10 + 4 = 14, write 4 ; 
 
 1-3462 carry 1 + 2 = 1+ I = + 1=1 + 2 = 1. 
 
 ^•^"^ Of course the figures printed in heavy type are the only ones pro- 
 
 1.4 nounced or mentally enforced. 
 
 Ezamples of some cases where the use of the notation by powers of 10 
 enable one to dispense with the characteristic in portions of computations are 
 given incidentally at page xxi. 
 
 Grouping by Fives in the Tables. — Throughout the entire set 
 of tables, it will be observed, the columns and lines are arranged in 
 groups of five. This not only aids the eye to readily follow any 
 desired line or column, but enables the computer with a little prac- 
 tice to enter a desired column or line without glancing at the num- 
 ber at the top of the column or side of the line, and similarly to read 
 off the nvmiber of column cr line without glancing off to the marginal 
 figure. Thus the middle column in the second group is 7, the last 
 in the first group is 4, and so on. The practice of working by 
 observed position rather than by the marginal number should be 
 pursued. It reduces fatigue and tends to prevent mistakes. 
 
 Indexing at Corners of Tables. — The bold type at the outer cor- 
 ners of the tables shows the contents of the page and its opposite. 
 Thus on the sixth page of the five-place log table, the larger black 
 figure 2 shows that these two pages contain the logs of all the num- 
 bers beginning with 2. The smaller black figures, 30, 47, in the 
 margin show that the mantissae on the two pages extend from 30 to 
 47 (first two figures). The indexing will be found a material help 
 in rapidly running the page corners under the finger torfind either a 
 desired table or a desired figure in a table. 
 
 Decimal Point in Logarithm Tables. — It is the almost universal 
 custom to omit the decimal point entirely from logarithm tables. 
 This tends toward compactness, but is by no means essential on that 
 score. The omission causes no serious inconvenience after slight 
 
ixx' LOGARITHMS. 
 
 practice. On the other hand, the retention of the point renders the 
 table complete and strictly self -consistent ; that is, any mantissa in 
 the table is then the completely expressed logarithm of the cor- 
 responding tabular number. This fact tends materially toward clear 
 comprehension on the part of the beginner or occasional computer. 
 The table is also then perfectly assimilated to the "Notaltion by 
 Powers of lo," page xv, which affords not only the clearest basis of 
 explanation of mantissa and characteristic, but by far the easiest 
 method of obtaining and following the characteristic in computations. 
 The points do not add necessarily to the bulk of the tables and are 
 no hindrance to their use by computers accustomed to other rules 
 than those here given respecting the characteristic. They are 
 therefore retained in these tables. 
 
 Antilogarithm = Number Corresponding. — Given the logarithm to 
 find the "number corresponding," i.e. the number of which this is 
 the logarithm. This number is also called the " antilogarithm." 
 
 From the Log Tables. — 
 
 Ilzample. — To And the antilog of 2.4857, inspect the body of the four-place 
 log table to find the mantissa .4857 (or the next smaller than this if the exact 
 value does not appear). It will be found to lie on line 3.0 and in column 6, and 
 Is, hence, the log of 3.06. The characteristic 2 is the log of lo^. 
 .•. antilog 2.4857 = 3.o6-io2 or 306. 
 
 Example. — To find the antilog of 2.4860. In the table this mantissa does 
 not appear exactly, but the next smaller is .4857, whose antilog is 3.06, and the 
 difference from this to the next larger is 14. 
 
 .4860 - .4857 = 3, and t'j = .2, 
 .". antilog .4860 is -j^ or 0.2 of the way from 3.06 to 3.07, 
 .•. antilog .4860 = 3.062, 
 also antilog 2. := lo^, 
 
 .'. antilog 2.4860 = 3.062-10^ or 306.2. 
 
 The interpolation can be mentally made by the marginal interpolation tables. 
 The tabular difference is 14, and it is desired to know what decimal fraction the 
 difference 3 is of this. Looking down the column under 14 for the number 
 nearest to 3 it is found to be 3 and to stand opposite to 2. .'. 3 is 0.2 of 14, and 
 antilog .4860 = 3.062. 
 
 It will be noticed that in the four-place and five-place log tables 
 those mantissse have been printed in heavier type in which the first 
 figure changes from one digit to the next. This serves as a guide 
 to the eye in looking for any desired mantissa whose antilog is sought. 
 
 From Tables of Antilogarithms. — Some computers prefer to employ 
 a special table for antilogarithms instead of working backward in 
 the ordinary logarithm table as in the preceding example. Whether 
 
LOGARITHMS. XXxi 
 
 the small saving in time effected by this means is an equivalent 
 to the slight additional mental effort incident to the employment in 
 alternation of tables differently arranged, may be questioned. Where 
 many antilogs are to be taken out in succession, the gain is, however, 
 sensible. 
 
 Ksample. — To find by the table of Antilogarithms the antilog 2.4857. 
 
 Taking the mantissa first, we find on line .48, column 5, the next smaller 
 number 3.055 with a tabular difference of 7. Hence, antilog .485 = 3.055. But 
 antilog .4857 will be 0.7 of the way from that of .485 to .486. The amount to be 
 added then for interpolation is o. 7 x 7 = 5. 
 
 antilog .4857 = 3.055 + 0.005 = 3-o6o, 
 antilog 2.4857 = 3.060-102 =306.0. 
 
 Interpolation tables are provided whose method of use is sufficiently 
 obvious. 
 
 Cologarithms = Logarithms of Reciprocals. — The colog of any 
 number jp is the- logarithm of the reciprocal of the number. 
 
 It is therefore log i — logp = o — logj9. 
 
 In substitution in ,a formula such as x = "•"•" ^ which is the product of 
 
 several numbers (one or more) divided by the product of several others (one or 
 more), the direct process would be to take the sum of the logarithms of the 
 factors in the numerator, and to subtract from this the sum of the logs of the 
 factors in the denominator. 
 
 Example. — log a = i. 2543 log = 3. 8642 
 
 l0g6 =3.8766 log(i = 5.2I2I 
 
 loge = 2.1345 
 
 Numerator sum = 1. 1309 Denominator sum = 1.2108 
 
 Subtract denominator sum= 1.2108 
 
 Difference = 3.9201 
 a; = number corresponding = 8.320'io"', or 0.008320. 
 
 This process may be simplified by employing the colog. It then becomes 
 
 logos =1.2543 
 
 log 6 = 3.8766 
 colog c =4.1358 
 colog (^ = 4.7879 
 colog e =3.8655 
 
 Sum = 3.9201 
 X = number corresponding = 8.320-10-3 
 
 This process is thus reduced to the simple addition of a series of numbers. 
 
 The colog may be easily taken out of the usual log table by 
 merely looking out the logarithm and subtracting mentally from o. 
 
XXXll 
 
 LOGARITHMS. 
 
 Example. — Desired the colog of 306.2. Log 306.2 = 2.4860, colog = 3.5140. 
 
 The use of cologs either with or without a table effects but small saving, 
 except in case a series of substitutions in a given formula are to be made, so 
 that a number of cologs may be looked out in immediate succession. 
 
 Table of Cologs. — The table of four-place cologarithms is arranged 
 similarly in every respect to the table of four-place logarithms, and 
 the cologs are taken from it just as logs from their table; noting, 
 however, that the cologs in the table have the characteristic i, and 
 that the differences are subtractive. 
 
 Example. — Desired the colog of 306.2. 
 
 In line 3.0, column 6, colog 3.06 
 0.2 X (— 14) by difference table 
 
 .-. colog 3.062 
 colog 10* 
 
 Separate into 3.o62-io2. 
 
 = 1-5143 
 = -3 
 
 Difference from 
 colog 3. 07 is — 14. 
 
 = 1^.5140 
 = 2. 
 
 colog 306.2 = colog 3.062- + colog io2 = 3-5140 
 
 Example. — Desired the colog of 0.00 713 6. 
 
 In line 7.1, column 3, is colog 7.13 = 
 
 0.6 (— 6) by difference table z 
 
 colog 7. 1 36 = 
 
 colog 10^3 = 
 
 colog 0.00 713 6 = colog 7.136 -f- colog IO~3= 
 
 1. 1469 
 
 7.1465 
 
 + 3- 
 2.1465 
 
 Difference is — 6. 
 
 Habit in Reading off Numbers or Logarithms. — Time can be econ- 
 omized, strain on the attention reduced, and liability to mistake 
 lessened by an easily acquired habit of grouping and emphasizing 
 the figures in reading off the numbers, the mantissa, and the num- 
 bers corresponding (antilogs) in using tables. 
 
 A good method of reading is as follows : 
 
 In reading a number or antilog pay no regard to the decimal 
 point. Emphasize the first figure; pause, read second and third 
 figures; pause, read remaining figures in groups of three. Thus: 
 Desired the log of 30.62 047 2. Read this as 3 06 204 72, i.e. three 
 . . . naught six . . . two naught four . . . seven two. 
 
 In reading off a mantissa use no emphasis, but group the first 
 two figures together, and the subsequent figures by threes. Thus, the 
 mantissa .4869 would be read as 48 69, i.e. forty-eight . . . sixty- 
 nine; and .48601 as 48 601, i.e. forty-eight . . . six naught one. 
 
 In taking from the log table the numbers corresponding (antilog) 
 to .48601, it would be read 306 2, three . . . naught six . . . two, 
 precisely as under the above rule for reading a number. 
 
LOGARITHMS. XXXlii 
 
 These rules apply equally well to four or five place tables. In 
 tables of six or seven places the first three figures of the mantissa 
 are grouped together in printing, and are therefore more conveniently 
 read oS together. Also, it is more convenient to read off six-place 
 numbers and antilogs with three figures instead of two in the second 
 group ; thus, 7 814 62. 
 
 The difierence between a number and a mantissa thus read off, whether 
 audibly or mentally, almost precludes the possibility of mistaking one for the 
 other, so that less strict attention will be required to avoid entering the number 
 column of a table with a mantissa, or vice versa. It also avoids the mental or 
 verbal employment of words of instruction. Thus, if a computer reads off 7 82 
 he knows, or his assistant using the log tables knows, as soon as the first figure 
 has been read that the logarithm of the number is desired. Conversely, if 
 he reads off 43 857, the first two figures alone show that the quantity is a man- 
 tissa, and that the antilog is required. Thus, no words of instruction need be 
 used throughout an entire computation, and yet no possibility of error need 
 enter. 
 
 It is also to be noted that this grouping is consistent with the symmetrical 
 grouping advocated at an earlier page ; adapts itself perfectly to the employment 
 of the notation by powers of 10 ; and coincides with the most convenient group- 
 ing in the flve-place tables. 
 
 Powers and Roots by Logarithms. — If a = lo" (so that m = log a) 
 then (a)" = (lo")" and log («■")= n log a. Here both m and n may 
 be either positive or negative, and either an integer or a fraction. 
 
 Hence, to raise any number, whole or fractional, to any power, 
 integral or fractional, and positive or negative, multiply the logarithm 
 of the number by the exponent of the power of the number. 
 
 Since a root is a fractional power, i.e. y« = ^s, the above rule 
 includes the extraction of a root. In the case of decimal fractions 
 the fact that the characteristic is negative while the mantissa is pos- 
 itive, must be regarded. The correct result will be assured if the 
 mantissa and characteristic are separately multiplied (or divided) 
 by the exponent, and the latter result then subtracted from the for- 
 mer, as will be further shown. Certain special procedures will also 
 be described. 
 
 The one exception to this is where the index of the power is a single figure 
 and positive. This case takes care of Itself without special attention. 
 
 It may seem that the use of the negative characteristic thus increases labor 
 over the usual notation explained at the foot of page xxviii. Inspection of 
 examples will show that the only case in which it does so is where the index of 
 the power or root is other than a single digit. 
 
XXxiv LOGAKITHMS. 
 
 Powers and Roots of Numbers greater than Unity. — 
 Examples. 
 
 Desired the cube of 
 
 47.16,1.6.(47.16)'. 
 
 log 47.16 
 Multiply by 
 
 = 1.673s 
 3 
 
 log a; 
 
 = 5.0205 .•. a; = i.048'ic 
 
 Desired \/47i.6. 
 
 
 log47i.6 
 Divide by 
 
 = 2.6735 
 5 
 
 log a; 
 
 = 0.5347 .-. a; =3.425, 
 
 Ezample. — Desired the 2.416 power of 65 830. 
 
 log 65 830. = 4.8184 
 
 Multiply by 2.416 
 
 96368 
 I 92736 
 
 4818 
 
 2892 
 
 .-.log (65 830)2-«« =11.6413 
 
 (65 83o)2«6 _ 4.378 • 10" = 437800000000. 
 
 To avoid the direct multiplication of the logarithm by the index of power, 
 when this contains several figures, their logs may be taken. Thus 
 
 (S pi. logs.) (4 pi. logs.) 
 
 log log 65 830 = log 4.8184 = 0.68291 0.6829 
 
 log 2.416 = 0.38310 0.3831 
 
 loglog (65 83o)2-^i«= 1.06601 1.0660 
 
 antilog 1.06 601 = log (65 83o)"'6 = 11.641 11.64 
 
 .-. (65830)2116= 4.376-1011 4.365-1011. 
 
 When the log of a log is thus taken, a table giving at least one 
 place more in the mantissa should be used than would be otherwise 
 needed in order to protect the last place of figures in the result, as 
 is shown in the above example, which is by no means an extreme 
 case. If the quantity is a decimal fraction, the negative character- 
 istic must be separately treated and the result subtracted from the 
 result obtained with the mantissa. 
 
 Powers of Decimal Fractions. — Here it is necessary to notice that 
 the logarithm of a decimal fraction is composed of two parts, one 
 positive the other negative. Thus, 
 
 logo.o6 831 = 2.8345 or 8.8345-10., 
 according to the notation chosen. In the first form (the one here 
 recommended) the logarithm consists of a negative characteristic 
 
LOGARITHMS. XXXV 
 
 and a positive mantissa ; in the second form it consists of a positive 
 logarithm (both characteristic and mantissa) followed by a negative 
 characteristic. 
 
 No new procedure is necessary, but it is essential to be consistent 
 as to sign of each part, and to remember that both parts must be 
 subjected to any operation performed upon either. Whenever the 
 exponent has more than one figure, the negative characteristic and 
 the positive mantissa should be separately multiplied by the index, 
 and the former subtracted from the latter. 
 
 Example. — Desired (0.004716)*. 
 
 logo.oo 4716 = 3.6735 or 7.6735-10 
 
 Multiply by 4 4 
 
 10.6940 or 30.6940 — 40, or 0.6940 — 10 
 
 .-. (0.004716)* = number corresponding, or antilog, 
 = 4.943.io~w or 0.00 000 000 049 43. 
 
 Example. — Desired (p.oo 4^16)*-^^. 
 
 logo.00 4716 =3.6735 or 
 4-32 
 
 7.6735 - 10 
 4-32 4-32 
 
 26940 
 20215 
 1348 
 
 306940- 43.2 
 230205 
 15348 
 
 2.9095 
 — 12.96 
 
 33-14953 
 -43-2 
 
 17.9495 
 
 1T.949S 
 
 (o.oo47i6)'*-32 = 2.962'io~ii. 
 
 
 Roots of Decimal Fractions. — To extract the root of a decimal 
 fraction, divide separately the negative characteristic and the posi- 
 tive mantissa by the index of the desired root. Subtract the former 
 quotient from the latter. The difference will be the logarithm of 
 the desired root. In other words, treat the characteristic separate 
 from the logarithm. This procedure is always the safest to adopt 
 when there is any doubt in the mind of the computer. 
 
 Example. — Desired Vo.oe 831. 
 
 log 0.06 831 = 2.8345 
 
 Dividing characteristic by 3 = — 0.6667 
 
 Dividing mantissa by 3=0. 2782 
 
 .. log V0.06831 = 1.6115 
 v'o.oe 831 = number corresponding — 4.088-10-1. 
 
XXXvi SQUARES AND SQUARE BOOTS. 
 
 A method easily understood by inspection is this : Add to the neg- 
 ative characteristic of the logarithm a number equal to mr where r 
 is the index of the desired root and m is a whole number large 
 enough to make mr larger than or equal to the characteristic, in 
 other words, large enough to extinguish the negative sign of the 
 characteristic. Write this number with- a negative sign after the 
 logarithm. Then divide the whole by the index r. The quotient 
 will be the logarithm of the desired root. Usually m = i, i.e. 
 
 Example. — Desired \/o.o6 83i- 
 log 0.06 831 = 2.8345, adding and subtracting 3 gives 1-8345 ~ 3 
 
 dividing by 3 gives 0.6115 — i = 1.6115 
 .*. ■\/o.o5 831 ="number corresponding = 4.o88'io-i or 0.4088. 
 
 SQUARES AND SQUARE ROOTS. 
 
 It is common to give separate tables of squares and- of square 
 roots by which, respectively, the square or square root of any num- 
 ber may be taken out. Inspection, however, shows that the four- 
 place table of square roots must occupy four pages, the first two 
 containing the numbers from i.o to 10., the second two from 10. to 
 100. ; the corresponding roots ranging from i. to 10. ; while a table of 
 squares would occupy but two pages, containing numbers from i.o to 
 10., the squares ranging from i. to 100. Hence the tabular diifer- 
 ences in the table of square roots will be much smaller than in the 
 table of squares. For this reason the table of squares may advan- 
 tageously be dispensed with, and squares be taken out when desired 
 from the table of square roots, as the numbers corresponding (anti- 
 logarithms) are taken out of a table of logarithms. The smallness 
 of the differences makes interpolation easier and more rapid than in 
 a table of squares, and this more than offsets the slight disadvan- 
 tage of the reverse process of interpolation. The tables at page 30 
 give square roots to four places. As in the logarithm tables, the 
 numbers in the body of the table are printed in stronger type wher- ' 
 ever the second figure changes, in order to assist the eye in the 
 reverse use of the table. 
 
 In the table of square roots the insertion of the extra section giving i.oo to 
 1. 10 to form places direct to avoid interpolation is not called for as in logarithms 
 because the interpolation is very easy, and because the squares of terms of the 
 form (i -^ a) are not frequently required. 
 
SQUARES AND SQUARE ROOTS. XXXVll 
 
 To find the square of any number, factor the number as described 
 in the "Notation by Powers of lo," page xv. Enter the body of 
 the table with the first factor, and find the corresponding marginal 
 reading and column heading which will be the first three figures 
 of the square. Interpolate for the fourth figure. Square the 
 factor lo*", which makes it io±^" Multiply together these two 
 squares. 
 
 Example. — Desired the square of 34 850. 
 
 34 850.2 =(3.485-101)2= 3.4852- I02X^. 
 
 In the table 3.479 (the next smallest value to 3485) stands in line 12, col- 
 umn I. The tabular difference is 14, of which our difference ( = 3.485 — 3.479=6) 
 is y\, or 0.4 (as may be seen at once from the interpolation table headed 14). 
 
 Hence 34850.2 = 12. 14-108= 121 400000. 
 
 Example. — Desired (0.00049 83)2. • 
 
 (0.0004981)2 = 4.98i2-io-*x2 = 24.83-io"8 = 0.00000024 83. 
 
 To find the square root of any number, factor it as in the " Nota- 
 tion by Powers of 10," page xv, except that n must be no-sv an even 
 number, -while the first factor must have either one or two digits pre- 
 ceding the decimal point, whichever may be necessary, in order to 
 permit n to be made even. 
 
 Find, then, from the table, interpolating if necessary, the square 
 root of the finst factor, and multiply this by 10-"^^, the square root 
 of the second factor ; the product is the desired square root. 
 
 Example. — Desired the square root of 347.6. 
 (347.6)i=(3.476-io2)i 
 
 In the table, line 3.4, column 7, gives (3.47)2 = 1.863 
 Interpolations by table gives 0.6 difference = i 
 
 (3.476)^=7^86^ 
 
 .. (347.6)^= 1. 864-ioi= 18.64. 
 
 Example. — Desired ■v/875 200. 
 
 V87.S2-I0* = 9-355''o^ = 93S-S- 
 
 Example. — Desired (0.05643) ?. 
 
 (5.643-10-2)7 = 2.376-10-1 = 0.2376. 
 
 Example. — Desired 0.00 006 784. 
 
 67.84- io"« = 8.236-10-3 = 0.008236. 
 
XXXviii KECIPKOCALS. 
 
 RECIPROCALS. 
 
 This table, page 34, contains tlie reciprocals to four places of 
 numbers from i. to 9.99, and by iaterpolation from i. to 9.999. The 
 reciprocal to four places of any number from zero to infinity is, 
 of course, one of these tabular values multiplied by a suitable 
 power of 10. In this table, the reciprocals of numbers from i. to 
 1. 1 00 are given directly in the first ten lines to avoid interpolation 
 in finding the reciprocals of terms of the form (i + a), where a is 
 
 a small decimal fraction. 
 
 * 
 
 N.B. — The approximation 1/(1 +a) = (i —a) approx., is frequently em- 
 ployed in computations to avoid dividing by (i + a). This useful approxima- 
 tion, however, must he used with caution. The error from its employment is 
 a^ ; that is, if a = o.i, the error from multiplying by (i — a) instead of divid- 
 ing by (i 4- a) is 0.12 = 0.01, or i per cent; if = 0.03, the error is 0.03^ 
 = 0.0009, 01' nearly o. i per cent, and so on. 
 
 To find the reciprocal of a number, factor it by the " Notation by 
 Powers of 10," page xv.' Find the reciprocal of the first factor by 
 the table and multiply this by the second factor 10=*=" with the alge- 
 braic sign of its exponent reversed, i.e. by lo'f". 
 
 Example. — Desired 1/4486,1.6: (4486) ~i. 
 
 (4486.)-! =(4.486- io8)-i =(4.486.)-i-io-3. 
 In table, line 4.4, col. 8, (4.48)-! = 0.2232 
 
 By difference table, 0.6 difference = — 3 
 
 Reciprocal of 4.486 = 0.2229 
 
 (4486.)-! = (4.486)~i-io-8 = 0.2229-IO"' = 0.0002229. 
 
 Example. — Desired i/o.oo 327 5. 
 
 (0.00 327 S)-i =(3.275)-i-(io-8)-i = o.3os4-io» = 305.4. 
 
 NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 
 
 It is frequently convenient to have a table giving rough values 
 of the natural trigonometric functions for use in preliminary, check, 
 or approximate computations. The four-place tables of the above 
 four functions cover all ordinary needs. Interpolation can be 
 made in these tables to o°.oi by the interpolation tables, or to i' 
 by mental computation, since the step between successive columns is 
 o°.i, or 6'. 
 
TEIGONOMETEIC FUNCTIONS. XXXIX 
 
 Example. — Desired the natural sine of 37°. 75. 
 
 On line 37° under heading °.'] is 0.61 15. To interpolate for the remaining 
 figure we must add o.j of the tabular difference, which, by inspection, is 14. 
 0.5 X 14 = 7, as can be seen at once in the interpolation table 14 opposite the 
 line 37°. 
 
 .-. sin 37°.75 =0.6115 + .0007 =0.6122. 
 
 Example. — Desired the natural cotangent of 72°. 28. 
 
 The cosines and cotangents read upward in the right-hand degree column. 
 
 Line 72°, column °.2, gives 0.321 1 
 
 0.8 of difference (19), to be subtracted, — 15 
 
 .•. natural cotangent 72°.28 =0.3196 
 
 All of the tables are used similarly. 
 
 LOGARITHMS OF SINES, COSINES, TANGENTS, AND COTANGENTS. 
 
 Two sets of tables are given, four-place and five-place, respec- 
 tively. The four-place tables read to tenths and hundredths of 
 degrees, and are convenient for general rough work and with instru- 
 ments reading to tenths of a degree. The five-place tables give 
 values to minutes direct. They are adapted to a very large part of 
 the angular measurements ordinarily made in experimental work. 
 Interpolation to half or quarter minutes is easily made in them 
 mentally. A computer working closer than that would naturally 
 employ the Vega, or other conveniently arranged six- or seven-place 
 tables, dropping unnecessary places. 
 
 For the reasons stated under the discussion of logarithm tables, 
 page xxviii, the negative characteristic is here retained instead of the 
 more customary 9, with the appended — 10. 
 
 The use of the tables needs little explanation. The four-place 
 tables are used precisely as the tables of the natural functions. In 
 the five-place tables, for less than 45", read the tables downwards, 
 using the minute column at the left hand. Tor angles greater than 
 45°, read the tables upwards, using the minute column at the right 
 hand of the table, and take care to employ the column-headings 
 given at the foot of the table. 
 
 Examples. — 
 
 Log sin 31° 22' = 7.71 643. 
 Log tan 54° 46' =0.15 loi. 
 
xl SLIDE WIliE RATIOS. 
 
 SLIDE WIRE RATIOS. 
 
 The increasing use of the slide wire in electrical measurements, 
 notably in connection with physical chemistry, renders the table of 
 values of 
 
 a decided convenience. The work to which the slide wire is thus 
 for the most part employed demands but four-place tables. 
 
 To use the table, let a be the reading in millimetres on the slide wire, 
 which is supposed to be one metre long with millimetre subdivision, 
 or of any other length with division into thousandths. Find the 
 first two figures of a in the first column, and run out on this line to 
 the column headed with the third figure. The number there found 
 will give the value of the above fraction, which is the ratio of the 
 length of one section of the wire to the other. If a contains a fourth 
 figure, that is, if read to tenths of a millimetre, interpolation must be 
 made in the usual manner. 
 
 Example. — The slider reads 415.6 millimetres. 
 
 In line 41 under 5 is found 0.7094. Interpolating by adding 0.6 of the 
 tabular diflerence 29, gives 
 
 X = 0.7094 + 0.6 X 29 
 
 = 0.7094+ .0017 =0.7111. 
 
DEFINITIONS AND EXPLANATIONS 
 
 UNDERLYING THE COMPUTATION RULES. 
 
 The following statements call for the attention of those only who find 
 unfamllar terms in the foregoing rules. 
 
 A Digit is any one of the ten characters i, 2, 3, 4, 5, 6, 7, 8, 9, o. 
 
 A Significant Figure is any digit used to denote or signify the amount of the 
 quantity in the place in which it stands. Thus zero may be a significant figure 
 when it is written not merely to locate the decimal point, but to indicate that 
 the quantity in the place in which it stands is known to be nearer to zero than 
 to any other digit. 
 
 For example, if a distance has been measured to the nearest fiftieth of an 
 inch and found to be 205.46 inches, all five of the figures, including the zero, are 
 significant. And similarly if the measurement had shown the distance to be 
 nearer to 205.40 than to 205.41 or to 205.39 the filial zero would be also signifi- 
 cant, and should invariably be retained, since its presence serves the most 
 useful purpose of showing that this place of figures had been measured as well as 
 the rest. If in such a case the quantity had been written 205.4 instead of 205.40, 
 the inference would be drawn either that the hundredths of an inch had not been 
 measured, or that the person who wrote the number was ignorant or careless of 
 the proper numerical usage. Failure to follow this simple rule is a common 
 source of annoyance and uncertainty. 
 
 A zero when used merely to enable the decimal point to be retained is of 
 course not a significant figure in the above sense. E.g. If the distance were 
 measured as 286. centimetres within ± i centimetre, it might be retained as 
 2.86 metres, or 0.00 286 liilometres, or 2860. millimetres. In this case neither of 
 the zeros would be significant. 
 
 From this last example it is obvious that when the first zero, or zeros, pre- 
 cede the decimal point, they fail to indicate intrinsically whether or not they are 
 significant. E.g. The number 2860. millimetres or 28 600. millimetres, standing 
 apart from explanatory context, would afford no clew to whether the last place, 
 or the last two places, had been measured. In writing such a number, therefore, 
 whenever it is desirable to convey this information some statement of the reliabil- 
 ity of the quantity must be appended. This is usually done by writing after the 
 number ± a where a is a number, of two significant figures only, representing 
 the estimated measure of the accuracy or unreliability of the result. (See later. ) 
 
 Places of Figures are the places in which figures stand in the number as 
 actually written. Places of significant figures are those in which significant 
 figures stand. These two terms being merely, although not actually, identical, 
 are often used interchangeably. 
 
 xli 
 
xlii DEFINITIONS AND EXPLANATIONS. 
 
 Example. — 426018. has six places of figures and of significant figures 
 3 479 100. has seven places of figures, hut whether its numher of places of signifi- 
 cant figures is more than five is indeterminate. 0.02 7680 has seven places of 
 figures with five places of significant figures. 2.76 8o-io-''' has five places of 
 figures and five significant figures. 
 
 Places of Decimals. — These, of course, are the places following the decimal 
 point as the numher happens to be vrritten. E.g. 0.027680 has six decimal 
 places. 2.7680-10'^ has four decimal places, although its magnitude is the 
 same as that of the preceding quantity. 
 
 From the foregoing six examples it will be seen that the number of deci- 
 mal places and the number of places of significant figures have no necessary- 
 mutual relation. 
 
 Accuracy ; Reliability. — To know the exact accuracy of a given quantity 
 it would be necessary, of course, to know the true value of that quantity. In 
 the case of a few mathematical constants (such as ir = 3.14 159 265 •.•) the true 
 value is known, at least far beyond ordinary requirements. But in case of all 
 measurements the same is obviously not true, for if the true value were known, 
 measurements would be unnecessary. Some approximate expression of the accu- 
 racy of a measured result can, however, usually be obtained, and is necessary. 
 Sometimes this is afforded by a knowledge of the instrument used and the degree 
 of care employed. Thus, suppose the distance of about 3 feet 6^^ inches 
 = 3-5039 feet between two marks to have been carefully once measured with a 
 good foot-rule, it could safely be assumed from our previous knowledge of such 
 vyork that if a series of these measurements were undertaken, the results would 
 vary from their mean by less than ± 3V of an inch ; also, that the error in the 
 rule itself, and from other unavoidable or unavoided sources, would not on the 
 average materially increase the error of measurement. Then ± -J^ inch 
 = ± 0.0026 ft. would be taken as the estimated measure of accuracy of the result. 
 Instead of expressing the accuracy in units, e.g. inches or feet, it is usually 
 more convenient or intelligible to express it as a fraction ; or, better still, in per- 
 centage. Thus, the foregoing will be 
 
 , 0.0026 , .74 / , 0.0026\ , i 
 
 ± = ± 0.00 074, I.e. — '-^ — , or looi ± ^ 1 = ± 0.074 per cent. 
 
 3-S looooo \ 3.5 j 
 
 If in this example the reliability had not been estimated at ^^ inch, but if 
 several measurements had been made, and these had been found upon inspec- 
 tion to deviate from their mean by about j^j of an inch, then, other things being 
 the same, the measure of accuracy of any single measurement taken without 
 knowledge of the others would be regarded as ± -r}^ inch, or ± 0.074 per cent. 
 
 Mean ; Average ; Deviation Measure. — When the result is the arithmetical 
 mean or average of several separate measurements of the same quantity, its 
 reliability or accuracy is taken to be in proportion to the square root of the 
 numher of such observations. Thus, in the last preceding example, if there had 
 been m = 9 single observations made, the measure of accuracy of the mean of 
 these vf ould be 
 
 ± -i- -7- Vre = ± -5 — \z = db 4: = ± o.oio inch, or ± 0.025 per cent. 
 32 32 ^9 96 
 
 The differences of the single observations taken under like conditions from 
 their mean will be called deviations, and their numerical average (i.e. their sum 
 
DEI'INITIONS AND EXPLANATIONS. xliii 
 
 omitting their algebraic sign, divided by their number) will be called the average 
 deviation of the single observation from the mean, and will be denoted by ad. 
 This quantity divided by the square root of n would be called the average devia- 
 tion of the mean, and will be denoted by AD. It is the averagS amount by 
 which any one such mean would be found to deviate from the average of a 
 number of such means all taken under like conditions. The term deviation 
 measure will be used in referring to either of these quantities. 
 
 Briefly, then, the meaning of the terms may be summarized as follows : By 
 the statement that the accuracy or reliability of a result is of a quoted amount 
 is meant that the deviation measure of this result is estimated or found to be of 
 this stated amount, and that so far as this can be discovered by inspection, no 
 other sources of error exist which aflect the result by an amount sensible as 
 compared with this.* 
 
 It is essential to bear ir» mind in connection with all quantities that are the 
 result of measurement that no absolute numerical expression of the accuracy 
 or error is possible ; that any expression which is given is usually merely a 
 deviation measure; that is, an approximate average value of the effect of 
 the variable parts of the errors, accompanied by an assurance, expressed or 
 implied, that a study of the discoverable sources of error of the process has 
 been made, and that these have been corrected for or found to be negligible 
 compared to the deviation measure. 
 
 In specifying the accuracy desired in the result, it must be understood that 
 merely the converse of this is meant ; or, at least, that only the converse is possi- 
 ble of attainment. 
 
 Rules for Significant Figures. — The rules are so framed that, barring mis- 
 takes, the greatest possible computation error entering into the result of any 
 ordinary computation (e.g. one involving a total of not much exceeding 20 
 component numbers, steps, or operations, where a rejection error may occur) 
 shall not be sensible compared with the errors of the measurements or data, or 
 shall not sensibly afEect the accuracy of the result. They are, therefore, safe 
 rules in the worst possible cases. But in order to be so they are necessarily 
 more than sufficiently stringent for some classes of comparatively rough work, 
 where the infrequent undetected entrance of a computation error two to four 
 times as large as the experimental error would be permissible. For such work 
 one less place of figures may be used, but when the rules are thus relaxed the 
 possible consequence should be borne in mind, and special scrutiny applied to 
 the various stages of the computation, special attention being directed to quan- 
 tities beginning with i or 2. 
 
 Rejection Error. — Whenever it becomes necessary to throw off places of 
 figures, a " rejection error " may enter into the result ; e.g. suppose that for any 
 reason the last two figures are to be rejected in 
 
 24 375 291, 
 making it 24 375 300. 
 
 The rejection error in the new form is evidently -|- 9. 
 
 In rejection, the last figure retained is always to be increased by i when the 
 rejected figure next it is 5 or over, but remains unchanged if that figure is less 
 than 5. 
 
 * For a more extended discussion of this and allied subjects see the author's 
 " Precision of Measurements." 
 
xliv DEFINITIONS AND EXPLANATIONS. 
 
 Thus, calling the last place retained the rth place, the limits of the rejection 
 error entering into that place are + 0.5 and — 0.5, and as all amounts between 
 these limits are equally likely to occur, the average rejection error in the long 
 run will be 6.25 in the rth place. 
 
 Law and Amount of Accumulated Rejection Error. — Let the last place 
 of significant figures retained in a number, e.g. the fourth, fifth, etc., be called 
 the rth place. Then the error entering from rejection of figures beyond the rth 
 will be at most ± 5 in the (»■ + i) place, and any error between these limits, 
 + 5 and — 5 in the (?• + i) place, will be equally likely to occur in any given 
 case, and therefore will be of equal frequency in the long run. The average 
 rejection error in any considerable number of rejections will therefore be ± 2.5 
 in the (r + i) place. If then in direct processes of multiplication, division, evolu- 
 tion, or involution (separate or combined) each factor, product, and quotient in 
 the operation be carried out to the same number r of places, what will be the accu- 
 mulated fractional rejection error if n such rejections are made during the entire 
 operation ? This error we shall call for brevity the computation error, or 
 simply the rejection error. This question might easily be answered in a form 
 giving the average accumulated error, but we are at present concerned chiefly 
 with the maximum possible error, since our object is to frame rules which will 
 reduce the worst possible computation error to negligible dimensions. The 
 maximum computation error would arise when every single rejection error was 
 5 in the (r 4- i) place, and all had the same Eign ; and this would be the greatest 
 fraction of the final result when that result and all the factors (and therefore all 
 the intermediate products, quotients, etc.) began with i and had o in the other 
 places, i.e. were each ic— ' with the decimal point wherever it might happen to 
 stand. If there were n of these factors, products, quotients, etc., at which 
 rejections were made, the maximum possible computation error in the result 
 ■would, therefore, be re x 5 in the (r+ i) place, and the fractional error would 
 be 5 re/ic. Since this maximum error would be exceedingly rare unless n were 
 very small, and any approaching one-half of it would be very rare, we may 
 properly assume that our rules will be sufficiently stringent if we allow this 
 maximum error to have the same magnitude as the desired accuracy in the 
 result as expressed on the basis of the precision measure, or deviation measure, 
 explained at page xlii. To determine most simply what number r of places this 
 limitation would call for in the processes under consideration, let us take specific 
 cases. Suppose the work is desired to possess an accuracy of i per cent. Then 
 5 re/ic must be equal to or less than i per cent; i.e. 5 re^i/ioo. Hence, we 
 have to solve 
 
 
 5 re _ I 
 IC 100 
 
 
 By inspection, if 
 
 '• = 3. Sn= 10, 
 
 .-. re = 2, 
 
 if 
 
 r = 4, 5 n = 100, 
 
 .'. re = 20. 
 
 But obviously n will almost never be as small as 2, and rarely as large as 20, 
 lying with greatest frequency between 5 and 10 and averaging below 7. This 
 will give a maximum error of 0.0035 o"" j P^r cent with re = 7, r = 4, which would 
 be insignificant, and rising to i per cent only when re = 20. Hence, in work of 
 multiplication, division, etc., where i per cent accuracy, or a little better, is 
 desired (remembering that by this we mean only a deviation measure of i per 
 cent) r = 4 will be an entirely safe but not an excessive value ; that is, the reten- 
 
DEFINITIONS AND EXPLANATIONS. xlv 
 
 tion of four significant figures throughout will insure entirely sufBoient freedom 
 from computation error in every case when the number of rejections is less than 
 the very unusual total of about 20, and fewer places would not be warranted. 
 Similarly five places will suffice for worlt to o.i per cent, i.e. better than i per 
 cent, but not much better than o.i per cent; six places for work of o.oi per 
 cent, and so on. 
 
 As to relaxation of the rules in special cases, it is evident that but little can 
 be safely done. The maximum error with n = 7, »■ = 4, will be 0.35 per cent, 
 and an error of \ of this, say, of 0.1 per cent, will not be of very uncommon 
 occurrence. In fact, with only two rejections the error might be 0.1 per cent. 
 Hence, four places cannot be considered as safe to o. i per cent, even for short 
 computations. Four places might properly enough be used in short computa- 
 tions up to J per cent. Similar statements of course hold for the other rules. 
 
 When logarithms are used for multiplication, division, etc., tables should be 
 used giving the mantissa to the same number of places of figures as required by 
 the. foregoing rules for direct multiplication and division. Hence, one would 
 employ four-place tables for i per cent work, five-place tables for o.i per cent 
 work, and so on. The numbers, antilogs, and mantissse should all be carried 
 out to the same number of places. This conforms to the customary and only 
 convenient practice. 
 
 This rule is based primarily on the fact, next to be shown, that under them 
 the maximum computation error in the use of logarithms arises chiefly from the 
 rejection in the numbers and antilogs themselves and not sensibly from the 
 rejected places in the logarithms. In logarithms, a change of the rth figure by i 
 produces the same fractional error in the antilog whatever its value, viz. 2.4/10'', 
 as may be seen easily by inspection of tables. Hence, as the maximum rejection 
 error in the tabular value of a logarithm is 5 in the (»• 4- i) place of the man- 
 tissse, which may be doubled by the process of interpolating, the maximum 
 fractional error in a result due to the maximum rejection error in any mantissa 
 is 2.4/10''. But if only r places are retained in the number or antilog, the 
 maximum error in it due to rejection of its further- places is s/ic, compared 
 to which 2.4/10' is negligible. Hence, as the number of rejections from num- 
 ber and antilog together is usually about the same as from mantissse, the accumu- 
 lated error will be due almost wholly to the rejections from the numbers and 
 antilogs. And of these rejections there will ordinarily be about as many if the 
 computation is carried out by logarithms as if by direct multiplication or 
 division. The above rule is thus justified. 
 
 In addition or subtraction the maximum rejection error will be obviously 
 5 TO in the (r -f i) place. Under the above stated rule that the weakest quantity 
 shall be carried to four significant figures (or two uncertain places) for i per 
 cent work, the smallest value of the deviation measure or uncertainty of the 
 result win be 10 in the rth place, which is 100 in the (r -f i) place. Hence, 
 
 5™^ 100. .-. n = 20. 
 
 The maximum accumulated error would then attain the size of the smallest 
 deviation measure, i.e. the worst possible case would occur, only when the num- 
 ber of rejections was as great as twenty. Hence, the rule of four places for 1 
 per cent work, five for 0.1 per cent work, and so on, as before given, is sufficient. 
 
TABLES 
 
LOGS. 4 PL. 
 
 FOUR PLACE LOGARITHMS. 
 
 No. 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 
 
 9 
 
 INTERPOLATION 
 TABLES. 
 
 1.00 
 
 .0000 
 
 .0004 
 
 .0009 
 
 .0013 
 
 .0017 
 
 .0022 
 
 .0026 
 
 .0030 .0035 
 
 .0039 
 
 38 36 34 32 
 
 .01 
 
 0043 
 
 0048 
 
 0052 
 
 0056 
 
 0060 
 
 0065 
 
 0069 
 
 0073 0077 
 
 0082 
 
 4 4 3 3 
 
 .02 
 
 0086 
 
 0090 
 
 0095 
 
 0099 
 
 0103 
 
 0107 
 
 OIII 
 
 0116 0120 
 
 0124 
 
 8776 
 
 •03 
 
 0128 
 
 0133 
 
 0137 
 
 0141 
 
 0145 
 
 0149 
 
 0154 
 
 0158 0162 
 
 0166 
 
 II II 10 10 
 
 .04 
 
 0170 
 
 0175 
 
 0179 
 
 0183 
 
 0187 
 
 0191 
 
 0195 
 
 0199 0204 
 
 0208 
 
 15 14 14 13 
 
 1.05 
 
 .0212 
 
 .0216 
 
 .0220 
 
 .0224 
 
 .0228 
 
 •0233 
 
 .0237 
 
 .0241 .0245 
 
 .0249 
 
 19 18 17 16 
 
 .06 
 
 0253 
 
 0257 
 
 0261 
 
 0265 
 
 0269 
 
 0273 
 
 0278 
 
 0282 0286 
 
 0290 
 
 23 22 20 19 
 
 .07 
 
 0294 
 
 0298 
 
 0302 
 
 0306 
 
 0316 
 
 0314 
 
 0318 
 
 0322 0326 
 
 0330 
 
 27 25 24 22 
 
 .08 
 
 0334 
 
 0338 
 
 0342 
 
 0346 
 
 0350 
 0390 \ 
 
 °354 
 
 035S 
 
 0362, 0366 
 
 0370 
 
 30 29 27 26 
 
 .09 
 
 0374 
 
 0378 
 
 0382 
 
 0386 
 
 0394 
 
 039^ 
 
 0402 0406 
 
 0410 
 
 34 32 31 29 
 30 28 26 24 
 
 1.0 
 
 .0000 
 
 .0043 
 
 .0086 
 
 .0128 
 
 .0170 
 
 .0212 
 
 .0253 
 
 .0294 .0334 
 
 ■0374 
 
 .1 
 
 0414 
 
 0453 
 
 0492 
 
 0531 
 
 0569 
 
 0607 
 
 0645 
 
 0682 0719 
 
 0755 
 
 3332 
 
 .2 
 
 0792 
 
 0828 
 
 0864 
 
 0899 
 
 0934 
 
 0969 
 
 1004 
 
 1038. 1072 
 
 1 106 
 
 6655 
 
 •3 
 
 "39 
 
 "73 
 
 1206 
 
 1239 
 
 1271 
 
 i3°3 
 
 1335 
 
 1367 1399 
 
 1430 
 
 9887 
 
 •4 
 
 1461 
 
 1492 
 
 1523 
 
 1553 
 
 1584 
 
 1614 
 
 1644 
 
 1673 1703 
 
 1732 
 
 12 II 10 10 
 
 '5 
 
 .1761 
 
 .1790 
 
 .1818 
 
 .1847 
 
 .1875 
 
 .1903 
 
 •1931 
 
 •1959 .i987«2014 
 
 15 14 13 12 
 
 .6 
 
 2041 
 
 2068 
 
 2095 
 
 2122 
 
 2148 
 
 2175 
 
 2201 
 
 2227 2253 
 
 2279 
 
 18 17 16 14 
 
 •7 
 
 2304 
 
 2330 
 
 2355 
 
 2380 
 
 2405 
 
 2430 
 
 2455 
 
 2480 2504 
 
 2529 
 
 21 20 18 17 
 
 .8 
 
 2553 
 
 2577 
 
 2601 
 
 2625 
 
 2648 
 
 2672 
 
 2695 
 
 2718 2742 
 
 2765 
 
 24 22 21 19 
 
 ■9 
 
 2788 
 
 2810 
 
 2833 
 
 2856 
 
 2878 
 
 2900 
 
 2923 
 
 2945 2967 
 
 2989 
 
 27 25 23 22 
 
 2.0 
 
 .3010 
 
 •3°32 
 
 ■3054 
 
 ■3075 
 
 .3096 
 
 .3118 
 
 •3139 
 
 .3160 .3181 
 
 .3201 
 
 22 20 18 16 
 
 .1 
 
 3222 
 
 3243 
 
 3263 
 
 3284 
 
 3304 
 
 3324 
 
 3345 
 
 3365 3385 
 
 3404 
 
 2222 
 
 .2 
 
 3424 
 
 3444 
 
 3464 
 
 3483 
 
 3502 
 
 3522 
 
 3541 
 
 3560 3579 
 
 3598 
 
 4 4 4 3 
 
 •3 
 
 3617 
 
 3636 
 
 3655 
 
 3674 
 
 3692 
 
 37" 
 
 3729 
 
 3747 3766 
 
 3784 
 
 7655 
 
 •4 
 
 3802 
 
 3820 
 
 3838 
 
 3856 
 
 3874 
 
 3892 
 
 3909 
 
 3927 3945 
 
 3962 
 
 9876 
 
 2-S 
 
 •3979 
 
 ■3997 
 
 .4014 
 
 .4031 
 
 .4048 
 
 .4065 
 
 .4082 
 
 .4099 .4116 
 
 •4133 
 
 II 10 9 8 
 
 .6 
 
 4150 
 
 4166 
 
 4183 
 
 4200 
 
 4216 
 
 4232 
 
 4249 
 
 4265 4281 
 
 4298 
 
 13 12 II 10 
 
 •7 
 
 43H 
 
 4330 
 
 4346 
 
 4362 
 
 4378 
 
 4393 
 
 4409 
 
 4425 4440 
 
 4456 
 
 15 14 13 II 
 
 .8 
 
 4472 
 
 4487 
 
 4502 
 
 45>8 
 
 4533 
 
 4548 
 
 4564 
 
 4579 4594 
 
 4609 
 
 18 16 14 13 
 
 •9 
 
 4624 
 
 4639 
 
 4654 
 
 4669 
 
 4683 
 
 4698 
 
 4713 
 
 4728 4742 
 
 4757 
 
 20 18 16 14 
 
 3.0 
 
 •4771 
 
 .4786 
 
 .4800 
 
 .4814 
 
 .4829 
 
 •4843 
 
 .4857 
 
 .4871 .4886 
 
 .4900 
 
 15 14 13 12 
 
 .1 
 
 4914 
 
 4928 
 
 4942 
 
 4955 
 
 4969 
 
 4983 
 
 49^7 
 
 6011 5024 
 
 5038- 
 
 2 I I I 
 
 .2 
 
 5051 
 
 5065 
 
 5079 
 
 5092 
 
 5105 
 
 5"9 
 
 5132 
 
 5145 5'S9 
 
 5172 
 
 3 3^3 2 
 
 •3 
 
 5185 
 
 5198 
 
 5211 
 
 5224 
 
 5237 
 
 5250 
 
 5263 
 
 5276 5289 
 
 5302 
 
 5 4 4.. 4 
 
 •4 
 
 5315 
 
 5328 
 
 5340 
 
 5353 
 
 5366 
 
 5378 
 
 5391 
 
 5403 5416 
 
 5428 
 
 6 6 5 5 
 
 35 
 
 •5441 
 
 •5453 
 
 .5465 
 
 •5478 
 
 •5490 
 
 .5502 
 
 •5515 
 
 ■5527 -5539 
 
 •5551 
 
 8776 
 
 .6 
 
 5563 
 
 5575 
 
 5587 
 
 5599 
 
 561 1 
 
 5623 
 
 5635 
 
 5647 5658 
 
 5670 
 
 9887 
 
 ■7 
 
 5682 
 
 5694 
 
 5705 
 
 5717 
 
 5729 
 
 S740 
 
 5752 
 
 5763 5775 
 
 5786 
 
 II 10 9 8 
 
 .8 
 
 5798 
 
 5809 
 
 5821 
 
 5832 
 
 5843 
 
 5855 
 
 5866 
 
 5877 5888 
 
 5899 
 
 12 II 10 10 
 
 •9 
 
 S9II 
 
 5922 
 
 5933 
 
 5944 
 
 5955 
 
 5966 
 
 5977 
 
 5988 5999 
 
 6010 
 
 14 13 12 II 
 
 4.0 
 
 .6021 
 
 .6031 
 
 .6042 
 
 •6053 
 
 .6064 
 
 .6075 
 
 .6085 
 
 .6096 .6107 
 
 .6117 
 
 11 10 9 8 
 
 .1 
 
 6128 
 
 6138 
 
 6149 
 
 6160 
 
 6170 
 
 6180 
 
 6191 
 
 6201 6212 
 
 6222 
 
 I I I I 
 
 .2 
 
 6232 
 
 6243 
 
 6253 
 
 6263 
 
 6274 
 
 6284 
 
 6294 
 
 6304 6314 
 
 6325 
 
 2222 
 
 ■3 
 
 633s 
 
 6345 
 
 6355 
 
 6365 
 
 6375 
 
 6385 
 
 6395 
 
 6405 6415 
 
 6425 
 
 "3332 
 
 •4 
 
 6435 
 
 6444 
 
 6454 
 
 6464 
 
 6474 
 
 6484 
 
 6493 
 
 6503 6513 
 
 6522 
 
 4 4 4 3 
 
 4-S 
 
 •6532 
 
 .6542 
 
 .6551 
 
 .6561 
 
 •6571 
 
 .6580 
 
 .6590 
 
 .6599 .6609 
 
 .6618 
 
 6554 
 
 .6 
 
 6628 
 
 6637 
 
 6646 
 
 6656 
 
 6665 
 
 6675 
 
 6684 
 
 6693 6702 
 
 6712 
 
 7655 
 
 ■7 
 
 6721 
 
 ^^12 
 6902 
 
 6730 
 
 6739 
 
 6749 
 
 6758 
 
 6767 
 
 6776 
 
 6785 6794 
 
 6803 
 
 8766 
 
 .8 
 
 6821 
 
 6830 
 
 6839 
 
 6848 
 
 6857 
 
 6866 
 
 6875 6884 
 
 6893 
 
 9876 
 
 •9 
 
 691 1 
 
 6920 
 
 6928 
 
 6937 
 
 6946 
 
 6955 
 
 6964 6972 
 
 6981 
 
 lo 9 8 7 
 
 tnc 
 
 i^'Dl'V' 
 
 
 
 
 
 ['>\ 
 
 
 
 
 
 LOGS 
 
FOUR PLACE LOGARITHMS. 
 
 4 PL. LOGS. 
 
 No. 
 
 
 
 I 
 
 2 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 nterpolationI 
 
 TABLES. 1 
 
 5.0 
 
 .6990 
 
 .6998 
 
 .7007 .7016 
 
 .7024 
 
 •7033 
 
 .7042 
 
 .7050 
 
 .7059 
 
 .7067 
 
 9 8 
 
 7 
 
 .1 
 
 7076 
 
 7084 
 
 7093 7101 
 
 7H0 
 
 7118 
 
 7126 
 
 7135 
 
 7143 
 
 7152 
 
 I I 
 
 I 
 
 .2 
 
 7160 
 
 7168 
 
 7177 7185 
 
 7193 
 
 7202 
 
 7210 
 
 7218 
 
 7226 
 
 7235 
 
 2 2 
 
 I 
 
 •3 
 
 7243 
 
 7251 
 
 7259 7267 
 
 727s 
 
 7284 
 
 7292 
 
 7300 
 
 7308 
 
 7316 
 
 3 2 
 
 ^ 
 
 •4 
 
 7324 
 
 7332 
 
 7340 7348 
 
 7356 
 
 7364 
 
 7372 
 
 7380 
 
 7388 
 
 7396 
 
 4 3 
 
 3 
 
 5-5 
 
 .7404 
 
 .7412 
 
 .7419 .7427 
 
 •7435 
 
 •7443 
 
 •7451 
 
 •7459 
 
 .7466 
 
 •7474 
 
 5 4 
 
 4 
 
 .6 
 
 7482 
 
 7490 
 
 7497 7505 
 
 7513 
 
 7520 
 
 7528 
 
 7536 
 
 7543- 
 
 7551 
 
 5 5 
 
 4 
 
 •7 
 
 . 7559 
 
 7566 
 
 7574 7582 
 
 7589 
 
 7597 
 
 7604 
 
 7612 
 
 7619 
 
 7627 
 
 6 6 
 
 5 
 
 .8 
 
 7634 
 
 7642 
 
 7649 7657 
 
 7664 
 
 7672 
 
 7679 
 
 7686 
 
 7694 
 
 7701 
 
 7 6 
 
 6 
 
 •9 
 
 7709 
 
 7716 
 
 7723 7731 - 
 
 ^7738 
 
 7745 
 
 7752 
 
 7760 
 
 7767 
 
 7774 
 
 8 7 
 
 6 
 
 6.0 
 
 .7782 
 
 .7789 
 
 .7796 .7803 
 
 .7810 
 
 .7818 
 
 .7825 
 
 •7832 
 
 •7839 
 
 .7846 
 
 7 
 
 6 
 
 .1 
 
 7853 
 
 7860 
 
 7868 7875 
 
 7882 
 
 7889 
 
 7896 
 
 7903 
 
 7910 
 
 7917 
 
 I 
 
 I 
 
 .2 
 
 7924 
 
 7931 
 
 7938 7945 
 
 7952 
 
 7959 
 
 7966 
 
 7973 
 
 7980 
 
 7987 
 
 I 
 
 I 
 
 •3 
 
 7993 
 
 8000 
 
 8007 8014 
 
 8021 
 
 8028 
 
 8035 
 
 8041 
 
 8048 
 
 8055 
 
 2 
 
 2 
 
 •4 
 
 8062 
 
 8069 
 
 8075 8082 
 
 8089 
 
 8096 
 
 8102 
 
 8109 
 
 8116 
 
 8122 
 
 3 
 
 2 
 
 6.5 
 
 .8129 
 
 .8136 
 
 .8142 .8149 
 
 .8156 
 
 .8162 
 
 .8169 
 
 .8176 
 
 .8182 
 
 .8189 
 
 4 
 
 3 
 
 .6 
 
 8195 
 
 8202 
 
 8209 8215 
 
 8222 
 
 8228 
 
 8235 
 
 8241 
 
 8248 
 
 8254 
 
 4 
 
 4 
 
 •7- 
 
 8261 
 
 8267 
 
 8274 8280 
 
 8287 
 
 8293 
 
 8299 
 
 8306 
 
 8312 
 
 8319 
 
 5 
 
 4 
 
 .8 
 
 8325 
 
 8331 
 
 8338 8344 
 
 8351 
 
 8357 
 
 8363 
 
 8370 
 
 8376 
 
 8382 
 
 6 
 
 5 
 
 ■9 
 
 8388 
 
 8395 
 
 8401 8407 
 
 8414 
 
 8420 
 
 8426 
 
 8432 
 
 8439 
 
 8445 
 
 6 
 
 5 
 
 7.0 
 
 .8451 
 
 •8457 
 
 .8463 .8470 
 
 .8476 
 
 .8482 
 
 .8488 
 
 .8494 
 
 .8500 
 
 .8506 
 
 6 
 
 5 
 
 .1 
 
 8513 
 
 8519 
 
 8525 8531 
 
 8537 
 
 8543 
 
 8549 
 
 8555 
 
 8561 
 
 8567 
 
 I 
 
 I 
 
 .2 
 
 8573 
 
 8579 
 
 8585 8591 
 
 8597 
 
 8603 
 
 8609 
 
 8615 
 
 8621 
 
 8627 
 
 I 
 
 I 
 
 •3 
 
 8633 
 
 8639 
 
 8645 8651 
 
 8657 
 
 8663 
 
 8669 
 
 8675 
 
 8681 
 
 8686 
 
 2 
 
 2 
 
 •4 
 
 8692 
 
 8698 
 
 8704 8710 
 
 8716 
 
 8722 
 
 8727 
 
 8733 
 
 8739 
 
 8745 
 
 2 
 
 2 
 
 7-5 
 
 .8751 
 
 .8756 
 
 .8762 .8768 
 
 .8774 
 
 .8779 
 
 .8785 
 
 .8791 
 
 .8797 
 
 .8802 
 
 3 
 
 3 
 
 .6 
 
 8808 
 
 8814 
 
 8820 8825 
 
 8831 
 
 8837 
 
 8842 
 
 8848 
 
 8854 
 
 8859 
 
 4 
 
 3 
 
 .7 
 
 8865 
 
 8871 
 
 8876 8882 
 
 8887 
 
 8893 
 
 8899 
 
 8904 
 
 8910 
 
 8915 
 
 4 
 
 4 
 
 .8 
 
 8921 
 
 8927 
 
 8932 8938 
 
 8943 
 
 8949 
 
 8954 
 
 8960 
 
 8965 
 
 8971 
 
 5 
 
 4 
 
 •9 
 
 .8976 
 
 8982 
 
 8987 8993 
 
 8998 
 
 9004 
 
 9009 
 
 9015 
 
 9020 
 
 9025 
 
 5 
 
 5 
 
 8.0 
 
 .9031 
 
 .9036 
 
 .9042 .9947 
 
 •9053 
 
 .9058 
 
 .9063 
 
 .9069 
 
 .9074 
 
 .9079 
 
 6 
 
 6 
 
 .1 
 
 9085 
 
 9090 
 
 9096 9101 
 
 9106 
 
 9112 
 
 9117 
 
 9122 
 
 9128 
 
 9133 
 
 I 
 
 I 
 
 .2 
 
 9138 
 
 9143 
 
 9149 9154 
 
 9159 
 
 9165 
 
 9170 
 
 9175 
 
 9180 
 
 9186 
 
 I 
 
 I 
 
 •3 
 
 9191 
 
 9196 
 
 9201 9206 
 
 9212 
 
 9217 
 
 9222 
 
 9227 
 
 9232 
 
 9238 
 
 2 
 
 2 
 
 •4 
 
 9243 
 
 9248 
 
 9253 9258 
 
 9263 
 
 9269 
 
 9274 
 
 9279 
 
 9284 
 
 9289 
 
 2 
 
 2 
 
 8.5 
 
 .9294 
 
 .9299 
 
 .9304 .9309 
 
 •9315 
 
 .9320 
 
 •9325 
 
 •9330 
 
 •9335 
 
 •9340 
 
 3 
 
 3 
 
 .6 
 
 9345 
 
 9350 
 
 9355 9360 
 
 9365 
 
 9370 
 
 9375 
 
 9380 
 
 9385 
 
 9390 
 
 4 
 
 3 
 
 .7 
 
 9395 
 
 9400 
 
 9405 9410 
 
 9415 
 
 9420 
 
 9425 
 
 9430 
 
 9435 
 
 9440 
 
 4 
 
 4 
 
 .8 
 
 9445 
 
 9450 
 
 9455 9460 
 
 9465 
 
 9469 
 
 9474 
 
 9479 
 
 9484 
 
 9489 
 
 5 
 
 4 
 
 •9 
 
 9494 
 
 9499 
 
 9504 9509 
 
 9513 
 
 9518 
 
 9523 
 
 9528 
 
 9533 
 
 9538 
 
 5 
 
 5 
 
 9.0 
 
 •9542 
 
 ■9547 
 
 ■9552 .9557 
 
 .9562 
 
 .9566 
 
 •9571 
 
 ■9576 
 
 .9581 
 
 .9586 
 
 5 
 
 4 
 
 .1 
 
 959° 
 
 9595 
 
 9600 9605 
 
 9609 
 
 9614 
 
 9619 
 
 9624 
 
 9628 
 
 9633 
 
 I 
 
 
 
 .2 
 
 9638 
 
 9643 
 
 9647 9652 
 
 9657 
 
 9661 
 
 9666 
 
 9671 
 
 9675 
 
 9680 
 
 I 
 
 I 
 
 •3 
 
 9685 
 
 9689 
 
 9694 9699 
 
 9703 
 
 9708 
 
 9713 
 
 9717 
 
 9722 
 
 9727 
 
 2 
 
 I 
 
 ■4 
 
 9731 
 
 9736 
 
 9741 9745 
 
 9750 
 
 9754 
 
 9759 
 
 9763 
 
 9768 
 
 9773 
 
 2 
 
 2 
 
 9-5 
 
 •9777 
 
 .9782 
 
 .9786 .9791 
 
 •9795 
 
 .98CXJ 
 
 .9805 
 
 .9809 
 
 .9814 
 
 .9818 
 
 3 
 
 2 
 
 .6 
 
 9823 
 
 9827 
 
 9832 9836 
 
 9841 
 
 9845 
 
 9850 
 
 9854 
 
 9859 
 
 9863 
 
 3 
 
 2 
 
 •7 
 
 9868 
 
 9872 
 
 9877 9881 
 
 9886 
 
 9890 
 
 9894 
 
 9899 
 
 9903 
 
 9908 
 
 4 
 
 3 
 
 .8 
 
 9912 
 
 9917 
 
 9921 9926 
 
 9930 
 
 9934 
 
 9939 
 
 9943 
 
 9948 
 
 9952 
 
 4 
 
 3 
 
 •9 
 
 9956 
 
 9961 
 
 9965 9969 
 
 9974 
 
 9978 
 
 9983 
 
 9987 
 
 9991 
 
 9996 
 
 5 
 
 4 
 
 (3) 
 
 4 PL. LOGS. 
 
FOUR PLACE ANTILOCARITHMS. 
 
 ANTILOGS. 4 PL. 
 
 
 
 
 T H 
 
 USA 
 
 N D T H 8. 
 
 
 
 INTERPOLA. 1 
 
 Mant. 
 
 
 
 I 
 
 2 3 
 
 4 
 
 567 
 
 8 
 
 9 
 
 TABLES. 1 
 
 .00 
 
 1. 000 
 
 1.002 
 
 1.005 '007 
 
 1.009 
 
 1.012 I.OI4 1.016 
 
 1.019 
 
 1.021 
 
 2 
 
 3 
 
 .01 
 
 1.023 
 
 1.026 
 
 1.028 1.030 
 
 1-033 
 
 1.03s '-038 1.040 
 
 1.042 
 
 1.045 
 
 
 
 
 
 .02 
 
 1.047 
 
 1.050 
 
 1.052 1.054 
 
 1.057 
 
 1.059 1.062 1.064 
 
 1.067 
 
 1.069 
 
 
 
 I 
 
 ■03 
 
 1.072 
 
 1.074 
 
 1.076 1.079 
 
 1.081 
 
 1.084 1086 1.089 
 
 1.091 
 
 1.094 
 
 
 1 
 
 .04 
 
 1.096 
 
 1.099 
 
 1.102 1.104 
 
 1.107 
 
 1.109 I-H2 1.114 
 
 1.117 
 
 1.119 
 
 
 1 
 
 . -05 
 
 1. 122 
 
 1.125 
 
 1.127 I-I30 
 
 1.132 
 
 1.135 I-I38 1.140 
 
 I -143 
 
 1. 146 
 
 
 2 
 
 .06 
 
 1. 148 
 
 1.151 
 
 1.153 1.156 
 
 1-159 
 
 1. 161 1.164 1-167 
 
 1.169 
 
 1.172 
 
 
 2 
 
 .07 
 
 1. 175 
 
 1.178 
 
 1. 180 1.183 
 
 1.186 
 
 1.189 1-191 I-I94 
 
 1.197 
 
 1.199 
 
 
 2 
 
 .08 
 
 1.202 
 
 1.205 
 
 1.208 1.21 1 
 
 1.213 
 
 1.216 1.219 1-222 
 
 1.225 
 
 1.227 
 
 2 
 
 2 
 
 •09 
 
 1.230 
 
 1-233 
 
 1.236 1.239 
 
 1.242 
 
 1.245 1-247 1^250 
 
 1-253 
 
 1.256 
 
 2 
 
 3 
 
 .lO 
 
 1.259 
 
 1.262 
 
 1.265 '-268 
 
 1.271 
 
 1.274 1.276 1.279 
 
 1.282 
 
 1.285 
 
 3 
 
 4 
 
 .11 
 
 1.288 
 
 1. 291 
 
 1.294 1-297 
 
 1.300 
 
 1.303 1.306 1.309 
 
 1.312 
 
 I-3I5 
 
 
 
 
 
 .12 
 
 I.318 
 
 1.321 
 
 1.324 1.327 
 
 1-33° 
 
 1-334 1-337 1-340 
 
 1-343 
 
 1.346 
 
 1 
 
 1 
 
 •13 
 
 1^349 
 
 1-352 
 
 1-355 1-358 
 
 1.361 
 
 1.365 1.368 1.371 
 
 1-374 
 
 1-377 
 
 1 
 
 1 
 
 .14 
 
 1.380 
 
 1.384 
 
 1.387 1.390 
 
 1^393 
 
 1.396 1.400 1.403 
 
 1.406 
 
 1.409 
 
 1 
 
 2 
 
 •15 
 
 1-413 
 
 1.416 
 
 1.419 1.422 
 
 1.426 
 
 1.429 1.432 1-435 
 
 1-439 
 
 1.442 
 
 2 
 
 2 
 
 .16 
 
 1.445 
 
 1.449 
 
 1.452 1.455 
 
 '•459 
 
 1.462 1.466 1.469 
 
 1.472 
 
 1.476 
 
 2 
 
 2 
 
 •17 
 
 1-479 
 
 1-483 
 
 1.486 1.489 
 
 1-493 
 
 1.496 1.500 1.503 
 
 1.507 
 
 1.510 
 
 2 
 
 3 
 
 .18 
 
 1.514 
 
 r.517 
 
 1.521 1.524 
 
 1.528 
 
 1-531 1-535 1-538 
 
 1.542 
 
 1-545 
 
 2 
 
 3 
 
 .19 
 
 1-549 
 
 1-552 
 
 1.556 1.560 
 
 1-563 
 
 1.567 1.570 1.574 
 
 1.578 
 
 1.581 
 
 3 
 
 4 
 
 .20 
 
 1.585 
 
 1-589 
 
 1.592 1.596 
 
 1.600 
 
 1.603 1-607 i.6n 
 
 1.614 
 
 1.618 
 
 3 4 
 
 6 
 
 .21 
 
 1.622 
 
 1.626 
 
 1.629 I -633 
 
 1-637 
 
 1.641 1.644 I-648 
 
 1.652 
 
 1.656 
 
 
 
 1 
 
 .22 
 
 1.660 
 
 1.663 
 
 1.667 1-671 
 
 1675 
 
 1.679 1.683 1-687 
 
 1.690 
 
 1.694 
 
 1 1 
 
 I 
 
 •23 
 
 1.698 
 
 1.702 
 
 1.706 1.710 
 
 1.714 
 
 1.718 1.722 1.726 
 
 1-730 
 
 1-734 
 
 1 1 
 
 ■ 2 
 
 .24 
 
 1-738 
 
 1.742 
 
 1.746 1.750 
 
 1-754 
 
 1.758 1.762 1.766 
 
 1.770 
 
 1-774 
 
 I 2 
 
 2 
 
 •25 
 
 1.778 
 
 1.782 
 
 1.786 1.791 
 
 1-795 
 
 1.799 1.803 1-807 
 
 1.811 
 
 1.816 
 
 2 2 
 
 3 
 
 .26 
 
 1.820 
 
 1.824 
 
 1.828 1.832 
 
 1-837 
 
 1.841 1.845 I-849 
 
 1.854 
 
 1.858 
 
 2 2 
 
 3 
 
 •27 
 
 1.862 
 
 1.866 
 
 1.871 1.875 
 
 1.879 
 
 1.884 1-888 1.892 
 
 1.897 
 
 1.901 
 
 2 3 
 
 4 
 
 .28 
 
 1-905 
 
 1.910 
 
 1-914 i-9>9 
 
 1.923 
 
 1.928 1.932 1.936 
 
 1.941 
 
 1-945 
 
 2 3 
 
 4 
 
 •29 
 
 1.950 
 
 1.954 
 
 1-959 1-963 
 
 1.968 
 
 1.972 1.977 1-982 
 
 1.986 
 
 1.991 
 
 3- 4 
 
 5 
 
 ■30 
 
 1-995 
 
 2.000 
 
 2.004 2.009 
 
 2.014 
 
 2.018 2.023 2.028 
 
 2.032 
 
 2.037 
 
 4 5 
 
 6 
 
 •31 
 
 2.042 
 
 2.046 
 
 2.051 2.056 
 
 2.061 
 
 2.065 2.070 2.075 
 
 2.080 
 
 2.084 
 
 I 
 
 I 
 
 •32 
 
 2.089 
 
 2.094 
 
 2.099 2.104 
 
 2.109 
 
 2.113 2.118 2.123 
 
 2.128 
 
 2.133 
 
 I 1 
 
 1 
 
 •33 
 
 2.138 
 
 2.143 
 
 2.148 2.153 
 
 2.158 
 
 2.163 2.168 2.173 
 
 2.178 
 
 2.183 
 
 1 2 
 
 2 
 
 •34 
 
 2.188 
 
 2.193 
 
 2.198 2.203 
 
 2.208 
 
 2.213 2.218 2.223 
 
 2.228 
 
 2-234 
 
 2 2 
 
 2 
 
 •35 
 
 2.239 
 
 2.244 
 
 2.249 2.254 
 
 2.259 
 
 2.265 2.270 2.275 
 
 2.280 
 
 2.286 
 
 2 3 
 
 3 
 
 •36 
 
 2.291 
 
 2.296 
 
 2.301 2.307 
 
 2.312 
 
 2.317 2.323 2.328 
 
 2-333 
 
 2.339 
 
 2 3 
 
 4 
 
 •37 
 
 2-344 
 
 2.350 
 
 2.355 2.360 
 
 2.366 
 
 2-371 2.377 2.382 
 
 2-388 
 
 2.393 
 
 3 4 
 
 4 
 
 •38 
 
 2-399 
 
 2.404 
 
 2.410 2.415 
 
 2.421 
 
 2.427 2.432 2.438 
 
 2-443 
 
 2.449 
 
 3 4 
 
 5 
 
 •39 
 
 2.455 
 
 2.460 
 
 2.466 2.472 
 
 2.477 
 
 2.483 2.489 2.495 
 
 2.500 
 
 2.506 
 
 4 5 
 
 5 
 
 .40 
 
 2.512 
 
 2.518 
 
 2.523 2.529 
 
 2-535 
 
 2.541 2.547 2.553 
 
 2-559 
 
 2.564 
 
 5 6 ' 
 
 r 8 
 
 .41 
 
 2.570 
 
 2.576 
 
 2.582 2.588 
 
 2.594 
 
 2.600 2.606 2.612 
 
 2.618 
 
 2.624 
 
 1 I 
 
 1 
 
 .42 
 
 2.630 
 
 2.636 
 
 2.642 2.649 
 
 2-655 
 
 2.661 2.667 2.673 
 
 2.679 
 
 2.685 
 
 1 I 
 
 2 
 
 •43 
 
 2.692 
 
 2.698 
 
 2.704 2.710 
 
 2.716 
 
 2.723 2.729 2.735 
 
 2.742 
 
 2.748 
 
 2 2 : 
 
 ! 2 
 
 ■44 
 
 2-754 
 
 2.761 
 
 2.767 2.773 
 
 2.780 
 
 2.786 2.793 2.799 
 
 2.805 
 
 2.812 
 
 2 2 ; 
 
 i 3 
 
 •45 
 
 2.818 
 
 2.825 
 
 2.831 2.838 
 
 2.844 
 
 2.851 2.858 2.864 
 
 2.871 
 
 2.877 
 
 3 3 4 4 
 
 .46 
 
 2.884 
 
 2.891 
 
 2.897 2.904 
 
 2.911 
 
 2.917 2.924 2.931 
 
 2.938 
 
 2-944 
 
 3 4 4 5 
 
 •47 
 
 2.951 
 
 2.958 
 
 2.965 2.972 
 
 2.979 
 
 2.985 2.992 2.999 
 
 3.006 
 
 3-013 
 
 4 4 ; 
 
 6 
 
 .48 
 
 3.020 
 
 3.027 
 
 3.034 3.041 
 
 3.048 
 
 3.055 3.062 3:069 
 
 3.076 
 
 3-083 
 
 4566 
 
 •49 
 
 3.090 
 
 3-097 
 
 3.105 3.112 
 
 3-"9 
 
 3.126 3.133 3.141 
 
 3.148 
 
 3-IS5 
 
 556-7 
 
 ANTILOGS. 4 PL. 
 
 (4) 
 
FOUR PLACE ANTILOCARITHMS. 
 
 4 PL. ANTILOGS. 
 
 
 
 
 
 THOUSANDTHS. 
 
 
 
 
 INTERPOLA. 
 
 Mant. 
 
 
 
 I 
 
 2 
 
 3 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 TABLES. 
 
 .50 
 
 3.162 
 
 3-170 
 
 3-177 
 
 3.184 3.192 
 
 3-199 
 
 3.206 
 
 3-214 
 
 3-221 
 
 3.228 
 
 7 8 9 
 
 •SI 
 
 3^236 
 
 3-243 
 
 3-251 
 
 3.258 3.266 
 
 3-273 
 
 3.281 
 
 3.289 
 
 3.296 
 
 3-304 
 
 I 1 I 
 
 .52 
 
 3^3 J I 
 
 3-319 
 
 3-327 
 
 3-334 3-342 
 
 3-350 
 
 3-357 
 
 3-365 
 
 3-373 
 
 3-381 
 
 122 
 
 •S3 
 
 3.388 
 
 3-396 
 
 3-404 
 
 3.412 3.420 
 
 3-428 
 
 3-436 
 
 3-443 
 
 3-451 
 
 3-459 
 
 223 
 
 •S4 
 
 3-467 
 
 3475 
 
 3-483 
 
 3.491 3.499 
 
 3.508 
 
 3-516 
 
 3-524 
 
 3-532 
 
 3-540 
 
 3 3 4 
 
 •SS 
 
 3-548 
 
 3-556 
 
 3-565 
 
 3-573 3.581 
 
 3-589 
 
 3-597 
 
 3.606 
 
 3.614 
 
 3.622 
 
 4 4 5 
 
 .56 
 
 3-631 
 
 3-639 
 
 3-648 
 
 3.656 3.664 
 
 3-673 
 
 3-681 
 
 3.690 
 
 3-698 
 
 3-707 
 
 4 5 5 
 
 •57 
 
 3-715 
 
 3-724 
 
 3-733 
 
 3-741 3-750 
 
 3-758 
 
 3-767 
 
 3-776 
 
 3-784 
 
 3-793 
 
 566 
 
 .58 
 
 3.802 
 
 3-8 1 1 
 
 3-819 
 
 3.828 3.837 
 
 3.846 
 
 3-855 
 
 3-864 
 
 3-873 
 
 3.882 
 
 667 
 
 •S9 
 
 3.890 
 
 3-899 
 
 3.908 
 
 3-917 3-926 
 
 3.936 
 
 3-945 
 
 3-954 
 
 3-963 
 
 3972 
 
 6 7 8 
 
 .60 
 
 3-981 
 
 3-99° 
 
 3-999 
 
 4.009 4.018 
 
 4.027 
 
 4.036 
 
 4.046 
 
 4.055 
 
 4.064 
 
 9 10 11 12 
 
 .6i 
 
 4.074 
 
 4.083 
 
 4-093 
 
 4.102 4.111 
 
 4.121 
 
 4. J 30 
 
 4.140 
 
 4-150 
 
 4-159 
 
 I I I 1 
 
 .62 
 
 4.169 
 
 4.178 
 
 4.188 
 
 4.198 4.207 
 
 4.217 
 
 4.227 
 
 4.236 
 
 4.246 
 
 4.256 
 
 2222 
 
 •63 
 
 4.266 
 
 4.276 
 
 4-285 
 
 4.295 4.305 
 
 4.315 
 
 4.325 
 
 4-335 
 
 4-345 
 
 4-355 
 
 3 3 3 4 
 
 .64 
 
 4-365 
 
 4-375 
 
 4.385 
 
 4.395 4.406 
 
 4.416 
 
 4.426 
 
 4-436 
 
 4-446 
 
 4-457 
 
 4 4 4 5 
 
 •6S 
 
 4.467 
 
 4-477 
 
 4.487 
 
 4.498 4.508 
 
 4.519 
 
 4-529 
 
 4-539 
 
 4-550 
 
 4.560 
 
 5 5 6 6 
 
 .66 
 
 4-571 
 
 4.581 
 
 4.592 
 
 4.603 4.613 
 
 4.624 
 
 4-634 
 
 4-645 
 
 4.656 
 
 4.667 
 
 5677 
 
 .67 
 
 4-677 
 
 4.688 
 
 4-699 
 
 4.710 4.721 
 
 4-732 
 
 4-742 
 
 4-753 
 
 4.764 
 
 4-775 
 
 6788 
 
 .68 
 
 4.786 
 
 4-797 
 
 4.808 
 
 4,819 4.831 
 
 4.842 
 
 4-853 
 
 4.864 
 
 4-875 
 
 4.887 
 
 7 8 9 10 
 
 .69 
 
 4.898 
 
 4.909 
 
 4.920 
 
 4.932 4.943 
 
 4.955 
 
 4.966 
 
 4-977 
 
 4-989 
 
 5.000 
 
 8 9 10 11 
 
 .70 
 
 5.012 
 
 5-023 
 
 5-035 
 
 5.047 5.058 
 
 5.070 
 
 5.082 
 
 5 -093 
 
 5.105 
 
 5.117 
 
 12 13 14 15 
 
 •71 
 
 S.129 
 
 5-140 
 
 5-152 
 
 5.164 5.176 
 
 5.188 
 
 5.200 
 
 5.212 
 
 5.224 
 
 5-236 
 
 1112 
 
 •72 
 
 5-248 
 
 5.260 
 
 5.272 
 
 5.284 5.297 
 
 5 -309 
 
 S-321 
 
 5-333 
 
 5.346 
 
 5-358 
 
 2333 
 
 •73 
 
 5-370 
 
 5-383 
 
 5-395 
 
 5.408 5.420 
 
 5-433 
 
 S-445 
 
 5-458 
 
 5.470 
 
 5-483 
 
 4 4 4 5 
 
 •74 
 
 5-495 
 
 5.508 
 
 5-521 
 
 ,5.534 5-546 
 
 5-559 
 
 5-57« 
 
 S-585 
 
 5.598 
 
 5.610 
 
 5566 
 
 •75 
 
 5-623 
 
 5^636 
 
 5-649 
 
 5-662 5.675 
 
 5.689 
 
 5-702 
 
 S-715 
 
 5-728 
 
 5-741 
 
 6778 
 
 .76 
 
 5-754 
 
 5.768 
 
 5.781 
 
 5.794 5.808 
 
 5-821 
 
 5-834 
 
 5-848 
 
 5.861 
 
 5-875 
 
 7889 
 
 •77 
 
 5.888 
 
 5.902 
 
 5.916 
 
 5-929 S-943 
 
 5-957 
 
 S-970 
 
 5-984 
 
 5-998 
 
 6.0J2 
 
 8 9 10 11 
 
 .78 
 
 6.026 
 
 6.039 
 
 6.053 
 
 6.067 6.081 
 
 6.095 
 
 6.109 
 
 6.124 
 
 6.138 
 
 6.152 
 
 10 10 11 12 
 
 •79 
 
 6.166 
 
 6.180 
 
 6.194 
 
 6.209 6.223 
 
 6.237 
 
 6.252 
 
 6.266 
 
 6.281 
 
 6-295 
 
 11 12 13 14 
 
 .80 
 
 6.310 
 
 6.324 
 
 6-339 
 
 6.353 6.368 
 
 6-383 
 
 6-397 
 
 6.412 
 
 6.427 
 
 6.442 
 
 16 17 18 19 
 
 .81 
 
 6.457 
 
 6.471 
 
 6.486 
 
 6.501 6.516 
 
 6-531 
 
 6.546 
 
 6.561 
 
 6.577 
 
 6.592 
 
 2222 
 
 .82 
 
 6.607 
 
 6.622 
 
 6.637 
 
 6.653 6.668 
 
 6.683 
 
 6.699 
 
 6.714 
 
 6.730 
 
 6-745 
 
 3 3 4 4 
 
 •83 
 
 6.761 
 
 6.776 
 
 6.792 
 
 6.808 6.823 
 
 6.839 
 
 6.855 
 
 6.871 
 
 6,887 
 
 6.902 
 
 5556 
 
 .84 
 
 6.918 
 
 6.934 
 
 6.950 
 
 6.966 6.982 
 
 6.998 
 
 7.015 
 
 7031 
 
 7-047 
 
 7.063 
 
 6778 
 
 •8S 
 
 7.079 
 
 7.096 
 
 7. 112 
 
 7.129 7.145 
 
 7.161 
 
 7.178 
 
 7- "94 
 
 7.211 
 
 7.228 
 
 8 9 9 10 
 
 .86 
 
 7.244 
 
 7.261 
 
 7.278 
 
 7-295 7-3" 
 
 7-328 
 
 7-345 
 
 7.362 
 
 7.379 
 
 7.396 
 
 10 1011 11 
 
 .87 
 
 7-413 
 
 7-430 
 
 7-447 
 
 7.464 7.482 
 
 7-499 
 
 7-516 
 
 7-534 
 
 7-551 
 
 7.568 
 
 II 121313 
 
 .88 
 
 7.586 
 
 7-603 
 
 7.621 
 
 7.638 7.646 
 
 7.674 
 
 7.691 
 
 7-709 
 
 7.727 
 
 7-745 
 
 13141415 
 
 .89 
 
 7.762 
 
 7.780 
 
 7.798 
 
 7.816 7.834 
 
 7-852 
 
 7.870 
 
 7.889 
 
 7-907 
 
 7.925 
 
 14 15 16 17 
 
 .90 
 
 7-943 
 
 7.962 
 
 7.980 
 
 7.998 8.017 
 
 8.035 
 
 8.054 
 
 8.072 
 
 8.091 
 
 8.110 
 
 20 2122 23 
 
 .91 
 
 8.128 
 
 8.147 
 
 8.166 
 
 8.185 8.204 
 
 8.222 
 
 8.241 
 
 8.260 
 
 8.279 
 
 8.299 
 
 2222 
 
 .92 
 
 8.318 
 
 8-337 
 
 8.356 
 
 8-375 8.395 
 
 8.414 
 
 8-433 
 
 8-453 
 
 ,8.472 
 
 8,492 
 
 4 4 4 5 
 
 ■93 
 
 8.5 1 1 
 
 8-531 
 
 8.551 
 
 8.570 8.590 
 
 8.610 
 
 8.630 
 
 8.650 
 
 8.670 
 
 8.690 
 
 6677 
 
 •94 
 
 8.710 
 
 8.730 
 
 8.750 
 
 8.770 8.790 
 
 8.810 
 
 8.831 
 
 8.851 
 
 8.872 
 
 8.892 
 
 8899 
 
 •95 
 
 8.913 
 
 8.933 
 
 8.954 
 
 8.974 8.995 
 
 9.016 
 
 9.036 
 
 9.057 
 
 9.078 
 
 9.099 
 
 10 11 11 12 
 
 .96 
 
 9.120 
 
 9.141 
 
 9.162 
 
 9.183 9.204 
 
 9.226 
 
 9.247 
 
 9.268 
 
 9.290 
 
 9-3^ J^ 
 
 12131314 
 
 •97 
 
 9-333 
 
 9-354 
 
 9-376 
 
 9-397 9-419 
 
 9.441 
 
 9.462 
 
 9,484 
 
 9.506 
 
 9.528 
 
 1415 15 16 
 
 .98 
 
 9-550 
 
 9-572 
 
 9-594 
 
 9.616 9.638 
 
 9.661 
 
 9-683 
 
 9-705 
 
 9.727 
 
 9-750 
 
 16 17 18 18 
 
 •99 
 
 9.772 
 
 9-795 
 
 9.817 
 
 9.840 9.863 
 
 9.886 
 
 9.908 
 
 9-931 
 
 9-954 
 
 9-977 
 
 18 19 20 20 
 
 (5) 
 
 4 PL. ANTILOGS. 
 
FOUR PLACE COLOGARITHMS. 
 
 COLOGS. 4 PL. 
 
 NOTE THE CHARACTERISTIC 1. 
 
 No. 
 
 01234 
 
 56789 
 
 INTERPOLATION 
 TABLES. 
 
 1,00 
 
 r.9996 T.9991 T.9987 ^-9983 
 
 7.9978 7.9974 7.9970 7.9965 7.9961 
 
 
 .01 
 
 1-9957 9953 9948 9944 9940 
 
 9935 9931 9927 9923 99i8 
 
 
 .02 
 
 9914 9910 9905 9901 9897 
 
 9893 9887 9884 9880 9876 
 
 
 •03 
 
 9S72 9867 9863 9859 9855 
 
 9851 9846 9842 9838 9834 
 
 
 .04 
 
 9830 9825 9821 9817 9813 
 
 9809 9805 9801 9796 9792 
 
 Use the flnl ten 
 liDes to avoid in- 
 
 1.05 
 
 T.9788 T.9784 T.9780 7.9776 T.9772 
 
 7.9767 7.9763 7.9759 7.9755 7.9751 
 
 terpolating 
 
 from liOOO 
 
 .06 
 
 9747 9743 9739 9735 9731 
 
 9727 9722 9718 9714 9710 
 
 to 1,100. 
 
 .07 
 
 9706 9702 -9698 9694 9690 
 
 9686 9682 9678 9674 9670 
 
 
 .08 
 
 9666 9662 9658 9654 9650 
 
 9646 9642 9638 9634 9630 
 
 
 .09 
 
 9626 9622 9618 9614 9610 
 
 9606 9602 9598 9594 9590 
 
 -44-40-36-32 
 
 1.0 
 
 0.0000 T.9957 7.9914 7.9872 7.9830 
 
 7.9788 7.9747 7.9706 7.9666 7.9626 
 
 .1 
 
 7.9586 9547 9508 9469 9431 
 
 9393 9355 93i8 9281 9245 
 
 4 4 4 3 
 
 .2 
 
 9208 9172 9136 9101 9066 
 
 9031 8996 8962 8928 8894 
 
 9876 
 
 •3 
 
 8861 8827 8794 8761 8729 
 
 8697 8665 8633 8601 8570 
 
 13 12 II 10 
 
 •4 
 
 8539 8508 8477 8447 8416 
 
 8386 8356 8327 8297 8268 
 
 18 16 14 13 
 
 i-S 
 
 7.8239 7.8210 7.8182 7.8153 7.8125 
 
 7.8097 7.8069 7.8041 7.8013 7.7986 
 
 22 20 18 16 
 
 .6 
 
 7959 7932 7905 7878 7852 
 
 7825 7799 7773 7747 772i 
 
 26 24 22 19 
 
 •7 
 
 7696 7670 7645 7620 7595 
 
 7570 7545 7520 7496 7471 
 
 31 28 25 22 
 
 .8 
 
 7447 7423 7399 7375 7352 
 
 7328 7305 7282 7258 7235 
 
 35 32 29 26 
 
 •9 
 
 7212 7190 7167 7144 7122 
 
 7100 7077 7055 7033 7011 
 
 40 36 32 29 
 
 2.0 
 
 7.6990 7.6968 7.6946 7.6925 7.6904 
 
 7.6882 7.6861 7.6840 7.6819 7.6799 
 
 -28-26-24-22 
 
 .1 
 
 6778 6757 6737 6716 6696 
 
 6676 6655 6635 6615 6596 
 
 3322 
 
 .2 
 
 6576 6556 6536 6517 6497 
 
 6478 6459 6440 6421 6402 
 
 6554 
 
 •3 
 
 6383 6364 6345 6326 6308 
 
 6289 6271 6253 6234 6216 
 
 8877 
 
 •4 
 
 6198 6180 6162 6144 6126 
 
 6108 6091 6073 6055 6038 
 
 II 10 10 9 
 
 2-S 
 
 7.6021 7.60037.59857.59697.5952 
 
 7.5935 7.5918 7.5901 7.58847.5867 
 
 14 13 12 II 
 
 .6 
 
 5850 5834 5817 5800 5784 
 
 5768 5751 5735 5719 5702 
 
 17 16 14 13 
 
 •7 
 
 5686 5670 5654 5638 5622 
 
 5607 5591 5575 5560 5544 
 
 20 18 17 15 
 
 .8 
 
 5528 5513 5498 5482 5467 
 
 5452 5436 5421 5406 5391 
 
 22 21 19 18 
 
 ■9 
 
 5376 5361 5346 5331 5317 
 
 5302 5287 5272 5258 5243 
 
 25 23 22 20 
 
 3.0 
 
 7.5229 7.5214 7.5200 7.5186 7.5 1 71 
 
 7.5157 7.5143 7.5129 7.5114 7.5100 
 
 -18-16-14r-12 
 
 .1 
 
 5086 5072 5058 5045 5031 
 
 5017 5003 4989 4976 4962 
 
 2 2 I I 
 
 .2 
 
 4948 4935 4921 4908 4895 
 
 4881 4868 4855 4841 4828 
 
 4332 
 
 •3 
 
 4815 4802 4789 4776 4763 
 
 475° 4737 4724 47" 4698 
 
 5 5 4 4 
 
 •4 
 
 4685 4672 4660 4647 4634 
 
 4622 4609 4597 4584 4572 
 
 7665 
 
 3-5 
 
 MS59 '■.4547 7-4535 M522 7.4510 
 
 7.4498 7.4486 7.4473 7.4461 7.4449 
 
 9876 
 
 .6 
 
 4437 4425 4413 4401 4389 
 
 4377 4365 4353 4342 4330 
 
 II 10 8 7 
 
 .7 
 
 4318 4306 4295 4283 4271 
 
 4260 4248 4237 4225 4214 
 
 13 II 10 8 
 
 .8 
 
 4202 4191 4179 4168 4157 
 
 4145 4134 4123 4112 4101 
 
 14 13 II 10 
 
 •9 
 
 4089 4078 4067 4056 4045 
 
 4034 4023 4012 4001 3990 
 
 16 14 13 II 
 
 4.0 
 
 7.3979 7-3969 7-3958 7.3947 7.3936 
 
 7.3925 7.3915 7.3904 7.3893 7.3883 
 
 -11-10 -9 -8 
 
 .1 
 
 3872 3862 3851 3840 3830 
 
 3820 3809 3799 3788 3778 
 
 I I I I 
 
 .2 
 
 3768 3757 3747 3737 3726 
 
 3716 3706 3696 3686 3675 
 
 2222 
 
 .3 
 
 3665 3655 3645 3635 3625 
 
 3615 3605 3595 3585 3575 
 
 3332 
 
 •4 
 
 3565 3556 3546 3536 3526 
 
 3516 3507 3497 3487 3478 
 
 4 4 4 3 
 
 4-S 
 
 7.3468 7.3458 7.3449 7.3439 7.3429 
 
 7.3420 7.3410 7.3401 7.3391 7.3382 
 
 6 5 5 4 
 
 .6 
 
 3372 3363 3354 3344 3335 
 
 3325 3316 3307 3298 3288 
 
 7655 
 
 .7 
 
 3279 3270 3261 3251 3242 
 
 3233 3224 3215 3206 3197 
 
 8766 
 
 .8 
 
 3188 3179 3170 3161 3152 
 
 3143 3134 3125 3116 3107 
 
 9876 
 
 ' 
 
 3098 3089 3080 3071 3063 
 
 3054 3045 3036 3028 3019 
 
 10 9 8 7 
 
 COLOGS. 4 PL. 
 
 (6) 
 
FOUR PLACE COLOCARITHMS. 
 
 4 PL. COLOGS. 
 
 No. 
 
 o I 2 3 4 
 
 56789 
 
 interpolation! 
 
 TABLES. 1 
 
 5.0 
 
 7.3010 T.3002 T.2993 T.2984 T.2976 
 
 7.2967 7.2958 7.2950 7.2941 7.2933 
 
 -9 
 
 -8 -7 
 
 .1 
 
 2924 2916 2907 2899 2890 
 
 2882 2874 2865 2857 2848 
 
 1 
 
 1 1 
 
 .2 
 
 2840 2832 2823 2815 2807 
 
 2798 2790 2782 2774 2765 
 
 2 
 
 2 I 
 
 ■3 
 
 2757 2749 2741 2733 2725 
 
 2716 2708 2700 2692 2684 
 
 3 
 
 2 2 
 
 •4 
 
 2676 2668 2660 2652 2644 
 
 2636 2628 2620 2612 2604 
 
 4 
 
 3 3 
 
 5-5 
 
 T.2595 T.2588 T.2581 T.2573 T.2565 
 
 7.25577.25497.2541 7.25347.2526 
 
 S 
 
 4 4 
 
 .6 
 
 2518 2510 2503 2495 2487 
 
 2480 2472 2464 2457 2449 
 
 S 
 
 5 4 
 
 ■7 
 
 2441 2434 2426 2418 241 1 
 
 2403 2396 2388 2381 2373 
 
 6 
 
 6 5 
 
 .8 
 
 2366 2358 2351 2343 2336 
 
 2328 2321 2314 2306 2299 
 
 7 
 
 6 6 
 
 •9 
 
 2291 2284 2277 2269 2262 
 
 2255 2248 2240 2233 2226 
 
 8 
 
 7 6 
 
 6.0 
 
 T.22I8T.22U 7.2204 T.2197 1.2190 
 
 7.2182 7.2175 7.2168 7.2161 7.2154 
 
 -7 
 
 -6 
 
 .1 
 
 2147 2140 2132 2125 2I18 
 
 2111 2104 2097 2090 2083 
 
 I 
 
 1 
 
 .2 
 
 2076 2069 2062 2055 2048 
 
 2041 2034 2027 2020 2013 
 
 1 
 
 1 
 
 ■3 
 
 2007 2000 1993 1986 1979 
 
 1972 1965 1959 1952 1945 
 
 2 
 
 2 
 
 •4 
 
 1938 I93I 1925 I918 I9II 
 
 1904 1898 1891 1884 1878 
 
 3 
 
 2 
 
 6.5 
 
 7.1871 7.1864 7.1858 7.185I 7.1844 
 
 7.18387.18317.18247.18187.1811 
 
 4 
 
 3 
 
 .6 
 
 1805 1798 1791 1785 1778 
 
 1772 1765 1759 1752 1746 
 
 4 
 
 4 
 
 ■7 
 
 1739 1733 1726 1720 1713 
 
 1707 1701 1694 1688 1681 
 
 5 
 
 4 
 
 .8 
 
 1675 1669 1662 1656 1649 
 
 1643 1637 '^3° '624 1618 
 
 6 
 
 5 
 
 ■9 
 
 1612 1605 1599 1593 1586 
 
 1580 1574 1568 1561 1555 
 
 6 
 
 5 
 
 7.0 
 
 7.1549 7.1543 7.1537 7.1530 7.1524 
 
 7.15187.15127.15067.15007.1494 
 
 -6 
 
 -5 
 
 .1 
 
 1487 I481 1475 1469 1463 
 
 1457 1451 1445 1439 1433 
 
 I 
 
 I 
 
 .2 
 
 1427 I42I 1415 1409 1403 
 
 1397 1391 1385 1379 1373 
 
 I 
 
 I 
 
 •3 
 
 1367 1361 1355 1349 1343 
 
 1337 1331 1325 '319 1314 
 
 2 
 
 2 
 
 •4 
 
 1308 1302 1296 1290 1284 
 
 1278 1273 1267 1261 1255 
 
 2 
 
 2 
 
 7-S 
 
 7. 1 249 7. 1 244 7. 1 238 7. 1 232 7. 1 226 
 
 7.1221 7.12157.12097.12037.1198 
 
 3 
 
 3 
 
 .6 
 
 H92 n86 1 180 1 1 75 1 169 
 
 1163 1158 1152 1146 1141 
 
 4 
 
 3 
 
 •7 
 
 1135 1129 1124 1118 1113 
 
 1107 1101 1096 1090 1085 
 
 4 
 
 4 
 
 .8 
 
 1079 1073 1068 1062 1057 
 
 1051 1046 1040 1035 1029 
 
 s 
 
 4 
 
 •9 
 
 1024 1018 1013 1007 1002 
 
 0996 0991 0985 0980 0975 
 
 5 
 
 5 
 
 8.0 
 
 7.0969 7.0964 7.0958 7.0953 7.0947 
 
 7.0942 7.0937 i^-°93i 7.0926 7.0921 
 
 -6 
 
 -5 
 
 .1 
 
 0915 0910 0904 0899 0894 
 
 0888 0883 0878 0872 0867 
 
 1 
 
 I 
 
 .2 
 
 0862 0857 0851 0846 0841 
 
 0835 0830 0825 0820 0814 
 
 1 
 
 I 
 
 •3 
 
 0809 0804 0799 0794 0788 
 
 0783 0778 0773 0768 0762 
 
 2 
 
 2 
 
 •4 
 
 0757 0752 0747 0742 0737 
 
 0731 0726 0721 0716 0711 
 
 2 
 
 2 
 
 8.S 
 
 7.0706 7.0701 7.0696 7.0691 7.0685 
 
 7.0680 7.0675 7.0670 7.0665 7.0660 
 
 3 
 
 3 
 
 .6 
 
 0655 0650 0645 0640 0635 
 
 0630 0625 0620 0615 0610 
 
 4 
 
 3 
 
 •7 
 
 0605 0600 0595 0590 0585 
 
 0580 0575 0570 0565 0560 
 
 4 
 
 4 
 
 .8 
 
 0555 0550 0545 0540 0535 
 
 0531 0526 0521 0516 0511 
 
 5 
 
 4 
 
 ■9 
 
 0506 0501 0496 0491 0487 
 
 0482 0477 0472 0467 0462 
 
 S 
 
 5 
 
 9.0 
 
 7.0458 7.0453 7.0448 1.0443 7.0438 
 
 7.0434 7.0429 7.0424 7.0419 7.0414 
 
 -5 
 
 -4 
 
 .1 
 
 0410 0405 0400 0395 0391 
 
 0386 0381 0376 0372 0367 
 
 I 
 
 
 
 .2 
 
 0362 0357 0353 0348 0343 
 
 0339 0334 0329 0325 0320 
 
 1 
 
 1 
 
 •3 
 
 0315 0311 0306 0301 0297 
 
 0292 0287 0283 0278 0273 
 
 2 
 
 1 
 
 •4 
 
 0269 0264 0259 0255 0250 
 
 0246 0241 0237 0232 0227 
 
 2 
 
 2 
 
 9.5 
 
 7.0223 7.0218 7.0214 7.0209 7.0205 
 
 7.02007.0195 7.0191 7.01867.0182 
 
 3 
 
 2 
 
 .6 
 
 0177 0173 0168 0164 0159 
 
 0155 0150 0146 0141 0137 
 
 3 
 
 2 
 
 •7 
 
 0132 0128 0123 0119 0114 
 
 0110 0106 0101 0097 0092 
 
 4 
 
 3 
 
 .8 
 
 0088 0083 0079 0074 0070 
 
 0066 0061 0057 0052 0048 
 
 4 
 
 3 
 
 •9 
 
 0044 0039 0035 0031 0026 
 
 0022 0017 0013 0009 0004 
 
 S 
 
 4 
 
 (7) 
 
 4 PL. COLOGS. 
 
5 PL. LOGS. 
 ABBREV, TAB. 
 
 TABLE OF FIVE PLACE LOGARITHMS, 
 
 CONTAINING 
 
 An Abbreviated Table for One and Two Place Numbers ; 
 A Table for Five Place Numbers from 1.0 to I.I Avoiding Interpolation ; 
 A Table for All Four Place Numbers with Interpolation Tables for the 
 Fifth Place. 
 
 No. 
 
 log. 
 
 No. 
 
 log. 
 
 No. 
 
 log. 
 
 No. 
 
 log. 
 
 No. 
 
 log. 
 
 
 
 — 00 
 
 2.0 
 
 .30 103 
 
 4.0 
 
 .60206 
 
 6.0 
 
 .77815 
 
 8.0 
 
 .90309 
 
 I 
 
 .ooooo 
 
 2.1 
 
 .32 222 
 
 4-1 
 
 .61 278 
 
 6.1 
 
 •78 533 
 
 8.1 
 
 .go 849 
 
 2 
 
 .30 103 
 
 2.2 
 
 .34242 
 
 4.2 
 
 •62 325 
 
 6.2 
 
 •79 239 
 
 8.2 
 
 .91 381 
 
 3 
 
 •47 7»2 
 
 2.3 
 
 •36 173 
 
 4-3 
 
 •63 347 
 
 6^3 
 
 •79 934 
 
 8.3 
 
 .91 908 
 
 4 
 
 .60206 
 
 2.4 
 
 .38021 
 
 4.4 
 
 •64345 
 
 6.4 
 
 .80618 
 
 8.4 
 
 .92 428 
 
 5 
 
 .69 897 
 
 2.5 
 
 •39 794 
 
 4.5 
 
 .65 321 
 
 6.5 
 
 .81 291 
 
 8.5 
 
 .92 942 
 
 6 
 
 .77815 
 
 2.6 
 
 .41 497 
 
 4.6 
 
 .66 276 
 
 6.6 
 
 .81 954 
 
 8.6 
 
 . ^93450 
 
 7 
 
 .84510 
 
 2.7 
 
 .43 136 
 
 47 
 
 .67 210 
 
 6.7 
 
 .82607 
 
 8.7 
 
 ■93 952 
 
 8 
 
 .90309 
 
 2.8 
 
 .44716 
 
 4.8 
 
 .68 124 
 
 6.8 
 
 .83251 
 
 8.8 
 
 .94448 
 
 9 
 
 •95 424 
 
 2.9 
 
 .46 240 
 
 4'.9 
 
 .69 O30 
 
 6.9 
 
 .83885 
 
 8.9 
 
 •94 939 
 
 1.0 
 
 .00000 
 
 3.0 
 
 .47712 
 
 5.0 
 
 .69 897 
 
 7.0 
 
 .84510 
 
 9.0 
 
 ■95 424 
 
 I.I 
 
 .04 139 
 
 3-1 
 
 •49 136 
 
 5^1 
 
 •70 757. 
 
 7^1 
 
 .85 126 
 
 91 
 
 •95 904 
 
 1.2 
 
 .07 918 
 
 32 
 
 ■SOS'S 
 
 5-2 
 
 .71 600 
 
 7.2 
 
 •85 733 
 
 9.2 
 
 •96 379 
 
 1-3 
 
 •"394 
 
 3-3 
 
 .51851 
 
 5^3 
 
 .72 428 
 
 7.3 
 
 .86332 
 
 9^3 
 
 .96 848 
 
 1.4 
 
 .14613 
 
 3-4 
 
 •53 148 
 
 5'4 
 
 •73 239 
 
 7-4 
 
 •86 923 
 
 9.4 
 
 •97313 
 
 i-S 
 
 .17609 
 
 3^5 
 
 •54407 
 
 5^5 
 
 •74036 
 
 7-5 
 
 .87 506 
 
 9-5 
 
 •97 772 
 
 1.6 
 
 .20412 
 
 3-6 
 
 •55 630 
 
 5.6 
 
 •74819 
 
 7.6 
 
 .88081 
 
 9.6 
 
 .98 227 
 
 1-7 
 
 .23045 
 
 3-7 
 
 .56 8?o 
 
 5-7 
 
 •75 587 
 
 7-7 
 
 .88 649 
 
 9^7 
 
 •98 677 
 
 1.8 
 
 .25 527 
 
 3^8 
 
 •57 978 
 
 5.8 
 
 •76 343 
 
 7.8 
 
 .89 209 
 
 9.8 
 
 •99 123 
 
 1-9 
 
 •27875 
 
 3^9 
 
 .59 106 
 
 5-9 
 
 •77 085 
 
 7.9 
 
 ■89 763 
 
 9-9 
 
 ■99 564 
 
 (9) 
 
 5 PL. LOGS. 
 ABBREV. TAB. 
 
1.0-1.1. 
 LOGS. 5 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 01234 
 
 5 6 
 
 7 
 
 8 
 
 9 
 
 1.000 
 
 .00000 .00004 .00009 .00013 .00017 
 
 .00022 .00026 
 
 .00030 
 
 .00035 
 
 .00039 
 
 .OOI 
 
 oo'043 00 048 00 052 00 056 00 o6i 
 
 00 065 00 069 
 
 00074 
 
 00078 
 
 00082 
 
 .002 
 
 00087 00091 00095 00 100 00104 
 
 00108 00113 
 
 00 117 
 
 00 121 
 
 00126 
 
 .003 
 
 00 130 00 134 00 139 00 143 00 147 
 
 00 152 00 156 
 
 00 160 
 
 00 165 
 
 00169 
 
 .004 
 
 00173 00178 00182 00 186 00 191 
 
 00 195 00 199 
 
 00204 
 
 ^00 208 
 
 00212 
 
 1.005 
 
 .QP217 .00221 .00225 .00230 .00234 
 
 .00238 .00243 
 
 .00 247 
 
 .00251 
 
 -00255 
 
 .006 
 
 00 260 00 264 00 268 00 273 00 277 
 
 00 281 00 286 
 
 00290 
 
 00294 
 
 00 299 
 
 .00/ 
 
 00303 00307 00312 00316 00320 
 
 00325 00329 
 
 00333 
 
 00337 
 
 00342 
 
 .008 
 
 00346 00350 00355 00359 00363 
 
 00 368 00 372 
 
 00376 
 
 00381 
 
 00385 
 
 .009 
 
 00 389 00 393 00 398 00 402 00 406 
 
 00411 00415 
 
 00419 
 
 00424 
 
 00428 
 
 1.010 
 
 .00432 .00436 .00441 .00445 -00449 
 
 .00454 .00458 
 
 .00462 
 
 .00467 
 
 .00471 
 
 .oil 
 
 00475 00479 00484 00488 00492 
 
 00497 00501 
 
 00505 
 
 00509 
 
 00514 
 
 .012 
 
 0051& 00522 00527 00531 00535 
 
 00 540 00 544 
 
 00548 
 
 00552 
 
 °os57 
 
 .013 
 
 00 561 00 565 00 570 00 574 00 578 
 
 00 582 00 587 
 
 00591 
 
 00595 
 
 00600 
 
 .014 
 
 00604 00608 00612 00617 00621 
 
 00 625 00 629 
 
 00634 
 
 00638 
 
 00642 
 
 I.OI5 
 
 .00647 -00651 .00655 .00659 .00664 
 
 .00668 .00672 
 
 .00677 
 
 .00681 
 
 .00685 
 
 .016 
 
 00 689 00 694 00 698 00 702 00 706 
 
 00711 00715 
 
 00719 
 
 00724 
 
 00728 
 
 .017 
 
 00 732 00 736 00 741 00 745 00 749 
 
 00753 00758 
 
 00762 
 
 00766 
 
 00771 
 
 .oi8 
 
 . 00 775 00 779 00 783 00 788 00 792- 
 
 00 796 00 800 
 
 00805 
 
 00809 
 
 00813 
 
 .019 
 
 00817 00822 00826 00830 00834 
 
 00839 00843 
 
 00847 
 
 00852 
 
 00856 
 
 1.020 
 
 .00 860 .00 864 .00 869 .00 873 .00 877 
 
 .00881 .00886 
 
 .00890 
 
 .00894 
 
 .00898 
 
 .021 
 
 00903 00907 00911 00915 00920 
 
 00924 00928 
 
 00932 
 
 00937 
 
 00941 
 
 .022 
 
 00945 00949 00954 00958 00962 
 
 00966 00971 
 
 00975 
 
 00979 
 
 00983 
 
 .023 
 
 00 988 00 992 00 996 01 000 01 005 
 
 01 009 01 013 
 
 01 017 
 
 01 022 
 
 01 026 
 
 .024 
 
 01 030 01 034 01 038 01 043 01 047 
 
 01051 01055 
 
 01 060 
 
 01 064 
 
 01 068 
 
 1.025 
 
 .01 072 K)i 077 .01 081 .01 085 .01 089 
 
 .01 094 .01 098 
 
 .01 102 
 
 .01 106 
 
 .01 111 
 
 .026 
 
 01 115 01 119 01 123 01 127 01 132 
 
 01 136 01 140 
 
 01 144 
 
 01 149 
 
 01 153 
 
 .027 
 
 01 157 01 161 01 166 01 170 01 174 
 
 01 178 01 182 
 
 01 187 
 
 01 191 
 
 01195 
 
 .028 
 
 01 199 01 204 01 208 01 212 01 216 
 
 01 220 01 225 
 
 01 229 
 
 01233 
 
 01237 
 
 .029 
 
 01 242 01 246 01 250 01 254 01 258 
 
 01 263 01 267 
 
 01 271 
 
 01275 
 
 01 280 
 
 1.030 
 
 .01 284 .01 288 .01 292 .01 296 .01 301 
 
 .01 305 .01 309 
 
 .01 313 
 
 .01 317 
 
 .01 322 
 
 .031 
 
 01 326 01 330 01 334 01 338 01 343 
 
 01347 01351 
 
 01 355 
 
 01360 
 
 01364 
 
 .032 
 
 01 368 01 372 01 376 01 381 01 385 
 
 01389 01393 
 
 01397 
 
 01 402 
 
 01406 
 
 •033 
 
 01 410 01414 01418 01423 01427 
 
 01 431 01435 
 
 01439 
 
 01444 
 
 01 448 
 
 ■034 
 
 01 452 01 456 01 460 01 465 01 469 
 
 01473 01477 
 
 oj 481 
 
 01 486 
 
 01 490 
 
 I -035 
 
 .01 494 .01 498 .01 502 .01 507 .01 511 
 
 .01 515 .01 519 
 
 -01 523 
 
 .01 528 
 
 .01 532 
 
 .036 
 
 01 536 01 540 01 544 01 549 01 553 
 
 01 557 01 561 
 
 01565 
 
 01570 
 
 01574 
 
 ■037 
 
 01 578 01 582 01 586 01 590 01 595 
 
 01 599 01 603 
 
 01 607 
 
 01 611 
 
 01 616 
 
 .038 
 
 01 620 01 624 oi 628 01 632 01 636 
 
 01 641 01 645 
 
 01 649 
 
 01653 
 
 01657 
 
 •039 
 
 01 662 01 666 01 670 01 674 OI 678 
 
 01 682 01 687 
 
 01 691 
 
 01 695 
 
 01699 
 
 1.040 
 
 .01 703 .01 708 .01 712 .01 716 .01 720 
 
 .01 724 .01 728 
 
 •01 733 
 
 •01 737 
 
 .01 741 
 
 .041 
 
 01 745 01 749 01 753 01 758 01 762 
 
 01 766 01 770 
 
 01774 
 
 01 778 
 
 01783 
 
 .042 
 
 01 787 01 791 01 795 01 799 oi 803 
 
 01 808 01 812 
 
 01 816 
 
 01 820 
 
 01 824 
 
 ■043 
 
 01 828 01 833 01 837 01 841 01 845 
 
 01 849 01 853 
 
 01858 
 
 01862 
 
 01866 
 
 .044 
 
 01 870 01 874 01 878 01 883 01 887 
 
 01 891 01 895 
 
 01899 
 
 01903 
 
 01907 
 
 I -045 
 
 .01 912 .01 916 .01 920 .01 924 .01 928 
 
 .01 932 .01 937 
 
 .01 941 
 
 ■01 945 
 
 .01 949 
 
 .046 
 
 01 953 01 957 01 961 01 966 01 970 
 
 01 974 01 978 
 
 01 982 
 
 01 986 
 
 01 991 
 
 .047 
 
 01995 01999 02003 02007 02 01 1 
 
 02015 02020 
 
 02024 
 
 02028 
 
 02032 
 
 .048 
 
 02036 02040 02044 02049 02053 
 
 02057 02061 
 
 02065 
 
 02069 
 
 02073 
 
 .049 
 
 02 078 02 082 02 086 02 ogo 02 094 
 
 02 098 02 102 
 
 02 107 
 
 02 III 
 
 02 115 
 
 LOGS. 5 PL. 
 1.0-1.1. 
 
 (10) 
 
FIVE PLACE LOGARITHMS. 
 
 1.0-1.1. ' 
 
 5 PL. LOGS. 
 
 No. 
 
 8 
 
 1.050 
 
 .051 
 .052 
 
 •053 
 .054 
 
 1-055 
 .056 
 
 ■057 
 .058 
 
 •059 
 
 1.060 
 
 .061 
 .062 
 .063 
 .064 
 
 1.065 
 .066 
 .067 
 .068 
 .069 
 
 1.070 
 
 ,.071 
 .072 
 
 •073 
 .074 
 
 1.075 
 .076 
 .077 
 .078 
 .079 
 
 1.080 
 
 .081 
 .082 
 .083 
 .084 
 
 1.08s 
 .086 
 .087 
 .088 
 .089 
 
 1.090 
 
 .091 
 .092 
 
 ■093 
 .094 
 
 1.095 
 .096 
 .097 
 .098 
 .099 
 
 .02119 .02123 .02127 .02131 .02135 
 
 02 160 02 164 02 169 02 173 02 177 
 
 02 202 02 205 02 210 02 214 02 2l8 
 
 02243 02247 02251 02255 02259 
 
 02 284 02 288 02 292 02 296 02 301 
 
 .02325 .02329 .02333 .02338 .02342 
 
 02366 02371 02375 02379 02383 
 
 02407 02412 02416 02420 02424 
 
 02449 02453 02457 02461 02465 
 
 02 490 02 494 02 498 02 502 02 506 
 
 .02531 .02535 .02539 .02543 .02547 
 
 02 572 02 576 02 580 02 584 02 588 
 
 02612 02617 02621 02625 02629 
 
 02 653 02 657 02 661 02 666 02 670 
 
 02 694 02 698 02 702 02 706 02 710 
 
 .02735 .02739 .02743 .02747 .02751 
 
 02 776 02 780 02 784 02 788 02 792 
 
 02816 02821 02825 02829 02833 
 
 02 857 02 861 02 865 02 869 02 873 
 
 02898 02902 02906 02910 02914 
 
 .02938 .02942 .02946 .02951 .02955 
 
 02 979 02 983 02 987 02 991 02 995 
 03019 03024 03028 03032 03036 
 
 03 060 03 064 03 068 03 072 03 076 
 03100 03104 03109 03113 03117 
 
 •03 157 
 03197 
 03238 
 03278 
 03318 
 
 .03 141 .03 145 .03 149 .03 153 
 
 03 181 03 185 03 189 03 193 
 
 03 222 03 226 03 230 03 234 
 
 03 262 03 266 03 270 03 274 
 
 03302 03306 03310 03314 
 
 •03 342 
 03383 
 03423 
 03463 
 03503 
 
 •03543 -03 547 •03551 -03555 -03559 
 
 03583 03587 03591 03595 03 599 
 
 03623 03627 03631 03635 03639 
 
 03663 03667 03671 0367s 03679 
 
 03703 03707 03711 03715 03719 
 
 -03743 -03747 -03751 -03755 -03759 
 
 03782 03786 03790 03794 03798 
 
 03 822 -03 826 03 830 03 834 03 838 
 
 03 862 03 866 03 870 03 874 03 878 
 
 03902 03906 03910 03914 03918 
 
 .03941 .03945 .03949 .03953 .03957 
 
 03981 03985 03989 03993 03997 
 
 04021 04025 04029 04033 04036 
 
 04060 04064 04068 04072 04076 
 04100 04104 04108 04112 04116 
 
 .03 346 .03 350 .03 354 .03 358 
 03387 03391 03395 03399 
 03427 03431 0343s 03439 
 03467 03471 0347s 03479 
 03507 03511 03515 03519 
 
 -03547 -03551 
 03587 03591 
 03627 03631 
 03667 03671 
 03707 03711 
 
 -03747 -03751 
 
 03786 03790 
 
 •03 826 03 830 
 
 03 866 03 870 
 
 03 906 03 910 
 
 .02 140 .02 144 .02 148 .02 152 .02 156 
 
 02 181 02 185 02 189 02 193 02 197 
 
 02 222 02 226 02 230 02 23s 02 239 
 
 02 263 02 268 02 272 02 276 02 280 
 
 02305 02309 02313 02317 02321 
 
 .02 346 .02 350 .02 354 .02 358 .02 362 
 02387 02391 02395 02399 02403 
 02428 02432 02436 02440 02444 
 02469 02473 02477 02481 02485 
 02510 02514 02518 02522 02526 
 
 .02551 .02555 .02559 .02563 .02567 
 02 592 02 596 02 600 02 604 02 608 
 02633 02637 02641 02645 02649 
 02 674 02 678 02 682 02 686 02 690 
 02715 02719 02723 02727 02731 
 
 .02 755 .02 759 .02 763 .02 768 .02 772 
 02796 02800 02804 02808 02812 
 02 837 02 841 02 845 02 849 02 853 
 02 877 02 882 02 886 02 890 02 894 
 02918 02922 02926 02930 02934 
 
 .02 959 
 02999 
 03040 
 03080 
 03 121 
 
 .03 161 
 03 201 
 03242 
 
 .02 963 
 03003 
 03044 
 03084 
 03125 
 
 .03 165 
 03205 
 03246 
 
 03 282 03 286 
 03322 03326 
 
 .02 967 
 03007 
 03048 
 03088 
 03129 
 
 .03169 
 03209 
 03250 
 03 290 
 03330 
 
 .02 971 
 03011 
 03052 
 03092 
 03133 
 
 •03 173 
 03214 
 
 03254 
 03294 
 03334 
 
 -02 975 
 03015 
 03056 
 03096 
 03137 
 
 -03 177 
 03 218 
 03258 
 03298 
 03338 
 
 .03 362 .03 366 .03 371 .03 375 .03 379 
 
 03403 03407 03411 03415 03419 
 
 03443 03447 03451 03455 03459 
 
 03483 03487 03491 03495 03499 
 
 03523 03527 03531 03535 03539 
 
 •03563 -03567 •03571 •OS 575 -03579 
 
 03603 03607 03611 03615 03619 
 
 03643 03647 03651 03655 03659 
 
 03683 03687 03691 03695 03699 
 
 03723 03727 03731 03735 03739 
 
 .03 763 -03 767 -03 771 •OS 775 -03 778 
 03 802 03 806 03 810 03 814 03 818 
 03842 03846 03850 03854 03858 
 
 03 882 03 886 03 890 03 894 03 898 
 03922 03926 93930 03933 03937 
 
 .03961 .03965 .03969 .03973 .03977 
 04001 04005 04009 04013 04017 
 04040 04044 04048 04052 04056 
 04080 04084 04088 04092 04096 
 
 04 120 04 123 04 127 04 131 04 135 
 
 5 PL. LOGS. 
 1.0-1.1. 
 
1. 
 
 LOGS. 5 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 8 
 
 1.00 
 
 .OI 
 .02 
 
 •03 
 
 .04 
 
 I. OS 
 
 .06 
 .07 
 .08 
 .09 
 
 1.10 
 
 .II 
 
 .13 
 
 •13 
 
 .14 
 i.iS 
 
 .16 
 
 •17 
 .18 
 .19 
 
 1.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 1. 25 
 .26 
 .27 
 .28 
 .29 
 
 1.30 
 
 ■31 
 
 ■P 
 •33 
 •34 
 
 '•35' 
 •36 
 ■37 
 •38 
 ■39 
 
 1.40 
 
 .41 
 .42 
 ■43 
 ■44 
 
 '•45 
 .46 
 
 ■47 
 .48 
 •49 
 
 .00 000 
 
 00432 
 
 00860 
 
 01 284 
 01703 
 
 .02 119 
 
 02 53-<, 
 02938 
 
 03342 
 
 03743 
 
 ■04 139 
 04532 
 04922 
 05308 
 05690 
 
 .06 070 
 06446 
 06819 
 07188 
 0755s 
 
 .07918 
 08279 
 08636 
 08991 
 09342 
 
 .09691 
 10037 
 10380 
 
 10 721 
 II 059 
 
 •II 394 
 
 11 727 
 
 .i?.°S7 
 12385 
 12710 
 
 •13033 
 13354 
 13672 
 13988 
 14 301 
 
 .00043 
 00475 
 00903 
 01 326 
 01745 
 
 .02 160 
 02572 
 02979 
 
 03383 
 03782 
 
 .04179 
 04571 
 04961 
 05346 
 05729 
 .06 108 
 06483 
 06856 
 07225 
 07591 
 
 .07954. 
 08314 
 08672 
 09026 
 09377 
 .09 726 . 
 10072 
 
 10415 
 10.755 
 1 1 093 
 
 .1 1 428 , 
 II 760 
 12090 
 12418 
 12743 
 
 .13066 . 
 13386 
 13704 
 14019 
 
 14333 
 
 .00087 
 00518 
 00945 
 01 3(18 
 
 01 787 
 
 .02 202 
 
 02 612 
 
 03 019 
 
 03423 
 03 822 
 
 .04 21^ . 
 
 04610 
 
 04999 
 
 05385 
 05767 
 
 .06 145 . 
 
 06 521 
 06893 
 
 07 262 
 07628 
 
 ,00 130 . 
 
 00 561 
 00988 
 
 01 410. 
 01 828 
 
 .02 243 , 
 
 02653 
 
 03060 
 
 03463 
 03862 
 
 .08 027 
 
 08386 
 
 08743 
 09096 
 09447 
 
 •09 795 
 
 10 140 
 10483 
 10823 
 
 11 160 
 
 •II 494 
 
 11 826 
 
 12 156 
 12483 
 12808 
 
 • 13 130 
 13450 
 
 13767 
 14082 
 
 14395 
 
 .14675. 
 
 14983 
 
 15 290 
 
 15594 
 15897 
 .16 197 . 
 
 16495 
 
 16 791 
 
 17085 
 17377 
 
 .00346 
 
 00 775 
 
 01 199 
 
 01 620 
 
 02 036 
 
 .04 297 
 04689 
 05077 
 05 46 r 
 05843 
 .06221 
 06595 
 06967 
 
 07335 
 
 07 700 
 
 .08063/ 
 
 08 422/ 
 08778 
 
 09 132 
 
 09 482 
 
 .09 830 
 
 10 175 
 10517 
 10857 
 
 11 193 
 
 .11528 
 
 11 860 
 
 12 189 
 12516 
 12840 
 
 .13162 
 13481 
 
 13799 
 14 114 
 14426 
 
 '•14737 
 
 : 15045 
 
 ' 15 351 
 
 15655 
 
 ' 15957 
 
 .16 256 
 
 16554 
 
 16 850 
 
 17 143 
 
 1743s 
 
 •04 376 
 04 766 
 
 05154 
 05538 
 05918 
 
 .06 296 
 06670 
 07041 
 07408 
 07773 
 
 .11 561 
 11893 
 
 12 222 
 12548 
 12872 
 
 •13 194 
 
 13 513 
 13830 
 
 14 145 
 14457 
 
 .14768 , 
 15076 
 
 15 381 
 15685 
 15987 
 
 .16286. 
 16584 
 16879 
 
 17 173 
 17464 
 
 ■II 594 
 II 926 
 12254 
 12581 
 12905 
 
 .13 226 
 
 13545 
 13862 
 14176 
 14489 
 
 14 799 
 
 15 106 
 15412 
 
 15 715 
 
 16 017 
 
 16316 
 
 16 613 
 16909 
 
 17 202 
 17493 
 
 04415 
 04805 
 
 05 192 
 05576 
 05956 
 ■06 '333 
 
 06 707 
 07078 
 
 07445 
 07809 
 
 .08171 
 08529 
 08884 
 I 09237 
 09587 
 
 ■09 934 
 10278 
 
 10 619 
 ■10 958 
 
 11 294 
 
 .11628 
 
 "959 
 12287 
 
 12 613 
 12937 
 
 .13258 
 13577 
 13893 
 14208 
 14520 
 
 .14829 
 
 15137 
 15442 
 
 15746 
 16047 
 
 .16 346 
 16643 
 16938 
 17231 
 17 522 
 
 .04454 
 04844 
 05231 
 05614 
 05994 
 ■06371 
 06744 
 
 0711$ 
 07482 
 07 846 
 
 .08 207 
 08565 
 08920 
 
 09 272 
 09621 
 
 .09 968 
 
 10 312 
 10653 
 10992 
 11327 
 
 ,00 389 
 00817 
 01 242 
 
 01 662 
 02078 
 .02 490 
 
 02 898 
 03302 
 
 03703 
 
 04 100 
 
 .04493 
 04883 
 
 05 269 
 05 652 
 06032 
 
 .08 243 
 08600 
 08955 
 09307 
 09656 
 .10 003 
 10346 
 10687 
 11025 
 II 361 
 
 11 661 .11 694 
 11992 12024 
 12320 12352 
 
 12 646 12 678 
 12969 13,001 
 
 13290.13322 
 13609 13640 
 
 13925 13956 
 14239 14270 
 14551 14582 
 
 14860 
 15168 
 15473 
 15776 
 16077 
 
 16376 
 16673 
 16967 
 17 260 
 17 551 
 
 .14891 
 
 15 198 
 
 15503 
 15806 
 
 16 X07 
 
 .16406 
 16 702 
 16997 
 17289 
 17580 
 
 INTERPO. 
 
 lABLES. 
 
 ForlogLO 
 
 tologl.l 
 
 interpolated 
 
 values are 
 
 Kiven on thf 
 
 preceding 
 
 two pages. 
 
 38 36 
 
 4 4 
 
 8 7 
 
 II II 
 
 15 14 
 
 19 18 
 
 23 22 
 
 27 25 
 
 30 29 
 
 34 32 
 
 34 33 
 
 3 3 
 
 7 7 
 
 10 ID 
 
 14 13 
 
 17 17 
 
 20 20 
 
 24 23 
 
 27 26 
 
 31 30 
 
 32 31 
 
 .3 3 
 
 6 6 
 
 10 9 
 
 13 12 
 
 16 16 
 
 19 19 
 
 22 22 
 
 26 25 
 
 29 28 
 
 30 29 
 
 3 3 
 
 6 6 
 
 9 9 
 
 12 12 
 
 15 15 
 
 18^17 
 
 21 20 
 
 24 23 
 
 27 26 
 
 LOGS. 5 PL. 
 
 (12) 
 
FIVE PLACE LOGARITHMS. 
 
 
 ^_,__ 
 
 6 PL. LOGS. 
 
 
 No. 
 
 01234 56789 
 
 INTERPO 
 TABLES. 
 
 
 
 1.50 
 
 .17 609 .17 638 .17 667 .17 696 .17 725 .17 754 .17 782 .17 811 .17 840 .17 869 
 
 29 27 
 
 .00 
 
 
 •51 
 
 17898 17926 17955 17984 18013 18041 18070 18099 18 127 18156 
 
 3 3 
 
 .30 
 
 
 •52 
 
 18 184 18213 18 241 18270 18298 18327 18355 '8384 18 412 18 441 
 
 6 5 
 
 
 
 ■53 
 
 18469 18498 18526 18554 18583 18 611 18639 18667 18696 18724 
 
 9 8 
 
 
 
 •54 
 
 18752 18780 18808 18837 18-865 18893 18 921 18949 18977 19 008 
 
 12 11 
 
 
 
 "•55 
 
 .19033 .19061 .19089 .19117 .19145 .19173 .19201 .19229 .19257 .19285 
 
 15 14 
 
 
 
 •55 
 
 19312 19340 19368 19396 19424 19451 19479 19507 19535 19562 
 
 17 16 
 
 
 
 •57 
 
 19590 19618^9645 19673 19700 19728 19756 19783 19 811 19838 
 
 20 19 
 
 
 
 •58 
 
 19866 19 893° 19 921 19948 19976 20 003 20030 20058 20085 20112 
 
 23 22 
 
 
 
 •59 
 
 20140 20167 20194 20222 20249 20276 20303 20330 20358 20385 
 
 26' 24 
 
 
 
 1.60 
 
 .20 412 .20 439 .20 466 .20 493 .20 520 .20 548 .20 575 .20 602 .20 629 .20 656 
 
 26 25 
 
 
 
 .61 
 
 20683 20710 20737 20763 20790 20817 20844 20371 20898 20925 
 
 3 3 
 
 
 
 .62 
 
 20952 20978 21005 21032 21059 21085 21 112 21139 211^5 21192 
 
 5 5 
 
 
 
 •63 
 
 21219 21245 21272 21299 21325 21352 21378 21405 21431 21458 
 
 8 8. 
 
 
 
 .64' 
 
 21484 21 511 21537 21564 21590 21617 21643 21669 21696 21722 
 
 10 ih 
 
 
 
 1.6s 
 
 , .21 748 .21 775 .21 801 .21 827 .21 854 .21 880 .21 906 .21 932 .21 958 .21 985 
 
 13 13 
 
 
 
 .66 
 
 22 011 22037 22063 22089 22115 22 141 22167 221^4 22220 22246 
 
 16 15 
 
 
 
 .67 
 
 22272 22298 22324- 22350 22376 22401 22427 22453 22479 22505 
 
 18 18 
 
 
 
 .68. 
 
 22531 22557 22583 22608 22634 22660 22686 22712 22737 22763 
 
 21 20 
 
 
 
 .69 
 
 22789 22814 22840 22866 22891 22917 22943 22968 22994 23 019 
 
 23 23 
 
 
 
 1.70 
 
 .23 045 .23 070 .23 096 .23 121 .23 147 .23 172 .23 198 .23 223 .23 249 .23 274 
 
 25 24 
 
 
 
 •71 
 
 23300 23325 23350 23376 23401 23426 23452 23477 23502 23528 
 
 3 2 
 
 
 
 .72 
 
 23553 23578 23603 23629 23654 23679 23704 23729 23754 23779 
 
 5 5 
 
 
 
 ■73 
 
 23S05 23830 23855 23880 23905 23930 23955 23980 24 005 24030 
 
 8 7 
 
 
 
 ■74 
 
 24055 24080 24105 24130 24155 24180 24204 24229 24254 24279 
 
 10 10 
 
 
 
 '•75 
 
 .24 304 .24 329 .24 353 .24 378 .24 403 .24 428 .24 452 .24 477 .24 502 .24 527 
 
 13 12 
 
 
 
 .76 
 
 ,24551 24576 24601 24625 24650 24674 24699 24724 24748 24773 
 
 15 14 
 
 
 
 •77 
 
 24797 24822 24846 24871 24895 24920 24944 24969 24993 25 018 
 
 18 17 
 
 
 
 •78 
 
 25 042 25 066 25 091 25 115 25 139 25 164 25 188 25 212 25 237 25 261 
 
 20 19 
 
 
 
 •79 
 
 25285 25310 25334 25358 25382 25406 25431 25455 25479 25503 
 
 23 22 
 
 
 
 1.80 
 
 ■25 527 ^25 551 ^25 575 ^25 600 .25 624 .25 648 .25 672 .25 696 .25 720 .25 744 
 
 24 23 
 
 
 
 .81 
 
 25 768 25 792 25 816 25 840 25 864 25 888 25,9,12 25 935 25 959 25 983 
 
 2 2 
 
 
 
 .82 
 
 26 007- 26 031 26055 26079 26102 26126 26150 26174 26198 26221 
 
 5 5 
 
 
 
 •83 
 
 26245 26269 26293 26316 26340 '26364 26387 26411 26435 26458 
 
 7 7 
 
 
 
 .84 
 
 26482 26505 26529 26553 26576 26600 26623 26647 26670 26694 
 
 10 9 
 
 
 
 1.8s 
 
 .26717 .26741 .26764 .26788 .26811 .26834 .26858 .26881 .26905 .26928 
 
 12 12 
 
 
 
 .86 
 
 26951 26975 26998 27 021 27045 27068 27091 27114 27138 27161 
 
 14 14 
 
 
 
 •87 
 
 27 184 27 207 27 231 27 254 27 277 27 300 27 323 27 346 27 370 27 393 
 
 17 16 
 
 
 
 .88 
 
 27416 27439 27462 27485 27508 27531 27554 27577 27600- 27 623 
 
 19 18 
 
 
 
 .•89 
 
 27646 27669 27692 27715 27738 27761 27784 27807 27830 27852 
 
 22 20 
 
 
 
 1.90 
 
 .27 875 .27 898 .27 921 .27 944 .27 967 .27 989 .28 012 .28 035 .28 058 .28 081 
 
 22 21 
 
 
 
 •91 
 
 28103 28126 28149 28 171 28194 28217 28240' 28262 28285 28307 
 
 2 2 
 
 
 
 .92 
 
 28330 28353 28375 28398 28421 28443 28466 28488 28511 28533 
 
 4 4 
 
 
 
 •93 
 
 28556 28578 28601 28623 28646 28668 28691 28713 28735 28758 
 
 7 6 
 
 
 
 ■94 
 
 28780 28803 28825 28847 28870 28892 28914 28937 28959 28981 
 
 9 8 
 
 
 
 ■95 
 
 .29 003 .29 026 .29 048 .29 070 .29 092 .29 115 .29 137 .29 159 .29 181 .29 203 
 
 11 11 
 
 
 
 .96 
 
 29226 29248 292.70 29292 29314 29336 29358 29380 29403 29425 
 
 13 13 
 
 00 
 
 
 ■97 ■ 
 
 29447 29469 29491 29513 29535 29557 29579 29601 29623 29645 
 
 15 15 
 
 .30 
 
 
 .98 
 
 29667 29688 29710 29732 29754 29776 29798 29820 29842 29863 
 
 18 17 
 
 
 
 ■99 
 
 29885 29907 29929 29951 29973 29994 30016 30038 30060 30081 
 
 20 19 
 
 
 
 
 (13) 5 PL 
 
 .. LOG 
 1. 
 
 s. 
 
2. 
 LOGS. 6 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 .30 
 
 .47 
 
 .80 
 
 .47 
 
 No. 
 
 2.00 
 
 .OI 
 .02 
 
 •03 
 
 .04 
 
 2.05 
 
 .06 
 .07 
 .08 
 .09 
 
 2.10 
 
 .II 
 
 .12 
 
 •13 
 .14 
 
 2.15 
 .16 
 
 •17 
 .18 
 
 .19 
 
 2.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 2.25 
 .26 
 .27 
 .28 
 .29 
 
 2.30 
 
 •31 
 •32 
 •33 
 •34 
 
 2-35 
 •36 
 •37 
 .38 
 •39 
 
 2.40 
 
 .41 
 .42 
 •43 
 
 ■44 
 
 2-45 
 .46 
 
 ■47 
 .48 
 •49 
 
 8 
 
 LOGS. 
 2. 
 
 •30 103 
 30320 
 
 30535 
 30750 
 30963 
 
 •31 175 
 31387 
 31597 
 31806 
 
 32 015 
 
 .32 222 
 32428 
 32634 
 32838 
 33041 
 
 •33244 
 
 33 445 
 33646 
 33846 
 34044 
 
 •34 242 
 34439 
 34635 
 34830 
 
 35025 
 •35 218 
 35 411 
 35603 
 
 35 793 
 35984 
 
 •36 173 
 36361 
 36549 
 36736 
 36922 
 
 •37 107 
 37291 
 
 37 475 
 37658 
 37840 
 
 .38 021 
 
 38 202 
 38382 
 38561 
 38739 
 
 •38917 
 39094 
 39270 
 
 39 445 
 39 620 
 
 6 PL. 
 
 ■30 125 
 30341 
 30557 
 30771 
 30984 
 
 •31 197 
 31408 
 31 618 
 31827 
 32035 
 
 ■32 243 
 32449 
 32654 
 32858 
 33062 
 
 •33 264 
 33465 
 33666 
 33866 
 34064 
 
 •34 262 
 34459 
 3465s 
 34850 
 35044 
 •35 238 
 35430 
 35622 
 
 35813 
 36 003 
 
 .30 146 , 
 
 30363 
 
 30578 
 
 30792 
 
 31006 
 
 .31 218 
 31429 
 31639 
 31848 
 32056 
 
 .32 263 
 
 32469 
 3267s 
 32879 
 33082 
 
 •33 284 
 33486 
 33686 
 33885 
 34084 
 
 ,34 282 
 
 34 479 
 34674 
 34869 
 
 35064 
 
 35 257 
 35 449 
 35641 
 35832 
 36021 
 
 .36 192 .36 211 
 36380 36399 
 
 36568 
 36754 
 36940 
 
 •37 J2S 
 37310 
 
 37 493 
 37676 
 
 37858 
 
 ■38039 
 
 38 220 
 
 38399 
 38578 
 38757 
 
 ■38 934 
 
 39 III 
 39287 
 39463 
 39637 
 
 36586 
 36773 
 36959 
 
 ■37144 
 37328 
 37 5" 
 37694 
 37876 
 
 •38057 
 38238 
 38417 
 38596 
 38775 
 
 •38 952 
 3? 129 
 
 39305 
 39480 
 
 39655 
 
 ,30 168 
 
 30384 
 
 30 600 
 30814 
 31027 
 
 •31 239 
 31450 
 
 31 660 
 31869 
 32077 
 
 .32 284 
 32490 
 32695 
 32899 
 33102 
 
 •33 304 
 33506 
 33706 
 33905 
 34104 
 
 •34 301 
 34498 
 34694 
 34889 
 35083 
 
 •35 276 
 35468 
 35660 
 
 35851 
 36040 
 
 .36 229 
 36418 
 3660s 
 36791 
 36977 
 •37 162 
 37346 
 37530 
 37712 
 37894 
 
 ■3807s 
 38256 
 
 3843s 
 38614 
 38792 
 
 ■38 970 
 39146 
 39322 
 39498 
 39672 
 
 ■30 190 
 30406 
 30621 
 30835 
 31048 
 
 .31 260 
 
 31471 
 31681 
 31890 
 32098 
 
 •32305 
 32510 
 
 32715 
 32919 
 33122 
 
 ■33 325 
 33526 
 33726 
 33925 
 34124 
 
 •34 321 
 34518 
 34713 
 34908 
 35102 
 
 •35 295 
 35488 
 35679 
 35870 
 36059 
 
 .36 248 
 
 36436 
 36624 
 36810 
 36996 
 
 •37 181 
 37365 
 37548 
 37 731 
 37912 
 
 •38093 
 38274 
 38453 
 38632 
 38810 
 
 .38 987 
 39164 
 39340 
 
 39515 
 39690 
 
 (14) 
 
 .30211 , 
 
 30428 
 
 30643 
 
 30856 
 
 31069 
 
 .31 281 
 31492 
 31 702 
 
 31 911 
 
 32 118 
 
 •32 325 
 32531 
 32736 
 32940 
 33143 
 
 •33 345 
 33546 
 33746 
 
 33 94S 
 34143 
 
 •34 341 
 
 34 537 
 
 34 733 
 34928, 
 
 35 122 
 
 •35 315 
 35507 
 35698 
 35889 
 36078 
 
 •36 267 
 
 36455 
 36642 
 36829 
 37 014 
 
 ■37 199 
 37383 
 37566 
 37 749 
 37931 
 
 .38112 
 38292 
 
 38471 
 38650 
 38828 
 
 .39 005 
 
 39182 
 39358 
 39 533 
 39707 
 
 •30 255 
 
 30471 
 30685 
 
 30899 
 
 31 112 
 
 ■31 323 
 31534 
 31744 
 31952 
 
 32 160 
 
 .32 366 
 32572 
 32777 
 32980 
 33183 
 
 •33 385 
 33586 
 33786 
 33985 
 34183 
 
 •30 233 
 30449 
 30664 
 30878 
 31091 
 .31 302 
 31 513 
 31723 
 31931 
 32139 
 
 ■32 346 
 32552 
 32756 
 32960 
 
 33163 
 
 •33 365 
 33566 
 33766 
 33965 
 34163 
 
 •34 361 
 34 557 
 34 753 
 
 34 947 
 
 35 141 
 
 •35 334 ^35 353 
 35526 35 545 
 35717 35736 
 35908 35927 
 36097 36 116 
 
 .36286 .36305 
 
 36474 36493 
 36661 36680 
 36847 36866 
 37033 37051 
 .37 218 .37 236 
 37401 37420 
 37585 ^7603 
 37 767 1 37 785 
 37 949 37967 
 
 .38 130 .38 148 
 38310 38328 
 
 38489 38507 
 38668 38686 
 38846 38863 
 
 .39023^.39041 
 39 199 39217 
 39 375 39 393 
 39550 39568 
 39724 39742 
 
 .30 276 
 30492 
 30707 
 30920 
 
 31 133 
 
 •31 345 
 31555 
 31765 
 31973 
 
 32 181 
 
 •32 387 
 32593 
 32797 
 
 33 001 
 33203 
 
 •33405 
 33606 
 33806 
 
 34 005 
 34203 
 
 •34380 ^34400 
 
 34 577 34596 
 34772 34792 
 34967 34986 
 
 35 160/ 35 180 
 
 •35 372 
 35564 
 35 755 
 35946 
 36135 
 
 ■30 298 
 30514 
 30728 
 30942 
 31 154 
 ■31 366 
 31576 
 31785 
 31994 
 32201 
 
 •32 408 
 32613 
 32818 
 33021 
 33224 
 
 •33425 
 33626 
 33826 
 34025 
 34223 
 
 .34420 
 34616 
 
 34 81 1 
 
 35 005 
 3S»i99 
 
 •35 392 
 35583 
 35 774 
 35965 
 36154 
 
 .36324 ^36342 
 36511 36530 
 36698 36717 
 36884 36903 
 37070 37088 
 
 •37 254 
 37438 
 37621 
 37803 
 37985 
 
 .38 166 
 38346 
 38525 
 38703 
 38881 
 
 •39 058 
 39235 
 39410 
 
 3958s 
 39 759 
 
 •37 273 
 37 457 
 37639 
 37822 
 38003 
 
 .38 184 
 38364 
 38543 
 38721 
 
 38899 
 .39076 
 39252 
 39428 
 39602 
 
 39 777 
 
FIVE PLACE LOGARITHMS. 
 
 5 PL. LOGS. 
 
 No. 
 
 8 
 
 INTP, 
 TAB. 
 
 2.50 
 
 •5' 
 
 •52 
 •S3 
 •54 
 
 ^•55 
 •56 
 ■57 
 .58 
 
 •59 
 
 2.60 
 
 .61 
 .62 
 
 •63 
 .64 
 
 2.65 
 .66 
 .67 
 .68 
 •69 
 
 2.70 
 
 •71 
 .72 
 
 ■73 
 •74 
 
 2^75 
 .76 
 
 ■77 
 .78 
 
 ■79 
 
 2.80 
 
 .81 
 .82 
 
 ■83 
 .84 
 
 2.85 
 .86 
 
 ■87 
 •.88 
 
 ■89 
 
 2.90 
 
 .91 
 ■92 
 ■93 
 ■94 
 
 2.95 
 .96 
 
 •97 
 .98 
 
 ■99 
 
 •39 794 
 39967 
 
 40 140 
 40312 
 40483 
 
 .40 654 
 40824 
 
 40993 
 
 41 162 
 
 41330 
 
 .41 497 
 
 41 664 
 41830 
 41996 
 
 42 160 
 
 •42 325 
 42488 
 42651 
 42813 
 42975 
 
 •43 136 
 43297 
 
 43 457 
 43616 
 
 43 775 
 
 •43 933 
 44091 
 44248 
 44404 
 44560 
 
 •44 716 
 44871 
 
 45025 
 45179 
 45332 
 
 •45 484 
 45637 
 45788 
 45 939 
 46090 
 
 .46 240 
 46389 
 46538 
 46687 
 46835 
 
 .46 982 
 47129 
 47276 
 47422 
 
 47567 
 
 .39811 
 39985 
 40157 
 40329 
 
 40SSP 
 .40671 
 40841 
 41010 
 41 179 
 41347 
 
 .41 514 
 41 681 
 41847 
 42012 
 
 42177 
 
 .42 341 
 42504 
 42-667 
 42830 
 42991 
 
 •43 152 
 43313 
 43 473 
 43632 
 43791 
 
 •43 949 
 44107 
 44264 
 44420 
 44576 
 
 ■44 731 
 44886 
 
 45040 
 45194 
 45 347 
 •45500 
 45652 
 45803 
 
 45 954 
 
 46 105 
 
 ■46 25 s 
 46404 
 
 46553 
 46702 
 46850 
 
 •46 997 
 47144 
 47290 
 47436 
 47582 
 
 •39 829 
 
 40 002 
 
 40175 
 40346 
 40518 
 
 .40 688 
 40858 
 
 41 027 
 41 196 
 41363 
 
 •41 531 
 41697 
 41863 
 42029 
 42193 
 
 •42 357 
 42521 
 42684 
 42846 
 
 43 008 
 
 ■43 169 
 43329 
 43489 
 43648 
 43807 
 
 •43 965 
 
 44 122 
 44279 
 44436 
 44592 
 
 •44 747 
 44902 
 
 45056 
 45209 
 45362 
 
 ■45 515 
 45667 
 45818 
 
 45969 
 46 120 
 
 .46 270 
 46419 
 46568 
 46716 
 46864 
 
 .47 012 
 
 47159 
 -47305 
 47451 
 47596 
 
 ■39 846 
 40019 
 
 40 192 
 40364 
 4P535 
 .40 705 
 40875 
 41044 
 
 41 212 
 41 380 
 
 ■39 863 
 40037 
 40209 
 40381 
 40552 
 
 .40 722 
 40892 
 41 061 
 41 229 
 41397 
 
 .41 547 .41 564 
 41 714 41 731 
 
 41 880 41 896 
 
 42 045 42 062 
 42 210 42 226 
 
 ■42 374 
 42537 
 
 42 700 
 42862 
 43024 
 
 •43 185 
 
 43 345 
 43505 
 43 664, 
 43823 
 
 ■43 981 
 44138 
 44295 
 
 44451 
 44607 
 
 .42 390 
 
 42553 
 
 42 716 
 42878 
 43040 
 
 ■43 201 
 43361 
 43521 
 
 43 680 
 43838 
 
 ■43 996 
 44154 
 
 44 31 1 
 44467 
 44623 
 
 .44762 .44778 
 44917 44932 
 45071 45086 
 45 225 45 240 
 45378 45 393 
 
 ■45-530 
 45 682 
 45834 
 45984 
 46135 
 
 .46 285 
 46434 
 46583 
 4673" 
 46879 
 
 .47 026 
 47173 
 47319 
 47465 
 47 61 1 
 
 •45 545 
 45697 
 45849 
 
 46 000 
 46150 
 
 .46300 
 46449 
 46598 
 46746 
 46894 
 
 •47 041 
 47188 
 
 47 334 
 47480 
 47625 
 
 .39 881 
 40054 
 40226 
 40398 
 40569 
 
 •40 739 
 40909 
 41 078 
 41 246 
 41414 
 
 ••41 581 
 41747 
 
 41 913 
 
 42 078 
 42243 
 
 .42 406 
 42570 
 42732 
 42894 
 43056 
 
 •43217 
 
 43 377 
 43 537 
 43696 
 
 43854 
 .44 012 
 
 44170 
 44326 
 
 44483 
 44638 
 
 •44 793 
 44948 
 45 102 
 45255 
 45408 
 
 ■45 561 
 45712 
 45864 
 46015 
 46165 
 
 •46315 
 46464 
 46613 
 46761 
 46909 
 
 ■47 056 
 47 202 
 
 47 349 
 47 494 
 47640 
 
 ■39 898 
 40071 
 40243 
 40415 
 40586 
 
 .40 756 
 40926 
 41095 
 41263 
 41430 
 
 •41 597 
 41764 
 41929 
 42095 
 42259 
 
 •42 423 
 42586 
 
 42749 
 
 42 911 
 43072 
 
 •43 233 
 
 43 393 
 43 553 
 43712 
 43870 
 .44028 
 44185 
 44342 
 44498 
 44654 
 
 .44 809 
 44963 
 45117 
 45271 
 45423 
 
 •45 576 
 45728 
 
 45879 
 46030 
 46 180 
 
 •46 330 
 46479 
 46627 
 
 46776 
 46923 
 
 •47 070 
 47217 
 
 47363 
 47509 
 47654 
 
 •39915 
 40088 
 40261 
 40432 
 40603 
 
 ■40 773 
 40943 
 41 III 
 41 280 
 41447 
 
 .41 614 
 
 41 780 
 41946 
 
 42 III 
 42275 
 
 •42 439 
 42602 
 
 42765 
 42927 
 43088 
 
 •43 249 
 43409 
 43569 
 43727 
 43886 
 
 •44044 
 44 201 
 
 44358 
 44514 
 44669 
 
 .44 824 
 
 44 979 
 45133 
 
 45 286 
 45 439 
 
 ■45 591 
 45 743 
 45894 
 46045 
 46195 
 
 •46 345 
 46494 
 46642 
 46790 
 46938 
 
 .47085 
 47232 
 47378 
 47524 
 47669 
 
 ■39 933 
 
 40 106 
 40278 
 40449 
 40620 
 
 •40 790 
 40960 
 
 41 128 
 
 41 296 
 41464 
 
 ■41 631 
 41797 
 41963 
 
 42 127 
 
 42 292 
 
 ■42 455 
 42619 
 42781 
 42943 
 43104 
 
 ■43 265 
 43425 
 43584 
 
 43 743 
 43902 
 
 •44059 .44075 
 44217 44232 
 
 44 373 44389 
 44529 44 545 
 44 685 44 700 
 
 •39 950 
 40123 
 40295 
 40466 
 40637 
 .40 807 
 40976 
 41 145 
 41313 
 41 481 
 
 .41 647 
 41 814 
 41979 
 42144 
 42308 
 
 ■42 472 
 42635 
 42797 
 
 42959 
 43120 
 
 .43 281 
 43441 
 43600 
 
 43 759 
 43917 
 
 .44840 
 
 44 994 
 45148 
 45301 
 
 45 454 
 .45 606 
 45758 
 
 45 909 
 46060 
 46210 
 
 .44855 
 45 010 
 
 45 163 
 45317 
 45469 
 
 .45 621 
 45 773 
 45924 
 46075 
 46225 
 
 (15) 
 
 •46 359 -46 374 
 46509 46523 
 46657 46672 
 
 46 805 46 820 
 46953 46967 
 .47 100 .47 114 
 
 47 246 47 261 
 47392 47407 
 47538 47 553 
 47683 47698 
 
 6 PL. 
 
 LOGS. 
 2. 
 
FIVE PLACE LOGARITHMS. 
 
 LOGS. 5 PL. 
 
 No. 
 
 8 
 
 3.00 
 
 .OI 
 
 .02 
 
 •03 
 .04 
 
 305 
 .06 
 .07 
 .oS 
 .09 
 
 3.10 
 
 .11 
 .12 
 
 •>3 
 .14 
 
 3-«5 
 .16 
 
 •17 
 .18 
 
 •19 
 
 3.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 3-25 
 .26 
 .27 
 .28 
 .29 
 
 3.30 
 
 ■31 
 •32 
 ■33 
 •34 
 
 3-35 
 ■36 
 •37 
 •38 
 •39 
 
 3.40 
 
 •4' 
 .42 
 
 •43 
 •44 
 
 3-45 
 .46 
 
 •47 
 .48 
 
 •49 
 
 LOGS. 
 3. 
 
 •47712 • 
 47857 
 
 48 001 
 
 48144 
 48287 
 
 •48 430 
 48572 
 48714 
 48855 
 48996 
 
 ■49 136 
 49276 
 
 49415 
 
 49 554 
 49693 
 
 •49 831 
 49969 
 
 50 106 
 5° 243 
 50379 
 
 .50515 
 50651 
 50786 
 50920 
 51055 
 .51 188 
 51322 
 51455 
 51587 
 51720 
 
 .51 851 
 
 5«983 
 52 114 
 52244 
 52375 
 
 ■52 504 
 52634 
 52763 
 52892 
 53020 
 
 ■53 148 
 53275 
 53403 
 53529 
 53656 
 
 ■53 782 
 53908 
 54033 
 54158 
 54283 
 
 6 PL. 
 
 47 727 
 47871 
 48015 
 
 48159 
 48302 
 
 .48444 
 48586 
 48728 
 48869 
 
 49 010 
 
 •49 150 
 49290 
 49429 
 49568 
 49707 
 
 •49 845 
 49982 
 
 50 120 
 50256 
 50393 
 
 •50 529 
 50664 
 
 50799 
 50934 
 51068 
 
 .51 202 
 
 51335 
 51468 
 
 51 601 
 51733 
 
 .51865 
 51996 
 52127 
 52257 
 52388 
 
 •52517 
 52647 
 52776 
 52905 
 53033 
 
 ■53 161 
 53288 
 
 53415 
 53542 
 53668 
 
 ■53 794 
 53920 
 
 54045 
 54170 
 
 54295 
 
 ■47 741 
 47885 
 48029 
 
 48173 
 48316 
 
 .48458 
 48601 
 48742 
 48883 
 49024 
 
 •49 164 
 49304 
 
 49 443 
 49582 
 49721 
 
 ■49 859 
 49996 
 
 50133 
 
 50 270 
 50406 
 
 .50 542 
 50678 
 50813 
 
 50947 
 
 51 081 
 
 .51215 
 51348 
 51481 
 51 614 
 5^746 
 
 .51 878 
 62 009 
 
 52140 
 52270 
 52401 
 
 •52 530 
 52660 
 52789 
 52917 
 53046 
 
 ■53 173 
 53301 
 53428 
 
 53 555 
 53681 
 
 ■53807 
 53 933 
 54058 
 54183 
 54307 
 
 •47 756 
 
 47900 
 
 48044 
 
 48187 
 
 48330 
 
 .48473 , 
 
 48615 
 
 48756 
 
 48897 
 
 49038 
 
 •49 178 
 49318 
 49 457 
 49596 
 
 49 734 
 
 •49 872 
 
 50 010 
 
 50147 
 50284 
 50420 
 
 •50556 
 50691 
 50826 
 50961 
 51095 
 
 .51 228 
 51362 
 
 51495 
 51627 
 
 51759 
 
 .51 891 
 52022 
 
 52153 
 52284 
 
 52414 
 
 •52 543 
 52673 
 52802 
 52930 
 53058 
 
 •53 186 
 53314 
 53441 
 53567 
 53694 
 •53 820 
 53 945 
 54070 
 
 54195 
 54320 
 
 •47 770 
 47914 
 48058 
 48202 
 48344 
 
 .48487 
 48629 
 
 48770 
 
 48 9H 
 49052 
 
 •49 192 
 49332 
 
 49 471 
 49610 
 49748 
 
 .49 886 
 50024 
 
 50 161 
 50297 
 50433 
 
 •50 569 
 50705 
 50840 
 
 50974 
 
 51 108 
 
 .51 242 
 
 51375 
 51508 
 
 51 640 
 51772 
 
 .51 904 
 
 52035 
 
 52 166 
 
 52297 
 52427 
 .52556 
 52686 
 52815 
 52943 
 53071 
 
 •53 199 
 53326 
 
 53 453 
 53580 
 53706 
 •53 832 
 53958 
 54083 
 54208 
 54332 
 
 •47 784 
 47929 
 48073 
 48216 
 48359 
 .48 501 
 48643 
 48785 
 48926 
 49066 
 
 •47 799 
 47 943 
 48087 
 48230 
 48373 
 .48515 
 48657 
 48799 
 48940 
 49080 
 
 •47 813 
 47958 
 48 lOI 
 48 244 
 48387 
 .48 530 
 48671 
 48813 
 48954 
 49094 
 
 ,47 828 .47 842 
 47972 47986 
 48 116 48 130 
 48259 48273 
 
 48 401 48 416 
 
 .48 544 .48 558 
 48686 48700 
 48827 48841 
 48968 48982 
 
 49 108 49 122 
 
 .49 206 .49 220 
 49346 49360 
 49485 49499 
 49624 49638 
 49762 49776 
 
 .49900 
 50037 
 50174 
 
 50 3" 
 50447 
 
 •50583 
 50718 
 50853 
 
 50987 
 
 51 121 
 
 •51 255 
 51388 
 51 521 
 51 654 
 51786 
 
 .51917 
 52048 
 52179 
 52310 
 52440 
 
 •52 569 
 52699 
 52827 
 52956 
 53084 
 
 .53212 
 
 53 339 
 53466 
 
 53 593 
 53719 
 
 ■53 845 
 53970 
 54095 
 54220 
 
 54 345 
 
 •49 914 
 50051 
 50188 
 
 50325 
 50461 
 
 .50 596 
 50732 
 50866 
 51001 
 51135 
 .51 268 
 51402 
 
 51534 
 51667 
 
 51799 
 
 •51 930 
 52061 
 52192 
 52323 
 52453 
 
 •52 582 
 
 52711 
 52840 
 
 52969 
 
 53097 
 
 •53 224 
 53352 
 
 53 479 
 53605 
 
 53732 
 
 •53 857 
 53983 
 
 54 108 
 
 54233 
 54 357 
 
 .49 234 .49 248 .49 262 
 49 374 49388 49402 
 49513 49527 49541 
 49651 49665 49679 
 49790 49803 49817 
 
 •49927 ^49 941 ^49 955 
 50065 50079 50092 
 50202 50215 50229 
 50338 50352 50365 
 50474 50488 50501 
 
 .50610 
 
 50745 
 50880 
 
 51014 
 51148 
 
 .51 282 
 
 51 415 
 51548 
 51680 
 51812 
 
 •51 943 
 5-2075 
 52205 
 
 52336 
 52466 
 
 •52 595 
 52724 
 52853 
 52982 
 53 no 
 
 •53 237 
 53364 
 53491 
 53618 
 
 53 744 
 
 •53 870 
 
 53 995 
 
 54 120 
 54245 
 54370 
 
 .50 623 
 50759 
 50893 
 
 51 028 
 51 162 
 
 .51 295 
 51428 
 51561 
 51693 
 51825 
 
 •51 957 
 52088 
 52218 
 52349 
 52479 
 .52608 
 
 52737 
 
 52 866 
 52994 
 .53 122 
 
 •53 250 
 
 53 377 
 53504 
 53631 
 53 757 
 •S3 882 
 54008 
 
 54133 
 54258 
 54382 
 
 •50 637 
 50772 
 50907 
 
 51041 
 pi75- 
 •51 308 
 51441 
 51574 
 
 51 706 
 51838 
 
 •51970 
 
 52 lOI 
 
 52231 
 52362 
 
 52492 
 .52 621 
 52750 
 
 52879 
 
 53 007 
 
 53135 
 
 •S3 263 
 53390 
 53517 
 53643 
 53769 
 
 •53895 
 54020 
 
 54145 
 54270 
 
 54 394 
 
 (16) 
 
FIVE PLACE LOGARITHMS. 
 
 
 
 5 PL. 
 
 LOGS 
 
 No. 
 
 01234 
 
 5 6, 7 8 9 
 
 INTP 
 TAB. 
 
 
 3.50 
 
 .54407 ^54419 ^54432 ^54 444 .54 456 
 
 •54469 ^54481 .54494 .54506 .54518 
 
 13 
 
 .4' 
 
 •S' 
 
 54 53" 54 543 54 555 54 568 54580 
 
 54 593 54605 54617 54630 54642 
 
 1 
 
 .6C 
 
 •52 
 
 54654 54667 54679 54691 54704 
 
 54716 54728 54741 54 753 54765 
 
 3 
 
 
 •S3 
 
 54 777 54790 54802 54814 54827 
 
 54839 54851 54864 54876 54888 
 
 4 
 
 
 •54 
 
 54900 54913 54925 54 937 54 949 
 
 54962 54 974 54986 54998 86 011 
 
 5 
 
 
 3-SS 
 
 •55 023 .55 035 -55 047 •SS 060 .55 072 
 
 .55084 .55096 .55 108 .55 121 .55 133 
 
 7 
 
 
 •56 
 
 55 "45 "^55 157 55169 55182 55194 
 
 55206 55218 55230 55242 55255 
 
 8 
 
 
 ■57 
 
 55267 55279 55291 55303 55315 
 
 55328 55340 55352 55364 55376 
 
 9 
 
 
 ■58 
 
 55388 55400 55413 55425 55437 
 
 55 449 55461 55473 55485 55497 
 
 10 
 
 
 •59 
 
 55509 55522 55534 55546 55558 
 
 55570 55582 55594 55606 55618 
 
 12 
 
 
 3.60 
 
 •55 630 .55 642 .55 654 ^55 666 .55 678 
 
 •55 691 -55 703 .55 715 •SS 727 ^55 739 
 
 13 
 
 
 .6i 
 
 55751 55763 55775 55787 55799 
 
 55811 ,55823 55835 55847 55859 
 
 I 
 
 
 .62 
 
 55871 55883 55895 55907 55919 
 
 55 931 55 943 55 955 55 967 55 979 
 
 2 
 
 
 ■63 
 
 55991 56 003 56015 56027 56038 
 
 56050 56062 56074 56086 56098 
 
 4 
 
 
 .64 
 
 56 no 56122 56134 56146 56158 
 
 56170 56182 56194 56205 56217 
 
 5 
 
 
 3-65 
 
 .56 229 .56 241 .56 253 .56 265 .56 277 
 
 .56289 .56301 .56312 .56324 .56336 
 
 6 
 
 
 .66 
 
 56348 56360 56372 56384 56396 
 
 56407 56419 56431 56443 56455 
 
 7 
 
 
 .67 
 
 56467 56478 56490 56502 56514 
 
 56526 56538 56549 56561 56573 
 
 8 
 
 
 .68 
 
 56585 56597 56608 56620 56632 
 
 56 644 56 656 56 667 56 679 56 691 
 
 10 
 
 
 .69 
 
 56703 56714 56726 56738 56750 
 
 56761 56773 56785 56797 56808 
 
 11 
 
 
 3.70 
 
 .56820 .56832 .56844 .56855 .56867 
 
 .56879 .56891 .56902 .56914 .56926 
 
 12 
 
 
 •71 
 
 56937 56949 56961 56972 56984 
 
 56996 57 008 57019 57031 57043 
 
 I 
 
 
 .72 
 
 57054 57066 57078 57089 57101 
 
 57113 57124 57136 57148 57159 
 
 2 
 
 
 ■73 
 
 57171 57183 57194 57206 57217 
 
 57229 57241 57252 57264 57276 
 
 4 
 
 
 •74 
 
 57287 57299 57310 57322 57334 
 
 57 345 57 357 57 368 57 380 57 392 
 
 5 
 
 
 3-75 
 
 •57403 ^57415 ^57426 .57438 .57449 
 
 ■57461 .57473 .57484 .57496 .57507 
 
 6 
 
 
 .76 
 
 57S"9 57530 57542 57553 57565 
 
 57576 57588 57.600 57 6u 57623 
 
 7 
 
 
 •77 
 
 57634 57646 57657 57669 57680 
 
 57692 57703 57715 57726 57738 
 
 8 
 
 
 .78 
 
 57 749 57761 57772 57784 57795 
 
 57807 57818 57830 57841 57852 
 
 10 
 
 
 •79 
 
 57864 57875 57887 57898 57910 
 
 57 921 57933 57944 57955 57967 
 
 11 
 
 
 3.80 
 
 ■57978 ^57990 .58 001 .58013 .58024 
 
 .58035 .58047 .58058 .58070 .58081 
 
 11 
 
 
 .81 
 
 58092 58104 58115 58127 58138 
 
 58 149 58 161 58 172 58 184 58 195 
 
 1 
 
 
 .82 
 
 58 206 58 218 58 229 58 240 58 252 
 
 58263 58274 58286 58297 58309 
 
 2 
 
 
 •83 
 
 58320 58.331 58343 58354 58365 
 
 58377 58388 58399 58410 58422 
 
 3 
 
 
 .84 
 
 58433 58444 58456 58467 58478 
 
 58490 58501 58512 58524 58535 
 
 4 
 
 
 3-85 
 
 .58 546 .58 557 .58 569 .58 580 .58 591 
 
 .58602 .58 614,. 58 625 .58636 .58647 
 
 6 
 
 
 .86 
 
 58659 58670 58681 58692 58704 
 
 58715 58726 58737 58749 58760 
 
 7 
 
 
 .87 
 
 58 771 58 782 58 794 "58 805 58 816 
 
 58827 58838 58850 58861 58872 
 
 8 
 
 
 .88 
 
 58883 58894 58906 58917 58928 
 
 58939 58950 58961 58973 58984 
 
 9 
 
 
 .89 
 
 58995 59 006 59017 59028 59040 
 
 59051 59062 59073 59084 59095 
 
 10 
 
 
 3.90 
 
 .59 106 .59 118 .59 129 .59 140 .59 151 
 
 .59 162 .59 173 .59 184 .59 195 .59 207 
 
 11 
 
 
 .91 
 
 59218 59229 59240 59251 59262 
 
 59273 59284 59295 59306 59318 
 
 1 
 
 
 .92 
 
 59329 59340 59351 59362 59 373 
 
 59384.59395 59406 59417 59428 
 
 2 
 
 
 •93 
 
 59 439 59450 5946/ 59472 59483 
 
 59 494 59506 59517 59528 59 539 
 
 3 
 
 
 .94 
 
 59550 59561 59 572 59583 59 594 
 
 59605 59616 59627 59638 59649 
 
 4 
 
 
 3-95 
 
 .59 660 .59 671 .59 682 .59 693 .59 704 
 
 ■59 715 -59 726 .59 737 ^59 748 .59 759 
 
 6 
 
 
 .96 
 
 59770 59780 59791 59802 59813 
 
 59824 59835 59846 59857 59868 
 
 7 
 
 .47 
 
 ■97 
 
 59879 59890 59901 59912 59923 
 
 59 934 59 945 59 956 59 966 59977 
 
 8 
 
 .60 
 
 .98 
 ■99 
 
 59988 59999 60 010 60021 60032 
 
 60043 60054 60065 60076 60086 
 
 9 
 
 
 60097 60108 60119 60130 60141 
 
 60 152 60 163 60 173 60 184 60 195 
 
 10 
 
 
 
 (17) 6 PL. I 
 
 .OG 
 3. 
 
 s. 
 
4. 
 LOGS. 6 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 8 
 
 4.00 
 
 .01 
 .02 
 
 •03 
 .04 
 
 4-05 
 .06 
 .07 
 .08 
 .09 
 
 4.10 
 
 .11 
 .12 
 
 •13 
 
 .14 
 
 4.15 
 .16 
 
 •17 
 .18 
 .19 
 
 4.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 4.25 
 .26 
 .27 
 .28 
 .29 
 
 4.30 
 
 •3J 
 ■32 
 •33 
 •34 
 
 4-35 
 •36 
 •37 
 •38 
 •39 
 
 4.40 
 
 .41 
 .42 
 ■43 
 •44 
 
 4-45 
 .46 
 
 •47 
 .48 
 ■49 
 
 .60 206 
 60314 
 60423 
 60531 
 60638 
 
 .60 746 
 60853 
 60959 
 61 066 
 61 172 
 
 .61 278 
 61384 
 61 490 
 
 61595 
 61 700 
 
 .61 805 
 
 61 909 
 62014 
 
 62 118 
 
 62 221 
 
 .62 325 
 62428 
 62531 
 62634 
 62737 
 
 •62 839 
 62941 
 63043 
 63144 
 63246 
 
 •63 347 
 63448 
 
 63548 
 63649 
 
 63 749 
 
 •63 849 
 63949 
 64048 
 64147 
 64246 
 
 •64 345 
 64444 
 64542 
 64640 
 64738 
 
 .64836 
 
 64933 
 65031 
 65 128 
 65225 
 
 ,60217 
 60325 
 
 60433 
 
 60 541 
 60649 
 
 .60 756 
 60863 
 60970 
 
 61 077 
 61 183 
 
 .61 289 
 
 61395 
 61 500 
 61 606 
 6i 711 
 
 .61 815 
 61 920 
 62024 
 62128 
 62232 
 
 •62.335 
 62439 
 62542 
 62644 
 62747 
 
 .62 849 
 62951 
 63053 
 63155 
 63256 
 
 •63 357 
 63458 
 63558 
 63659 
 63759 
 .63 859 
 63959 
 64058 
 64157 
 64256 
 
 •64355 
 64454 
 64552 
 64650 
 64748 
 
 .64 84^ 
 
 64943 
 65040 
 
 65137 
 65234 
 
 .60 228 , 
 
 60336 
 
 60444 
 
 60552 
 
 60660 
 
 .60 767 
 60874 
 60981 
 61087 
 61 194 
 
 .61 300 
 61 405 
 61 511 
 61 616 
 
 61 721 
 
 .61 826 
 61930 
 62034 
 
 62 138 
 62242 
 
 .62 346 
 62449 
 62552 
 62655 
 62757 
 
 .62 859 
 62961 
 63063 
 63165 
 63266 
 
 •63 367 
 63468 
 63568 
 63669 
 63769 
 
 ■63 869 
 63969 
 64068 
 64167 
 64266 
 
 .64 365 
 64464 
 64562 
 64660 
 64758 
 .64856 
 
 64953 
 65 050 
 65147 
 65244 
 
 .60 239 
 60347 
 60455 
 60563 
 60670 
 
 .60 778 
 60885 
 60991 
 61 098 
 61 204 
 
 .61 3l[o 
 61 416 
 61 521 
 61 627 
 61 731 
 
 .61 836 
 
 61 941 
 62045 
 
 62 149 
 62252 
 
 •62 356 
 62459 
 62562 
 62665 
 62 767 
 
 .62 870 
 62972 
 63073 
 63175 
 63276 
 
 ■63 377 
 63478 
 63579 
 63679 
 
 63779 
 
 •63 879 
 63979 
 64078 
 64177 
 64276 
 
 ■64 375 
 64473 
 64572 
 64670 
 64768 
 
 .64 865 
 64963 
 65 060 
 
 65157 
 65254 
 
 .60 249 
 60358 
 60466 
 60574 
 60681 
 
 .60788 
 60895 
 61002 
 61 109 
 61 215 
 
 .61 321 
 61 426 
 61532 
 61637 
 61 742 
 
 .61 847 
 61 951 
 62055 
 62159 
 62263 
 
 .62 366 
 62469 
 62572 
 62675 
 62778 
 
 .62 880 
 62982 
 63083 
 63185 
 63286 
 
 ■63387 
 63488 
 63589 
 63689 
 
 63789 
 .63 889 
 63988 
 64088 
 64187 
 64286 
 
 ■64 385 
 64483 
 64582 
 64680 
 64777 
 
 .64875 
 64972 
 65070 
 65 167 
 65263 
 
 .60 260 
 60 369 
 60477 
 
 60 584 
 60692 
 
 .60 799 
 60906 
 
 61 013 
 61 119 
 61 225 
 
 ■61 331 
 61437 
 61 542 
 61648 
 61 752 
 
 .61 857 
 
 61 962 
 62066 
 
 62 170 
 62273 
 
 ■62 377 
 62480 
 62583 
 62685 
 62788 
 
 .62 890 
 62992 
 63094 
 
 63195 
 63296 
 
 •63 397 
 63498 
 
 63599 
 63699 
 
 63799 
 ■63 899 
 63998 
 64098 
 64197 
 64296 
 
 •64 395 
 64493 
 64591 
 64689 
 64787 
 
 .64 885 
 64982 
 
 65079 
 65 176 
 
 65273 
 
 .60 271 
 60379 
 60487 
 
 60595 
 60703 
 
 .60810 
 60917 
 61 023 
 61 130 
 61 236 
 
 •61 342 
 61 448 
 
 61553 
 61658 
 61 763 
 
 .61 868 
 
 61 972 
 62076 
 
 62 180 
 62 284 
 
 .62 387 
 62490 
 
 62593 
 62696 
 
 62 798 
 .62900 
 
 63 003 
 63104 
 63205 
 63306 
 
 .63 407 
 63508 
 63609 
 63709 
 63809 
 
 .63 909 
 64008 
 
 64 108 
 64207 
 64306 
 
 .64 404 
 
 64503 
 64601 
 64699 
 64797 
 .64 895 
 64992 
 65089 
 
 65 186 
 65283 
 
 .60 282 
 60390 
 60498 
 60606 
 60713 
 
 .60821 
 60927 
 61034 
 61 140 
 61247 
 
 .61 352 
 61458 
 61563 
 
 61 669 
 61773 
 .61 878 
 61982 
 62086 
 
 62 190 
 62294 
 
 •62 397 
 62500 
 62603. 
 
 62 706 
 62808 
 .62910 
 63012 
 63114 
 63215 
 63317 
 
 •63417 
 63518 
 63619 
 
 63 7«9 
 63819 
 
 •63 919 
 64018 
 64118 
 64217 
 64316 
 
 .64414 
 
 64513 
 64611 
 64709 
 64807 
 
 .64 904 
 66 002 
 
 65099 
 65 196 
 65292 
 
 .60 304 
 60412 
 60520 
 60627 
 6073s 
 
 .60842 
 60949 
 61055 
 61 162 
 61268 
 
 •61 374 
 61479 
 61584 
 
 61 690 
 61794 
 
 .61 899 
 
 62 003 
 
 62 107 
 
 62 211 
 62315 
 
 .62418 
 62521 
 62624 
 62 726 
 62829 
 
 •62931 
 63033 
 63134 
 63236 
 
 63337 
 
 .63438 
 63538 
 63639 
 63739 
 63839 
 
 .63929 .63939 
 64 028 64 038 
 
 64 128 64 137 
 64227 64237 
 64326 64335 
 
 .64424 .64434 
 64523 64532 
 64621 64631 
 64719 64729 
 64816 64826 
 
 .64914 .64924 
 65011 65021 
 
 65 108 65 118 
 65205 65215 
 65302 65312 
 
 ,60 293 
 60401 
 60509 
 60617 
 60724 
 
 .60 831 
 60938 
 61045 
 61 151 
 61 257 
 
 •61 363 
 61 469 
 
 61574 
 
 61 679 
 
 6i 784 
 
 .61 888 
 
 61993 
 62097 
 62201 
 62304 
 
 .62 408 
 62511 
 .62 613 
 
 62 716 
 62818 
 
 .62 921 
 63022 
 63124 
 63225 
 63327 
 
 .63 428 
 63528 
 63629 
 63729 
 63829 
 
 LOGS. 5 PL. 
 4. 
 
 (i8) 
 
FIVE PLACE LOGARITHMS. 
 
 
 
 . 5 PL. 
 
 LOGS 
 
 No. 
 4.50 
 
 01234 
 
 56789 
 
 INTP 
 TAB. 
 
 
 .65 321 .65 331 .65 341 .65 350 .65 360 
 
 •65 369 65 379 .65 389 .65 398 .65 408 
 
 10 
 
 .6( 
 
 •SI 
 
 65418 65427 65437 65447 65456 
 
 65466 65475 65485 65495 65504 
 
 I 
 
 .6£ 
 
 ■52 
 
 65514 65523 65533 65543 65552 
 
 ■ 65 562 65 571 65 581 65 591 65 600 
 
 2 
 
 
 •53 
 
 65 610 65 619 65 629 65 639 65 648 
 
 65 658 65 667 65 677 65 686 65 696 
 
 3 
 
 
 •54 
 
 65 706 65 715 65 725 65 734 .65 744 
 
 65 753 65 763 65 772 65 782 65 792 
 
 4 
 
 
 4-55 
 
 .65 8oi .65 81 1 .65 820 .65 830 .65 839 
 
 .65 849 .65 858 .65 868 .65 877 .65 887 
 
 5 
 
 
 •56 
 
 65896 65906 65916 65925 65935 
 
 65944 65954 65963 65973 65982 
 
 6 
 
 
 •57 
 
 65 992 66 001 66 01 1 66 020 66 030 
 
 66039 66049 66058 66068 66077 
 
 7 
 
 
 •58 
 
 66087 66096 66106 66 115 66124 
 
 66134 66143 66153 66162 66172 
 
 8 
 
 
 •59 
 
 66 181 66 191 66200 66210 66219 
 
 66229 66238 66247 66257 66266 
 
 9 
 
 
 4.60 
 
 .66276 .66285 -66295 .66304 .66314 
 
 .66323 .66332 .66342 .66351 .66361 
 
 9 
 
 
 .61 
 
 66370 66380 66389 66398 66408 
 
 66417 66427 66436 66445 66455 
 
 1 
 
 
 .62 
 
 66464 66474 66483 66492 66502 
 
 66 511 66521 66530 66539 66549 
 
 2 
 
 
 •63 
 
 66558 66567 66577 66586 66596 
 
 66605 66614 66624 66633 66642 
 
 3 
 
 
 .64 
 
 66652 66661 66671 66680 66689 
 
 66699 66708 66717 66727 66736 
 
 4 
 
 
 4-65 
 
 .66745 .66755 .66764 .66773 -66783 
 
 .66792 .66801 .66811 .66820 .66829 
 
 5 
 
 
 .66 
 
 66839 66848 66857 66867 66876 
 
 66885 66894 66904.66913 66922 
 
 5 
 
 
 .67 
 
 66 932 66 941 66 950 66 960 66 969 
 
 66978 66987 66997 67 006 67015 
 
 6 
 
 
 .68 
 
 67025 67034 67043 67052 67062 
 
 67071 67080 67089 67099 67108 
 
 7 
 
 
 .69 
 
 67 117 67127 67136 67145 67154 
 
 67 164 67 173 67 182 67 191 67 201 
 
 8 
 
 
 4,70 
 
 .67 210 .'67 219 .67 228 .67 237 .67 247 
 
 .67256 .67265 .67274 .67284 .67293 
 
 9 
 
 
 •71 
 
 67302 67 311 67321 67330 67339 
 
 67348 67357 67367 67376 67385 
 
 1 
 
 
 .72 
 
 67394 67403 67413 67422 67431 
 
 67440 67449 67459 67468 67477 
 
 2 
 
 
 •73 
 
 67486 67495 67504 67514 67523 
 
 67532 67541 67550 67560 67569 
 
 3 
 
 
 •74 
 
 67578 67587 67596 67605 67614 
 
 67624 67633 67642 67651 67660 
 
 4 
 
 
 4^75 
 
 .67 669 .67 679 .67 688 .67 697 .67 706 
 
 .67 715 .67 724 .67 733 .67 742 .67 752 
 
 5 
 
 
 .76 
 
 67 761 67 770 67 779 67 788 67 797 
 
 67806 67815 67825 67834 67843 
 
 5 
 
 
 ■77 
 
 67852 67861 67870 67879 67888 
 
 67897 67906 67916 67925 67934 
 
 6 
 
 
 .78 
 
 67943 67952 67961 67970 67979 
 
 67988 67997 68 006 68015 68024 
 
 7 
 
 
 •79 
 
 68034 68043 68052 68061 68070 
 
 68079 68088 68097 68106 68115 
 
 8 
 
 
 4.80 
 
 .68 124 .68 133 .68 142 .68 151 .68 160 
 
 .68 169 .68 178 .68 187 .68 196 .68 205 
 
 9 
 
 
 .81 
 
 68215 68224 68233 68242 68251 
 
 68260 68 269 68 278 68287 68296 
 
 I 
 
 
 .82 
 
 68305 68314 68323 68332 68341 
 
 68350 68359 68368 68377 68386 
 
 2 
 
 
 •83 
 
 68395 68404 68413 68422 68431 
 
 68440 68449 68458 68467 68476 
 
 3 
 
 
 .84 
 
 68485 68494 68502 68511 68520 
 
 68529 68538 68547 68556 68565 
 
 4 
 
 
 4.85 
 
 .68574 .68583 .68592 .68601 .68610 
 
 .68 619 .68 628 .68 637 .68 646 .68 655 
 
 5 
 
 
 .86 
 
 68 664 68 673 68 681 68 690 68 699 
 
 68708 68717 68726 68735 68744 
 
 5 
 
 
 •87 
 
 68753 68762 68771 68780 68789 
 
 68797 68806 68815 68824 68833 
 
 6 
 
 
 .88 
 
 68842 68851 68860 68869 68878 
 
 68 886 68895 68904 68913 68922 
 
 7 
 
 
 .89 
 
 68931 68940 68949 68958 68966 
 
 68975 68984 68993 69 002 69011 
 
 8 
 
 
 4.90 
 
 .69020 .69028 .69037 .69046 .69055 
 
 .69064 .69073 .69082 .69090 .69099 
 
 8 
 
 
 •91 
 
 69108 69 117 69126 69135 69144 
 
 69 152 69 161 69 170 69 179 69 188 
 
 1 
 
 
 .92 
 
 69 197 69 205 69 214 69 223 69 232 
 
 69 241 69 249 69 258 69 267 69 276 
 
 2 
 
 
 •93 
 
 69285 69294 69302 69 311 69320 
 
 69329 69338 69346 69355 69364 
 
 2 
 
 
 •94 
 
 69373 69381 69390 69399 69408 
 
 69417 69425 69434 69443 69452 
 
 3 
 
 
 4-95 
 
 .69 461 .69 469 .69 478 .69 487 .69 496 
 
 .69504 -69513 .69522 .69531 .69539 
 
 4 
 
 .60 
 
 .96 
 
 69548 69557 69566 69574 69583 
 
 69 592 69 601 69 609 69 618 69 627 
 
 S 
 
 .69 
 
 •97 
 
 69 636 69 644 69 653 69 662 69 671 
 
 69 679 69 688 69 697 69 705 69 714 
 
 6 
 
 
 .98 
 
 69723 69732 69740 69749 69758 
 
 69767 69775 69784 69793 69801 
 
 6 
 
 
 ■99 
 
 69 810 69 819 69 827 69 836 69 845 
 
 69854 69862 69871 69880 69888 
 
 7 
 
 
 
 (19) 5 PL. I 
 
 -OG 
 4. 
 
 S. 
 
5. 
 LOGS. 5 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 8 
 
 5.00 
 
 .OI 
 .02 
 
 •°3 
 .04 
 
 5°5 
 .06 
 .07 
 .08 
 .09 
 
 5.10 
 
 .11 
 .12 
 
 •13 
 .14 
 
 S-I5 
 .16 
 
 ■>7 
 .18 
 
 •19 
 
 5.20 
 
 .21 
 
 .22 
 
 •23 
 .24 
 
 5'2S 
 .26 
 .27 
 .28 
 .29 
 
 5.30 
 
 •31 
 •32 
 •33 
 
 •34 
 
 5^35 
 •36 
 •37 
 •38 
 ■39 
 
 5.40 
 
 .41 
 .42 
 ■43 
 ■44 
 
 S-45 
 .46 
 
 •47 
 
 ■49 
 
 logs! 
 5. 
 
 .69 897 
 69984 
 70070 
 70157 
 70243 
 •70 329 
 
 7041.5 
 70 501 
 70586 
 70672 
 
 •70 757 
 70842 
 
 70927 
 71 012 
 71 096 
 
 .71 181 
 71265 
 71349 
 71433 
 71517 
 
 .71 600 
 71 684 
 71767 
 71850 
 71933 
 .72016 
 72099 
 
 72 i8i 
 72263 
 72346 
 
 .72428 
 72509 
 72591 
 72673 
 72754 
 
 •72 83s 
 72916 
 
 72997 
 73078 
 73159 
 
 •73 239 
 73320 
 73400 
 73480 
 
 73 560 
 
 •73 640 
 73719 
 73 799 
 73878 
 73 957 
 
 5 PL. 
 
 .69 go6 
 69992 
 70079 
 70165 
 70252 
 
 •70 338 
 70424 
 70509 
 
 70595 
 70680 
 
 .70 766 
 70851 
 
 70935 
 71 020 
 71 105 
 
 .71 189 
 71273 
 
 71357 
 71441 
 
 71525 
 
 ,71 609 
 
 71 692 
 
 7177s 
 71858 
 71941 
 
 .72 024 
 
 72 107 
 72 189 
 72 272 
 72354 
 
 ■72 436 
 72518 
 
 72599 
 72681 
 
 72 762 
 
 .72 843 
 
 72925 
 
 73 006 
 73086 
 73167 
 
 ■73 247 
 73328 
 73408 
 73488 
 73568 
 
 •73 648 
 73727 
 73807 
 73886 
 
 73965 
 
 .69914 
 70 001 
 
 70088 
 70174 
 70 260 
 
 .70 346 
 70432 
 70518 
 70603 
 70689 
 
 ■70 774 
 
 70 859- 
 70944 
 
 71 029 
 71 "3 
 .71 198 
 71 282 
 71366 
 71450 
 71533 
 
 .71617 
 71 700 
 71784 
 
 71 867 
 71950 
 .72032 
 
 72115 
 
 72 198 
 72 280 
 72362 
 
 .72444 
 72 526 
 72607 
 72689 
 
 72 770 
 
 .72852 
 72933 
 73014 
 73094 
 73175 
 
 ■73255 
 73336 
 73416 
 73496 
 73576 
 
 •73656 
 
 73 735 
 73 815 
 73894 
 73 973 
 
 ,69 923 
 70010 
 70096 
 70183 
 70269 
 
 •70355 
 70441 
 
 70 526 
 70612 
 70697 
 
 •70 783 
 70868 
 70952 
 71037 
 
 71 122 
 
 .71 206 
 71 290 
 71374 
 71458 
 71542 
 
 .71 625 
 
 71 709 
 71792 
 71875 
 71958 
 
 .72 041 
 
 72 123 
 72206 
 72288 
 72370 
 
 •72452 
 72534 
 72616 
 72697 
 72779 
 ,72860 
 72941 
 73022 
 73102 
 73183 
 
 •73 263 
 
 73 344 
 73424 
 73504 
 73584 
 
 ■73 664 
 73 743 
 73823 
 73902 
 73981 
 
 .69 932 
 ,70018 
 70 105 
 70191 
 70 278 
 
 ■70 364 
 
 70449 
 
 70535 
 70621 
 
 70 706 
 
 •70 791 
 70876 
 70961 
 
 71 046 
 71 130 
 
 .71 214 
 71299 
 
 71383 
 71 466 
 
 71550 
 
 •71 634 
 71717 
 71 800 
 71883 
 
 71 966 
 
 .72049 
 72132 
 
 72 214 
 72296 
 72378 
 
 .72 460 
 72542 
 72624 
 72705 
 
 72 787 
 .72 868 
 72949 
 73030 
 
 73 III 
 73 191 
 
 ■73 272 
 73352 
 73432 
 73512 
 73 592 
 ■73672 
 
 73751 
 73830 
 73910 
 73989 
 
 .69 940 
 70027 
 70 1 14 
 
 70 200 
 70286 
 
 •70372 
 70458 
 70544 
 70629 
 70714 
 
 .70800 
 70885 
 70969 
 71054 
 
 71 139 
 .71 223 
 
 71307 
 71 391 
 71475 
 71559 
 
 .71 642 
 71725 
 71 809 
 
 71 892 
 71975 
 .72057 
 
 72 140 
 
 72 222 
 72304 
 72387 
 
 •72 469 
 72550 
 72632 
 
 72713 
 72795 
 
 .72876 
 72957 
 73038 
 
 73 "9 
 73199 
 
 .73 280 
 73360 
 73440 
 73520 
 73600 
 
 •73 679 
 73 759 
 
 73918 
 73 997 
 
 ,69 949 
 70036 
 70 122 
 
 70 209 
 70295 
 
 .70 381 
 70467 
 
 70552 
 70638 
 
 70723 
 
 .70 S08 
 70893 
 70978 
 71063 
 
 71 147 
 
 .71 231 
 
 71315 
 71399 
 71483 
 71567 
 
 .71 650 
 
 71734 
 71817 
 
 71 900 
 71983 
 .72066 
 
 72 148 
 72230 
 72313 
 72395 
 
 .72477 
 
 72558 
 72 640 
 72 722 
 72803 
 
 .72 884 
 72965 
 73046 
 73127 
 73207 
 
 .73 288 
 73368 
 73448 
 73528 
 73608 
 
 ■73687 
 Z376Z 
 
 73926 
 74 005 
 
 .69958 , 
 70044 
 70131 
 70217 
 70303 
 ■70 389 
 70475 
 70561 
 70646 
 70731 
 
 .70817 
 70902 
 70986 
 71 071 
 71155 
 .71 240 
 
 71324 
 71 408 
 71492 
 71575 
 
 .71 659 
 71742 
 71825 
 71 908 
 71991 
 
 .72074 
 72156 
 
 72239 
 72321 
 
 72403 
 
 .72485 
 72567 
 72648 
 72730 
 72811 
 
 .72 892 
 72973 
 73054 
 73135 
 73215 
 
 •73 296 
 73376 
 73456 
 73536 
 73616 
 
 •73 695 
 73 775 
 73854 
 73 933 
 74013 
 
 ,69 966 
 70053 
 
 70 140 
 70226 
 70312 
 
 ■70 398 
 70484 
 70569 
 70655 
 70740 
 
 .70 825 
 70910 
 70995 
 71079 
 
 71 164 
 
 .71 248 
 71332 
 71416 
 
 71 500 
 71584 
 
 .71 667 
 71750 
 
 71834 
 71917 
 71999 
 
 .72 082 
 
 72 165 
 72247 
 72329 
 72411 
 
 ■72493 
 72575 
 72656 
 
 72738 
 72819 
 
 .72900 
 72981 
 73062 
 
 73143 
 73223 
 
 ■73 304 
 73384 
 73464 
 
 73 544 
 73624 
 
 ■73 703 
 73783 
 73862 
 
 73941 
 74020 
 
 ■69 975 
 
 70 062 
 70148 
 70234 
 70321 
 
 .70 406 
 70492 
 70578 
 70663 
 70749 
 
 .70834 
 70919 
 71003 
 71088 
 71172 
 
 •71 257 
 71341 
 71425 
 71508 
 71592 
 
 •71 675 
 71759 
 
 71 842 
 
 71925 
 
 72 008 
 
 .72 090 
 72173 
 72255 
 72337 
 72419 
 
 •72 501 
 72583 
 72665 
 72746 
 72827 
 
 .72 908 
 
 72989 
 73070 
 
 73151 
 73231 
 
 •73312 
 73392 
 73472 
 73552 
 73632 
 
 ■73711' 
 
 73791 
 
 73870 
 
 73 949 
 74028 
 
 (20) 
 
FIVE PLACE LOGARITHMS. 
 
 5 PL. LOGS. 
 
 No. 
 
 8 
 
 5.50 
 
 •51 
 •52 
 
 •53 
 •54 
 
 5^55 
 .56 
 
 ■57 
 •58 
 •59 
 
 5.60 
 
 .61 
 .62 
 
 •63 
 .64 
 
 5-65 
 .66 
 
 .67 
 .68 
 .69 
 
 5.70 
 
 •7> 
 
 .72 
 
 •73 
 •74 
 
 5-75 
 .76 
 
 •77 
 .78 
 
 •79 
 
 5.80 
 
 .81 
 .82 
 
 •83 
 .84 
 
 5.85 
 .86 
 .87 
 
 5.90 
 
 •91 
 .92 
 
 •93 
 •94 
 
 5-95 
 .96 
 
 •97 
 :98 
 
 •99 
 
 .74036 
 
 74 "5 
 74194 
 
 74 273 
 74351 
 
 •74 429 
 74507 
 74586 
 74663 
 74741 
 
 .74819 
 74896 
 74974 
 75051 
 75128 
 
 ■75 205 
 75282 
 75358 
 
 75 435 
 
 75 5" 
 
 •75 587 
 75664 
 
 75740 
 75815 
 75891 
 
 •75 967 
 76042 
 
 76 118 
 
 76193 
 76268 
 
 ■76 343 
 76418 
 76492 
 76567 
 76641 
 
 .76 716 
 
 76 790 
 76864 
 
 76938 
 77012 
 
 •77085 
 
 77159 
 77232 
 
 77305 
 
 77 379 
 •77452 
 
 77525 
 77 597 
 77 670 
 
 77 743 
 
 .74044 
 
 74123 
 74202 
 74280 
 74 359 
 
 •74437 
 745'5 
 74 593 
 74671 
 
 74 749 
 
 •74 827 
 74904 
 74981 
 75059 
 75136 
 
 •75213 
 75289 
 
 75366 
 75442 
 75519 
 
 ■75 595 
 75671 
 
 75 747 
 75823 
 75899 
 
 ■75 974 
 76050 
 76125 
 76200 
 76275 
 
 •76 350 
 76425 
 76500 
 
 76574 
 76649 
 
 •76 723 
 
 76797 
 76871 
 
 76945 
 77019 
 
 •77 093 
 77 166 
 77 240 
 
 77313 
 77386 
 
 •77 459 
 77532 
 77605 
 77677 
 77750 
 
 •74 052 
 7413J 
 
 74 2IO 
 74288 
 74367 
 
 •74 445 
 74523 
 74601 
 74679 
 
 74 757 
 
 •74 S34 
 74912 
 74989 
 75066 
 75143 
 
 .75 220 
 
 75297 
 
 75 374 
 75450 
 75526 
 
 •75 603 
 75679 
 
 75 755 
 75831 
 75906 
 
 •75 982 
 76057 
 
 76133 
 76208 
 76283 
 
 •76358 
 76433 
 76507 
 76582 
 76656 
 
 .76 730 
 76805 
 
 76 879 
 76953 
 77026 
 
 .77 100 
 
 77173 
 77247 
 77320 
 
 77 393 
 .77 466 
 
 77 539 
 77 612 
 77685 
 77 757 
 
 .74 060 
 
 74139 
 74218 
 74296 
 74 374 
 
 ■74 453 
 74 531 
 74609 
 74687 
 74764 
 
 .74 842 
 74920 
 
 74 997 
 75074 
 75151 
 
 .75 228 
 75305 
 75381 
 75458 
 
 75 534 
 
 .75 610 
 75686 
 75762 
 75838 
 75914 
 
 •75 989 
 76065 
 
 76 140 
 76215 
 76290 
 
 •76365 
 76440 
 
 76515, 
 
 76589 
 
 76664 
 
 •76 738 
 76812 
 76886 
 76960 
 77034 
 
 •77 107 
 
 77 181 
 
 77254 
 77327 
 77401 
 
 •77 474 
 77546 
 77619 
 77 692 
 77764 
 
 .74 068 
 
 74147 
 74225 
 
 74304 
 74382 
 
 .74461 
 
 74 539 
 74617 
 74695 
 74772 
 
 ■74 850 
 74927 
 
 75 005 
 
 75 082 
 75159 
 
 ■75 236 
 75312 
 75389 
 75465 
 75542 
 
 .75618 
 75694 
 75770 
 75846 
 75921 
 
 ■75 997 
 76072 
 76148 
 76223 
 
 76 298 
 
 •76 373 
 76448 
 76522 
 
 76597 
 76671 
 
 ■76 745 
 76819 
 
 76893 
 76967 
 77041 
 
 ■77 "5 
 77188 
 
 77 262 
 
 77 335 
 77408 
 
 ■77481 
 77 554 
 77 627 
 77699 
 77772 
 
 .74076 
 74155 
 74233 
 74312 
 74390 
 
 .74 468 
 
 74 547 
 74624 
 74702 
 74780 
 
 .74858 
 
 74 935 
 75012 
 75089 
 
 75 i66 
 
 •75 243 
 75320 
 75 397 
 75 473 
 75 549 
 
 ■75 626 
 75702 
 75778 
 75853 
 75929 
 .76 005 
 76080 
 76155 
 76230 
 76305 
 
 .76 380 
 
 76455 
 76530 
 76604 
 76678 
 
 ■76753 
 76827 
 76901 
 
 7697s 
 77048 
 
 ■77 122 
 77 195 
 77269 
 77342 
 77415 
 
 ■77 488 
 77561 
 
 77634 
 77 706 
 
 77 779 
 
 .74084 
 74162 
 
 74241 
 74320 
 74398 
 
 ■74476 
 74 554 
 74632 
 74710 
 74788 
 
 •74865 
 
 74 943 
 
 75 020 
 
 75 097 
 75174 
 
 •75251 
 75328 
 75404 
 75481 
 
 75 557 
 
 •75 633 
 75709 
 75785 
 75861 
 
 75 937 
 .76012 
 76087 
 
 76 163 
 76238 
 76313 
 
 .76388 
 76462 
 
 76537 
 76612 
 76686 
 
 .76 760 
 
 76834 
 76908 
 76982 
 77056 
 
 ■77 129 
 77203 
 
 77 276 
 
 77 349 
 77422 
 
 ■77 495 
 77568 
 77641 
 
 77714 
 77786 
 
 .74092 
 74170 
 74249 
 74327 
 74406 
 
 •74 484 
 74562 
 
 74 640 
 74718 
 74796 
 
 •74873 
 74950 
 75028 
 75105 
 75182 
 
 •75 259 
 
 75 335 
 75412 
 
 75488 
 
 75565 
 
 •75 641 
 75717 
 75 793 
 75868 
 
 75 944 
 .76 020 
 76095 
 
 76 170 
 76245 
 76320 
 
 •76395 
 76470 
 
 76545 
 76619 
 76693 
 
 .76 768 
 76842 
 76916 
 76989 
 77063 
 
 ■77137 
 
 77 210 
 
 77283 
 77 357 
 77430 
 
 •77 503 
 77576 
 77648 
 77721 
 77 793 
 
 74099 .74107 
 74 178 74 186 
 74257 74265 
 74 335 74 343 
 74414 74421 
 
 74492 .74500 
 74570 74578 
 74648 74656 
 74726 74733 
 74803 74 81 1 
 
 .74 881 
 74958 
 75035 
 75 "3 
 75189 
 
 •75 266 
 75 343 
 75420 
 
 75496 
 75572 
 
 •75 648 
 75724 
 
 75 800 
 75876 
 75952 
 
 .76027 
 
 76 103 
 76178 
 76253 
 76328 
 
 .76403 
 76477 
 76552 
 76626 
 
 76 701 
 
 •76 775 
 76849 
 76923 
 
 76997 
 77070 
 
 ■77 144 
 77217 
 77291 
 
 77364 
 
 77 437 
 
 .74 889 
 
 74966 
 
 75043 
 75120 
 
 75197 
 •75 274 
 75351 
 75427 
 75504 
 75580 
 
 ■75 656 
 75732 
 75808 
 75884 
 
 75 959 
 
 ■76 035 
 
 76 110 
 76185 
 76 260 
 7633s 
 
 .76410 
 76485 
 76559 
 76634 
 
 76 708 
 
 .76 782 
 76856 
 76930 
 
 77 004 
 77078 
 
 ■77 151 
 77225 
 77298 
 
 77371 
 77 444 
 
 .77510 .77517 
 
 77583 77590 
 
 77656 77663 
 
 77728 77735 
 
 77 801 77 808 
 
 INTP. 
 TAB. 
 
 (21) 
 
 5 PL. LOGS. 
 5. 
 
FIVE PLACE LOGARITHMS. 
 
 LOGS. 
 
 5 PL. 
 
 
 
 
 No. 
 
 01234 
 
 56789 
 
 INTP. 
 TAB. 
 
 .77 
 .84 
 
 6.00 
 
 .OI 
 .02 
 
 •03 
 .04 
 
 .77815 .77822 .77830 .77837 .77844 
 77887 77895 77902 77909 77916 
 77960 77967 77974 77981 77988 
 78032 78039 78046 78053 78061 
 78104 78 III 78118 78125 78132 
 
 .77851 .77859 -77866 .77873 .77880 
 77924 77931 77938 77945 77952 
 77996 78 003 78010 78017 78025 
 78068 78075 78082 78089 78097 
 78 140 78 147 78 154 78 161 78 168 
 
 8 
 I 
 
 2 
 2 
 3 
 
 
 6.05 
 .06 
 .07 
 .08 
 .09 
 
 .78 176 .78 183 .78 190 .78 197 .78204 
 78247 78254 78262 78269 78276 
 78319 78326 78333 78340 78347 
 78390 78398 78405 78412 78419; 
 78462 78469 78476 78483 78490 
 
 .78211 .78219 .78226 .78233 .78240 
 78283 78290 78297 78305 78312 
 78355 78362 78369 78376 78383 
 78426 78433 78440 78447.78455 
 78497 78504 78512 78519 78526 
 
 4 
 5 
 6 
 
 6 
 7 
 
 
 6.10 
 
 .11 
 .12 
 
 •13 
 .14 
 
 -78533 -78540 -78547 -78554 -78561 
 78604 78611 78618 78625 78633 
 78675 78682 78689 78696 78704 
 78746 78753 78760 78767 78774 
 78817 78824 78831 78838 78845 
 
 .78569 .78576 .78583 .78590 .78597 
 78640 78647 78654 78661 78668 
 78711 78718 78725 78732 78739 
 78781 78789 78796 78803 78810 
 78852 78859 78866 78873 78880 
 
 7 
 
 1 
 1 
 2 
 3 
 
 
 6.15 
 .16 
 
 ■17 
 .18 
 .19 
 
 -78888 -78895 .78902 .78909 .78916 
 78958 78965 78972 78979 78986 
 79029 79036 79043 79050 79057 
 79099 79106 79113 79120 79127 
 79,169 79176 79183 79190 79197 
 
 .78923 .78930 .78937 .78944 .78951 
 78993 79 000 79007 79014 79021 
 79064 79071 79078^79085 79092 
 79134 79141 79148 79155 79162 
 79204 79 2U 79218 79225 79232 
 
 4 
 4 
 5 
 6 
 6 
 
 
 6.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 -79 239 -79 246 -79 253 .79 260 .79 267 
 79309 79316 79323 79330 79 337 
 79 379 79386 79 393 79 400 79407 
 79 449 79456 79463 79470 79 477 
 79518 79525 79532 79 539 79546 
 
 •79 274 -79 281 .79 288 ..79 295 .79 302 
 79 344 79351 79358 79365 79372 
 79414 79421 79428 79435 79442 
 79484 79491 79498 79505 79 511 
 79 553 79560 79567 79 574 79 581 
 
 7 
 
 1 
 I 
 2 
 3 
 
 
 6.25 
 .26 
 .27 
 .28 
 .29 
 
 .79 588 .79 595 .79 602 .79 609 .79 616 
 79657 79664 79671 79678 79685 
 79727 79 734 79741 79748 79 754 
 79 796 79 803 79 810 79 817 79 824 
 79865 79872 79879 79886 79893 
 
 •79 623 .79 630 .79 637 .79 644 .79 650 
 79692 79699 79706 79713 79720 
 79761 79768 79775 79782 79789 
 79831 79837 79844 79851 79858 
 79900 79906 79913 79920 79927 
 
 4 
 4 
 5 
 6 
 6 
 
 
 6.30 
 
 ■31 
 •32 
 •33 
 •34 
 
 •79 934 -79 941 .79948 -79 955 -79962 
 80 003 80010 80017 80024 80030 
 80072 80079 80085 80092 80099 
 80 140 80 147 80 154 80 161 80 168 
 80209 80216 80223 80229 80236 
 
 •79 969 ^79 975 ^79 982 .79 989 -79 996 
 80037 80044 80051 80058 80065 
 80106 80113 80120 80127 80134 
 80175 80182 80188 80195 80202 
 80 243 80 250 80 257 80 264 80 271 
 
 7 
 
 1 
 1 
 2 
 3 
 
 
 6.35 
 -36 
 •37 
 •38 
 •39 
 
 .80 277 .80 284 .80 291 .80 298 .80 305 
 80346 80353 80359 80366 80373 
 80414 80421 80428 80434 80441 
 80 482 80 489 80 496 80 502 80 509 
 80550 80557 80564 80570 80577 
 
 .80312 .80318 .80325 .80332 .80339 
 80380 80387 80393 80400 80407 
 80448 80455 80462 80468 80475 
 80516 80523 80530 80536 80543 
 80584 80591 80598 80604 80611 
 
 4 
 4 
 5 
 6 
 6 
 
 
 6.40 
 
 ■41 
 .42 
 
 •43 
 •44 
 
 .80618 .80625 -80632 .80638 .80645 
 80686 80693 80699 80706 80713 
 80 754 80 760 80 767 80 774 80 781 
 80821 80828 80835 80841 80848 
 80889 80895 80902 80909 80916 
 
 .80652 .80659 .80665 -80672 .80679 
 80 720 80 726 80 733 80 740 80 747 
 80787 80794 80801 80808 80814 
 80855 80862 80868 80875 80882 
 80 922 80 929 80 936 80 943 80 949 
 
 6 
 
 I 
 1 
 2 
 2 
 
 .77 
 .84 
 
 6-45 
 .46 
 
 -47 
 .48 
 -49 
 
 .80956 .80963 .80969 .80976 .80983 
 81023 81030 81037 81043 81050 
 81090 81097 81104 81111 81117 
 81 158 81 164 81 171 81 178 81 184 
 81224 81231 81238 81245 81251 
 
 .80990 .80996 .81003 .81010 .81017 
 81 057 81 064 81 070 81 077 81 084 
 81 124 81 131 8i 137 81 144 81 151 
 81191 81198 81204 81 2U 81218 
 81 258 81 265 81 271 81 278 81 285 
 
 3 
 
 4 
 4 
 5 
 5 
 
 LO 
 
 e 
 
 GS. 
 
 5 PL. (22) 
 
 
 
FIVE PLACE LOGARITHMS. 
 
 
 
 
 
 
 6 PL. 
 
 LOGS 
 
 No. 
 
 12 
 
 3 4 
 
 5 
 
 6 
 
 789 
 
 INTP. 
 TAB. 
 
 6 
 
 
 6.50 
 
 .81 291 .81 298 .81 305 
 
 .81311 .81318 
 
 .81 325 
 
 •81 331 
 
 .81338 .81 345 -81351 
 
 .7' 
 
 •5' 
 
 81 358 81 365 81 371 
 
 81378 81385 
 
 81 391 
 
 81398 
 
 81405 81411 81418 
 
 1 
 
 .84 
 
 •52 
 
 81425 81 431 81438 
 
 81445 '81451 
 
 81458 
 
 81465 
 
 81471 81478 81485 
 
 I 
 
 
 •53 
 
 81 491 81 498 81 505 
 
 81 511 81 518 
 
 81525 
 
 81 531 
 
 81538 81544 81-551 
 
 2 
 
 
 •54 
 
 81 558 81564 81 571 
 
 81 578 81 584 
 
 81591 
 
 81598 
 
 81 604 81 611 81617 
 
 2 
 
 
 6.55 
 
 .8i 624 .81 631 .81 637 
 
 .81 644 .81 651 
 
 ■81 657 
 
 .81 664 
 
 .81 671 .81 677 .81 684 
 
 3 
 
 
 .56 
 
 81 690 8i 697 81 704 
 
 81 710 81 717 
 
 81723 
 
 81730 
 
 81 737 81 743 81 750 
 
 4 
 
 
 ■57 
 
 81 757 81 763 81 770 
 
 81 776 81 783 
 
 81790 
 
 81796 
 
 81 803 81 809 81 816 
 
 4 
 
 
 .58 
 
 81 823 81 829 81 836 
 
 81 842 81 849 - 
 
 81856 
 
 81862 
 
 81 869 81 875 81 882 
 
 5 
 
 
 •59 
 
 81 889 81 895 81 902 
 
 81 908 81 915 
 
 81 921 
 
 81928 
 
 81 935 81 941 81 948 
 
 5 
 
 
 6.60 
 
 .81 954 .81 961 .81 968 
 
 .81 974 .81 981 
 
 .81 987 
 
 .81 994 
 
 .82 000 .82007 -82014 
 
 % 
 
 
 .61 
 
 82020 82027 82033 
 
 82 040 82 046 
 
 82053 
 
 82060 
 
 82 066 82 073 82 079 
 
 I 
 
 
 .62 
 •63 
 
 82 086 82 092 82 099 
 82 151 82158 82164 
 
 82105 82 112 
 82 171 82178 
 
 82 119 
 82184 
 
 82 12£ 
 
 82 132 82 138 82 145 
 
 I 
 2 
 
 
 8219^1 
 
 82 197 82 204 82 210 
 
 
 .64 
 
 82217 82223 82230 
 
 82 236 82 243 
 
 82 249 
 
 82256 
 
 82263-82269 82276 
 
 3. 
 
 
 6.65 
 
 .82282 .82289 .82^295 
 
 .82 302 .82 308 
 
 .82315 
 
 .82321 
 
 .82328 .82334 .82341 
 
 4 
 
 
 .66 
 
 82347 82354 82360 
 
 82367 82373 
 
 82380 
 
 82387 
 
 82 393 82 400 82 406 
 
 4 
 
 
 .67 
 
 82413 82419 82426 
 
 82432 82439 
 
 82445 
 
 82452 
 
 82458 82465 82471 
 
 5 
 
 
 .68 
 
 82478 82484 82491 
 
 82 497 82 504 
 
 82 510 
 
 82517 
 
 82523 82530 82536 
 
 6 
 
 
 .69 
 
 82543 82549 82556 
 
 82 562 82 569 
 
 82575 
 
 82 582 
 
 82588 82595 82601' 
 
 6 
 
 
 6.70 
 
 .82 607 .82 614 .82 620 
 
 .82627 .82633 
 
 .82 640 
 
 .82 646 
 
 .82 653 .82 659* .82 666 
 
 6 
 
 
 •71 
 
 82672 82679 82685 
 
 82692 82698 
 
 82705 
 
 82 71 I 
 
 82 718 82 724 82 730 
 
 I 
 
 
 .72 
 
 82737 82743 82750 
 
 82756 82763 
 
 82 769 
 
 82776 
 
 82782 82789 82795 
 
 I 
 
 
 ■73 
 
 82802 82808 82814 
 
 82821 82827 
 
 82834 
 
 82840 
 
 82847 82853 82860 
 
 2 
 
 
 •74 
 
 82866 82872 82879 
 
 82885 82892 
 
 82898 
 
 82 905 
 
 82911 82918 82924 
 
 2 
 
 
 6.75 
 
 .'82 930 .82 937 .82 943 
 
 .82950 .82956 
 
 ■82 963 
 
 .82 969 
 
 .82975 .82982 .82988 
 
 3 
 
 
 .76 
 
 82995 83 001 83008 
 
 83 014 83 020 
 
 ' 83027 
 
 83033 
 
 83040 83046 83052 
 
 4 
 
 
 •77 
 
 83059 83065 83072 
 
 83078 83085 
 
 83091 
 
 83097 
 
 83104 83110 83117 
 
 4 
 
 
 .78 
 
 83 123 83 129 83 136 
 
 83 142 83 149 
 
 83155 
 
 83 161 
 
 83 168 83 174 83 181 
 
 5 
 
 
 •79 
 
 83 187 83 193 83 200 
 
 83 206 83 213 
 
 83219 
 
 83225 
 
 83232 83238 83245 
 
 5 
 
 
 6.80 
 
 .83251 .83257 .83264 
 
 .83270 .83276 
 
 •83 283 
 
 .83 289 
 
 .83 296 .83 302 .83 308 
 
 7 
 
 
 .81 
 
 83315 83321 83327 
 
 83334 83340 
 
 83347 
 
 83353 
 
 83359 83366 83372 
 
 1 
 
 
 .82 
 
 83"378 83385 83391 
 
 83398 83404 
 
 83410 
 
 83417 
 
 83423 83429 83436 
 
 1 
 
 
 •83 
 
 83442 83448 83455 
 
 83461 83467 
 
 83474 
 
 83480 
 
 83487 83493 83499 
 
 2 
 
 
 .84 
 
 83506 83512 83518 
 
 83525 83531 
 
 83537 
 
 83544 
 
 83550 83556 83563 
 
 3 
 
 
 6.85 
 
 ■83 569 ^83 575 •SS 582 
 
 •83 588 .83 594 
 
 .83 601 
 
 .83 607 
 
 .83613 .83620 .83626 
 
 4 
 
 
 .86 
 
 83632 83639 83645 
 
 83651 83658 
 
 83664 
 
 83670 
 
 83677 83683 83689 
 
 ,4 
 
 
 .87 
 
 83696 83702 83708 
 
 83715 83721 
 
 83727 
 
 83734 
 
 83740 83746 83753 
 
 5 
 
 
 .88 
 
 83759 83765 83771 
 
 83778 83784 
 
 83790 
 
 83797 
 
 83803 83809 83816 
 
 6 
 
 
 .89 
 
 83822 83828 83835 
 
 83841 83847 
 
 83853 
 
 83860 
 
 83866 83872 83879 
 
 6 
 
 
 6.90 
 
 .83885 .83891 .83897 
 
 .83904 .83910 
 
 .83916 
 
 •83 923 
 
 -83 929 -83 935 -83 942 
 
 6 
 
 
 •91 
 
 83948 83954 83960 
 
 83967 83^973 
 
 83979 
 
 83985 
 
 83992 83998 84 004 
 
 1 
 
 
 .92 
 
 84 on 84017 84023 
 
 84 029 84 036 
 
 84042 
 
 84048 
 
 84 055 84 061 84 067 
 
 1 
 
 
 ■93 
 
 84073 84080 84086 
 
 84 092 84 098 
 
 84105 
 
 84 III 
 
 84 117 84123 84130 
 
 2 . 
 
 
 ■94 
 
 84136 84142 84148 
 
 84155 84 161 
 
 84167 
 
 84173 
 
 84180 84186 84192 
 
 2 
 
 
 6.95 
 
 .84198 .84205 .84211 
 
 .84217 .84 223 
 
 .84 230 
 
 .84 236 
 
 .84 242 .84 248 .84 255 
 
 3 
 
 
 .96 
 
 84 261 84 267 84 273 
 
 84280 84286 
 
 84 292 
 
 84298 
 
 84305 84311 84317 
 
 4 
 
 .Ti 
 
 •97 
 
 84323 84330 84336 
 
 84342 84348 
 
 84354 
 
 84361 
 
 84367 84373 84379 
 
 4 
 
 .84 
 
 .98 
 
 84386 84392 84398 
 
 84404 84410 
 
 84417 
 
 84423 
 
 84429 84435 84442 
 
 5 
 
 
 ■99 
 
 84448 84454 84460 
 
 84 466 84 473 
 
 84479 
 
 84485 
 
 84491 84497 84504 
 
 5 
 
 
 ^ 
 
 
 (23) 
 
 
 6 PL. 
 
 -OC 
 6. 
 
 s 
 
7. 
 LOGS. 6 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 7.00 
 
 .OI 
 .02 
 
 •03 
 
 .04 
 
 7-05 
 .06 
 .07 
 .08 
 .09 
 
 7.10 
 
 .II 
 
 .12 
 
 •13 
 .14 
 
 7-"5 
 .16 
 
 •17 
 .18 
 .19 
 
 7.20 
 
 .21 
 .22 
 
 •23 
 
 .24 
 
 7-25 
 .26 
 
 •27 
 .28 
 .29 
 
 7.30 
 
 •31 
 •32 
 ■33 
 •34 
 
 7-35 
 •36 
 •37 
 •38 
 •39 
 
 7.40 
 
 .41 
 •42 
 •43 
 ■44 
 
 7-45 
 .46 
 
 •47 
 .48 
 
 •49 
 
 LOGS. 
 7, 
 
 8 
 
 .84 510 .84516 
 S4572 84578 
 84 634 84 640 
 84 696 84 702 
 84757 84763 
 
 .84819 .84825 
 84880 84887 
 
 84 942 84 948 
 
 85 003 85009 
 85065 85071 
 
 .85 126 
 85187 
 85248 
 85309 
 85370 
 
 •85 431 
 85491 
 
 85552 
 85612 
 
 85673 
 
 •85 733 
 85794 
 85854 
 85914 
 85974 
 
 .86 034 
 86094 
 86153 
 86213 
 86273 
 
 •86 332 
 86392 
 86451 
 86510 
 86570 
 
 .86 629 
 86 688 
 
 86747 
 86806 
 86864 
 
 .86 923 
 86982 
 87040 
 87099 
 87157 
 
 .87216 
 87274 
 87332 
 87390 
 87448 
 
 5 PL. 
 
 .85 132 
 85193 
 85254 
 85315 
 85378 
 
 85 437 
 85497 
 85558 
 85618 
 85679 
 
 ■85 739 
 85800 
 85860 
 85 920 
 
 85 980 
 ,86 040 
 
 86 100 
 86159 
 86219 
 86 279 
 
 ,86 338 
 86398 
 86457 
 86516 
 86576 
 
 ,86 635 
 86694 
 
 86753 
 86812 
 86870 
 
 .86 929 
 86988 
 87046 
 87105 
 87163 
 
 .87 221 
 87280 
 87338 
 87396 
 87454 
 
 .84 522 
 
 84584 
 84646 
 84708 
 84770 
 
 .84 831 
 84893 
 84954 
 85016 
 85077 
 
 .85 138 
 
 85199 
 85260 
 
 85321 
 85382 
 
 ■85443 
 85503 
 85564 
 85625 
 85685 
 
 •85 745 
 85806 
 85866 
 85926 
 85986 
 
 .86 046 
 86106 
 86165 
 86225 
 86285 
 
 .86 344 
 86404 
 86463 
 86522 
 86581 
 
 .86 641 
 
 86 700 
 
 86759 
 86817 
 86876 
 
 •86935 
 86994 
 87052 
 
 87 III 
 87169 
 
 .87 227 
 87286 
 
 87344 
 87402 
 87460 
 
 .84 528 
 84590 
 84652 
 84714 
 84776 
 
 .84837 
 84899 
 84960 
 
 85 022 
 85083 
 
 •85 144 
 85205 
 85266 
 
 85327 
 85388 
 
 ■85449 
 85509 
 85570 
 85631 
 85691 
 
 .85751 
 85812 
 85.872 
 85932 
 85992 
 
 .86052 
 
 86 112 
 
 86 171 
 86231 
 86291 
 
 .86 350 
 86410 
 86469 
 86528 
 86587 
 
 .86 646 
 86705 
 86764 
 86823 
 86882 
 
 .86 941 
 86999 
 87058 
 
 87 116 
 
 8717s 
 
 •87 233 
 87291 
 
 87349 
 87408 
 87466 
 
 .84 535 
 84597 
 84658 
 
 84 720 
 84782 
 
 .84844 
 
 84905 
 84967 
 85028 
 85089 
 
 .85 150 
 
 85 211 
 
 85 272 
 85333 
 85394 
 
 •85 455 
 85516 
 85576 
 
 85637 
 85697 
 
 •85 757 
 85818 
 85878 
 85938 
 85998 
 
 .86058 
 
 86 118 
 86177 
 86237 
 86 297 
 
 .86356 
 86415 
 
 86475 
 86534 
 86593 
 .86 652 
 86 711 
 86 770 
 86829 
 
 86 888 
 
 •S6947 
 
 87 005 
 
 87064 
 87 122 
 87 181 
 
 •87 239 
 .87 297 
 
 87355 
 87413 
 87471 
 
 (24) 
 
 .84 541 
 84603 
 84665 
 84 726 
 84788 
 
 .84850 
 84 91 1 
 84973 
 85034 
 85095 
 
 .85 156 
 85217 
 85278 
 
 85339 
 85400 
 
 .85 461 
 85522 
 85582 
 85643 
 85703 
 
 •85 763 
 85824 
 85884 
 
 85944 
 86 004 
 
 .86 064 
 
 86 124 
 86183 
 86243 
 86303 
 
 .86 362 
 86421 
 86481 
 86540 
 86599 
 
 .86 658 
 86717 
 86776 
 86835 
 86894 
 
 ■86953 
 
 87 01 1 
 87070 
 87 128 
 87186 
 
 ■87 245 
 87303 
 87361 
 87419 
 87477 
 
 ,84 547 
 84609 
 84671 
 
 84733 
 84794 
 
 .84 856 
 84917 
 84979 
 85 040 
 85 101 
 
 .85 163 
 85 224 
 85285 
 
 85345 
 85406 
 
 .85 467 
 85528 
 85588 
 85649 
 85709 
 
 .85 769 
 85 830 
 85890 
 85950 
 86010 
 
 ■84553 
 84615 
 84677 
 
 84739 
 84800 
 
 .84 862 
 84924 
 
 84985 
 85046 
 85107 
 
 .85 169 
 85 230 
 85291 
 
 85352 
 85 412 
 
 •85 473 
 85534 
 85594 
 85655 
 8571S 
 
 •85 775 
 85836 
 85896 
 85956 
 86016 
 
 •84 559 
 84621 
 84683 
 
 84745 
 84807 
 
 .84 868 
 84930 
 84991 
 85 052 
 85114 
 
 •85 17s 
 85236 
 
 85297 
 85358 
 85418 
 
 •85 479 
 85540 
 85 600 
 85661 
 85721 
 
 .84 566 
 84628 
 84689 
 
 84751 
 84813 
 
 .84 874 
 84936 
 
 84997 
 85058 
 85 120 
 
 .85 181 
 85 242 
 85303 
 85364 
 85425 
 
 •85 485 
 85546 
 85606 
 85667 
 85727 
 
 .86070 .86076 
 86130 86136 
 86 189 86 195 
 86 249 86 255 
 86308 86314 
 
 .85 781 .85 788 
 85842 85848 
 
 85 902 85 908 
 85962 85968 
 86022 86028 
 
 .86082 .86088 
 
 86 141 86 147 
 86 201 86 207 
 86261 86267 
 86320 86326 
 
 .86 368 
 86427 
 86487 
 86546 
 86605 
 
 .86 664 
 86723 
 86782 
 86841 
 86900 
 
 .86 958 
 87017 
 87075 
 87134 
 87192 
 
 .87 251 
 87309 
 87367 
 87425 
 
 87483 
 
 .86374 
 86433 
 86493 
 86552 
 
 86 61 1 
 
 .86 670 
 86729 
 86788 
 86847 
 86906 
 
 .86 964 
 87023 
 87081 
 
 87 140 
 87198 
 
 .87 256 
 
 87315 
 
 87373- 
 
 87431 
 
 87489 
 
 ,86 380 
 86439 
 86499 
 86558 
 86617 
 
 .86 676 
 
 86735 
 86794 
 86853 
 86 91 1 
 
 ,86 970 
 87029 
 87087 
 87146 
 87204 
 
 .87 262 
 87320 
 87379 
 87437 
 87495 
 
 ,86 386 
 86445 
 86504 
 86564 
 86623 
 
 ,86 682 
 86741 
 86800 
 86859 
 86917 
 
 .86976 
 
 87035 
 87093 
 87 151 
 87 210 
 
 .87 268 
 87326 
 
 87384 
 87442 
 87 500 
 
FIVE PLACE LOGARITHMS. 
 
 6 PL. LOGS. 
 
 No. 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 789 
 
 INTR 
 TAB. 
 
 7.50 
 
 .87 506 .87 512 
 
 .87518 
 
 •87 523 
 
 .87 529 
 
 •87 535 
 
 •87 541 
 
 ■87547 -87552 .87558 
 
 6 
 
 •5' 
 
 87564 87570 
 
 87576 
 
 87581 
 
 87587 
 
 87593 
 
 87599 
 
 87 604 87 610 87 616 
 
 1 
 
 •52 
 
 87622 8762S 
 
 87633 
 
 87639 
 
 87645 
 
 87651 
 
 87656 
 
 87662 87668 87674 
 
 1 
 
 •S3 
 
 87.679 87685 
 
 87691 
 
 87697 
 
 87703 
 
 87708 
 
 87714 
 
 87 720 87 726 87 731 
 
 2 
 
 •54 
 
 87737 87743 
 
 87749 
 
 87754 
 
 87760 
 
 87766 
 
 87772 
 
 87777 87783 87789 
 
 2 
 
 7^55 
 
 .87 795 .87 800 
 
 .87 806 
 
 .87812 
 
 .87818 
 
 ■87 823 
 
 .87 829 
 
 .87835 .87841 .87846 
 
 3 
 
 .56 
 
 87852 87858 
 
 87864 
 
 87869 
 
 87875 
 
 87881 
 
 87887 
 
 87892 87898 87904 
 
 4 
 
 •57 
 
 87910 87915 
 
 87921 
 
 87927 
 
 87933 
 
 87938 
 
 87944 
 
 87950 87955 87961 
 
 4 
 
 ■58 
 
 87967 87973 
 
 87978 
 
 87984 
 
 87990 
 
 87996 
 
 88 001 
 
 88007 88013 88018 
 
 5 
 
 •59 
 
 88024 88030 
 
 88036 
 
 88041 
 
 88047 
 
 88053 
 
 88058 
 
 88064 88070 88076 
 
 5 
 
 7.60 
 
 .88081 .88087 
 
 .88093 
 
 .88 098 
 
 .88 104 
 
 .88110 
 
 .88116 
 
 .88 121 .88 127 .88 133 
 
 S 
 
 .61 
 
 88138 88144 
 
 88150 
 
 88156 
 
 88161 
 
 88167 
 
 88173 
 
 88 178 88 184 88 190 
 
 1 
 
 .62 
 
 88195 88201 
 
 88207 
 
 88213 
 
 88218 
 
 88224 
 
 88230 
 
 88235 88241 88247 
 
 1 
 
 •63 
 
 88252 88258 
 
 88264 
 
 88270 
 
 88275 
 
 88281 
 
 88287 
 
 88292 88298 88304 
 
 2 
 
 .64 
 
 88309 88315 
 
 88321 
 
 88326 
 
 88332 
 
 88338 
 
 88343 
 
 88349 88355 88360 
 
 2 
 
 7-65 
 
 .88 366 .88 372 
 
 ■88 377 
 
 .88 383 
 
 .88 389 
 
 ■88 395 
 
 .88 400 
 
 .88406 .88412 .88417 
 
 3 
 
 .66 
 
 88423 88429 
 
 88434 
 
 88440 
 
 88446 
 
 88451 
 
 88457 
 
 88463 88468 88474 
 
 3 
 
 .67 
 
 88480 88485 
 
 88491 
 
 88497 
 
 88502 
 
 88508 
 
 88513 
 
 88519 88525 88530 
 
 4 
 
 .68 
 
 88536 88542 
 
 88547 
 
 88553 
 
 88559 
 
 88564 
 
 88570 
 
 88576 88581 88587 
 
 4 
 
 .69 
 
 88593 88598 
 
 88604 
 
 88610 
 
 88615 
 
 88621 
 
 88627 
 
 88632 88638 88-.643 
 
 5 
 
 7.70 
 
 .88649 .88^55 
 
 .88 660 
 
 .88 666 
 
 .88 672 
 
 .88 677 
 
 !88 683 
 
 .88 689 .88 694 .88 700 
 
 6 
 
 •71 
 
 88705 88 711 
 
 88717 
 
 88722 
 
 88728 
 
 88734 
 
 88739 
 
 88745 88750 88756 
 
 1 
 
 .72 
 
 88762 88767 
 
 88773 
 
 88779 
 
 88784 
 
 88790 
 
 88795 
 
 88801 88807 88812 
 
 I 
 
 •73 
 
 88818 88824 
 
 88829 
 
 88835 
 
 88840 
 
 88846 
 
 88852 
 
 88857 88863 88 868 
 
 2 
 
 •74 
 
 88874 88880 
 
 88885 
 
 88891 
 
 88897 
 
 88902 
 
 88908 
 
 88913 88919 88925 
 
 2 
 
 7-75 
 
 .88930 .88936 
 
 .88 941 
 
 .88 947 
 
 .88953 
 
 .88 958 
 
 .88 964 
 
 .88969 .88975 .88981 
 
 3 
 
 .76 
 
 88986 88992 
 
 88997 
 
 89 003 
 
 89009 
 
 89014 
 
 89020 
 
 89025 89031 89037 
 
 4 
 
 •77 
 
 89 042 89 048 
 
 89053 
 
 89059 
 
 89064 
 
 89070 
 
 89076 
 
 89081 89087 89092 
 
 4 
 
 .78 
 
 89 098 89 104 
 
 89 109 
 
 89 115 
 
 89 120 
 
 89126 
 
 89131 
 
 89 137 89 143 89 148 
 
 5 
 
 •79 
 
 89154 89159 
 
 89165 
 
 89 170 
 
 89176 
 
 89182 
 
 89187 
 
 89 193 89 198 89 204 
 
 5 
 
 7.80 
 
 .89209 .89215 
 
 .89 221 
 
 .89 226 
 
 .89 232 
 
 .89 237 
 
 .89 243 
 
 .89248 .89254 .89260 
 
 5 
 
 .81 
 
 89 265 89 271 
 
 89276 
 
 89282 
 
 89287 
 
 89293 
 
 89298 
 
 89304 89310 89315 
 
 1 
 
 .82 
 
 89 321 89 326 
 
 89.332 
 
 89337 
 
 89343 
 
 89348 
 
 89354 
 
 89360 89365 89371 
 
 1 
 
 •83 
 
 89376 89382 
 
 89387 
 
 89393 
 
 89398 
 
 89404 
 
 89409 
 
 89415 89421 89426 
 
 2 
 
 .84 
 
 89432 89437 
 
 89443 
 
 89448 
 
 89454 
 
 89459 
 
 89465 
 
 89470 89476 89481 
 
 2 
 
 7-85 
 
 .89 487 .89 492 
 
 .89498 
 
 .89 504 
 
 .89 509 
 
 •89515 
 
 .89 520 
 
 .89 526 .89 531 .89 537 
 
 3 
 
 .86 
 
 89542 89548 
 
 89553 
 
 89559 
 
 89564 
 
 89570 
 
 89575 
 
 89581 89586 89592 
 
 3 
 
 •87 
 
 89597 89 6»3 
 
 89609 
 
 89614 
 
 89 620 
 
 89625 
 
 89631 
 
 89 636 89 642 89 647 
 
 4 
 
 .88 
 
 89653 89658 
 
 89664 
 
 89669 
 
 89675 
 
 89680 
 
 89686 
 
 89 691 89 697 89 702 
 
 4 
 
 .89 
 
 89 708 89 713 
 
 89719 
 
 89724 
 
 89730 
 
 89735 
 
 89741 
 
 89746 89752 89757 
 
 5 
 
 7.90 
 
 .89 763 .89 768 
 
 ■89 774 
 
 .89 779 
 
 •89 785 
 
 •89 790 
 
 ■89 796 
 
 .89 801 .89 807 .89 812 
 
 6 
 
 •91 
 
 89818 89823 
 
 89829 
 
 89834 
 
 89840 
 
 89845 
 
 89851 
 
 89856 89862 89867 
 
 1 
 
 .92 
 
 89873 89878 
 
 89883 
 
 89889 
 
 89894 
 
 89900 
 
 89905 
 
 89911 89916 89922 
 
 1 
 
 •93 
 
 89927 89933 
 
 89938 
 
 89944 
 
 89949 
 
 89955 
 
 89 960 
 
 89966 89971 89977 
 
 2 
 
 •94 
 
 89982 89988 
 
 89993 
 
 89998 
 
 90 00i 
 
 90009 
 
 90015 
 
 90020 90026 90031 
 
 2 
 
 7^95 
 
 .90037 .90042 
 
 .90 048 
 
 .90053 
 
 .90059 
 
 .90 064 
 
 .90 069 
 
 .90075 .90080 .90086 
 
 3 
 
 .96 
 
 90091 90097 
 
 90 102 
 
 90 108 
 
 90 113 
 
 90119 
 
 90 124 
 
 90 129 90 135 90 140 
 
 4 
 
 •97 
 
 90 146 90 151 
 
 90157 
 
 90 162 
 
 90 168 
 
 90173 
 
 90179 
 
 90 184 90 189 90 195 
 
 4 
 
 .98 
 
 90 200 90 206 
 
 90 21 1 
 
 90 217 
 
 90222 
 
 90 227 
 
 90233 
 
 90 238 90 244 90 249 
 
 5 
 
 ■99 
 
 90 255 90 260 
 
 90266 
 
 90271 
 
 90 276 
 
 90 282 
 
 90287 
 
 90 293 90 298 90 304 
 
 5 
 
 (25) 
 
 5 PL. 
 
 LOGS. 
 7. 
 
8. 
 LOGS. 5 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 8.00 
 
 .OI 
 .02 
 
 •03 
 
 .04 
 
 8.05 
 .06 
 .07 
 .08 
 .09 
 
 8.10 
 
 .II 
 
 .12 
 
 •13 
 
 .14 
 
 8.15 
 .16 
 
 ■17 
 .18 
 
 •19 
 
 8.20 
 
 .21 
 .22 
 
 •23 
 .24 
 
 8.25 
 .26 
 
 •27 
 .28 
 .29 
 
 8.30 
 
 •31 
 •32 
 ■33 
 
 •34 
 
 8^35 
 •36 
 •37 
 •38 
 •39 
 
 8.40 
 
 .41 
 .42 
 •43 
 ■44 
 
 8.45 
 .46 
 
 •47 
 .48 
 
 •49 
 
 2 
 
 8 
 
 .90 309 
 90363 
 90417 
 90472 
 90526 
 
 .90 580 
 90634 
 90687 
 90741 
 90795 
 
 .90 849 
 90902 
 90956 
 91 009 
 91 062 
 
 .91 116 
 91 169 
 91 222 
 91275 
 91328 
 
 •91 381 
 91434 
 91487 
 
 91 540 
 91593 
 .91 645 
 916518 
 
 91 751 
 91803 
 91855 
 
 .91 908 
 
 91 960 
 92012 
 
 92 065 
 92 117 
 
 .92 169 
 92 221 
 92273 
 92324 
 92376 
 
 .92428 
 92480 
 92531 
 92583 
 92634 
 
 .92686 . 
 
 92737 
 92788 
 92 840 
 92891 
 
 .90314 
 90369 
 90423 
 90477 
 90531 
 .90 585 
 90639 
 90693 
 90747 
 90800 
 
 •90 854 
 90907 
 90961 
 91 014 
 91 068 
 
 .91 121 
 
 91 174 
 91 228 
 91 281 
 91334 
 
 •91' 387 
 91440 
 91492 
 
 91545 
 91598 
 
 .91 651 
 
 91703 
 91756 
 91 808 
 
 91 861 
 
 •91 913 
 91965 
 92018 
 92070 
 
 92 122 
 
 •92 174 
 92 226 
 92 278 
 92330 
 92381 
 
 •92 433 
 92485 
 92536 
 92588 
 92639 
 
 .92 691 
 92742 
 92793 
 92845 
 92896 
 
 .90 320 
 
 90374 
 90428 
 90482 
 90536 
 .90 590 
 
 90 644 
 90698 
 90752 
 90806 
 
 •90 859 
 90913 
 90966 
 
 91 020 
 91073 
 .91 126 
 91 180 
 
 91233 
 91286 
 
 9>339 
 
 .91 392 
 
 91445 
 91498 
 
 91 551 
 91603 
 
 .91 656 
 91709 
 91 761 
 91 814 
 91866 
 
 .91 918 
 
 91 971 
 92023 
 92075 
 
 92 127 
 
 ■92179 
 92231 
 92283 
 92335 
 92387 
 
 •92 438 
 92490 
 92542 
 
 92593 
 92645 
 
 .92 696 
 92747 
 92799 
 92 850 
 92901 
 
 .90 325 
 90380 
 
 90434 
 90488 
 90542 
 
 ■90 596 
 90650 
 90703 
 90757 
 
 90 811 
 
 .90 865 
 90918 
 90972 
 
 91 025 
 91 078 
 .91 132 
 91 185 
 91238 
 91 291 
 91344 
 
 ■91 397 
 91450 
 
 91503 
 91556 
 91 609 
 
 .91 661 
 
 91714 
 91 766 
 91 819 
 
 91 871 
 
 .91 924 
 91976 
 92028 
 92080 
 
 92 132 
 .92 184 
 92236 
 92288 
 92340 
 92392 
 
 •92 443 
 92495 
 92547 
 92598 
 92650 
 
 .92 701 
 92752 
 92804 
 92855 
 92906 
 
 •90 331 
 90385 
 90439 
 90493 
 90547 
 .90 601 
 90655 
 
 90 709 
 90763 
 90816 
 
 .90 870 
 90924 
 
 90977 
 91030 
 
 91 084 
 
 •91 «37 
 91 190 
 91243 
 91297 
 91350 
 
 .91 402 
 
 91455 
 91 508 
 91 561 
 91 614 
 
 .91' 666 
 91 719 
 91 772 
 91 824 
 91 876 
 
 .91 929 
 
 91 981 
 92033 
 92085 
 92137 
 .92 189 
 
 92 241 
 92293 
 92345 
 92397 
 
 •92449 
 92500 
 
 92552 
 92 603 
 92655 
 .92 706 
 
 92758 
 92 809 
 92860 
 92911 
 
 •90 336 
 90390 
 
 90445 
 90499 
 90553 
 .90 607 
 90660 
 90714 
 90768 
 90822 
 
 .90 875 
 90929 
 90982 
 91036 
 91 089 
 .91 142 
 91 196 
 91249 
 91302 
 9135s 
 
 .91 408 
 91 461 
 91 514 
 91 566 
 91 619 
 
 .91 672 
 91 724 
 91 777 
 91 829 
 91 882 
 
 ■91 934 
 
 91 986 
 92038 
 92091 
 92143 
 .92 195 .92 200 
 92247 92252 
 92298 92304 
 92350 92355 
 
 92 402 92 407 
 
 ,90 342 
 90396 
 90450 
 90504 
 90558 
 .90612 
 90666 
 
 90 720 
 
 90773 
 90827 
 
 .90 881 
 
 90934 
 90988 
 
 91 041 
 91094 
 
 .91 148 
 91 201 
 91254 
 
 91307 
 91360 
 
 •91 413 
 91 466 
 
 91519 
 91572 
 91 624 
 
 .91 677 
 
 91 730 
 91 782 
 
 91834 
 91887 
 
 •91 939 
 
 91 991 
 92044 
 92096 
 
 92 148 
 
 •92 454 
 92505 
 92557 
 92 609 
 92 660 
 
 .92711 
 92763 
 92814 
 92865 
 92.916 
 
 •92459 
 92511 
 92562 
 92614 
 92665 
 
 .92 716 
 92 768 
 92819 
 92 870 
 92921 
 
 •90 347 
 90401 
 
 90455 
 90509 
 
 90563 
 .90617 
 90671 
 90725 
 
 90779 
 90832 
 
 .90 886 
 90940 
 
 90993 
 91 046 
 91 100 
 
 •91 153 
 91 206 
 91259 
 91 312 
 91365 
 
 .91 418 
 91471 
 91524 
 91577 
 91630 
 
 .91 682 
 
 91735 
 91787 
 91 840 
 
 91 892 
 
 .91944 
 91997 
 92049 
 
 92 lOI 
 92153 
 .92 205 
 92257 
 92309 
 92361 
 92412 
 
 .92464 
 92 516 
 
 92567 
 92619 
 92 670 
 
 .92 722 .92 727 
 
 92773 92778 
 
 92 824 92 829 
 
 92875 92881 
 
 92927 92932 
 
 •90 352 
 90407 
 90461 
 90515 
 90569 
 •90 623 
 90677 
 90730 
 90784 
 90838 
 
 .90 891 
 
 90945 
 90998 
 91 052 
 91 105 
 
 .91 158 
 91 212 
 91 265 
 91318 
 91 371 
 
 .91 424 
 
 91477 
 91529 
 91582 
 91635 
 .91 687 
 91740 
 
 91793 
 91845 
 91897 
 
 •90 358 
 90412 
 90466 
 90520 
 90574 
 .90 628 
 90682 
 90736 
 90789 
 90843 
 
 •90 897 
 90950 
 91004 
 91057 
 91 no 
 
 .91 164 
 91 217 
 91 270 
 91323 
 91376 
 
 .91 429 
 91 482 
 91535 
 91587 
 91 640 
 
 .91 693 
 
 91745 
 91798 
 91850 
 91903 
 
 .91 950 .91 955 
 92 003 92007 
 92054 92059 
 92106 92 III 
 92 158 92 163 
 
 .92210 .92215 
 92 262 92 267 
 92314 92319 
 92366 92371 
 92418 92423 
 
 .92 469 
 92521 
 92572 
 92624 
 92675 
 
 .92 474 
 92526 
 92578 
 92629 
 92681 
 .92 732 
 
 92783 
 92834 
 92886 
 92937 
 
 LOGS. 5 PL. 
 8. 
 
 (26) 
 
FIVE PLACE LOGARITHMS. 
 
 8. 
 6 PL. LOGS. 
 
 No. 
 
 8.50 
 
 •51 
 
 •52 
 •53 
 •54 
 
 8.55 
 .56 
 
 ■57 
 .58 
 
 •59 
 
 8.60 
 
 .61 
 
 .62 
 
 •63 
 .64 
 
 8.65 
 .66 
 .67 
 .68 
 .69 
 
 8.70 
 
 •71 
 .72 
 
 ■73 
 
 •74 
 
 8.75 
 
 .76 
 
 •77 
 .78 
 
 ■79 
 
 8.80 
 
 .81 
 .82 
 
 •83 
 
 .84 
 
 8.85 
 .86 
 .87 
 
 8.90 
 
 .91 
 .92 
 •93 
 ■94 
 8.95 
 .96 
 
 •97 
 .98 
 
 ■99 
 
 8 
 
 .92 942 
 92993 
 93044 
 93095 
 93146 
 
 ■93 197 
 93247 
 93298 
 93 349 
 93 399 
 
 •92 947 
 92998 
 
 93049 
 93 100 
 
 93 151 
 ■93 202 
 93252 
 93303 
 93 354 
 93404 
 
 ■93450.93455 
 93500 93505 
 93551 93556 
 93601 93606 
 
 93651 93656 
 
 •93 702 
 93752 
 93802 
 93852 
 93902 
 
 •93 952 
 94 002 
 
 94052 
 
 94 101 
 
 94 151 
 .94 201 
 94250 
 94300 
 94 349 
 94 399 
 
 ■94 448 
 94498 
 
 94 547 
 94596 
 
 94645 
 •94 694 
 94 743 
 94792 
 94841 
 94890 
 
 ■94 939 
 94988 
 95036 
 95085 
 95134 
 .95 182 
 95231 
 95279 
 95328 
 95376 
 
 ■93 707 
 
 93 757 
 93807 
 
 93857 
 93907 
 
 •93 957 
 94007 
 
 94057 
 
 94 106 
 94156 
 
 .94 206 
 94255 
 94305 
 94 354 
 94404 
 
 •94 453 
 94503 
 94552 
 94601 
 94650 
 
 •94 699 
 94748 
 
 94 797 
 94846 
 94895 
 
 •94 944 
 94 993 
 95041 
 95090 
 
 95139 
 •95 187 
 95236 
 95284 
 95332 
 95381 
 
 .92952 
 93 003 
 
 93054 
 93105 
 93156 
 
 •93 207 
 93258 
 93308 
 93 359 
 93409 
 
 •93 460 
 93510 
 93561 
 
 93 611 
 93661 
 
 •93 712 
 93762 
 93812 
 93862 
 93912 
 
 •93 962 
 94012 
 94062 
 
 94 HI 
 94 161 
 
 .94 21 1 
 94260 
 94310 
 
 94 359 
 94409 
 
 .94458 
 94507 
 94 557 
 94606 
 
 94655 
 
 •94 704 
 
 94 753 
 94802 
 94851 
 94900 
 
 •94 949 
 94998 
 95046 
 95095 
 95143 
 
 •95 192 
 95240 
 95289 
 
 95 337 
 95386 
 
 •92957 
 93008 
 
 93059 
 93 HO 
 
 93 161 
 
 ■93 212 
 93263 
 93313 
 93364 
 93414 
 
 •93 465 
 93515 
 93566 
 93616 
 93666 
 
 •93717 
 93767 
 93817 
 94867 
 93917 
 
 •93 967 
 94017 
 94067 
 
 94 1 16 
 94 1 56 
 
 .94216 
 94265 
 94315 
 94364 
 94414 
 
 •94463 
 94512 
 94562 
 
 94 61 1 
 94660 
 
 •94 709 
 94758 
 94807 
 94856 
 94905 
 
 ■94 954 
 
 95 003 
 
 95051 
 95 loo 
 95148 
 
 •95 197 
 95245 
 95294 
 95342 
 95390 
 
 .92 962 
 
 93013 
 93064 
 
 93115 
 93166 
 
 •93217 
 93268 
 93318 
 
 93369 
 93420 
 
 •93 470 
 93520 
 
 93571 
 93621 
 
 93671 
 
 ■93 722 
 93772 
 93822 
 93872 
 93922 
 
 •93 972 
 94022 
 94072 
 
 94 121 
 94171 
 
 .94 221 
 94270 
 94320 
 
 94369 
 94419 
 
 .94 468 
 94517 
 94567 
 94616 
 94665 
 
 •94 714 
 94763 
 94812 
 94861 
 94910 
 
 •94 959 
 95007 
 
 95056 
 95105 
 
 95153 
 .95 202 
 95250 
 95299 
 
 95 347 
 95 395 
 
 .92 967 
 93018 
 93069 
 93120 
 93 171 
 .93 222 
 93273 
 93323 
 93 374 
 93425 
 
 •93 475 
 93526 
 93576 
 93 626 
 93676 
 
 •93 727 
 
 93 777 
 93827 
 
 93877 
 93927 
 
 •93 977 
 94027 
 
 94077 
 
 94 126 
 94176 
 
 .94 226 
 94275 
 94325 
 
 94 374 
 94424 
 
 •94473 
 94522 
 
 94571 
 94621 
 94670 
 
 ■94 719 
 94768 
 94817 
 94866 
 94915 
 
 ■94 963 
 95012 
 95061 
 
 95 109 
 95158 
 ■95 207 
 95255 
 95303 
 95352 
 95400 
 
 ■92 973 
 93024 
 
 93075 
 93125 
 93176 
 ■93 227 
 93278 
 93328 
 
 93 379 
 93430 
 
 •93 480 
 93531 
 93581 
 93631 
 93682 
 
 •93 732 
 93782 
 93832 
 93882 
 93932 
 
 •93 982 
 94032 
 94082 
 
 94131 
 
 94 181 
 
 •94 231 
 94280 
 94330 
 94 379 
 94429 
 
 •94 478 
 94527 
 94576 
 94626 
 
 94675 
 
 •94 724 
 
 94 773 
 94822 
 
 94871 
 94919 
 
 .94 968 
 95017 
 
 95 066 
 95114 
 95163 
 ■95211 
 95 260 
 95308 
 95 357 
 95405 
 
 .92 978 
 93029 
 93080 
 93131 
 93181 
 
 •93 232 
 93283 
 93 334 
 93384 
 93 435 
 
 ■93 485 
 93536 
 93586 
 93636 
 93687 
 
 ■93 737 
 93787 
 93837 
 93887 
 
 93 937 
 
 ■93 987 
 94037 
 94086 
 94136 
 
 94 186 
 
 •94 236 
 94285 
 94 335 
 94384 
 
 94 433 
 
 •94 483 
 94532 
 94581 
 94630 
 94680 
 
 •94 729 
 94778 
 94827 
 94876 
 94924 
 
 •94 973 
 
 95 022 
 
 95071 
 95 119 
 95168 
 
 .95 216 
 95265 
 95313 
 95361 
 95410 
 
 .92983 .92988 
 
 93034 93039 
 93085 93090 
 93 136 93 141 
 93 186 93 192 
 
 •93 237 
 93288 
 
 93 339 
 93389 
 93440 
 
 •93 490 
 93541 
 93591 
 93641 
 93692 
 
 •93 742 
 93792 
 93842 
 93892 
 93942 
 
 ■93 992 
 94042 
 
 94091 
 94141 
 94191 
 .94 240 
 94290 
 94340 
 94389 
 94438 
 
 .94 488 
 
 94 537 
 94586 
 
 94635 
 94685 
 
 ■94 734 
 94783 
 94832 
 94880 
 94929 
 
 •94 978 
 95027 
 
 95075 
 
 95 124 
 95173 
 .95 221 
 95270 
 95318 
 95366 
 95415 
 
 (27) 
 
 .93 242 
 93293 
 93 344 
 93 394 
 93 445 
 
 •93 495 
 93546 
 93596 
 93646 
 
 93697 
 
 •93 747 
 93 797 
 93847 
 93897 
 
 93 947 
 
 •93 997 
 94047 
 94096 
 
 94146 
 94196 
 
 •94 245 
 94295 
 
 94 345 
 94 394 
 94 443 
 
 •94 493 
 94542 
 94591 
 94640 
 94689 
 
 •94 738 
 94 7.87 
 94836 
 94885 
 
 94 934 
 
 ■94 983 
 95032 
 
 95 080 
 95 129 
 95177 
 .95 226 
 95274 
 95323 
 95371 
 95419 
 
 5 PL. 
 
 INTP. 
 TAB. 
 
 LOGS. 
 8. 
 
9. 
 LOGS. 5 PL. 
 
 FIVE PLACE LOGARITHMS. 
 
 No. 
 
 .01234 
 
 5 67 8 9 
 
 INTP. 
 TAB. 
 
 5 
 
 I 
 I 
 2 
 2 
 
 . 9.00 
 
 .OI 
 .02 
 
 •03 
 .04 
 
 •95 424 -95 429 -95 434 -95 439 '95 444 
 95472 95 477 95482 95487 95492 
 95521 95525 95530 95535 95540 
 
 95569 95 574 95578 95583 95588 
 95617 95622 95626 95631 95636 
 
 •95 448 .95 453 •gs 458 .95 463 .95 468 
 
 95 497 95501 95506 95511 95516 
 95 545 95550 95 554 95 559 95564 
 95 593 95598 95602 95607 95612 
 95641 95646 95650 95655 95660 
 
 9-05 
 .06 
 .07 
 .08 
 .09 
 
 •95 66^ ^95 670 .95 674 ^95 679 ^95 684 
 95713 95718 95722 95727 95732 
 95 761 95 766 95 770 95 775 95 78° 
 95 809 95 813 95 818 95 823 95 828 
 95856 95861-95866 95871 95875 
 
 .95 689 .95 694 .95 698 .95 703 .95 708 
 95 737 95 742 95 746 95 751 95 756 
 95785 95789 95 794 95 799 95804 
 95832 95837 95842 95847 95852 
 95880 95885 95890 95895 95899 
 
 3 
 3 
 4 
 4 
 5 
 
 9.10 
 
 .11 
 
 .12 
 
 ■13 
 .14 
 
 .95904 .95909 .95914 ^95918 .95923 
 95952 95 957 95961 95966 95971 
 95 999 96 004 96009 96014 96019 
 96047 96052 96057 96061 96066 
 96095 96099 96104 96109 96114 
 
 •95 928 .95 933 .95 938 .95 942 .95 947 
 95976 95980 95985 95990 95995 
 96023 96028 96033 96038 96042 
 96071 96076 96080 96085 96090 
 96 118 96123 96128 96133 96137 
 
 4 
 
 I 
 1 
 2 
 
 9.I5 
 .16 
 
 •17 
 .18 
 .19 
 
 .96 142 .96 147 .96 152 .96 156 .96 161 
 96190 96194 96199 96204 96209 
 96237 96242 96246 96251 96256 
 96 284 96 289 96 294 96 298 96 303 
 96332 96336 96341 96346 96350 
 
 .96166 .96171 .96175 .96180 .96185 
 96 213 96 2i8 96 223 96 227 96 232 
 96 261 96 265 96 270 96 275 96 280 
 96308 96313 96317 96322 96327 
 96355 96360 96365 96369 96374 
 
 2 
 2 
 3 
 3 
 4- 
 
 9.20 
 
 .21 
 
 .22 
 
 ■23 
 
 .24 
 
 •96 379 96 384 -96 388 .96 393 .96 398 
 96426 96431 96435 96440 96445 
 96473 96478 96483 96487 96492 
 96520 96525 96530 96534 96539- 
 96567 96572 96577 96581 96586 
 
 .96402 .96407 .96412 .96417 .96421 
 96450 96454 96459 96464 96468 
 96497 96501 96506 96511 96515 
 96544 96^48 96553 96558 96562, 
 96 591 96 595 96 600 96 605 96 609 
 
 5 
 I 
 
 1 
 2 
 2 
 
 9.25 
 .26 
 .27 
 .28 
 .29 
 
 .96 614 .96 619 .96 624 .96 628 .96 633 
 96 661 96 666 96 670 96 675 96 680 
 96708 96713 96717 96722 96727 
 
 96755 96759 96764 96769 96774 
 96802 96806 96 811 96816 96820 
 
 .96638 .96642 .96647 .96652 .96656 
 96 685 96 689 96 694 96 699 96 703 
 
 96731 96736 96741 96745 96750 
 96778 96783 96788 96792 96797 
 96 825 96 830 96 834 96 839 96 844 
 
 3 
 3 
 4 
 4 
 5 
 
 9.30 
 
 •3' 
 
 •32 
 •33 
 •34 
 
 .96848 .96853 .96858 .96862 .96867 
 96895 96900 96904 96909 96914 
 96942 96946 96951 96956 96960 
 96988 96993 96997 97 002 97007 
 97035 97039 97044 97049 97053 
 
 .96872 .96876 .96881 .96886 .96890 
 96918 96923 96928 96932 96937 
 
 96965 96970 96974 96979 96984 
 97 01 1 97016 97021 97025 97030 
 97058 97063 97067 97072 97077 
 
 4 
 
 1 
 1 
 2 
 
 9-35 
 •36 
 •37 
 .38 
 ■39 
 
 .97081 .97086 .97090 .97095 .97100 
 97128 97132 97137 97142 97146 
 97174 97179 97183 97188 97192 
 97220 97225 97230 97234 97239 
 97 267 97 271 97 276 97 280 97 285 
 
 .97 104 .97 109 .97 114 .97 118 .97 123 
 97 151 97155 97160 97165 97169 
 97197 97202 97206 97211 97216 
 97243 97248 97253 97257 9/262 
 97290 97294 97299 97304 97308 
 
 2 
 2 
 3 
 3 
 4 
 
 9.40 
 
 .41 
 
 .42 
 
 ■43 
 .44 
 
 ■97313 .97317 ^97322 .97327 .97331 
 97 359 97364 97368 97 373 97 377 
 97405 97410 97414 97419 97424 
 97451 97456 97460 97465 97470 
 97497 97502 97506 97511 97516 
 
 •97 336 -97 340 .97 345 ^97 35o .97 354 
 97382 97387 97391 97.396 97400 
 97428 97433 97437 97442 97 447 
 97 474 97 479 97 483 97 488 97 493 
 97520 97525 97529 97534 97539 
 
 6 
 
 I 
 1 
 2 
 2 
 
 9-45 
 .46 
 
 •47 
 .48 
 ■49 
 
 •97 543 ^97 548 .97 552 .97 557 ^97 562 
 97589 97 594 97598 97603 97607 
 97635 97-640 97644 97649 97653 
 97681 97685 97690 97695 97699 
 97727 97731 97736 97740 97745 
 
 •97566 .97571 ^97 575 -97580 .97585 
 97612 97617 97621 97626 97630 
 97 658 97 663 97 667 97 672 97 676 
 97704 97708 97713 97717 97722 
 97 749 97 754 97 759 97 763 97 768 
 
 3 
 3 
 4 
 4 
 
 5 
 
 LOGS. 6 PL. 
 9. 
 
 (28) 
 
FIVE PLACE LOGARITHMS. 
 
 5 PL. LOGS. 
 
 No. 
 
 01234 
 
 56789 
 
 INTP, 
 TAB. 
 
 9.50 
 
 •51 
 
 •52 
 ■53 
 •54 
 
 •97 772 -97 777 ^97 782 .97 786 .97 79i 
 97818 97823 97827 97832 97836 
 97864 97868 97873 97877 97882 
 97909 97914 97918 97923 97928 
 97 955 97 959 97 9^4 97 968 97 973 
 
 •97 795 -97800 .97804 ,97809 .97813 
 97841 97845 97850 97855 97859 
 97 886 97 891 97 896 97 900 97 905 
 
 97932 97 937 97 941 97 946 97 950 
 97978 97982 97987 97991 97996 
 
 4 
 
 1 
 I 
 2 
 
 9-55 
 .56 
 
 •57 
 •58 
 •59 
 
 .98 000 .98 005 .98 009 .98 014 .98 019 
 98046 98050 98055 98059 98064 
 98091 98096 98100 98105 98109 
 98 137 98 141 98 146 98 150 98 155 
 9_8 182 98186 98191 98195 98200 
 
 .98 023 .98 028 .98 032 .98 037 .98 041 
 98068 98073 98078 98082 98087 
 98114 98118 98123 98127 98132 
 98 159 98 164 98 168 98 173 98 177 
 98 204 98 209 98 214 98 218 98 223 
 
 2 
 2 
 3 
 
 3 
 4 
 
 9.60 
 
 .61 
 .62 
 ■63 
 .64 
 
 .98 227 .98 232 .98 236 .98 241 .98 245 
 98 272 98 277 98 281 98 286 98 290 
 98318 98322 98327 98331 98336 
 
 98363 98367 98372 98376 98381 
 98408 98412 98417 98421 98426 
 
 .98250 .98254 .98259 .98263 .98268 
 98295 98299 98304 98308 98313 
 98340 98345 98349 98354 98358 
 
 98385 98390 98394 98399 98403 
 98430 98435 98439 98444 98448 
 
 5 
 1 
 
 1 
 2 
 2 
 
 9-65 
 
 .66 
 .67 
 .68 
 .69 
 
 .98453 .98457 .98462 .98466 .98471 
 98498 98502 98507 98511 98516 
 
 98543 98547 98552 98556 98561 
 98588 98592 98597 98601 98605 
 98 632 98 637 98 641 98 646 98 650 
 
 .98475 .98480 .98484 .98489 .98493 
 98520 98525 98529 98534 98538 
 
 98565 98570 98574 98579 98583 
 98610 98614 98619 98623 98628 
 98655 98659 98664 98668 98673 
 
 3 
 3 
 
 4 
 4 
 5 
 
 9.70 
 
 ■71 
 .72 
 
 •73 
 •74 
 
 .98677 .98682 .98686 .98691 .98695 
 98722 98726 98731 98735 98740 
 98767 98771 98776 98 7S0 98784 
 98 811 98816 98820 98825 98829 
 98856 98860 98865 98869 98874 
 
 .98700 .98704 .98709 .98713 .98717 
 
 98744 98749 98753 98758 98762 
 98789 98793 98798 98802 98807 
 98834 98838 98843 98847 98851 
 98878 98883 98887 98892 98896 
 
 4 
 
 
 I 
 
 1 
 2 
 
 9-75 
 .76 
 
 •77 
 .78 
 
 •79 
 
 .98900 .98905 .98909 .98914 ,98918 
 98945 98949 98954 98958 98963 
 98989 98994 98998 99 003 99007 
 99034 99038 99043 99047 99052 
 99078 99083 99087 99092 99096 
 
 .98923 .98927 .98932 .98936 .98941 
 98967 98972 98976 98981 98985 
 99012 99016 99021 99025 99029 
 99056 99061 99065 99069 99074 
 99100 99105 99109 99 114 99118 
 
 2 
 2 
 3 
 3 
 4 
 
 9.80 
 
 .81 
 .82 
 
 •83 
 .84 
 
 •99 123 .99 127 .99 131 .99 136 .99 140 
 99 167 99 171 99 176 99 180 99 185 
 
 99 2H 99216 99220 99224 99229 
 99255 99260 99264 99269 99273 
 99300 99304 99308 99313 99317 
 
 •99 145 ^99 149 -99 154 -99 158 -99 162 - 
 99 189 99 193 99 198 99 202 99 207 
 99233 99238 99242 99247 99251 
 99 277 99 282 99 286 99 291 99 295 
 99322 99326 99330 99335 99339 
 
 5 
 
 1 
 I 
 2 
 2 
 
 9-85 
 .86 
 
 •87 
 .88 
 .89 
 
 •99 344 .99348 ^99352 ^99 357 -99 361 
 99388 99392 99396 99401 99405 
 99432 99436 99441 99445 99449 
 99476 99480 99484 99489 99493 
 99520 99524 99528 99533 99537 
 
 •99 366 .99 370 .99 374 ^99 379 -99 383 
 99410 99414 99419 99423 99427 
 
 99 454 99458 99463 99467 99471 
 99498 99502 99506 99511 99515 
 
 99542 99546 99550 99 555 99 559 
 
 3 
 3 
 4 
 4 
 5 
 
 9.90 
 
 •91 
 .92 
 
 •93 
 •94 
 
 •99564 .99568 .99572 .99 577 ^99581 
 99607 99612 99616 99621 99625 
 99651 99656 99660 99664 99669 
 99695 99699 99704 99708 99712 
 99 739 99 743 99 747 99 752 99 756 
 
 •99 585 ^99 590 .99 594 .99 599 ^99 603 
 99 629 99 634 99 638 99 642 99 647 
 99673 99677 99682 99686 99691 
 99717 99721 99726 99730 99734 
 99760 99765 99769 99 774 99778 
 
 4 
 
 
 1 
 1 
 2 
 
 9-95 
 .96 
 
 •97 
 .98 
 
 •99 
 
 ■99 782 .99 787 ^99 791 .99 795 .99 800 
 99826 99830 99835 99839 99843 
 99 870 99 874 99 878 99 883 99 887 
 99913 99917 99922 99926 99930 
 99 957 99961 99965 99970 99974 
 
 .99804 .99808 .99813 .99817 .99822 
 99 848 99 852 99 856 99 861 99 865 
 99891 99896 99900 99904 99909 
 99 935 99 939 99 944 99 948 99952 
 99978 99983 99987 99 991 99996 
 
 2 
 2 
 3 
 3 
 
 4 
 
 (29) 
 
 5 PL. LOGS. 
 9. 
 
1.-10. 
 SQ. RTS. 
 
 86 SQRS. 
 
 SQUARE ROOTS AND SQUARES. 
 
 Note. The table gives roots directly, squares by inverse interpolation. 
 
 No. 
 
 Interpola. 
 for Thousandths. 
 
 1.0 
 
 .1 
 
 .2 
 
 •3 
 
 •4 
 
 i-S 
 .6 
 
 •7 
 .8 
 
 •9 
 
 2.0 
 
 .1 
 
 .2 
 
 •3 
 ■4 
 
 2.5 
 
 .6 
 
 •9 
 
 3.0 
 
 .1 
 
 .2 
 
 •3 
 
 •4 
 
 3-5 
 .6 
 
 •7 
 .8 
 
 •9 
 
 4.0 
 
 .1 
 
 .2 
 
 •3 
 
 •4 
 
 4-5 
 .6 
 
 ■7 
 
 I.OOO 
 
 1.049 
 1.095 
 1. 140 
 1. 183 
 1.225 
 1.265 
 1.304 
 1.342 
 1-378 
 
 1.414 
 1.449 
 1.483 
 1.517 
 1.549 
 
 1.581 
 1.612 
 1.643 
 1-673 
 1703 
 
 1.732 
 1. 761 
 1.789 
 1. 81 7 
 
 1.844 
 
 1.871 
 1.897 
 1.924 
 1.949 
 1-975 
 
 2.000 
 
 2.025 
 2.049 
 2.074 
 2.098 
 
 2.121 
 
 2.145 
 2.168 
 2. 191 
 2.214 
 
 .005 
 .054 
 .100 
 
 .145 
 .187 
 
 .229 
 .269 
 .308 
 
 •345 
 .382 
 
 .418 
 
 -453 
 .487 
 .520 
 -552 
 
 .584 
 .616 
 .646 
 .676 
 .706 
 
 ■735 
 .764 
 
 •792 
 .819 
 
 .847 
 
 -873 
 .900 
 
 .926 
 .952 
 -977 
 
 2.027 
 2.052 
 2.076 
 2.100 
 
 2.124 
 2.147 
 2.170 
 2.193 
 2.216 
 
 .010 
 -058 
 .105 
 .149 
 .192 
 
 -233 
 •273 
 ■3" 
 -349 
 -386 
 
 .421 
 .456 
 .490 
 -523 
 ■556 
 .587 
 .619 
 .649 
 .679 
 .709 
 
 -738 
 .766 
 
 ■794 
 .822 
 .849 
 
 .876 
 
 -903 
 .929 
 
 •954 
 .980 
 
 2.005 
 2.030 
 2.054 
 2.078 
 2.102 
 
 2.126 
 2.149 
 2-173 
 2^i95 
 2.218 
 
 1.015 
 1.063 
 1. 109 
 
 1^153 
 1. 196 
 
 1^237 
 1.277 
 
 '•315 
 '•353 
 i^389 
 
 1.425 
 '•459 
 '•493 
 1.526 
 
 '■559 
 1.591 
 1.622 
 1.652 
 1.682 
 1. 712 
 
 1-741 
 1.769 
 1.797 
 1.825 
 1.852 
 
 1.879 
 1.905 
 
 1-931 
 
 1-957 
 1.982 
 
 2.007 
 2.032 
 2.057 
 2.081 
 2.105 
 
 2.128 
 2.152 
 
 2-175 
 2.198 
 2.220 
 
 .020 
 .068 
 .114 
 .158 
 .200 
 
 .241 
 .281 
 -319 
 -356 
 •393 
 
 .428 
 •463 
 ■497 
 -530 
 .562 
 
 •594 
 .625 
 .655 
 .685 
 •715 
 
 •744 
 -772 
 .800 
 
 .828 
 -855 
 .881 
 .908 
 
 -934 
 .960 
 
 •985 
 
 2.010 
 2.035 
 2.059 
 2.083 
 2.107 
 
 2.131 
 
 2.154 
 2.177 
 2.200 
 2.223 
 
 1.025 
 1.072 
 1.118 
 1.162 
 1.204 
 
 1.245 
 1.285 
 
 1-323 
 1.360 
 1.396 
 
 1.432 
 1.466 
 1.500 
 
 1-533 
 1.565 
 
 1-597 
 1.628 
 1.658 
 1.688 
 1.718 
 
 1.746 
 
 1-775 
 1.803 
 1.830 
 1-857 
 1.884 
 1.910 
 1-936 
 1.962 
 
 1-987 
 
 2.012 
 2.037 
 2.062 
 2.086 
 2.110 
 
 2-133 
 2.156 
 2.179 
 2.202 
 2.225 
 
 1 .030 ] 
 
 -034 
 
 -039 1 
 
 1.077 
 
 .082 
 
 .086 1 
 
 1.122 1 
 
 .127 ] 
 
 -131 1 
 
 1.166 
 
 .170 
 
 -175 I 
 
 1.208 ] 
 
 .212 
 
 .217 1 
 
 1.249 
 
 -253 
 
 •257 1 
 
 1.288 
 
 .292 
 
 .296 1 
 
 1-327 
 
 -330 
 
 -334 1 
 
 1.364 
 
 -367 
 
 -371 1 
 
 1.400 
 
 .404 
 
 .407 I 
 
 1-435 1 
 
 -439 
 
 .442 I 
 
 1.470 
 
 -473 
 
 .476 1 
 
 i-5°3 
 
 .507 
 
 .510 1 
 
 1-536 
 
 -539 
 
 •543 1 
 
 1.568 
 
 '•572 
 
 •575 1 
 
 1.600 
 
 -603 
 
 .606 1 
 
 1.631 
 
 •634 
 
 -637 1 
 
 1.661 
 
 .664 
 
 .667 1 
 
 1.691 
 
 .694 
 
 -697 1 
 
 1.720 1 
 
 -723 
 
 .726 1 
 
 1-749 
 
 -752 
 
 •755 1 
 
 1.778 
 
 .780 
 
 •783 I 
 
 1.806 
 
 [.808 
 
 [.8n 1 
 
 1-8.33 
 
 -836 
 
 .838 I 
 
 1.860 
 
 .863 
 
 .865 I 
 
 1.887 ' 
 
 .889 1 
 
 .892 I 
 
 1-913 
 
 .916 
 
 .918 I 
 
 1-939 
 
 .942 
 
 ■944 I 
 
 1.965 1 
 
 .967 ] 
 
 .970 1 
 
 1.990 
 
 .992 
 
 -995 1 
 
 2.015 
 2.040 
 2.064 
 
 2.088 
 
 2.112 
 
 2.135 
 2.159 
 2.182 
 2.205 
 2.227 
 
 2.017 
 2.042 
 2.066 
 2.090 
 2.114 
 
 2.138 
 2.161 
 2.184 
 2.207 
 2.229 
 
 2.020 
 2.045 
 2.069 
 2.093 
 2.117 
 
 2.140 
 2.163 
 2.186 
 2.209 
 2.232 
 
 .044 
 .091 
 .136 
 -179 
 .221 
 
 .261 
 
 .300 
 
 -338 
 
 -375 
 .411 
 
 .446 
 .480 
 
 -513 
 -546 
 -578 
 .609 
 .640 
 .670 
 .700 
 .729 
 
 •758 
 .786 
 .814 
 .841 
 .868 
 
 •895 
 .921 
 
 •947 
 •972 
 -997 
 
 2.022 
 2.047 
 2.071 
 2.095 
 2.119 
 
 2.142 
 2.166 
 2.189 
 2.211 
 2.234 
 
 SQ. RTS. & SQRS. 
 1.-10 
 
 (30) 
 
SQUARE ROOTS AND SQUARES. i.-io. 
 
 SQ. RTS. & SQRS. 
 
 No. 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Interpola. for 1 
 Thousandths. 1 
 
 5.0 
 
 2.236 
 
 2.238 
 
 2.241 
 
 2.243 
 
 2.245 
 
 .2.247 
 
 2.249 
 
 2.252 
 
 2-254 
 
 2.256 
 
 3 
 
 2 
 
 .1 
 
 2.258 
 
 2.261 
 
 2.263 
 
 2.265 
 
 2.267 
 
 2.269 
 
 2.272 
 
 2.274 
 
 2.276 
 
 2.278 
 
 
 
 
 
 .2 
 
 2.280 
 
 2.283 
 
 2.285 
 
 2.287 
 
 2.289 
 
 2.291 
 
 2.293 
 
 2.296 
 
 2.298 
 
 2300 
 
 I 
 
 
 
 •3 
 
 2.302 
 
 2.304 
 
 2.307 
 
 2.309 
 
 2.311 
 
 2.313 
 
 2.315 
 
 2.317 
 
 2-319 
 
 2.322 
 
 1 
 
 
 •4 
 
 2.324 
 
 2.326 
 
 2.328 
 
 2.330 
 
 2.332 
 
 2.335 
 
 2.337 
 
 2.339 
 
 2.341 
 
 2.343 
 
 1 
 
 
 S-S 
 
 2-345 
 
 2.347 
 
 2-349 
 
 2.352 
 
 2.354 
 
 2.356 
 
 2.358 
 
 2.360 
 
 2.362 
 
 2.364 
 
 2 
 
 
 .6 
 
 2.366 
 
 2.369 
 
 2-371 
 
 2-373 
 
 2-375 
 
 2.377 
 
 2.379 
 
 2.381 
 
 2.383 
 
 2-385 
 
 2 
 
 
 •7 
 
 2-387 
 
 2.390 
 
 2.392 
 
 2-394 
 
 2.396 
 
 2.398 
 
 2.400 
 
 2.402 
 
 2.404 
 
 2.406 
 
 2 
 
 
 .8 
 
 2.408 
 
 2.410 
 
 2.412 
 
 2.415 
 
 2.417 
 
 2.419 
 
 2.421 
 
 2.423 
 
 2.425 
 
 2.427 
 
 2 
 
 2 
 
 •9 
 
 2.429 
 
 2-431 
 
 2.433 
 
 2.435 
 
 2.437 
 
 2.439 
 
 2.441 
 
 2.443 
 
 2.445 
 
 2.447 
 
 3 
 
 2 
 
 6.0 
 
 2.449 
 
 2.452 
 
 2.454 
 
 2.456 
 
 2.458 
 
 2.460 
 
 2.462 
 
 2.464 
 
 2.466 
 
 2.468 
 
 3 
 
 2 
 
 .1 
 
 2.470 
 
 2.472 
 
 2.474 
 
 2.476 
 
 2.478 
 
 2.480 
 
 2.482 
 
 2.484 
 
 2.486 
 
 2.488 
 
 
 
 
 
 .2 
 
 2.490 
 
 2.492 
 
 2.494 
 
 2.496 
 
 2.498 
 
 2.500 
 
 2.502 
 
 2.504 
 
 2.506 
 
 2.508 
 
 1 
 
 
 
 •3 
 
 2.510 
 
 2.512 
 
 2.514 
 
 2.516 
 
 2.518 
 
 2.520 
 
 2.522 
 
 2.524 
 
 2.526 
 
 2.528 
 
 1 
 
 
 •4 
 
 2.530 
 
 2-532 
 
 2-534 
 
 2.536 
 
 2.538 
 
 2-540 
 
 2.542 
 
 2.544 
 
 2.546 
 
 2.548 
 
 I 
 
 
 6.5 
 
 2.550 
 
 2.551 
 
 2-553 
 
 2-555 
 
 2-557 
 
 2-559 
 
 2.561 
 
 2-563 
 
 2.565 
 
 2.567 
 
 2 
 
 
 .6 
 
 2.569 
 
 2-571 
 
 2-573 
 
 2-575 
 
 2-577 
 
 2-579 
 
 2.581 
 
 2.583 
 
 2.585 
 
 2.587 
 
 2 
 
 
 •7 
 
 2.588 
 
 2.590 
 
 2.592 
 
 2.594 
 
 2.596 
 
 2.598 
 
 2.600 
 
 2.602 
 
 2.604 
 
 2.606 
 
 2 
 
 
 .8 
 
 2.608 
 
 2.610 
 
 2.612 
 
 2.613 
 
 2.615 
 
 2.617 
 
 2.619 
 
 2.621 
 
 2.623 
 
 2.625 
 
 2 
 
 2 
 
 •9 
 
 2.627 
 
 2.629 
 
 2.631 
 
 2.632 
 
 2.634 
 
 2.636 
 
 2.638 
 
 2.640 
 
 2.642 
 
 2.644 
 
 3 
 
 2 
 
 7.0 
 
 2.646 
 
 2.648 
 
 2.650 
 
 2.651 
 
 2-653 
 
 2.655 
 
 2.657 
 
 2.659 
 
 2.661 
 
 2.663 
 
 2 
 
 1 
 
 .1 
 
 2.665 
 
 2.666 
 
 2.668 
 
 2.670 
 
 2.672 
 
 2.674 
 
 2.676 
 
 2.678 
 
 2.680 
 
 2.681 
 
 
 
 
 
 .2 
 
 2.683 
 
 2.685 
 
 2.687 
 
 2.689 
 
 2.691 
 
 2.693 
 
 2.694 
 
 2.696 
 
 2.698 
 
 2.700 
 
 
 
 
 
 ■3 
 
 2.702 
 
 2.704 
 
 2.706 
 
 2.707 
 
 2.709 
 
 2.711 
 
 2.713 
 
 2.71S 
 
 2.717 
 
 2.718 
 
 
 
 
 ■4 
 
 2.720 
 
 2.722 
 
 2.724 
 
 2.726 
 
 2.728 
 
 2.729 
 
 2.731 
 
 2-733 
 
 2.735 
 
 2.737 
 
 
 
 
 7-5 
 
 2.739 
 
 2.740 
 
 2.742 
 
 2.744 
 
 2.746 
 
 2.748 
 
 2.750 
 
 2-751 
 
 2.753 
 
 2.755 
 
 
 
 .6 
 
 2.757 
 
 2.759 
 
 2.760 
 
 2.762 
 
 2.764 
 
 2.766 
 
 2.768 
 
 2.769 
 
 2.771 
 
 2.773 
 
 
 
 •7 
 
 2-775 
 
 2.777 
 
 2.778 
 
 2.780 
 
 2.782 
 
 2.784 
 
 2.786 
 
 2-787 
 
 2.789 
 
 2.791 , 
 
 
 
 .8 
 
 2-793 
 
 2.795 
 
 2.796 
 
 2.798 
 
 2.800 
 
 2.802 
 
 2.804 
 
 2.805 
 
 "2.807 
 
 2.809 
 
 2 
 
 
 •9 
 
 2.81 1 
 
 2.8l2 
 
 2.814 
 
 2.816 
 
 2.818 
 
 2.820 
 
 2.821 
 
 2.823 
 
 2.825 
 
 2.827 
 
 2 
 
 
 8.0 
 
 2.828 
 
 2.830 
 
 2.832 
 
 2.834 
 
 2.835 
 
 2837 
 
 2.839 
 
 2.841 
 
 2.843 
 
 2.844 
 
 2 
 
 1 ■ 
 
 .1 
 
 2.846 
 
 2.848 
 
 2.850 
 
 2.851 
 
 2.853 
 
 2.855 
 
 2.857 
 
 2.858 
 
 2.860 
 
 2.862 
 
 
 
 
 
 .2 
 
 2.864 
 
 2.865 
 
 2.867 
 
 2.869 
 
 2.871 
 
 2.872 
 
 2.874 
 
 2.876 
 
 2-877 
 
 2.879 
 
 
 
 
 
 •3 
 
 2.881 
 
 2.883 
 
 2.884 
 
 2.886 
 
 2.888 
 
 2.890 
 
 2.891 
 
 2.893 
 
 2.895 
 
 2.897 
 
 
 
 
 ■4 
 
 2.898 
 
 2.900 
 
 2.902 
 
 2.903 
 
 2.905 
 
 2.907 
 
 2.909 
 
 2.910 
 
 2.912 
 
 2-914 
 
 
 
 
 8.S 
 
 2.915 
 
 2.917 
 
 2.919 
 
 2.921 
 
 2.922 
 
 2.924 
 
 2.926 
 
 2.927 
 
 2.929 
 
 2.931 
 
 
 
 .6 
 
 2-933 
 
 2.934 
 
 2.936 
 
 2.938 
 
 2-939 
 
 2.941 
 
 2.943 
 
 2.944 
 
 2.946 
 
 2.948 
 
 
 
 •7 
 
 2.950 
 
 2.951 
 
 2.953 
 
 2-955 
 
 2.956 
 
 2.958 
 
 2.960 
 
 2.961 
 
 2.963 
 
 2.965 
 
 
 
 .8 
 
 2.966 
 
 2.968 
 
 2.970 
 
 2.972 
 
 2.973 
 
 2-975 
 
 2.977 
 
 2.978 
 
 2.980 
 
 2.982 
 
 2 
 
 
 •9 
 
 2.983 
 
 2.985 
 
 2.987 
 
 2.988 
 
 2.990 
 
 2.992 
 
 2.993 
 
 2.995 
 
 2.997 
 
 2.998 
 
 2 
 
 
 9.0 
 
 3.000 
 
 3.002 
 
 3-003 
 
 3.005 
 
 3.007 
 
 3.008 
 
 3.010 
 
 3.012 
 
 3-013 
 
 3015 
 
 2 
 
 1 
 
 .1 
 
 3-017 
 
 3-Oi8 
 
 3.020 
 
 3.022 
 
 3.023 
 
 3.025 
 
 3.027 
 
 3.028 
 
 3030 
 
 3.032 
 
 
 
 
 
 .2 
 
 3-033 
 
 3-035 
 
 3-036 
 
 3-038 
 
 3.040 
 
 3-041 
 
 3.043 
 
 3-045 
 
 3-046 
 
 3.048 
 
 
 
 
 
 ■3 
 
 3.050 
 
 3-051 
 
 3-053 
 
 3-055 
 
 3-056 
 
 3.058 
 
 3.059 
 
 3.061 
 
 3-063 
 
 3-064 
 
 
 
 
 •4 
 
 3.066 
 
 3.068 
 
 3-069 
 
 3-071 
 
 3.072 
 
 3-074 
 
 3.076 
 
 3-077 
 
 3-079 
 
 3.081 
 
 
 
 
 9-S 
 
 3.082 
 
 3.084 
 
 3.085 
 
 3.087 
 
 3.089 
 
 3.090 
 
 3.092 
 
 3-094 
 
 3.095 
 
 3097 
 
 
 
 .6 
 
 3.098 
 
 3.100 
 
 3.102 
 
 3-103 
 
 3.105 
 
 3.106 
 
 3.108 
 
 3.110 
 
 3.1 11 
 
 3-113 
 
 
 
 •7 
 
 3- "4 
 
 3.116 
 
 3.118 
 
 3-119 
 
 3.121 
 
 3.122 
 
 3.124 
 
 3.126 
 
 3.127 
 
 3.129 
 
 
 
 .8 
 
 3-130 
 
 3-132 
 
 3-134 
 
 3-135 
 
 3.137 
 
 3-138 
 
 3.140 
 
 3.142 
 
 3-143 
 
 3-145 
 
 2 
 
 
 •9 
 
 3.146 
 
 3.148 
 
 3-150 
 
 3-151 
 
 3.153 
 
 3.154 
 
 3.156 
 
 3-158 
 
 3-159 
 
 3.161 
 
 2 
 
 
 (31) 
 
 SQ. RTS. 
 
 86 SQRS. 
 1.-10. 
 
lO.-lOO. 
 SQ. RTS. 
 
 & SQRS. 
 
 SQUARE ROOTS AND SQUARES. 
 
 No. 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Interpola. 1 
 for Hundredths. | 
 
 10. 
 
 3.162 
 
 3-178 
 
 3-194 
 
 3.209 
 
 3-225 
 
 3.240 
 
 3.256 
 
 3-271 
 
 3.286 
 
 3-302 
 
 16 
 
 14 
 
 II. 
 
 3-317 
 
 3-332 
 
 3-347 
 
 3-362 
 
 3-376 
 
 3-391 
 
 3-406 
 
 3-421 
 
 3-435 
 
 3450 
 
 2 
 
 I 
 
 12. 
 
 3464 
 
 3-479 
 
 3-493 
 
 3.507 
 
 3-521 
 
 3-536 
 
 3-550 
 
 3564 
 
 3-578 
 
 3-592 
 
 3 
 
 3 
 
 13- 
 
 3.606 
 
 3-619 
 
 3-633 
 
 3-647 
 
 3-661 
 
 3-674 
 
 3.688 
 
 3-701 
 
 3-715 
 
 3-728 
 
 5 
 
 4 
 
 14. 
 
 3-742 
 
 3-755 
 
 3.768 
 
 3.782 
 
 3-795 
 
 3.808 
 
 3.821 
 
 3-834 
 
 3-847 
 
 3.860 
 
 6 
 
 6 
 
 15- 
 
 3-873 
 
 3.886 
 
 3-899 
 
 3.912 
 
 3-924 
 
 3-937 
 
 3-950 
 
 3.962 
 
 3-975 
 
 3-987 
 
 8 
 
 7 
 
 16. 
 
 4.000 
 
 4.012 
 
 4.025 
 
 4-037 
 
 4.050 
 
 4.062 
 
 4-074 
 
 4.087 
 
 4-099 
 
 4.1 1 1 
 
 10 
 
 8 
 
 17- 
 
 4-123 
 
 4-135 
 
 4.147 
 
 4-159 
 
 4.171 
 
 4.183 
 
 4-195 
 
 4.207 
 
 4-219 
 
 4-231 
 
 II 
 
 10 
 
 18. 
 
 4-243 
 
 4.254 
 
 4.266 
 
 4.278 
 
 4.290 
 
 4.301 
 
 4-313 
 
 4-324 
 
 4-336 
 
 4-347 
 
 13 
 
 II 
 
 19. 
 
 4-359 
 
 4-370 
 
 4.382 
 
 4-393 
 
 4.405 
 
 4.416 
 
 4-427 
 
 4-438 
 
 4-450 
 
 4.461 
 
 14 
 
 13 
 
 20. 
 
 4-472 
 
 4483 
 
 4-494 
 
 4.506 
 
 4-517 
 
 4.528 
 
 4-539 
 
 4-550 
 
 4.561 
 
 4-572 
 
 12 
 
 10 
 
 21. 
 
 4-583 
 
 4-593 
 
 4.604 
 
 4.615 
 
 4.626 
 
 4-637 
 
 4.648 
 
 4.658 
 
 4.669 
 
 4.680 
 
 I 
 
 I 
 
 22. 
 
 4.690 
 
 4.701 
 
 4.712 
 
 4.722 
 
 4-733 
 
 4-743 
 
 4-754 
 
 4-764 
 
 4-775 
 
 4-785 
 
 2 
 
 2 
 
 23. 
 
 4.796 
 
 4.806 
 
 4.817 
 
 4.827 
 
 4-837 
 
 4.848 
 
 4.858 
 
 4.868 
 
 4.879 
 
 4.889 
 
 4 
 
 3 
 
 24. 
 
 4-899 
 
 4-909 
 
 4.919 
 
 4-930 
 
 4.940 
 
 4.950 
 
 4.960 
 
 4.970 
 
 4.980 
 
 4.990 
 
 5 
 
 4 
 
 25. 
 
 5.000 
 
 5.010 
 
 5.020 
 
 5.030 
 
 5-040 
 
 5.050 
 
 5.060 
 
 5.070 
 
 S-079 
 
 5.089 
 
 6 
 
 5 ■ 
 
 26. 
 
 S-099 
 
 5.109 
 
 5. 119 
 
 5.128 
 
 5-138 
 
 5.148 
 
 5-158 
 
 5.167 
 
 5-177 
 
 5.187 
 
 7 
 
 6 
 
 27. 
 
 5.196 
 
 5.206 
 
 5.215 
 
 5-225 
 
 5-235 
 
 5-244 
 
 5-254 
 
 5-263 
 
 5-273 
 
 5.282 
 
 . 8 
 
 7 
 
 28. 
 
 5.292 
 
 S-301 
 
 5-310 
 
 5-320 
 
 5-329 
 
 5-339 
 
 5-348 
 
 5-357 
 
 5-367 
 
 5-376 
 
 10 
 
 8 
 
 29. 
 
 5-385 
 
 5-394 
 
 5.404 
 
 5-413 
 
 5-422 
 
 5-431 
 
 5-441 
 
 5.450 
 
 5-459 
 
 5.468 
 
 II 
 
 9 
 
 30. 
 
 5-477 
 
 5.486 
 
 5-495 
 
 5.505 
 
 5-514 
 
 5-523 
 
 5-532 
 
 S-541 
 
 5-550 
 
 5-559 
 
 9 
 
 8 
 
 31- 
 
 5.568 
 
 5-577 
 
 5-586 
 
 5-595 
 
 5,604 
 
 5.612 
 
 5.621 
 
 5.630 
 
 S-639 
 
 5.648 
 
 I 
 
 I 
 
 32. 
 
 5-657 
 
 5.666 
 
 5-675 
 
 5.683 
 
 5.692 
 
 5-701 
 
 5.710 
 
 5.718 
 
 5-727 
 
 5-736 
 
 2 
 
 2 
 
 33- 
 
 5-745 
 
 5-753 
 
 5-762 
 
 5-771 
 
 5-779 
 
 5-788 
 
 5-797 
 
 5.805 
 
 5.814 
 
 5.822 
 
 3 
 
 2 
 
 34- 
 
 5-831 
 
 5-840 
 
 5-848 
 
 5-857 
 
 5.865 
 
 5-874 
 
 5.882 
 
 5.891 
 
 5-899 
 
 5.908 
 
 .4 
 
 3 
 
 35- 
 
 5-916 
 
 5-925 
 
 5-933 
 
 5-941 
 
 5-950 
 
 5-958 
 
 5-967 
 
 5-975 
 
 5-983 
 
 5.992 
 
 5 
 
 4 
 
 36. 
 
 6.000 
 
 6.008 
 
 6.017 
 
 6.025 
 
 6-033 
 
 6.042 
 
 6.050 
 
 6.058 
 
 6.066 
 
 6-075 
 
 5 
 
 5 
 
 37- 
 
 6.083 
 
 6.091 
 
 6.099 
 
 6.107 
 
 6.1:6 
 
 6.124 
 
 6.132 
 
 6.140 
 
 6.148 
 
 6.156 
 
 6 
 
 6 
 
 38- 
 
 6.164 
 
 6-173 
 
 6.181 
 
 6.189 
 
 6.197 
 
 6.205 
 
 6.213 
 
 6.221 
 
 6.229 
 
 6.237 
 
 7 
 
 6 
 
 39- 
 
 6.245 
 
 6.253 
 
 6.261 
 
 6.269 
 
 6.277 
 
 6.285 
 
 6.293 
 
 6.301 
 
 6.309 
 
 6.317 
 
 8 
 
 7 
 
 40. 
 
 6-325 
 
 6-332 
 
 6.340 
 
 6.348 
 
 6.356 
 
 6.364 
 
 6.372 
 
 6.380 
 
 6.387 
 
 6-395 
 
 8 
 
 7 
 
 41. 
 
 6.403 
 
 6.41 1 
 
 6.419 
 
 6.427 
 
 6.434 
 
 6.442 
 
 6.450 
 
 6.458 
 
 6.465 
 
 6.473 
 
 I 
 
 I 
 
 42. 
 
 6.481 
 
 6.488 
 
 6.496 
 
 6.504 
 
 6.512 
 
 6.519 
 
 6.527 
 
 6-535 
 
 6.542 
 
 6.550 
 
 2 
 
 I 
 
 43- 
 
 6-557 
 
 6.56s 
 
 6-573 
 
 6.580 
 
 6.588 
 
 6.595 
 
 6.603 
 
 6.61 1 
 
 6.618 
 
 6.626 
 
 2 
 
 2 
 
 44. 
 
 6.633 
 
 6.641 
 
 6.648 
 
 6.656 
 
 6.663 
 
 6.671 
 
 6.678 
 
 6.686 
 
 6.693 
 
 6.701 
 
 3 
 
 3 
 
 45- 
 
 6.708 
 
 6.716 
 
 6.723 
 
 6.731 
 
 6.738 
 
 6.745 
 
 6.753 
 
 6.760 
 
 6.768 
 
 6-775 
 
 4 
 
 4 
 
 46. 
 
 6.782 
 
 6.790 
 
 6-797 
 
 6.804 
 
 6.812 
 
 6.819 
 
 6.S26 
 
 6.834 
 
 6.841 
 
 6.848 
 
 5 
 
 4 
 
 47- 
 
 6.856 
 
 6.863 
 
 6.870 
 
 6.877 
 
 6.885 
 
 6.892 
 
 6.899 
 
 6.907 
 
 6.914 
 
 6.921 
 
 6 
 
 5 
 
 48. 
 
 6.928 
 
 6-935 
 
 6.943 
 
 6.950 
 
 6.957 
 
 6.964 
 
 6.971 
 
 6-979 
 
 6.986 
 
 6.993 
 
 6 
 
 6 
 
 49. 
 
 7.000 
 
 7.007 
 
 7.014 
 
 7.021 
 
 7.029 
 
 7.036 
 
 7-043 
 
 7.050 
 
 7-057 
 
 7.064 
 
 7 
 
 6 
 
 "rt 
 
 S. & SQRS. 
 
 
 
 (32) 
 
 
 
 
 
 
 
 lO.-lOO. 
 
SQUARE ROOTS AND 
 
 SQUARES. 10.-100. 
 
 SQ. RTS. & SQRS. 
 
 No. 
 
 
 
 I 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Interpola. for 1 
 Hundredttis. 1 
 
 50. 
 
 7.071 
 
 7.078 7.085 
 
 7.092 
 
 7.099 
 
 7.106 
 
 7-"3 
 
 7.120 
 
 7.127 
 
 7-"34 
 
 7 
 
 6 
 
 51- 
 
 7-141 
 
 7-148 7-155 
 
 7.162 
 
 7.169 
 
 7.176 
 
 7-183 
 
 7.190 
 
 7-197 
 
 7.204 
 
 I 
 
 1 
 
 52. 
 
 7.2II 
 
 7.218 7.225 
 
 7.232 
 
 7-239 
 
 7-246 
 
 7-253 
 
 7.259 
 
 7.266 
 
 7-273 
 
 1 
 
 1 
 
 53- 
 
 7.280 
 
 7.287 7.294 
 
 7-301 
 
 7-308 
 
 7-314 
 
 7-321 
 
 7-328 
 
 7-335 
 
 7-342 
 
 2 
 
 2 
 
 54- 
 
 7-348 
 
 7-355 7-362 
 
 7-369 
 
 7-376 
 
 7.382 
 
 7-389 
 
 7-396 
 
 7403 
 
 7.409 
 
 3 
 
 2 
 
 55- 
 
 7.416 
 
 7.423 7.430 
 
 7-436 
 
 7-443 
 
 7-450 
 
 7-457 
 
 7-463 
 
 7.470 
 
 7-477 
 
 4 
 
 3 
 
 56. 
 
 7-483 
 
 7.490 7.497 
 
 7.503 
 
 7.510 
 
 7-517 
 
 7-523 
 
 7-530 
 
 7-537 
 
 7-543 
 
 4 
 
 4 
 
 57- 
 
 7-55° 
 
 7.556 7.563 
 
 7.570 
 
 7.576 
 
 7-583 
 
 7-589 
 
 7-596 
 
 7-603 
 
 7.609 
 
 5 
 
 4 
 
 58- 
 
 7.616 
 
 7.622 7.629 
 
 7-635 
 
 7.642 
 
 7.649 
 
 7-655 
 
 7.662 
 
 7.668 
 
 7.675 
 
 6 
 
 5 
 
 59- 
 
 7.681 
 
 7.688 7.694 
 
 7.701 
 
 7.707 
 
 7-7H 
 
 7.720 
 
 7.727 
 
 7-733 
 
 7.740 
 
 6 
 
 5 
 
 60. 
 
 7.746 
 
 7-752 7.759 
 
 7-765 
 
 7-772 
 
 7.778 
 
 7-785 
 
 7.791 
 
 7-797 
 
 7.804 
 
 7 
 
 6 
 
 61. 
 
 7.810 
 
 7.817 . 7.823 
 
 7.829 
 
 7.836 
 
 7.842 
 
 7.849 
 
 7-855 
 
 7.861 
 
 7.868 
 
 I 
 
 1 
 
 62. 
 
 7.874 
 
 7.880 7.887 
 
 7-893 
 
 7.899 
 
 7.906 
 
 7.912 
 
 7.918 
 
 7-925 
 
 7-931 
 
 1 
 
 1 
 
 63- 
 
 7-937 
 
 7-944 7-950 
 
 7-956 
 
 7.962 
 
 7-969 
 
 7-975 
 
 7.981 
 
 7.987 
 
 7-994 
 
 2 
 
 2 
 
 64. 
 
 8.000 
 
 8.006 8.012 
 
 8.019 
 
 8.025 
 
 8.031 
 
 8.037 
 
 8.044 
 
 8.050 
 
 8.056 
 
 3 
 
 2 
 
 65. 
 
 8.062 
 
 8.068 8.07s 
 
 8.081 
 
 8.087 
 
 8.093 
 
 8.099 
 
 8.106 
 
 8.112 
 
 8.118 
 
 4 
 
 3 
 
 66. 
 
 8.124 
 
 8.130 8.136 
 
 8.142 
 
 8.149 
 
 8-155 
 
 8.161 
 
 8.167 
 
 8-173 
 
 8.179 
 
 4 
 
 4 
 
 67. 
 
 8.185 
 
 8.191 8.198 
 
 8.204 
 
 8.210 
 
 8.216 
 
 8.222 
 
 8.228 
 
 8.234 
 
 8.240 
 
 5 
 
 4 
 
 68. 
 
 8.246 
 
 8.252 8.258 
 
 8.264 
 
 8.270 
 
 8.276 
 
 8.283 
 
 8.289 
 
 8.295 
 
 8.301 
 
 6 
 
 5 
 
 69. 
 
 8.307 
 
 8.313 8.319 
 
 8.325 
 
 8-331. 
 
 8.337 
 
 8-343 
 
 8-349 
 
 8-355 
 
 8-361 
 
 6 
 
 S 
 
 70. 
 
 8.367 
 
 8-373 8.379 
 
 8-385 
 
 8.390 
 
 8-396 
 
 8.402 
 
 8.408 
 
 8.414 
 
 8.420 
 
 6 
 
 5 
 
 71- 
 
 8.426 
 
 8.432 8.438 
 
 8.444 
 
 8.450 
 
 8.456 
 
 8.462 
 
 8.468 
 
 8-473 
 
 8.479 
 
 1 
 
 I 
 
 72- 
 
 8.485 
 
 8.491 8.497 
 
 8.803 
 
 8.509 
 
 8-515 
 
 8.521 
 
 8.526 
 
 8-532 
 
 8.538 
 
 1 
 
 I 
 
 73- 
 
 8.544 
 
 8.550 8.556 
 
 8.562 
 
 8.567 
 
 8-573 
 
 8-579 
 
 8.585 
 
 8.591 
 
 8-597 
 
 2 
 
 2 
 
 74- 
 
 8.602 
 
 8.608 8.614 
 
 8.620 
 
 8.626 
 
 8.631 
 
 8-637 
 
 8.643 
 
 8.649 
 
 8.654 
 
 2 
 
 2 
 
 75- 
 
 8.660 
 
 8.666 8.672 
 
 8.678 
 
 8.683 
 
 8.689 
 
 8-695 
 
 8.701 
 
 8.706 
 
 8.712 
 
 3 
 
 3 
 
 76. 
 
 8.718 
 
 8.724 8.729 
 
 8-735 
 
 8.741 
 
 8.746 
 
 8-752 
 
 8.758 
 
 8.764 
 
 8.769 
 
 4 
 
 3 
 
 77- 
 
 8-77S 
 
 8.781 8.786 
 
 8.792 
 
 8.798 
 
 8.803 
 
 8.809 
 
 8.815 
 
 8.820 
 
 8.826 
 
 4 
 
 4 
 
 78. 
 
 8.832 
 
 8.837 8.843 
 
 8.849 
 
 8.854 
 
 8.860 
 
 8.866 
 
 8.871 
 
 8.877 
 
 8.883 
 
 5 
 
 4 
 
 79- 
 
 8.888 
 
 8.894 8.899 
 
 8.905 
 
 8.911 
 
 8.916 
 
 8.922 
 
 8.927 
 
 8-933 
 
 8-939 
 
 5 
 
 5 
 
 80. 
 
 8.944 
 
 8.950 8.955 
 
 8.961 
 
 8.967 
 
 8.972 
 
 8-978 
 
 8.983 
 
 8.989 
 
 8.994 
 
 6 
 
 5 
 
 8i. 
 
 9.000 
 
 9.006 9.01 1 
 
 9.017 
 
 9.022 
 
 9.028 
 
 9-033 
 
 9-039 
 
 9.044 
 
 9.050 
 
 1 
 
 1 
 
 82. 
 
 9-055 
 
 9.061 9.066 
 
 9.072 
 
 9-077 
 
 9.083 
 
 9.088 
 
 9.094 
 
 9.099 
 
 9.105 
 
 1 
 
 1 
 
 83. 
 
 9.110 
 
 9.116 9.121 
 
 9.127 
 
 9.132 
 
 9-138 
 
 9-143 
 
 9.149 
 
 9.154 
 
 9.160 
 
 2 
 
 2 
 
 84. 
 
 9- 1 65 
 
 9.171 9.176 
 
 9.182 
 
 9.187 
 
 9.192 
 
 9.198 
 
 9.203 
 
 9.209 
 
 9-214 
 
 2 
 
 2 
 
 85. 
 
 9.220 
 
 9.225 9.230 
 
 9.236 
 
 9.241 
 
 9.247 
 
 9.252 
 
 9-257 
 
 9.263 
 
 9.268 
 
 3 
 
 3 
 
 86. 
 
 9.274 
 
 9.279 9.284 
 
 9.290 
 
 9-295 
 
 9-301 
 
 9.306 
 
 9-3II 
 
 9-317 
 
 9.322 
 
 4 
 
 3 
 
 87. 
 
 9-327 
 
 9-333 9-338 
 
 9-343 
 
 9-349 
 
 9-354 
 
 9-359 
 
 9-365 
 
 9-370 
 
 9-375 
 
 4 
 
 4 
 
 88. 
 
 9-381 
 
 9.386 9.391 
 
 9-397 
 
 9402 
 
 9-407 
 
 9-413 
 
 9.418 
 
 9-423 
 
 9-429 
 
 5 
 
 4 
 
 89. 
 
 9-434 
 
 9-439 9-445 
 
 9.450 
 
 9-455 
 
 9.460 
 
 9.466 
 
 9-471 
 
 9-476 
 
 9.482 
 
 5 
 
 5 
 
 90. 
 
 9.487 
 
 9.492 9.497 
 
 9.503 
 
 9.508 
 
 9-513 
 
 9-518 
 
 9-524 
 
 9-529 
 
 9-534 
 
 5 
 
 
 91- 
 
 9-539 
 
 9-545 9-550 
 
 9-555 
 
 9.560 
 
 9-566 
 
 9-571 
 
 9-576 
 
 9.581 
 
 9.586 
 
 I 
 
 
 92. 
 
 9.592 
 
 9.597 9.602 
 
 9.607 
 
 9.612 
 
 9.618 
 
 9-623 
 
 9.628 
 
 9-633 
 
 9-638 
 
 I 
 
 
 93- 
 
 9.644 
 
 9.649 9.654 
 
 9-659 
 
 9.664 
 
 9.670 
 
 9-675 
 
 9.680 
 
 9.685 
 
 9.690 
 
 2 
 
 
 94- 
 
 9-695 
 
 9.701 9.706 
 
 9-7" 
 
 9.716 
 
 9.721 
 
 9.726 
 
 9-731 
 
 9-737 
 
 9.742 
 
 2 
 
 
 95- 
 
 9-747 
 
 9.752 9.757 
 
 9.762 
 
 9.767 
 
 9.772 
 
 9.778 
 
 9-783 
 
 9-788 
 
 9-793 
 
 3 
 
 
 96. 
 
 9-798 
 
 9.803 9.808 
 
 9-813 
 
 9.818 
 
 9-823 
 
 9.829 
 
 9-834 
 
 9-839 
 
 9.844 
 
 3 
 
 
 97- 
 
 9.849 
 
 9.854 9.859 
 
 9.864 
 
 9.869 
 
 9.874 
 
 9-879 
 
 9.884 
 
 9.889 
 
 9-894 
 
 4 
 
 
 98. 
 
 9.899 
 
 9-905 9-9IO 
 
 9-915 
 
 9.920 
 
 9-925 
 
 9-930 
 
 9-935 
 
 9.940 
 
 9-945 
 
 4 
 
 
 99- 
 
 9.950 
 
 9.955 9.960 
 
 9-965 
 
 9.970 
 
 9-975 
 
 9.980 
 
 9.985 
 
 9.990 
 
 9-995 
 
 5 
 
 
 (33) 
 
 SQ. RTS. & SQRS. 
 10.-100. 
 
RECIPROCALS. 
 
 RECIP. 
 
 No. 
 
 01234 
 
 56789 
 
 INTERPOLATION 
 TABLES. 
 
 1.00 
 
 .01 
 .02 
 
 •03 
 .04 
 
 0.9990 0.9980 0.9970 0.9960 
 
 0.9901 9891 9881 9872 9862 
 
 9804 9794 9785 9775 9766 
 
 9709 9699 9690 9680 9671 
 
 9615 9606 9597 9588 9579 
 
 0.9950 0.9940 0.9930 0.9921 0.991 1 
 9852 9843 9833 9823 9814 
 
 9756 9747 9737 9728 9718 
 9662 9653 9643 9634 9625 
 9569 9560 9551 9542 9533 
 
 -85- 
 
 9 
 17 
 26 
 
 34 
 
 75-65-65 
 
 876 
 15 13 II 
 23 20 17 
 30 26 22 
 
 1.05 
 .06 
 .07 
 .08 
 .09 
 
 0.9524 0.95 1 5 0.9506 0.9497 0.9488 
 9434 9425 9416 9407 9399 
 9346 9337 9328 9320 93" 
 9259 9251 9242 9234 9225 
 9174 9166 9158 9149 9141 
 
 0.9479 0.9470 0.9461 0.9452 0.9443 
 9390 9381 9372 9363 9355 
 9302 9294 9285 9276 9268 
 9217 9208 9200 9191 9183 
 9132 9124 9116 9107 9099 
 
 43 38 33 28 
 51 45 39 33 
 60 53 46 39 
 68 60 52 44 
 77 68 59 50 
 
 -45-35-25-22 
 
 5432 
 
 9 7 5 4 
 14 n 8 7 
 18 14 10 9 
 
 1.0 
 .1 
 
 .2 
 •3 
 •4 
 
 0.9901 0.9804 0.9709 0.9615 
 
 0.9091 9009 8929 8850 8772 
 
 8333 8264 8197 8130 8065 
 
 7692 7634 7576 7519 7463 
 
 7143 7092 7042 6993 6944 
 
 0.9524 0.9434 0.9346 0.9259 0.9174 
 8696 8621 8547 8475 8403 
 8000 -7937 7874 7813 7752 
 
 7407 7353 7299 7246 7194 
 6897 6849 6803 6757 67 I I 
 
 I -5 
 .6 
 
 •7 
 .8 
 
 •9 
 
 0.6667 0.6623 0-6579 0.6536 0.6494 
 6250 621 1 6173 6135 6098 
 5882 5848 5814 5780 5747 
 
 5556 5525 5495 5464 5435 
 5263 5236 5208 5181 5155 
 
 0.6452 0.6410 0.6369 0.6329 0.6289 
 6061 6024 5988 5952 5917 
 5714 5682 5650 5618 5587 
 5405 5376 5348 5319 5291 
 5128 5102 5076 5051 5025 
 
 23 
 27 
 32 
 36 
 41 
 
 18 13 II 
 21 15 13 
 25 18 15 
 28 20 18 
 32 23 20 
 
 2.0 
 
 .1 
 
 .2 
 •3 
 4 
 
 0.5000 0.4975 0.4950 0.4926 0.4902 
 4762 4739 4717 4695 4673 
 
 4545 4525 4505 4484 4464 
 4348 4329 4310 4292 4274 
 4167 4149 4132 4115 4098 
 
 0.4878 0.4854 0.4831 0.4808 0.4785 
 4651 4630 4608 4587 4566 
 4444 4425 4405 4386 4367 
 4255 4237 4219 4202 4184 
 4082 4065 4049 4032 4016 
 
 -18-16-14-12 
 2211 
 4332 
 
 5 5 4 4 
 7665 
 
 2-5 
 
 .6 
 
 •7 
 .8 
 
 •9 
 
 0.4000 0.3984 0.3968 0.3953 0.3937 
 3846 3831 3817 3802 3788 
 3704 3690 3676 3663 3650 
 357« 3559 3545 3534 3521 
 3448 3436 3425 3413 3401 
 
 0.3922 0.3906 0.3891 0.3876 0.3861 
 
 3774 3759 3745 373i 371? 
 3636 3623 3610 3597 3584 
 
 3509 3497 3484 3472 3460 
 3390 3378 3367 3356 3344 
 
 9 
 II 
 
 13 
 14 
 16 
 
 876 
 
 10 8' 7 
 
 11 10 8 
 
 13 II 10 
 
 14 13 II 
 
 3.0 
 
 .1 
 
 .2 
 •3 
 
 •4 
 
 0.3333 0.3322 0.331 1 0.3300 0.3289 
 3226 3215 3205 3195 3185 
 3125 31 15 3106 3096 3086 
 3030 3021 3012 3003 2994 
 2941 2933 2924 2915 2907 
 
 0.3279 0.3268 0.3257 0.3247 0.3236 
 
 3175 3165 3155 3145 3135 
 3077 3067 3058 3049 3040 
 2985 2976 2967 2959 2950 
 2899 2890 2882 2874 2865 
 
 -11 
 
 I 
 2 
 3 
 4 
 
 -9 -8 -7 
 
 1 I I 
 
 2 2 I 
 
 3 2 :i 
 
 4 3 3 
 
 3-5 
 .6 
 
 7 
 .8 
 
 •9 
 
 0.2857 0.2849 0.2841 0.2833 0.2825 
 2778 2770 2762 2755 2747 
 2703 2695 2688 2681 2674 
 2632 2625 2618 261 1 2604 
 2564 2558 2551 2545 2538 
 
 0.2817 0.2809 0.2801 0.2793 0.2786 
 2740 2732 2725 2717 2710 
 2667 2660 2653 2646 2639 
 2597 2591 2584 2577 2571 
 2532 2525 2519 2513 2506 
 
 6 
 
 7 
 8 
 
 9 
 10 
 
 5 4 4 
 
 5 5 4 
 
 6 6 5 
 766 
 8 7 6 
 
 4.0 
 
 .1 
 .2 
 •3 
 •4 
 
 0.2500 0.2494 0.2488 0.2481 0.2475 
 2439 2433 2427 2421 2415 
 2381 2375 2370 2364 2358 
 2326 2320 2315 2309 2304 
 2273 2268 2262 2257 2252 
 
 0.2469 0.2463 0.2457 0.2451 0.2445 
 2410 2404 2398 2392 2387 
 2353 2347 2342 2336 2331 
 2299 2294 2288 2283 2278 
 2247 2242 2237 2232 2227 
 
 -6 
 
 I 
 2 
 2 
 
 -5 -4 
 I 
 
 1 I 
 
 2 I 
 2 2 
 
 4-S 
 .6 
 
 •7 
 .8 
 
 •9 
 
 0.2222 0.2217 0.22120.22080.2203 
 2274 2169 2165 2160 2155 
 2128 2123 2119 2114 2110 
 2083 2079 2075 2070 2066 
 2041 2037 2033 2028 2024 
 
 0.21980.21930.21880.21830.2179 
 2151 2146 2141 2137 2132 
 2105 2101 2096 2092 2088 
 2062 2058 2053 2049 2045 
 2020 2016 2012 2008 2004 
 
 3 
 4 
 4 
 
 5 
 
 5 
 
 3 2 
 
 3 2 
 
 4 3 
 
 4 3 
 
 5 4 
 
 RECIP. 
 
 (34) 
 
RECIPROCALS. 
 
 RECIP. 
 
 No. 
 
 12 3 4 
 
 56789 
 
 interpolation! 
 for thous. 1 
 
 5.0 
 .1 
 
 .2 
 
 •3 
 
 •4 
 
 0.2000 0.1996 0.1992 0.1988 0.1984 
 I96I 1957 1953 1949 1946 
 1923 I919 1916 I9I2 1908 
 1887 1883 1880 1876 1873 
 1852 1848 1845 1842 1838 
 
 0.1980 0.1976 0.1972 0.1969 0.1965 
 1942 1938 1934 1931 1927 
 1905 1901 1898 1894 1890 
 1869 1866 1862 1859 1855 
 1835 1832 1828 1825 1821 
 
 -A 
 
 
 1 
 
 1 
 2 
 
 -3 
 
 
 
 I 
 I 
 1 
 
 5-5 
 .6 
 
 •7 
 .8 
 
 •9 
 
 O.1818 0.1815 O.1812 0.1808 0.1805 
 1786 1783 1779 1776 1773 
 
 1754 1751 1748 1745 1742 
 1724 I72I I718 I715 I712 
 1695 1692 1689 1686 1684 
 
 0. 1 802 0. 1 799 0. 1 795 0. 1 792 0. 1 789 
 1770 1767 1764 1761 1757 
 
 1739 1736 1733 1730 1727 
 1709 1706 1704 1701 1698 
 1681 1678 1675 1672 1669 
 
 2 
 2 
 3 
 3 
 
 4 
 
 2 
 2 
 2 
 2 
 3 
 
 6.0 
 
 .1 
 
 .2 
 
 ■3 
 ■4 
 
 0.1667 0.1664 O.I66I 0.1658 0.1656 
 1639 1637 1634 163I 1629 
 1613 1610 1608 1605 1603 
 1587 1585 1582 1580 1577 
 1563 1560 1558 1555 1553 
 
 0. 1 653 0. 1 650 0. 1 647 0. 1 645 0. 1 642 
 1626 1623 1621 1618 1616 
 1600 1597 1595 1592 1590 
 1575 1572 1570 1567 1565 
 1550 1548 1546 1543 1541 
 
 -3 
 
 
 
 1 
 I 
 
 I 
 
 -2 
 
 
 
 
 6-S 
 .6 
 
 ■7 
 .8 
 
 •9 
 
 0.1538 0.1536 0.1534 O.I53I 0.1529 
 I515 I513 I5II 1508 1506 
 1493 1490 1488 i486 1484 
 1471 1468 1466 1464 1462 
 1449 1447 1445 1443 1441 
 
 0.1527 0.1524 0.1522 0.1520 0.1517 
 1504 1502 1499 1497 1495 
 1481 1479 1477 1475 1473 
 1460 1458 1456 1453 145 I 
 1439 1437 1435 1433 1431 
 
 2 
 
 2 
 2 
 2 
 3 
 
 2 
 2 
 
 7.0 
 
 .1 
 
 .2 
 
 •3 
 ■4 
 
 0.1429 0.1427 0.1425 0.1422 0.1420 
 1408 1406 1404 1403 I4OI 
 1389 1387 1385 1383 I381 
 1370 1368 1366 1364 1362 
 1351 1350 1348 1346 1344 
 
 0.1418 0.1416 0.14140.1412 0.1410 
 1399 1397 139s 1393 1391 
 1379 1377 1376 1374 1372 
 1361 1359 1357 1355 1353 
 1342 1340 1339 1337 1335 
 
 -2 
 
 
 
 
 -1 
 
 
 
 
 
 
 7-S 
 .6 
 
 ■7 
 .8 
 
 ■9 
 
 0.1333 O.I332 0.1330 0.1328 0.1326 
 1316 1314 1312 1311 1309 
 1299 1297 1295 1294 1292 
 1282 1280 1279 1277 1276 
 1266 1264 1263 1261 1259 
 
 0.1325 0.1323 0.1321 0.1319 0.1318 
 1307 1305 1304 1302 1300 
 1290 1289 1287 1285 1284 
 1274 1272 1271 1269 1267 
 1258 1256 1255 1253 1252 
 
 2 
 2 
 
 
 8.0 
 
 .1 
 
 .2 
 
 •3 
 
 •4 
 
 0.1250 0.1248 0.1247 0.1245 0.1244 
 1235 1233 1232 1230 1229 
 1220 1218 1217 1215 1214 
 1205 1203 1202 1200 1199 
 1190 1189 1188 1186 1185 
 
 0.1242 0.1241 0.1239 0.1238 0.1236 
 1227 1225 1224 1222 1221 
 1212 1211 1209 1208 1206 
 1198 1196 1195 1193 1192 
 1183 1182 1181 1179 1178 
 
 -3 
 
 
 
 
 
 
 
 
 
 8-5 
 .6 
 
 •7 
 .8 
 
 •9 
 
 0.11760.11750.11740.11720.1171 
 1163 1161 1160 1159 1157 
 H49 1148 1147 1145 1144 
 1136 1135 1134 1133 1131 
 1124 1122 1121 1120 1119 
 
 0.1 170 0.1 168 0.1 167 0.1 166 0.1 164 
 1156 1155 1153 1152 1151 
 1143 1142 1140 1139 1138 
 1130 1129 1127 1126 1125 
 1117 1116 1115 1114 1112 
 
 2 
 2 
 
 
 9.0 
 
 .1 
 
 .2 
 
 •3 
 •4 
 
 iiii 0.11100.1109 0.H07 0.1106 
 1099 1098 1096 1095 10.94 
 1087 1086 1085 1083 1082 
 1075 1074 1073 1072 1071 
 1064 1063 1062 1060 1059 
 
 0.1105 0.11040.11030.1101 0.1100 
 1093 1092 1091 1089 1088 
 ro8i 1080 1079 1078 1076 
 1070 1068 1067 1066 1065 
 1058 1057 1056 1055 1054 
 
 -3 
 
 
 
 
 
 
 
 
 
 9-S 
 .6 
 
 •7 
 .8 
 
 •9 
 
 0.1053 0.1052 0.1050 0.1049 0.1048- 
 1042 1041 1040 1038 1037 
 1031 1030 1029 1028 1027 
 1020 1019 1018 1017 1016 
 1010 1009 1008 1007 1006 
 
 0.1047 0.1046 0.1045 0.1044 0.1043 
 1036 1035 1034 1033 1032 
 1026 1025 1024 1022 1021 
 1015 1014 1013 1012 1011 
 1005 1004 1003 1002 1001 
 
 2 
 2 
 
 
 (35) 
 
 RECIP. 
 
SLIDE-WIRE RATIOS. 
 
 S. W. RATIOS. 
 
 cm. 
 
 Qinm. jmm. 2^^* omm. ^mm. 
 
 gmm. 
 
 gmm. 
 
 nmm. 
 
 gmm. 
 
 gnun. 
 
 
 
 0.0000 0.00 10 0.0020 0.0030 0.0040 
 
 0.0050 
 
 0.0060 
 
 0.0071 
 
 0.0081 
 
 0.0091 
 
 I 
 
 oioi oiii 0122 0132 0142 
 
 0152 
 
 0163 
 
 0173 
 
 0183 
 
 0194 
 
 2 
 
 0204 0215 0225 0235 0246 
 
 0256 
 
 0267 
 
 0278 
 
 0288 
 
 0299 
 
 3 
 
 0309 0320 0331 0341 0352 
 
 0363 
 
 0373 
 
 0384 
 
 0395 
 
 0406 
 
 4 
 
 0417 0428 0438 0449 0460 
 
 0471 
 
 0482 
 
 0493 
 
 0504 
 
 0515 
 
 5 
 
 0.0526 0.0537 0.0549 0.0560 0.0571 
 
 0.0582 
 
 0.0593 
 
 0.0605 
 
 0.0616 
 
 0.0627 
 
 6 
 
 0638 0650 0661 0672 0684 
 
 0695 
 
 0707 
 
 0718 
 
 0730 
 
 0741 
 
 7 
 
 0753 0764 0776 0788 0799 
 
 081 1 
 
 0823 
 
 0834 
 
 0846 
 
 0858 
 
 8 
 
 0870 0881 0893 0905 0917 
 
 0929 
 
 0941 
 
 0953 
 
 0965 
 
 0977 
 
 9 
 
 0989 looi 1013 1025 1038 
 
 1050 
 
 1062 
 
 1074 
 
 1087 
 
 1099 
 
 10 
 
 o.iiii 0.1124 0.1136 0.1148 0.1161 
 
 0.1173 
 
 0.1186 
 
 0.1 198 
 
 0.1211 
 
 0.1223 
 
 II 
 
 1236 1249 I26I 1274 1287 
 
 1299 
 
 1312 
 
 1325 
 
 1338 
 
 1351 
 
 12 
 
 1364 1377 1390 1403 I4I6 
 
 1429 
 
 1442 
 
 H55 
 
 1468 
 
 I48I 
 
 13 
 
 1494 1508, 1521 1534 1547 
 
 1561 
 
 1574 
 
 1588 
 
 1601 
 
 I6I4 
 
 14 
 
 1628 1641 1655 1669 1682 
 
 1696 
 
 1710 
 
 1723 
 
 1737 
 
 I75I 
 
 IS 
 
 0.1765 0.1779 0.1793 0.1806 0.1820 
 
 0.1834 
 
 0.1848 
 
 0.1862 
 
 0.1877 
 
 0.I89I 
 
 i6 
 
 1905 I9I9 1933 1947 1962 
 
 1976 
 
 1990 
 
 2005 
 
 2019 
 
 2034 
 
 17 
 
 2048 2063 2077 2092 2107 
 
 2121 
 
 2136 
 
 2151 
 
 2166 
 
 2180 
 
 i8 
 
 2195 2210 2225 2240 2253 
 
 2270 
 
 2285 
 
 2300 
 
 2315 
 
 2331 
 
 19 
 
 2346 2361 2376 2392 2407 
 
 2422 
 
 2438 
 
 2453 
 
 2469 
 
 2484 
 
 20 
 
 0.2500 0.2516 0.2531 0.2547 0.2563 
 
 0.2579 
 
 0.2595 
 
 0.2610 
 
 0.2626 
 
 0.2642 
 
 21 
 
 2658 2674 2690 2707 2723 
 
 2739 
 
 2755 
 
 2771 
 
 2788 
 
 2804 
 
 22 
 
 2821 2837 2854 2870 2887 
 
 2903 
 
 2920 
 
 2937 
 
 2953 
 
 2970 
 
 23 
 
 2987 3004 3021 3038 3055 
 
 3072 
 
 3089 
 
 3106 
 
 3123 
 
 3I4I 
 
 24 
 
 3'58 3175 3193 3210 3228 
 
 3245 
 
 3263 
 
 3280 
 
 3298 
 
 3316 
 
 25 
 
 0-3333 0.3351 0.3369 0.3387 0.3405 
 
 0.3423 
 
 0.3441 
 
 0.3459 
 
 0.3477 
 
 0.3495- 
 
 26 
 
 3514 3532 3550 3569 3587 
 
 3605 
 
 3624 
 
 3643 
 
 3661 
 
 3680 
 
 27 
 
 3699 3717 3736 3755 3774 
 
 3793 
 
 3812 
 
 3831 
 
 3850 
 
 3870 
 
 28 
 
 3889 3908 3928 3947 3967 
 
 3986 
 
 4006 
 
 4025 
 
 4045 
 
 4065 
 
 29 
 
 4085 4104 4124 4144 4164 
 
 4184 
 
 4205 
 
 4225 
 
 4245 
 
 4265 
 
 30 
 
 0.4286 0.4306 0.4327 0.4347 0.4368 
 
 0.4389 
 
 0.4409 
 
 0.4430 
 
 0.4451 
 
 0.4472 
 
 3' 
 
 4493 4SH 4535 455^ 4577 
 
 4599 
 
 4620 
 
 4641 
 
 4663 
 
 4684 
 
 32 
 
 4706 4728 4749 4771 4793 
 
 4815 
 
 4837 
 
 4859 
 
 4881 
 
 4903 
 
 33 
 
 4925 4948 4970 4993 5015 
 
 5038 
 
 5060 
 
 5083 
 
 5106 
 
 5129 
 
 34 
 
 5152 5175 5198 5221 5244 
 
 5267 
 
 5291 
 
 5314 
 
 5337 
 
 5361 
 
 35 
 
 0.5385 0.5408 0.5432 0.5456 0.5480 
 
 0.5504 
 
 0.5528 
 
 0.5552 
 
 0.5576 
 
 0.5601 
 
 36 
 
 5625 5650 5674 5699 5723 
 
 5748 
 
 5773 
 
 5798 
 
 5823 
 
 5848 
 
 37 
 
 5873 5898 5924 5949 5974 
 
 6000 
 
 6026 
 
 6051 
 
 6077 
 
 6103 
 
 38 
 
 6129 6155 6181 6208 6234 
 
 6260 
 
 6287 
 
 6313 
 
 6340 
 
 6367 
 
 39 
 
 6393 6420 6447 6475 6502 
 
 6529 
 
 6556 
 
 6584 
 
 661 1 
 
 6639 
 
 40 
 
 0.6667 0-5695 0.6722 0.6750 0.6779 
 
 0.6807 
 
 0.6835 
 
 0.6863 
 
 0.6892 
 
 0.6921 
 
 4' 
 
 6949 6978 7007 7036 7065 
 
 7094 
 
 7123 
 
 7153 
 
 7182 
 
 7212 
 
 42 
 
 7241 7271 7301 7331 7361 
 
 7391 
 
 7422 
 
 7452 
 
 7483 
 
 7513 
 
 43 
 
 7544 7575 7606 7637 7668 
 
 7699 
 
 7731 
 
 7762 
 
 7794 
 
 7825 
 
 44 
 
 7857 7889 7921 7953 7986 
 
 8018 
 
 8051 
 
 8083 
 
 8116 
 
 8149 
 
 45 
 
 0.8182 0.8215 0.8248 0.8282 0.8315 
 
 0.8349 
 
 0.8382 
 
 0.8416 
 
 0.8450 
 
 0.8484 
 
 46 
 
 8519 8553 8587 8622 8657 
 
 8692 
 
 8727 
 
 8762 
 
 8797 
 
 8832 
 
 47 
 
 8868 8904 8939 8975 901 I 
 
 9048 
 
 9084 
 
 9121 
 
 9157 
 
 9194 
 
 48 
 
 9231 9268 9305 9342 9380 
 
 9418 
 
 9455 
 
 9493 
 
 9531 
 
 9570 
 
 49 
 
 9608 9646 9685 9724 9763 
 
 9802 
 
 9841 
 
 9881 
 
 9920 
 
 9960 
 
 S. W. RATIOS. 
 
 (36) 
 
SLIDE-WIRE RATIOS. 
 
 S. W. RATIOS. 
 
 cm. 
 
 qUUII* 
 
 jnun. 
 
 2iiiin. 
 
 3"™- 
 
 ^mm. 
 
 gum. 
 
 gmm. 
 
 wmm. 
 
 gmm. 
 
 
 50 
 
 1. 000 
 
 1.004 
 
 1.008 
 
 1.012 
 
 1.016 
 
 1.020 
 
 1.024 
 
 1.028 
 
 1-033 
 
 1-037 
 
 51 
 
 1.041 
 
 1.045 
 
 1.049 
 
 1-053 
 
 1.058 
 
 1.062 
 
 1.066 
 
 1.070 
 
 1-075 
 
 1.079 
 
 52 
 
 1.083 
 
 1.088 
 
 1.092 
 
 1.096 
 
 1. 101 
 
 1.105 
 
 1. 110 
 
 1.114 
 
 1.119 
 
 1.123 
 
 53 
 
 I.I28 
 
 1. 132 
 
 I-137 
 
 r.141 
 
 1.146 
 
 1.151 
 
 1-155 
 
 i.i6o 
 
 1.165 
 
 1.169 
 
 54 
 
 1-174 
 
 1.179 
 
 1-183 
 
 1.188 
 
 1-193 
 
 1.198 
 
 1-203 
 
 1.208 
 
 1.212 
 
 1.217 
 
 55 
 
 1.222 
 
 1.227 
 
 1.232 
 
 1-237 
 
 1.242 
 
 1-247 
 
 1.252 
 
 1-257 
 
 1.262 
 
 1.268 
 
 56 
 
 1'273 
 
 1.278 
 
 1.283 
 
 1.288 
 
 1.294 
 
 1.299 
 
 1.304 
 
 1-309 
 
 1-315 
 
 1.320 
 
 57 
 
 1.326 
 
 1-331 
 
 1-336 
 
 1-342 
 
 1-347 
 
 1-353 
 
 1-358 
 
 1.364 
 
 1-370 
 
 1-375 
 
 58 
 
 1-381 
 
 1-387 
 
 1.392 
 
 1-398 
 
 1.404 
 
 1.410 
 
 1-415 
 
 1.421 
 
 1.427 
 
 1-433 
 
 59 
 
 1-439 
 
 1-445 
 
 1.451 
 
 1-457 
 
 1.463 
 
 1.469 
 
 1-475 
 
 1.481 
 
 1.488 
 
 1.494 
 
 60 
 
 1.500 
 
 1.506 
 
 I-SI3 
 
 1.519 
 
 1-525 
 
 1-532 
 
 1-538 
 
 1-545 
 
 1-551 
 
 . i;558 
 
 6i 
 
 1.564 
 
 1.571 
 
 1-577 
 
 1.584 
 
 1.591 
 
 1-597 
 
 1.604 
 
 1.611 
 
 1.618 
 
 1.625 
 
 62 
 
 1.632 
 
 1-639 
 
 1.646 
 
 1-653 
 
 1.660 
 
 1.667 
 
 1-674 
 
 1.681 
 
 1.688 
 
 1-695 
 
 63 
 
 1-703 
 
 1.710 
 
 1.717 
 
 1-725 
 
 1-732 
 
 1.740 
 
 1.747 
 
 1-755 
 
 1.762 
 
 1.770 
 
 64 
 
 1.778 
 
 1.7S6 
 
 1-793 
 
 1.801 
 
 1.809 
 
 1.817 
 
 1.825 
 
 1-833 
 
 1.841 
 
 1.849 
 
 65 
 
 1-857 
 
 1.865 
 
 1.874 
 
 1.882 
 
 1.890 
 
 1.899 
 
 1.907 
 
 1.915 
 
 1.924 
 
 1-933 
 
 66 
 
 1. 941 
 
 1-950 
 
 1-959 
 
 1.967 
 
 1.976 
 
 1.985 
 
 1.994 
 
 2.003 
 
 2.012 
 
 2.021 
 
 67 
 
 2.030 
 
 2.040 
 
 2.049 
 
 2.058 
 
 2.067 
 
 2.077 
 
 2.086 
 
 2.096 
 
 2.106 
 
 2.115 
 
 68 
 
 2.125 
 
 2-I3S 
 
 2.145 
 
 2-155 
 
 2.165 
 
 2-175 
 
 2.185 
 
 2.195 
 
 2.205 
 
 2.215 
 
 69 
 
 2.226 
 
 2.236 
 
 2.247 
 
 2.257 
 
 2.268 
 
 2-279 
 
 2.289 
 
 2.300 
 
 2.311 
 
 2.322 
 
 70 
 
 2-333 
 
 2.344 
 
 2-356 
 
 2-367 
 
 2-378 
 
 2.390 
 
 2.401 
 
 2-413 
 
 2-425 
 
 2.436 
 
 71 
 
 2.448 
 
 2.460 
 
 2.472 
 
 2.484 
 
 2.497 
 
 2.509 
 
 2.521 
 
 2-534 
 
 2.546 
 
 2-559 
 
 72 
 
 2-571 
 
 2.584 
 
 2-597 
 
 2.610 
 
 2.623 
 
 2.636 
 
 2.650 
 
 2.663 
 
 2.676 
 
 2.690 
 
 73 
 
 2.704 
 
 2.717 
 
 2-731 
 
 2-745 
 
 2-759 
 
 2-774 
 
 2.788 
 
 2.802 
 
 2.817 
 
 2.831 
 
 74 
 
 2.846 
 
 2.861 
 
 2.876 
 
 2.891 
 
 2.906 
 
 2.922 
 
 2.937 
 
 2-953 
 
 2.968 
 
 2.984 
 
 75 
 
 3.000 
 
 3.016 
 
 3032 
 
 3049 
 
 3.065 
 
 3.082 
 
 3.098 
 
 3-115 
 
 3132 
 
 3-149 
 
 76 
 
 3-167 
 
 3.184 
 
 3.202 
 
 3.219 
 
 3-237 
 
 3-255 
 
 3-274 
 
 3.292 
 
 3-310 
 
 3-329 
 
 77 
 
 3-348 
 
 3-367 
 
 3-386 
 
 3-405 
 
 3-425 
 
 3-444 
 
 3464 
 
 3-484 
 
 3-505 
 
 3-525 
 
 78 
 
 3-545 
 
 3-566 
 
 3-587 
 
 3.608 
 
 3-630 
 
 3-651 
 
 3-673 
 
 3-695 
 
 3-717 
 
 3-739 
 
 79 
 
 3.762 
 
 3-785 
 
 3.808 
 
 3-831 
 
 3-854 
 
 3-878 
 
 3.902 
 
 3-926 
 
 3-950 
 
 3-975 
 
 80 
 
 4.000 
 
 4.025 
 
 4.051 
 
 4.076 
 
 4.102 
 
 4.128 
 
 4-155 
 
 4.181 
 
 4.208 
 
 4.236 
 
 81 
 
 4.263 
 
 4.291 
 
 4-319 
 
 4-348 
 
 4-376 
 
 4.405 
 
 4-435 
 
 4-465 
 
 4-495 
 
 4.525 
 
 82 
 
 4-556 
 
 4-587 
 
 4.618 
 
 4.650 
 
 4.682 
 
 4-714 
 
 4-747 
 
 4.780 
 
 4.814 
 
 4.848 
 
 83 
 
 4.882 
 
 4-917 
 
 4-952 
 
 4.988 
 
 5.024 
 
 5.061 
 
 5.098 
 
 5-135 
 
 5-173 
 
 5.211 
 
 84 
 
 5.250 
 
 5-289 
 
 5-329 
 
 5-369 
 
 5-410 
 
 5.452 
 
 5-494 
 
 5-536 
 
 5-579 
 
 5.623 
 
 85 
 
 5.667 
 
 5-7" 
 
 5-757 
 
 5.803 
 
 5.849 
 
 5-897 
 
 5-944 
 
 5-993 
 
 6.042 
 
 6.092 
 
 86 
 
 6.143 
 
 6.194 
 
 6.246 
 
 6.299 
 
 6-353 
 
 6.407 
 
 6.463 
 
 6.519 
 
 6-576 
 
 6.634 
 
 87 
 
 6.692 
 
 6.752 
 
 6.813 
 
 6.874 
 
 6-937 
 
 7.000 
 
 7.065 
 
 7-130 
 
 7.197 
 
 7.264 
 
 88 
 
 7-333 
 
 7-403 
 
 7-475 
 
 7-547 
 
 7.621 
 
 7.696 
 
 7.772 
 
 7.850 
 
 7.929 
 
 8.009 
 
 89 
 
 8.091 
 
 8.174 
 
 8.259 
 
 8-346 
 
 8-434 
 
 8.524 
 
 8.615 
 
 8-709 
 
 8.804 
 
 8.901 
 
 90 
 
 9.000 
 
 9.101 
 
 9-204 
 
 9309 
 
 9-417 
 
 9-526 
 
 9.638 
 
 9.753 
 
 9.870 
 
 9.989 
 
 91 
 
 10. 1 1 
 
 10.33 
 
 10.36 
 
 10.49 
 
 10.63 
 
 10-77 
 
 10.90 
 
 11.05 
 
 11.20 
 
 11-35 
 
 92 
 
 11.50 
 
 11.66 
 
 11.82 
 
 11.99 
 
 12.16 
 
 12-33 
 
 12.51 
 
 12.70 
 
 12.89 
 
 13.08 
 
 93 
 
 13.29 
 
 13-49 
 
 13-71 
 
 13-93 
 
 14-15 
 
 14-38 
 
 14-63 
 
 14.87 
 
 15-13 
 
 15-39 
 
 94 
 
 15.67 
 
 15-95 
 
 16.24 
 
 16.54 
 
 16.86 
 
 17.18 
 
 17-52 
 
 17.87 
 
 18.23 
 
 18.61 
 
 95 
 
 19.00 
 
 19.41 
 
 19-83 
 
 20.28 
 
 20.74 
 
 21.22 
 
 21-73 
 
 22.26 
 
 22.81 
 
 23-39 
 
 96 
 
 24.00 
 
 24.64 
 
 25.32 
 
 26.03 
 
 26.78 
 
 27-57 
 
 28.41 
 
 29.30 
 
 30.25 
 
 31-26 
 
 97 
 
 32-33 
 
 33-48 
 
 34-71 
 
 36-04 
 
 37-46 
 
 39.00 
 
 40.67 
 
 42.48 
 
 44-45 
 
 46.62 
 
 98 
 
 49.00 
 
 51.6 
 
 54-6 
 
 57-8 
 
 61.5 
 
 65.7 
 
 70.4 
 
 75-9 
 
 82.3 
 
 89.9 
 
 99 
 
 99.0 
 
 110. 
 
 124. 
 
 142. 
 
 166. 
 
 199- 
 
 249. 
 
 332- 
 
 499- 
 
 999. 
 
 
 
 
 
 
 (37) 
 
 
 
 s. w. 
 
 RATIO 
 
NAT. SIN. 4 PL. 
 
 NATURAL SINES AND COSINES 
 
 TO 
 FOUR PLACES. 
 
 Note. For cosines use right-hand column of degrees and lower line of tenths. 
 
 Deg. 
 
 ".0 ".I ".2 ".3 °.4 
 
 °.5 °.6 °.7 °-8 ".9 
 
 
 Interpola. 
 for h'dth! 
 
 0° 
 
 0.0000 0.0017 0.0035 0.0052 0.0070 
 
 0.0087 0.0105 0.0122 0.01400.0157 
 
 89 
 
 18 17 
 
 I 
 
 0175 0192 0209 0227 0244 
 
 0262 0279 0297 0314 0332 
 
 88 
 
 2 2 
 
 2 
 
 0349 0366 0384 0401 0419 
 
 0436 0454 0471 0488 0506 
 
 87 
 
 4 3 
 
 3 
 
 0523 0541 0558 0576 0593 
 
 o6io 0628 0645 0663 0680 
 
 86 
 
 5 5 
 
 4 
 
 0698 0715 0732 0750 0767 
 
 0785 0802 0819 0837 0854 
 
 85 
 
 -7 7 
 
 S 
 
 0.0872 0.0889 0.0906 0.0924 0.0941 
 
 0.0958 0.0976 0.0993 0.1011*0.1028 
 
 84 
 
 9 9 
 
 6 
 
 1045 1063 1080 1097 I I 15 
 
 1132 1149 1167 1184 1201 
 
 83 
 
 II 10 
 
 7 
 
 1219 1236 1253 1271 1288 
 
 1305 1323 1340 1357 1374 
 
 82 
 
 13 12 
 
 8 
 
 1392 1409 1426 ii\i\/\ 1461 
 
 1478 1495 1513 1530 1547 
 
 81 
 
 14 14 
 
 9 
 
 1564 1582 1599 1616 1633 
 
 1650 1668 1685 1702 1719 
 
 80° 
 
 16 15 
 
 10° 
 
 0.17360.17540.17710.17880.1805 
 
 0.1822 0.1840 0.1857 0.1874 0.1891 
 
 79 
 
 17 16 
 
 II 
 
 1908 1925 1942 1959 1977 
 
 1994 201 I 2028 2045 2062 
 
 78 
 
 2 2 
 
 12 
 
 2079 2096 2113 2130 2147 
 
 2164 2181 2198 2215 2232 
 
 77 
 
 3 3 
 
 '3 
 
 2250 2267 2284 2300 2317 
 
 2334 2351 2368 2385 2402 
 
 76 
 
 5 5 
 
 14 
 
 2419 2436 2453 2470 2487 
 
 2504 2521 2538 2554 2571 
 
 75 
 
 7 6 
 
 IS 
 
 0.2588 0.2605 0.2622 0.2639 0.2656 
 
 0.2672 0.2689 0.2706 0.2723 0.2740 
 
 74 
 
 9 8 
 
 i6 
 
 2756 2773 2790 2807 2823 
 
 2840 2857 2874 2890 2907 
 
 73 
 
 10 10 
 
 17 
 
 2924 2940 2957 2974 2990 
 
 3007 3024 3040 3057 3074 
 
 72 
 
 12 II 
 
 i8 
 
 3090 3107 3123 3140 3156 
 
 3173 3190 3206 3223 3239 
 
 7« 
 
 14 13 
 
 19 
 
 3256 3272 3289 3305 3322 
 
 3338 3355 3371 3387 3404 
 
 70° 
 
 15 14 
 
 20° 
 
 0.3420 0.3437 0.3453 0.3469 0.3486 
 
 0.3502 0.3518 0.3535 0.3551 0.3567 
 
 69 
 
 16 15 
 
 21 
 
 3584 3600 3616 3633 3649 
 
 3665 3681 3697 3714 3730 
 
 68 
 
 2 2 
 
 22 
 
 3746 3762 3778 3795 381 I 
 
 3827 3843 3859 3875 3891 
 
 67 
 
 3 3 
 
 23 
 
 3907 3923 3939 3955 397' 
 
 3987 4003 4019 4035 4051 
 
 66 
 
 5 5 
 
 24 
 
 4067 4083 4099 4115 4131 
 
 4147 4163 4179 4195 4210 
 
 65 
 
 6 6 
 
 25 
 
 0.4226 0.4242 0.4258 0.4274 0.4289 
 
 0.4305 0.4321 0.4337 0.4352 0.4368 
 
 64 
 
 8 8 
 
 26 
 
 4384 4399 4415 443' 4446 
 
 4462 4478 4493 4509 4524 
 
 63 
 
 10 9 
 
 27 
 
 4540 4555 4571 4586 4602 
 
 4617 4633 4648 4664 4679 
 
 62 
 
 II II 
 
 28 
 
 ^4695 4710 4726 4741 4756 
 
 4772 4787 4802 4818 4833 
 
 61 
 
 13 12 
 
 29 
 
 4848 4863 4879 4894 4909 
 
 4924 4939 4955 4970 4985 
 
 60° 
 
 14 14 
 
 30° 
 
 0.5000 0.5015 0.5030 0.5045 0.5060 
 
 0.5075 0.5090 0.5105 0.5120 0.5135 
 
 59 
 
 U 13 
 
 31 
 
 5150 5165 5180 5195 5210 
 
 5225 5240 5255 5270 5284 
 
 58 
 
 I I 
 
 32 
 
 5299 5314 5329 5344 5358 
 
 5373 5388 5402 5417 5432 
 
 57 
 
 3 3 
 
 33 
 
 5446 5461 5476 5490 5505 
 
 5519 5534 5548 5563 5577 
 
 56 
 
 4 4 
 
 34 
 
 5592 5606 5621 5635 5650 
 
 5664 5678 5693 5707 5721 
 
 55 
 
 6 5 
 
 35 
 
 0-5736 05750 0-5764 0.5779 0-5793 
 
 0.5807 0.5821 0.5835 0.5850 0.5864 
 
 54 
 
 7 7 
 
 36 
 
 5878 5892 5906 5920 5934 
 
 5948 5962 5976 5990 6004 
 
 53 
 
 8 8 
 
 37 
 
 6018 6032 6046 6060 6074 
 
 6088 6101 6115 6129 6143 
 
 52 
 
 10 9 
 
 38 
 
 6157 6170 6184 6198 6211 
 
 6225 6239 6252 6266 6280 
 
 51 
 
 II 10 
 
 39 
 
 6293 6307 6320 6334 6347 
 
 6361 6374 6388 6401 6414 
 
 50° 
 
 13 12 
 
 
 i°.o ".9 °-8 °.7 °.6 
 
 °.5 °.4 ".3 °.2 °.i 
 
 Deg. 
 
 Interpola. 
 for h'dth! 
 
 NAT. COS. 4 PL. 
 
 (38) 
 
NATURAL SINES AND COSINES. 
 
 4 PL. NAT. SIN. 
 
 Oeg. 
 
 °.o °.I °.2 ^.3 °.4 
 
 ^.5 °.6 °.7 °-8 ;.9 
 
 
 Interpola. 
 for h'dths 
 
 40° 
 
 0.6428 0.6441 0.6455 0.6468 0.6481 
 
 0.64940.65080.6521 0.65340.6547 
 
 49 
 
 13 12 
 
 41 
 
 6561 6574 6587 6600 6613 
 
 6626 6639 6652 6665 6678 
 
 48 
 
 I I 
 
 42 
 
 6691 6704 6717 6730 6743 
 
 6756 6769 6782 6794 6807 
 
 47 
 
 3 2 
 
 43 
 
 6820 6833 6845 6858 6871 
 
 6884 6896 6909 6921 6934 
 
 46 
 
 4 4 
 
 44 
 
 6947 6959 6972 6984 6997 
 
 7009 7022 7034 7046 7059 
 
 -45 
 
 5 5 
 
 45 
 
 0.7071 0.7083 0.7096 0.7108 0.7120 
 
 0.7133 0.7145 0.7157 0.7169 0.7181 
 
 44 
 
 7 6 
 
 46 
 
 7193 7206 7218 7230 7242 
 
 7254 7266 7278 ,7290 7302 
 
 43 
 
 8 7 
 
 47 
 
 73*4 7325 7337 7349 736i 
 
 7373 7385 7396 7408 7420 
 
 42 
 
 9 8 
 
 48 
 
 7431 7443 7455 7466 7478 
 
 7490 7501 7513 7524 7536 
 
 41 
 
 10 10 
 
 49 
 
 7547 7559 757° 7S8i 7593 
 
 7604 7615 7627 7638 7649 
 
 40° 
 
 12 II 
 
 50° 
 
 0.7660 0.7672 0.7683 0.7694 0.7705 
 
 0.7716 0.7727 0.7738 0.7749 0.7760 
 
 39 
 
 11 9 
 
 51 
 
 7771 7782 7793 7804 7815 
 
 7826 7837 7848 7859 7869 
 
 38 
 
 I I 
 
 52 
 
 7880 7891 7902 7912 7923 
 
 7934 7944 7955 7965 7976 
 
 37 
 
 2 2 
 
 53 
 
 7986 7997 8007 8018 8028 
 
 8039 8049 8059 8070 8080 
 
 36 
 
 3 3 
 
 54 
 
 .8090 8100 81H 8121 8131 
 
 8141 8151 8161 8171 8181 
 
 35 
 
 4 4 
 
 55 
 
 0.8192 0.8202 0.821 1 0.8221 0.8231 
 
 0.8241 0.8251 0.8261 0.8271 0.8281 
 
 34 
 
 6 5 
 
 56 
 
 8290 8300 8310 8320 8329 
 
 8339 8348 8358 8368 8377 
 
 33 
 
 7 5 
 
 57 
 
 8387 8396 8406 84fs 8425 
 
 8434 8443 8453 8462 8471 
 
 32 
 
 8 6 
 
 58 
 
 8480 8490 8499 8508 8517 
 
 8526 8536 8545 8554 8563 
 
 31 
 
 9 7 
 
 59 
 
 8572 8581 8590 8599 8607 
 
 8616 8625 8634 8643 8652 
 
 30° 
 
 10 8 
 
 60° 
 
 0.8660 0.8669 0.8678 0.8686 0.8695 
 
 0.8704 0.8712 0.8721 0.87290.8738 
 
 29 
 
 8 7 
 
 61 
 
 8746 8755 8763 8771 8780 
 
 8788 8796 8805 8813 8821 
 
 28 
 
 I I 
 
 62 
 
 8829 8838 8846 8854 8862 
 
 8870 8878 8886 8894 8902 
 
 27 
 
 2 I 
 
 63 
 
 8910 8918 8926 8934 8942 
 
 8949 8957 8965 8973 8980 
 
 26 
 
 2 2 
 
 64 
 
 8988 8996 9003 901 I 9018 
 
 9026 9033 9041 9048 9056 
 
 25 
 
 3 3 
 
 6s 
 
 0.9063 0.9070 0.9078 0.9085 0.9092 
 
 0.91000.91070.91140.9121 0.9128 
 
 24 
 
 4 4 
 
 66 
 
 9135 9143 915° 9157 9164 
 
 9171 9178 9184 9191 9198 
 
 23 
 
 5 4 
 
 67 
 
 9205 9212 9219 9225 9232 
 
 9239 9245 9252 9259 9265 
 
 22 
 
 6 5 
 
 68 
 
 9272 9278 9285 9291 9298 
 
 9304 -9311 9317 9323 9330 
 
 21 
 
 6 6 
 
 69 
 
 9336 9342 9348 9354 9361 
 
 9367 9373 9379 9385 939i 
 
 20° 
 
 7 6 
 
 70° 
 
 0.9397 0.9403 0.9409 0.9415 0.9421 
 
 0.9426 0.9432 0.9438 0.9444 0.9449 
 
 19 
 
 6 4 
 
 71 
 
 9455 9461 9466 9472 9478 
 
 9483 9489 9494 9500 9505 
 
 18 
 
 I 
 
 72 
 
 95H 9516 9521 9527 9532 
 
 9537 9542 9548 9553 9558 
 
 17 
 
 I I 
 
 73 
 
 9563 9568 9573 9578 9583 
 
 9588 9593 9598 9603 9608 
 
 16 
 
 2 I 
 
 74 
 
 9613 9617 9622 9627 9632 
 
 9636 9641 9646 9650 9655 
 
 15 
 
 2 2 
 
 75 
 
 0.9659 0.9664 0.9668 0.9673 0.9677 
 
 0.9681 0.9686 0.9690 0.9694 0.9699 
 
 14 
 
 3 2 
 
 76 
 
 9703 9707 971 1 9715 9720 
 
 9724 9728 9732 9736 9740 
 
 13 
 
 4 2 
 
 77 
 
 9744 9748 9751 9755 9759 
 
 9763 9767 9770 9774 9778 
 
 12 
 
 4 3 
 
 78 
 
 9781 9785 9789 9792 9796 
 
 9799 9803 9806 9810 9813 
 
 II 
 
 5 3 
 
 79 
 
 9816 9820 9823 9826 9829 
 
 9833 9836 9839 9842 9845 
 
 10° 
 
 5 4 
 
 80° 
 
 0.9848 0.9851 0.9854 0.9857 0.9860 
 
 0.9863 0.9866 0.9869 0.9871 0.9874 
 
 9 
 
 3 2 
 
 81 
 
 9877 9880 9882 9885 9888 
 
 9890 9893 9895 9898 9900 
 
 8 
 
 
 
 82 
 
 9903 9905 9907 9910 9912 
 
 9914 9917 9919 9921 9923 
 
 7 
 
 I 
 
 83 
 
 9925 9928 9930 9932 9934 
 
 9936 9938 9940 9942 9943 
 
 6 
 
 I I 
 
 84 
 
 9945 9947 9949 995 i 9952 
 
 9954 9956 9957 9959 9960 
 
 5 
 
 I I 
 
 85 
 
 0.9962 0.9963 0.9965 0.9966 0.9968 
 
 0.9969 0.9971 0.9972 0.9973 0.9974 
 
 4 
 
 2 I 
 
 86 
 
 9976 9977 9978 9979 9980 
 
 9981 9982 9983 9984 9985 
 
 3 
 
 2 I 
 
 87 
 
 9986 9987 9988 9989 9990 
 
 9990 9991 9992 9993 9993 
 
 2 
 
 2 I 
 
 88 
 
 9994 9995 9995 999^ 999^ 
 
 9997 9997 9997 9998 9998 
 
 I 
 
 2 2 
 
 89 
 
 9998 9999 9999 9999 9999 
 
 1. 000 1. 000 1. 000 1. 000 1. 000 
 
 0° 
 
 3 2 
 
 
 i°.o ".9 °.8 °.7 °-6 
 
 °.5 °.4 -.3 °.2 °.i 
 
 Deg. 
 
 Interpola. 
 for h'dths 
 
 (39) 
 
 4 PL. NAT. COS. 
 
NAT. TAN. 4 PL. 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 TO 
 
 FOUR PLACES. 
 
 Note. For cotangents use right-hand column of degrees and lower line of tenths 
 
 Deg. 
 
 ".0 \i ".2 °.3 °.4 
 
 ".5 °-6 °.7 °.8 ''.9 
 
 
 Interpola. 
 for h'dthi 
 
 0° 
 
 0.00000.0017 0.0035 0.0052 0.0070 
 
 0.0087 0.0105 O.OI22 0.0140 0.0157 
 
 89 
 
 17 18 
 
 I 
 
 0175 0192 0209 0227 0244 
 
 0262 0279 0297 0314 0332 
 
 88 
 
 2 2 
 
 2 
 
 0349 0367 0384 0402 0419 
 
 0437 0454 0472 0489 0507 
 
 87 
 
 3 4 
 
 3 
 
 0524 0542 055^ 0577 0594 
 
 o6i2 0629 0647 0664 0682 
 
 86 
 
 5 5 
 7 7 
 
 4 
 
 0699 0717 0734 0752 0769 
 
 0787 0805 0822 0840 0857 
 
 85 
 
 S 
 
 0.0875 0.0892 0.0910 0.0928 0.0945 
 
 0.09630.0981 0.0998 O.IOI6 0.1033 
 
 84 
 
 9 9 
 
 6 
 
 1051 1069 1086 1104 1122 
 
 "39 1157 1175 1192 1210 
 
 83 
 
 10 II 
 
 7 
 
 1228 1246 1263 1281 1299 
 
 1317 1334 1352 1370 1388 
 
 82 
 
 12 13 
 
 8 
 
 1405 1423 1441 1459 1477 
 
 1495. 1512 1530 1548 1566 
 
 81 
 
 14 14 
 
 9 
 
 1584 1602 1620 1638 1655 
 
 1673 1691 1709 1727 1745 
 
 80° 
 
 15 16 
 
 10° 
 
 0.1763 0.1781 0.1799 0.1817 0.1835 
 
 0.18530.18710.18900.19080.1926 
 
 79 
 
 19 30 
 
 II 
 
 1944 ici2 1980 1998 2016 
 
 2035 2053 2071 2089 2107 
 
 78 
 
 2 2 
 
 12 
 
 2126 2144 2162 2180 2199 
 
 2217 2235 2254 2272 2290 
 
 77 
 
 4 4 
 
 13 
 
 2309 2327 2345 2364 2382 
 
 2401 2419 2438 2456 2475 
 
 76 
 
 6 6 
 
 14 
 
 2493 2512 2530 2549 2568 
 
 2586 2605 2623 2642 2661 
 
 75 
 
 8 8 
 
 IS 
 
 0.2679 0.2698 0.2717 0.2736 0.2754 
 
 0.2773 0.2792 0.281 1 0.2830 0.2849 
 
 74 
 
 10 10 
 
 16 
 
 2867 2886 2905 2924 2943 
 
 2962 2981 3000 3019 J038 
 
 73 
 
 II 12 
 
 17 
 
 3057 3076 3096 31:5 3134 
 
 3153 3172 3191 3211 3230 
 
 72 
 
 13 14 
 
 18 
 
 3249 3269 3288 3307 3327 
 
 3346 3365 3385 3404 3424 
 
 71 
 
 15 16 
 
 19 
 
 3443 3463 3482 3502 3522 
 
 3541 3561 3581 3600 3620 
 
 70° 
 
 17 18 
 
 20° 
 
 0.3640 0.3659 0.3679 0.3699 0.3719 
 
 0-3739 0.3759 0.3779 0.3799 0.3819 
 
 69 
 
 22 24 
 
 21 
 
 3839 3859 3879 3899 3919 
 
 3939 3959 3979 4000 4020 
 
 68 
 
 2 2 
 
 22 
 
 4040 4061 4081 4101 4122 
 
 4142 4163 4183 4204 4224 
 
 67 
 
 4 5 
 
 23 
 
 4245 4265 4286 4307 4327 
 
 4348 4369 4390 44" 4431 
 
 66 
 
 7 7 
 
 24 
 
 4452 4473 4494 45iS 453^ 
 
 4557 4578 4599 4621 4642 
 
 65 
 
 9 10 
 
 25 
 
 0.4663 0.4684 0.4706 0.4727 0.4748 
 
 0.4770 0.4791 0.4813 0.4834 0.4856 
 
 64 
 
 11 12 
 
 26 
 
 4877 4899 4921 4942 4964 
 
 4986 5008 5029 5051 5073 
 
 63 
 
 13 14 
 
 27 
 
 5095 5117 5139 5161 5184 
 
 5206 5228 5250 5272 5295 
 
 62 
 
 15 17 
 
 28 
 
 5317 5340 5362 5384 5407 
 
 5430 5452 5475 5498 5520 
 
 61 
 
 18 19 
 
 29 
 
 5543 5566 5589 5612 5635 
 
 5658 5681 5704 5727 5750 
 
 60° 
 
 20 22 
 
 30° 
 
 0-5774 0-5797 0-5820 0.5844 0.5867 
 
 0.5890 0.5914 0.5938 0.5961 0.5985 
 
 59 
 
 26 28 
 
 31 
 
 6009 6032 6056 6080 6104 
 
 6128 6152 6176 6200 6224 
 
 58 
 
 3 3 
 
 32 
 
 6249 6273 6297 6322 6346 
 
 6371 6395 6420 6445 6469 
 
 57 
 
 6 6 
 
 33 
 
 6494 6519 6544 6569 6594 
 
 6619 6644 6669 6694 6720 
 
 56 
 
 8 8 
 
 34 
 
 6745 6771 6796 6822 6847 
 
 6873 6899 6924 6950 6976 
 
 55 
 
 10 II 
 
 35 
 
 0.7002 0.7028 0.7054 0.7080 0.7107 
 
 0.7133 0.7159 0.7186 0.7212 0.7239 
 
 54 
 
 13 '4 
 
 36 
 
 7265 7292 7319 7346 7373 
 
 7400 7427 7454 7481 7508 
 
 53 
 
 16 17 
 
 37 
 
 7536 7563 7590 7618 7646 
 
 7673 7701 7729 7757 7785 
 
 52 
 
 18 20 
 
 38 
 
 7813 7841 7869 7898 7926 
 
 7954 7983 8012 8040 8069 
 
 51 
 
 21 22 
 
 39 
 
 8098 8127 8156 8185 8214 
 
 8243 8273 8302 8332 8361 
 
 50° 
 
 23 25 
 
 
 i°.o ".9 °.8 °7 °-6 
 
 "■5 °.4 °.3 ".2 ".I 
 
 Deg. 
 
 Interpola. 
 or h'dtha 
 
 NAT. COT. 4 PL. 
 
 (40) 
 
NATURAL TANGENTS AND COTANGENTS. 
 
 4 PL. NAT. TAN. 
 
 Deg. 
 
 °.o ".I ".2 °.3 °.4 
 
 °.S °.6 °.7 °-8 °.9 
 
 
 Interpol a, 
 forh'dths 
 
 40° 
 
 0.8391 0.8421 0.8451 0.8481 0.85 1 1 
 
 0.8541 0.8571 0.8601 0.8632 0.8662 
 
 49 
 
 30 40 
 
 41 
 
 8693 8724 8754 8785 8816 
 
 8847 8878 8910 8941 8972 
 
 48 
 
 3 4 
 
 42 
 
 9004 9036 9067 9099 9131 
 
 9163 9195 9228 9260 9293 
 
 47 
 
 6 8 
 
 43 
 
 9325 9358 9391 9424 9457 
 
 9490 9523 9556 9590 9623 
 
 46 
 
 9 12 
 
 44 
 
 9657 9691 9725 9759 9793 
 
 9827 9861 9896 9930 9965 
 
 45 
 
 12 16 
 
 45 
 
 i.oooo 1.0035 1.0070 1.0105 1.0141 
 
 1.0176 1.0212 1.0247 1.0283 1.0319 
 
 44 ' 
 
 15 20 
 
 46 
 
 0355 0392 0428 0464 0501 
 
 0538 0575 0612 0649 0686 
 
 43 
 
 18 24 
 
 47 
 
 0724 0761 0799 0837 0875 
 
 0913 0951 0990 1028 1067 
 
 42 
 
 21 28 
 
 48 
 
 1106 1145 1184 1224 1263 
 
 1303 1343 1383 1423 1463 
 
 41 
 
 24 32 
 
 49 
 
 1504 1544 1585 1626 1667 
 
 1708 1750 1792 1833 1875 
 
 40° 
 
 27 36 
 
 50° 
 
 1. 1918 1. 1960 1.2002 1.2045 i-2o88 
 
 1.2131 1.2174 1.22l8 1.2261 1.2305 
 
 39 
 
 50 60 
 
 ^ 
 
 2349 2393 2437 2482 2527 
 
 2572 2617 2662 2708 2753 
 
 38 
 
 5 6 
 
 52 
 
 2799 2846 2892 2938 2985 
 
 3032 3079 3127 3175 3222 
 
 37 
 
 10 12 
 
 S3 
 
 3270 3319 3367 3416 3465 
 
 3514 3564 3613 3663 3713 
 
 36 
 
 15 18 
 
 54 
 
 3764 3814 3865 3916 3968 
 
 4019 4071 4124 4176 4229 
 
 35 
 
 20 24 
 
 55 
 
 1.4281 1.4335 14388 1.4442 1.4496 
 
 1.4550 1.4605 1.4659 1.4715 1.4770 
 
 34 
 
 25 30 
 
 56 
 
 4826 4882 4938 4994 5051 
 
 5108 5166 5224 5282 5340 
 
 33 
 
 30 36 
 
 57 
 
 5399 5458 5517 5577 S637 
 
 5697 5757 5818 5880 5941 
 
 32 
 
 35 42 
 
 58 
 
 6003 6066 6128 6191 6255 
 
 6319 6383 6447 6512 6577 
 
 31 
 
 40 48 
 
 59 
 
 6643 6709 6775 6842 6909 
 
 ■6977 7045 7113 7182 7251 
 
 30° 
 
 45 54 
 
 60° 
 
 1.73211.73911.7461 1.7532 1.7603 
 
 1.7675 1-7747 1.7820 1.7893 1.7966 
 
 29 
 
 70 80 
 
 61 
 
 8040 81 1 5 8190 8265 8341 
 
 8418 8495 8572 8650 8728 
 
 28 
 
 7 8 
 
 62 
 
 8807 8887 8967 9047 9128 
 
 9210 9292 9375 9458 9542 
 
 27 
 
 14 16 
 
 63 
 
 1.9626 1.9711 1-9797 1.9883 1.9970 
 
 2.0057 2.0145 2.0233 2.0323 2.0413 
 
 26 
 
 ,21 24 
 
 64 
 
 2.0503 2.0594 2.0686 2.0778 2.0872 
 
 2.0965 2.10602.1155 2.1251 2.1348 
 
 25 
 
 28 32 
 
 65 
 
 2.1445 2.1543 2.1642 2.1742 2.1842 
 
 2.1943 2.2045 2.2148 2.2251 2.2355 
 
 24 
 
 35 40 
 
 66 
 
 2460 2566 2673 2781 2889 
 
 2998 3109 3220 3332 3445 
 
 23 
 
 42 48 
 
 67 
 
 3SS9 3673 3789 3906 4023 
 
 4142 4262 4383 4504 4627 
 
 22 
 
 49 56 
 
 68 
 
 4751 4876 5002 5129 5257 
 
 5386 5517 5649 5782 5916 
 
 21 
 
 56 64 
 
 69. 
 
 6051 6187 6325 6464 6605 
 
 6746 6889 7034 7179 7326 
 
 20° 
 
 63 72 
 
 70° 
 
 2.7475 2.7625 2.7776 2.7929 2.8083 
 
 2.8239 2.8397 2.8556 2.8716 2.8878 
 
 19 
 
 90 
 
 71 
 
 2.9042 2.9208 2.9375 2.9544 2.9714 
 
 2.9887 3.0061 3.0237 3.0415 3.0595 
 
 18 
 
 9 
 
 72 
 
 3.0777 3.0961 3.1146 3.1334 3.1524 
 
 3.1716 3.1910 3.2106 3.2305 3.2506 
 
 17 
 
 18 
 
 73 
 
 2709 2914 3122 3332 3544 
 
 3759 3977 4197 4420 4646 
 
 16 
 
 27 
 
 74 
 
 4874 5105 5339 5576 5816 
 
 6059 6305 6554 6806 7062 
 
 15 
 
 36 
 
 75 
 
 3.7321 3.7583 3.7848 3.81 18 3.8391 
 
 3.8667 3.8947 3.9232 3.9520 3.9812 
 
 14 
 
 45 
 
 76 
 
 4.0108 4.0408 4.0713 4.1022 4.133s 
 
 4.1653 4.1976 4.2303 4.2635 4.2972 
 
 13 
 
 54 
 
 77 
 
 4.3315 4.3662 4.4015 4.4374 4.4737 
 
 4.5107 4.5483 4.5864 4.6252 4.6646 
 
 12 
 
 63 
 
 78 
 
 4.7046 4.7453 4.7867 4.8288 4.8716 
 
 4.91524.9594 5.0045 5.0504 5.0970 
 
 11 
 
 72 
 
 79 
 
 5.1446 5.1929 5.2422 5.2924 5.3435 
 
 5.3955 5-4486 5.5026 5.5578 5.6140 
 
 10° 
 
 81 
 
 80° 
 
 5.6713 5.7297 5.7894 5.8502 5.9124 
 
 5.9758 6.0405 6.1066 6.1742 6.2432 
 
 9 
 
 
 81 
 
 6.3138 6.3859 6.4596 6.5350 6.6122 
 
 6.6912 6.7720 6.8548 6.9395 7-0264 ■ 
 
 8 
 
 
 82 
 
 7.1154 7.2066 7.3002 7.3962 7.4947 
 
 7-5958 7.6996 7.8062 7.9158 8.0285 
 
 7 
 
 
 83 
 
 8.1443 8.2636 8.3863 8.5126 8.6427 
 
 8.7769 8.9152 9.0579 9.2052 9.3572 
 
 6 
 
 
 84 
 
 9.5144 9.677 9.845 10.02 10.20 
 
 10.39 10.58 10,78 10.99 11-20 
 
 5 
 
 
 8s 
 
 11.43 11.66 11.91 12.16 12.43 
 
 12.71 13.00 13.30 13.62 13.95 
 
 4 
 
 
 86 
 
 14.30 14.67 15.06 15.46 15,89 
 
 16.35 16.83 17.34 17.89 18-46 
 
 3 
 
 
 87 
 
 19.08 19.74 20.45 21.20 22.02 
 
 22.90 23.86 24,90 26.03 27.27 
 
 2 
 
 
 88 
 
 28.64 30.14 31.82 33.69 35.80 
 
 38.19 40.92 44.07 47.74 52.08 
 
 I 
 
 
 89 
 
 57.29 63.66 71.62 81.85 95.49 
 
 114.6 143.2 191.0 286.5 5730 
 
 0° 
 
 
 
 i°.o ".9 °.8 °.7 °.6 
 
 ".5 °.4 ^.3 °.2 °.I 
 
 Deg, 
 
 Interpola, 
 for h'dths 
 
 (41) 
 
 4 PL. NAT. COT. 
 
LOG. SIN. 4 PL. 
 
 LOGARITHMS OF SINES AND COSINES 
 
 TO 
 
 FOUR PLACES. 
 
 Note. For log. cos. use right-hand column of degrees and lower line of tenths. 
 
 Deg. 
 
 °.o ".I •'.7. \z °.4 
 
 °.S °-6 °.7 °.8 °.9 
 
 
 Interpola. 
 for h'dths 
 
 0° 
 
 -00 3.24193.54293.71903.8439 
 
 3.9408 5.0200 5.0870 5.1450 5.1961 
 
 89 
 
 35 25 
 
 I 
 
 2.2419 2.2832 2.3210 2.3558 2.3880 
 
 2.4179 5.4459 5.4723 5.49^1 5.5206 
 
 88 
 
 4 3 
 
 2 
 
 2.5428 2.5640 2.5842 2.6035 26220 
 
 2.6397 2.6567 2.6731 2.6889 2.7041 
 
 87 
 
 7 5 
 
 3 
 
 2.7188 2.7330 2.7468 2.7602 2.7731 
 
 2.7857 2.7979 2.8098 2.8213 2.8326 
 
 86 
 
 II 8 
 
 4 
 
 2.8436 2.8543 2.8647 2.8749 2.8849 
 
 2.8946 2.9042 2.9135 2.92265.9315 
 
 85 
 
 14 10 
 
 S 
 
 5.9403 5.9489 5.9573 2.9655 29736 
 
 5.9816 2.9894 5.9970 7.0046 7.01 20 
 
 84 
 
 18 13 
 
 6 
 
 1.0192 1.0264 '•0334 1-0403 1.0472 
 
 1 -0539 7.0605 7.0670 7.0734 7.0797 
 
 83 
 
 21 15 
 
 7 
 
 7.0859 T.0920 7.0981 7.10407.1099 
 
 1.1157 1.12147.1271 1.13267.1381 
 
 82 
 
 25 18 
 
 8 
 
 7.1436 7.1489 7.1542 7.1594 7.1646 
 
 1^.16971.17471.17977.18477.1895 
 
 81 
 
 28 20 
 
 9 
 
 1. 1943 1.1991 1.2038 1.2085 1^-2131 
 
 1. 2176 1.2221 1.2266 1.2310 1.2353 
 
 80° 
 
 32 23 
 
 10° 
 
 7.2397 7.2439 7.2482 7.2524 7.2565 
 
 7.2606 7.2647 7.2687 7-2727 7.2767 
 
 79 
 
 21 18 
 
 II 
 
 2806 2845 2883 2921 2959 
 
 2997 3034 3070 3107 3143 
 
 78 
 
 2 2 
 
 12 
 
 3179 3214 3250 3284 3319 
 
 3353 3387 3421 3455 3488 
 
 77 
 
 4 4 
 
 '3 
 
 3521 3554 3586 3618 3650 
 
 3682 3713 3745 3775 3806 
 
 76 
 
 6 5 
 
 "4 
 
 3837 3867 3897 3927 3957 
 
 3986 4015 -4044 4073 4102 
 
 75 
 
 8 7 
 
 '5 
 
 7.4130 7.4158 7.4186 7.4214 7.4242 
 
 7.4269 7.4296 7.4323 7.4350 7.4377 
 
 74 
 
 II 9 
 
 i6 
 
 4403 4430 4456 4482 4508 
 
 4533 4559 4584 4609 4634 
 
 73 
 
 13 II 
 
 '7 
 
 4659 4684 4709 4733 4757 
 
 4781 4805 4829 4853 4876 
 
 72 
 
 15 13 
 
 i8 
 
 4900 4923 4946 4969 4992 
 
 5015 5037 5060 5082 5104 
 
 71 
 
 17 14 
 
 19 
 
 5126 5148 5170 5192 5213 
 
 5235 5256 5278 5299 5320 
 
 70° 
 
 19 16 
 
 20° 
 
 I-S34I i'.536i 7.53827.54027.5423 
 
 7.5443 7.5463 7.5484 7.5504 7.5523 
 
 69 
 
 IS 13 
 
 21 
 
 5543 5563 5583 5602 5621 
 
 5641 5660 5679 5698 5717 
 
 68 
 
 2 1 
 
 22 
 
 5736 5754 5773 5792 5810 
 
 5828 5847 5865 5883 5901 
 
 67 
 
 3 3 
 
 23 
 
 5919 5937 5954 5972 599o 
 
 6007 6024 6042 6059 6076 
 
 66 
 
 5 4 
 
 24 
 
 6093 6110 6127 6144 6161 
 
 6177 6194 6210 6227 6243 
 
 65 
 
 6 5 
 
 2S 
 
 7.6259 7.6276 7.6292 7.6308 7.6324 
 
 7.6340 7.6356 7.6371 7.6387 7.6403 
 
 64 
 
 8 7 
 
 26 
 
 6418 6434 6449 6465 6480 
 
 6495 6510 6526 6541 6556 
 
 63 
 
 9 8 
 
 27 
 
 6570 6585 6600 6615 6629 
 
 6644 6659 6673 6687 6702 
 
 62 
 
 II 9 
 
 28 
 
 6716 6730 6744 6759 6773 
 
 6787 6801 6814 6828 6842 
 
 61 
 
 12 10 
 
 29 
 
 6856 6869 6883 6896 6910 
 
 6923 6937 6950 6963 6977 
 
 60° 
 
 14 12 
 
 30° 
 
 7.6990 7.7003 7.7016 7.7029 7.7042 
 
 7.7055 7.7068 7.7080 7.7093 7.7106 
 
 59 
 
 11 9 
 
 31 
 
 7118 7131 7144 7156 7168 
 
 7181 7193 7205 7218 7230 
 
 58 
 
 I I 
 
 32 
 
 7242 7254 7266 7278 7290 
 
 7302 7314 7326 7338 7349 
 
 57 
 
 2 2 
 
 33 
 
 7361 7373 7384 7396 7407 
 
 7419 7430 7442 7453 7464 
 
 56 
 
 3 3 
 
 34 
 
 7476 7487 7498 7509 7520 
 
 7S3I 7542 7553 7564 7575 
 
 55 
 
 4 4 
 
 35 
 
 7.7586 7.7597 7.7607 7.761 8 7.7629 
 
 7.76407.76507.7661 7.7671 7.7682 
 
 54 
 
 6 5 
 
 36 
 
 7692 7703 7713 7723 7734 
 
 7744 7754 7764 7774 7785 
 
 S3 
 
 7 5 
 
 37 
 
 7795 7805 7815 7825 7835 
 
 7844 7854 7864 7874 7884 
 
 52 
 
 8 6 
 
 38 
 
 7893 7903 7913 7922 7932 
 
 7941 7951 7960 7970 7979 
 
 S> 
 
 9 7 
 
 39 
 
 7989 7998 8007 8017 8026 
 
 8035 8044 8053 8063 8072 
 
 50° 
 
 10 8 
 
 
 i°.o °.9 °.8 °.7 °.6 
 
 °.5 °.4 °.3 °.2 =.i 
 
 Deg. 
 
 Interpola. 
 for h'dth! 
 
 LOG. COS. 4 PL. 
 
 (42) 
 
LOGARITHMS OF SINES AND COSINtS. 
 
 4 PL. LOG. SIN. 
 
 Deg. 
 
 °.o °.i °.2 °.3 °.4 
 
 ".5 °.6 °.7 °-8 °.9 
 
 
 Interpola. 
 tables. 
 
 40^ 
 
 T.8081 T.8090T.8099T.8108T.8117 
 
 7.8125 T.8134 7.8143 7.8152 7.8161 
 
 49 
 
 9 8 7 
 
 41 
 
 8169 8178 8187 8195 8204 
 
 8213 8221 8230 8238 8247 
 
 48 
 
 1 1 I 
 
 42 
 
 8255 8264 8272 8280 8289 
 
 8297 8305 8313 8322 8330 
 
 47 
 
 2 2 1 
 
 43 
 
 8338 8346 8354 8362 8370 
 
 8378 8386 8394 8402 8410 
 
 46 
 
 322 
 
 44 
 
 8418 8426 8433 8441 8449 
 
 8457 8464 8472 8480 8487 
 
 45 
 
 4 3 3 
 
 45 
 
 7.8495 1-8502 T.8510 1.8517 1.8525 
 
 7.8532 7.8540 7.8547 7.8555 7.8562 
 
 44 
 
 5 4 4 
 
 46 
 
 8569 8577 8584 8591 8598 
 
 8606 8613 8620 8627 8634 
 
 43 
 
 5 5 4 
 
 47 
 
 8641 8648 8655 8662 8669 
 
 8676 8683 8690 8697 8704 
 
 43 
 
 665 
 
 48 
 
 871 I 8718 8724 8731 8738 
 
 8745 8751 8758 8765 8771 
 
 41 
 
 766 
 
 49 
 
 8778 8784 8791 8797 8804 
 
 8810 8817 8823 8830 8836 
 
 40° 
 
 876 
 
 50° 
 
 T.8843 T.8849 1-8855 'f-8862 7.8868 
 
 7,8874 7.8880 7.8887 7.8893 7-8899 
 
 39 
 
 6 5 4 
 
 SI 
 
 8905 8911 8917 8923 8929 
 
 8935 8941 8947 8953 8959 
 
 38 
 
 1 I 
 
 52 
 
 8965 8971 8977 8983 8989 
 
 8995 9000 9006 9012 9018 
 
 37 
 
 1 I 1 
 
 53 
 
 9023 9029 9035 9041 9046 
 
 9052 9057 9063 9069 9074 
 
 36 
 
 2 2 I 
 
 54 
 
 go8o 9085 9091 9096 9101 
 
 9107 9112 9118 9123 9128 
 
 35 
 
 .222 
 
 55 
 
 7.9134 7.9139 7.9144 7.9149 7.915s 
 
 7.91607.9165 7.9170 7.9175 7.9181 
 
 34 
 
 332 
 
 56 
 
 9186 9191 9196 9201 9206 
 
 9211 9216 9221 9226 9231 
 
 33 
 
 432 
 
 57 
 
 9236 9241 9246 9251 925s 
 
 9260 9265 9270 9275 9279 
 
 32 
 
 4 4 3 
 
 58 
 
 9284 9289 9294 9298 9303 
 
 9308 9312 9317 9322 9326 
 
 31 
 
 5 4 3 
 
 59 
 
 9331 9335 9340 9344 9349 
 
 9353 9358 9362 9367 937' 
 
 30° 
 
 5 5 4 
 
 60° 
 
 I 9375 7.9380 7.9384 7.9388 7.9393 
 
 7-9397 7.9401 7.9406 7.9410 7.9414 
 
 29 
 
 4 3 2 
 
 6i 
 
 9418 9422 9427 9431 9435 
 
 9439 9443 9447 945' 9455 
 
 28 
 
 000 
 
 62 
 
 9459 9463 9467 9471 9475 
 
 9479 9483 9487 9491 9495 
 
 27 
 
 1 I 
 
 63 
 
 9499 9503 9506 9510 95 '4 
 
 9518 9522 9525 9529 9533 
 
 26 
 
 1 I 1 
 
 64 
 
 9537 9540 9544 9548 955' 
 
 9555 9558 9562 9566 9569 
 
 25 
 
 2 1 I 
 
 65 
 
 i'-95 73 I -95 76 1-9580 7.9583 7.9587 
 
 7.95907.95947.9597 7.9601 7.9604 
 
 24 
 
 221 
 
 66 
 
 9607 9611 9614 9617 9621 
 
 9624 9627 9631 9634 9637 
 
 23 
 
 2 2 1 
 
 67 
 
 9640 9643 9647 9650 9653 
 
 9656 9659 9662 9666 9669 
 
 22 
 
 3 2 1 
 
 68 
 
 9672 9675 9678 9681 9684 
 
 9687 9690 9693 9696 9699 
 
 21 
 
 322 
 
 69 
 
 9702 9704 9707 9710 9713 
 
 9716 9719 9722 9724 9727 
 
 20° 
 
 432 
 
 70° 
 
 7.9730 7.9733 "'-9735 T.9738 i'.974i 
 
 7.9743 7.9746 7.9749 7.9751 7.9754 
 
 19 
 
 3 2 1 
 
 71 
 
 9757 9759 9762 9764 97^7 
 
 9770 9772 9775 9777 9780 
 
 18 
 
 000 
 
 72 
 
 9782 9785 9787 9789 9792 
 
 9794 9797 9799 9801 9804 
 
 17 
 
 100 
 
 73 
 
 9806 9808 9811 9813 9815 
 
 9817 9820 9822 9824 9826 
 
 16 
 
 I 1 
 
 74 
 
 9828 9831 9833 9835 9837 
 
 9839 9841 9843 9845 9847 
 
 15 
 
 1 1 
 
 75 
 
 7.9849 7.9851 7.9853 7.9855 7.9857 
 
 7.9859 7.9861 7.9863 7.9865 7.9867 
 
 14 
 
 2 1 1 
 
 76 
 
 9869 9871 9873 9875 9876 
 
 9878 9880 9882 9884 9885 
 
 13 
 
 211 
 
 77 
 
 9887 9889 9891 9892 9894 
 
 9896 9897 9899 9901 9902 
 
 12 
 
 2 1 I 
 
 78 
 
 9904 9906 9907 9909 9910 
 
 9912 9913 9915 9916 9918 
 
 11 
 
 2 2 1 
 
 79 
 
 9919 9921 9922 9924 9925 
 
 9927 9928 9929 9931 9932 
 
 10° 
 
 3 2 I 
 
 80° 
 
 7.9934 7.9935 7-9936 1-9937 1-9939 
 
 7.9940 7.9941 7.9943 7.9944 7.9945 
 
 9 
 
 2 1 
 
 81 
 
 9946 9947 9949 9950 9951 
 
 9952 9953 9954 9955 9956 
 
 8 
 
 
 
 82 
 
 9958 9959 9960 9961 9962 
 
 9963 9964 9965 9966 9967 
 
 7 
 
 
 
 83 
 
 9968 9968 9969 9970 9971 
 
 9972 9973 9974 9975 9975 
 
 6 
 
 1 
 
 84 
 
 9976 9977 9978 9978 9979 
 
 9980 9981 9981 9982 9983 
 
 5 
 
 I 
 
 85 
 
 7.9983 7.9984 7.9985 7.9985 7.9986 
 
 7.9987 7.9987 7.9988 7.9988 7.9989 
 
 4 
 
 I I 
 
 86 
 
 9989 9990 9990 9991 9991 
 
 9992 9992 9993 9993 9994 
 
 3 
 
 I 1 
 
 87 
 
 9994 9994 9995 9995 9996 
 
 9996 9996 9996 9997 9997 
 
 2 
 
 1 1 
 
 88 ■ 
 
 9997 9998 9998 9998 9998 
 
 9999 9999 9999 9999 9999 
 
 I 
 
 2 I 
 
 89 
 
 9999 9999 zero zero zero 
 
 zero zero zero zero zero 
 
 0° 
 
 2 I 
 
 
 i°.o °.9 °.8 °.^ °.6 
 
 °.5 °.4 ".3 "-2 ".I 
 
 Deg. 
 
 Interpola. 
 for h'dths 
 
 (43) 
 
 4 PL. LOG. COS. 
 
LOG. TAN. 4 PL. 
 
 LOGARITHMS OF TANGENTS AND COTANGENTS 
 
 TO 
 
 FOUR PLAGES. 
 
 Note. For log. cot. use right-hand column of degrees and lower line of tenth 
 
 Deg. 
 
 °.o ".I °.2 °.3 °.4 
 
 °.5 °-6 °.7 °-8 °.9 
 
 
 Interpola. 
 For h'dths 
 
 0° 
 
 -00 3.2419 3.5429 3.7190 3.8439 
 
 3.9409 2.0200 2.0870 2.1450 2.1962 
 
 89 
 
 35 27 
 
 I 
 
 2.2419 2.2833 2.3211 2.3559 2.3881 
 
 2.4181 2.4461 2.4725 2.49732.5208 
 
 88 
 
 4 3 
 
 2 
 
 2.5431 2.5643 2.5845 2.6038 2.6223 
 
 2.6401 2.6571 2.67362,68942.7046 
 
 87 
 
 7 5 
 
 3 
 
 2.7194 2.7337 2.7475 2.7609 2.7739 
 
 2.7865 2.7988 2.8107 2.8223 2.8336 
 
 86 
 
 II 8 
 
 4 
 
 ,2.8446 2.8554 2.8659 2.8762 2.8862 
 
 2.8960 2.9056 2.9150 2.9241 2.9331 
 
 85 
 
 14 11 
 
 5 
 
 2.9420 2.9506 2.9591 2.96742.9756 
 
 2.9836 2.9915 2.9992 7.0068 7.0143 
 
 84 
 
 18 14 
 
 6 
 
 1 .02 1 6 1 .0289 1 .0360 1 .0430 1 .0499 
 
 £.0567 1.0633 1.06997.07647.0828 
 
 83 
 
 21 16 
 
 7 
 
 T.0891 7.09547.10157.10761.1135 
 
 1.11941.12521.13107.13677.1423 
 
 82 
 
 25 19 
 
 « 8 
 
 7.1478 7.1533 7.1587 7.1640 7.1693 
 
 1. 1745 1.1797 1.1848 1.18987.1948 
 
 81 
 
 28 22 
 
 9 
 
 1. 1997 1.2046 1.2094 1. 2142 1. 2189 
 
 1 .2236 1 .2282 7.2328 7.2374 7.2419 
 
 80° 
 
 32 24 
 
 10° 
 
 7.24637.25077.2551 7.25947.2637 
 
 7.2680 7.2722 7.2764 7.2805 7.2846 
 
 79 
 
 25 23 
 
 II 
 
 2887 2927 2967 3006 3046 
 
 3085 3123 3162 3200 3237 
 
 78 
 
 3 2 
 
 12 
 
 327s 3312 3349 3385 3422 
 
 3458 3493 3529 3564 3599 
 
 77 
 
 5 5 
 
 "3 
 
 3634 3668 3702 3736 3770 
 
 3804 3837 3870 3903 3935 
 
 76 
 
 8 7 
 
 H 
 
 3968 4000 4032 4064 4095 
 
 4127 4*58 4189 4220 4250 
 
 75 
 
 10 9 
 
 IS 
 
 7.4281 7.431 1 7.4341 1.4371 7.4400 
 
 7.4430 7.4459 7.4488 7.4517 7.4546 
 
 74 
 
 13 12 
 
 i6 
 
 4575 4603 4632 4660 4688 
 
 47 '6 4744 477' 4799 4826 
 
 73 
 
 «s 14 
 
 17 
 
 4853 4880 4907 4934 4961 
 
 4987 5014 5040 5066 5092 
 
 72 
 
 18 16 
 
 i8 
 
 5118 5143 5169 5195 5220 
 
 5245 527° 5295 5320 5345 
 
 71 
 
 20 18 
 
 19 
 
 5370 5394 5419 5443 5467 
 
 5491 5516 5539 5563 5587 
 
 70° 
 
 23 21 
 
 20° 
 
 7.5611 7.56347.56587.5681 7.5704 
 
 ^•5727 7.5750 1-5773 7.5796 7.5819 
 
 69 
 
 21 19 
 
 21 
 
 5842 5864 5887 5909 5932 
 
 5954 5976 5998 6020 6042 
 
 68 
 
 2 2 
 
 22 
 
 6064 6086 6108 6129 6151 
 
 6172 6194 6215 6236 6257 
 
 67 
 
 4 4 
 
 23 
 
 6279 6300 6321 6341 6362 
 
 6383 6404 6424 6445 6465 
 
 66 
 
 6 6 
 
 24 
 
 6486 6506 6527 6547 6567 
 
 6587 6607 6627 6647 6667 
 
 65 
 
 8 8 
 
 25 
 
 7.6687 7.6706 7.6726 7.6746 7.6765 
 
 7.6785 7.6804 7.6824 7.6843 7.6863 
 
 64 
 
 II 10 
 
 26 
 
 6882 6901 6920 6939 6958 
 
 6977 6996 7015 7034 7053 
 
 63 
 
 13 11 
 
 27 
 
 7072 7090 7109 7128 7146 
 
 7165 7183 7202 7220 7238 
 
 62 
 
 15 13 
 
 28 
 
 7257 727s 7293 731 1 7330 
 
 7348 7366 7384 7402 7420 
 
 61 
 
 17 15 
 
 29 
 
 7438 7455 7473 7491 7509 
 
 7526 7544 7562 7579 7597 
 
 60° 
 
 19 17 
 
 30° 
 
 7.7614 7.7632 7.7649 7.7667 7.7684 
 
 7.7701 7.7719 7.7736 7.7753 7.7771 
 
 59 
 
 17 15 
 
 3> 
 
 7788 7805 7822 7839 7856 
 
 7873 7890 7907 7924 7941 
 
 58 
 
 2 2 
 
 32 
 
 7958 7975 7992 8008 8025 
 
 8042 8059 8075 8092 8109 
 
 57 
 
 3 3 
 
 33 
 
 8125 8142 8158 8175 8191 
 
 8208 8224 8241 8257 8274 
 
 56 
 
 5 5 
 
 34 
 
 8290 8306 8323 8339 8355 
 
 8371 8388 8404 8420 8436 
 
 55 
 
 7 6 
 
 35 
 
 7.8452 7.8468 7.8484 7.8501 7.85 1 7 
 
 7.8533 7.8549 7.8565 7.8581 7.8597 
 
 54 
 
 9 8 
 
 36 
 
 8613 8629 8644 8660 8676 
 
 8692 8708 8724 8740 8755 
 
 53 
 
 10 9 
 
 37 
 
 8771 8787 8803 8818 8834 
 
 8850 8865 8881 8897 8912 
 
 52 
 
 12 II 
 
 38 
 
 8928 8944 8959 8975 8990 
 
 9006 9022 9037 9053 9068 
 
 5' 
 
 14 12 
 
 39 
 
 9084 9099 9115 9130 9146 
 
 9161 9176 9192 9207 9223 
 
 50° 
 
 15 14 
 
 
 i°.o ".9 °.8 °.7 ".6 
 
 ".5 °.4 ".3 ■'■2 ''.I 
 
 Deg. 
 
 Interpola, 
 for h'dths 
 
 LOG. COT. 4 PL. 
 
 (44) 
 
LOGARITHMS OF TANGENTS AND COTANGENTS. 
 
 4 PL. LOG. TAN. 
 
 Deg. 
 
 °.0 °.I °.2 ".3 °.4 
 
 .5 .0 .7 -8 -9 
 
 
 Interpola. 
 for hdths 
 
 40° 
 
 T.9238 T.9254 T.9269 T.9284 T.9300 
 
 T.931S 1.9330 T.9346T.9361 T.9376 
 
 49 
 
 15 16 
 
 41 
 
 1.9392 1.9407 1.9422 T.9438 7.9453 
 
 1.9468 1.9483 1.9499 1. 95 14 1-9529 
 
 48 
 
 2 2 
 
 42 
 
 1.9544 1.9560 1.9575 I-9S90 1-9605 
 
 1.9621 1.9636 1.9651 1.9666 1.9681 
 
 47 
 
 3 3 
 
 43 
 
 1.9697 1.9712 1.9727 1.9742 1.9757 
 
 T.9772 T.9788 T.9803 T.9818 T.9833 
 
 46 
 
 5 5 
 
 44 
 
 1.9848 1.9864 1.9879 1.9894 1.9909 
 
 r.9924 T.9939 T.9955 1-9970 ^-9985 
 
 45 
 
 6 6 
 
 45 
 
 0.0000 0.0015 0-0030 0.0045 0.0061 
 
 0.00760.0091 0.01060.0121 0.0136 
 
 44 
 
 8 8 
 
 46 
 
 0152 0167 0182 0197 0212 
 
 0228 0243 0258 0273 0288 
 
 43 
 
 9 10 
 
 47 
 
 0303 0319 0334 0349 0364 
 
 0379 0395 0410 0425 0440 
 
 42 
 
 11 II 
 
 48 
 
 0456 0471 0486 0501 0517 
 
 0532 0547 0562 0578 0593, 
 
 41 
 
 12 13 
 
 49 ■ 
 
 0608 0624 0639 0654 0670 
 
 0685 0700 0716 0731 0746 
 
 40° 
 
 14 14 
 
 50° 
 
 0.0762 0.0777 O-0793 0.0808 0.0824 
 
 0.0839 0.0854 0.0870 0.0885 0.0901 
 
 39 
 
 17 18 
 
 S« 
 
 0916 0932 0947 0963 0978 
 
 0994 1010 1025 1041 1056 
 
 38 
 
 2 2 
 
 52 
 
 1072 1088 1 103 1 1 19 1 135 
 
 1150 1166 1182 1197 1213 
 
 37 
 
 3 4 
 
 S3 
 
 1229 1245 1260 1276 1292 
 
 1308 1324 1340 1356 1371 
 
 36 
 
 5 5 
 
 S4 
 
 1387 1403 1419 1435 1451 
 
 1467 1483 1499 1516 1532 
 
 35 
 
 7 7 
 
 SS 
 
 0.1548 0.1564 0.1580 0.1596 0.1612 
 
 0.1629 0.1645 0.1661 0.1677 0.1694 
 
 34 
 
 9 9 
 
 56 
 
 1710 1726 1743 1759 1776 
 
 1792 1809 1825 1842 1858 
 
 33 
 
 lo 11 
 
 57 
 
 1875 1891 1908 1925 1941 
 
 1958 1975 '992 2008 2025 
 
 32 
 
 12 13 
 
 S» 
 
 2042 2059 2076 2093 21 10 
 
 2127 2144 2161 2178 2195 
 
 31 
 
 14 14 
 
 59 
 
 2212 2229 2247 2264 2281 
 
 2299 2316 2333 2351 2368 
 
 30° 
 
 15 16 
 
 60° 
 
 0.2386 0.2403 0.2421 0.2438 0.2456 
 
 0.2474 0.2491 0.2509 0.2527 0.2545 
 
 29 
 
 21 23 
 
 61 
 
 2562 2580 2598 2616 2634 
 
 2652 2670 2689 2707 2725 
 
 28 
 
 2 2 
 
 62 
 
 2743 2762 2780 2798 2817 
 
 2835 2854 2872 2891 2910 
 
 27 
 
 4 5 
 
 63 
 
 Z928 2947 2966 2985 3004 
 
 3023 3042 3061 3080 3099 
 
 26 
 
 6 7 
 
 64 
 
 3118 3137 3157 3176 3196 
 
 3215 3235 3254 3274 3294 
 
 25 
 
 8 9 
 
 65 
 
 0.3313 0.3333 0.3353 0.3373 0.3393 
 
 0.3413 0.3433 0.3453 0.3473 0.3494 
 
 24 
 
 11 12 
 
 66 
 
 3514 3535 3555 357^ 3596 
 
 3617 3638 3659 3679 3700 
 
 23 
 
 13 14 
 
 67 
 
 3721 3743 3764 3785 3806 
 
 3828 3849 3871 3892 3914 
 
 22 
 
 15 16 
 
 68 
 
 3936 3958 3980 4002 4024 
 
 4046 4068 4091 4113 4136 
 
 21 
 
 17 18 
 
 69 
 
 4158 4181 4204 4227 4250 
 
 4273 4296 4319 4342 4366 
 
 20° 
 
 19 21 
 
 70° 
 
 0.4389 0.4413 0.4437 0.4461 0.4484 
 
 0.4509 0.4533 0.4557 0.4581 0.4606 
 
 19 
 
 25 27 
 
 71 
 
 4630 4655 4680 4705 4730 
 
 4755 4780 4805 4831 4857 
 
 18 
 
 3 3 
 
 72 
 
 4882 4908 4934 4960 4986 
 
 5013 5039 5066 5093 5120 
 
 17 
 
 5 5 
 
 73 
 
 S'47 5174 5201 5229 5256 
 
 5284 5312 5340 5368 5397 
 
 16 
 
 8 8 
 
 74 
 
 5425 5454 5483 55 "2 5541 
 
 5570 5600 5629 5659 5689 
 
 15 
 
 10 11 
 
 75 
 
 0.5719 0.5750 0.5780 0.581 1 0.5842 
 
 0.5873 0.5905 0.5936 0.5968 0.6000 
 
 14 
 
 13 14 
 
 76 
 
 6032 6065 6097 6130 6163 
 
 6196 6230 6264 6298 6332 
 
 *3 
 
 15 i6 
 
 77 
 
 6366 6401 6436 6471 6507 
 
 6542 6578 6615 6651 6688 
 
 12 
 
 18 19 
 
 78 
 
 6725 6763 6800 6838 6877 
 
 6915 6954 6994 7033 7073 
 
 11 
 
 20 22 
 
 79 
 
 7113 7154 7195 7236 7278 
 
 7320 7363 7406 7449 7493 
 
 10° 
 
 23 24 
 
 80° 
 
 0-7537 0.7581 0.7626 0.7672 0.7718 
 
 0.7764 0.781 1 0.7858 0.7906 0.7954 
 
 9 
 
 35 45 
 
 81 
 
 0.8003 0.8052 0.8102 0.8152 0.8203 
 
 0.8255 0.83070.83600.84130.8467 
 
 8 
 
 4 5 
 
 82 
 
 0.8522 0.8577 0.8633 0.8690 0.8748 
 
 0.8806 0.8865 0.8924 0.8985 0.9046 
 
 7 
 
 7 9 
 
 83 
 
 0.91090.91720.92360.9301 0.9367 
 
 0.9433 0.9501 0.9570 0.9640 0.971 1 
 
 6 
 
 11 14 
 
 84 
 
 0.97840.9857 0.9932 1.0008 1.0085 
 
 1.0164 1.0244 1.0326 1.0409 1.0494 
 
 5 
 
 14 18 
 
 85 
 
 1.0580 1.6669 1-0759 1.0850 1.0944 
 
 1.1040 1.1138 1.1238 1.1341 1.1446 
 
 4 
 
 18 23 
 
 86 
 
 1.1554 1.1664 I-I777 1-1893 I-20I2 
 
 1.2135 1.2261 1.2391 1.2525 1.2663 
 
 3 
 
 21 27 
 
 87 
 
 1.2806 1.2954 1.3106 1.3264 1.3429 
 
 1-3599 1-3777 1-3962 1.4155 1-4357 
 
 2 
 
 25 32 
 
 88 
 
 1.4569 1.4792 1.5027 1.5275 1.5539 
 
 1.5819 1.6119 1.6441 1.6789 1.7167 
 
 1 
 
 28 36 
 
 89 
 
 1.7581 1.8038 1.8550 1.9130 1.9800 
 
 2.0591 2.1561 2.28102.4571 2.7581 
 
 0° 
 
 32 41 
 
 
 i°.o °.9 °.8 °.7 °.6 
 
 -.5 °.4 "-3 '-2 ".1 
 
 Deg. 
 
 Interpola. 
 for h'dths 
 
 (45) 
 
 4 PL. LOG. COT. 
 
LOG SIN, etc. 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 TO 
 
 FIVE PLACES. 
 
 Note. The table gives the log of the natural value of the function, and hence the char- 
 acteristic is negative when that value is fractional. The common practice of adding 10. to 
 avoid the negative characteristic is not recommended. 
 
 0° 
 
 log cos 
 
 
 0° 
 
 log COS 
 
 
 o'-i6' 
 
 .i7'-28' 
 
 29'-36' 
 
 37'-43' 
 
 0.00 000 
 
 T.99 999 
 1.99998 
 1.99997 
 
 44'-6o' 
 
 32'-43' 
 24'-3i' 
 i7'-23' 
 
 44'-49' 
 5o'-54' 
 
 S5'-59' 
 60' 
 
 1.99 996 
 
 1-99 995 
 1.99994 
 
 1-99 993 
 
 Ii'-i6' 
 6'-io' 
 
 I'-S' 
 0' 
 
 
 log sin 
 
 89° 
 
 
 log sin * 
 
 89° 
 
 
 
 0° 
 
 
 
 
 
 0° 
 
 
 
 r 
 
 log sin 
 
 log tan 
 
 log cot 
 
 
 / 
 
 log sin 
 
 log tan 
 
 log oot 
 
 
 0' 
 
 00" 
 
 00 
 
 00 
 
 60' 
 
 30' 
 
 3-94 084 
 
 3.94086 
 
 2.05 914 
 
 30' 
 
 I 
 
 4-46 373 
 
 4-46 373 
 
 3-53 627 
 
 59 
 
 31 
 
 95508 
 
 95510 
 
 04490 
 
 29 
 
 2 
 
 4.76476 
 
 4.76476 
 
 3-23 524 
 
 58 
 
 32 
 
 96887 
 
 96889 
 
 03 III 
 
 28 
 
 3 
 
 494085 
 
 4-94 085 
 
 3-05 915 
 
 57 
 
 33 
 
 98223 
 
 - 98 225 
 
 01775 
 
 27 
 
 4 
 
 3.06 579 
 
 3.06 579 
 
 2.93 421 
 
 56 
 
 34 
 
 3.99 520 
 
 3-99 522 
 
 2.00478 
 
 26 
 
 s 
 
 3.16 270 
 
 3.16270 
 
 2.83 730 
 
 55 
 
 35 
 
 2.00 779 
 
 2.00 781 
 
 1.99 219 
 
 25 
 
 6 
 
 24188 
 
 24188 
 
 75812 
 
 54 
 
 36 
 
 02002 
 
 02004 
 
 97996 
 
 24 
 
 7 
 
 30882 
 
 30822 
 
 69 118 
 
 53 
 
 37 
 
 03192 
 
 03194 
 
 96806 
 
 23 
 
 8 
 
 36682 
 
 36682 
 
 63318 
 
 52 
 
 38 
 
 04350 
 
 04353 
 
 95647 
 
 22 
 
 9 
 
 41797 
 
 41797 
 
 58203 
 
 51 
 
 39 
 
 05478 
 
 05481 
 
 94519 
 
 21 
 
 10 
 
 3-46 373 
 
 346 373 
 
 2.53 627 
 
 50 
 
 40 
 
 2.06 578 
 
 2.06 581 
 
 1-93419 
 
 20 
 
 II 
 
 50512 
 
 50512 
 
 49488 
 
 49 
 
 41 
 
 07 650 
 
 07653 
 
 92347 
 
 19 
 
 12 
 
 54291 
 
 54291 
 
 45709 
 
 48 
 
 42 
 
 08696 
 
 08 700 
 
 91300 
 
 18 
 
 13 
 
 57767 
 
 57767 
 
 42233 
 
 47 
 
 43 
 
 09718 
 
 09722 
 
 90278 
 
 17 
 
 14 
 
 60985 
 
 60986 
 
 39014 
 
 46 
 
 44 
 
 10 717 
 
 10720 
 
 89280 
 
 16 
 
 15 
 
 3.63 982 
 
 3-63982 
 
 2.36018 
 
 45 
 
 45 
 
 2.11693 
 
 2. 1 1 696 
 
 1.88304 
 
 15 
 
 16 
 
 66784 
 
 66785 
 
 33215 
 
 44 
 
 46 
 
 12647 
 
 12 651 
 
 87349 
 
 14 
 
 17 
 
 69417 
 
 69418 
 
 30582 
 
 43 
 
 47 
 
 13581 
 
 13585 
 
 86415 
 
 13 
 
 18 
 
 71 900 
 
 71900 
 
 28 100 
 
 42 
 
 48 
 
 14495 
 
 14500 
 
 85 500 
 
 12 
 
 19 
 
 74248 
 
 74248 
 
 25 752 
 
 41 
 
 49 
 
 15 391 
 
 15395 
 
 84605 
 
 II 
 
 20 
 
 3-76475 
 
 3.76476 
 
 2.23 524 
 
 40 
 
 50 
 
 i.i6 268 
 
 2.16 273 
 
 1.83 727 
 
 10 
 
 21 
 
 78594 
 
 78595 
 
 21405 
 
 39 
 
 51 
 
 17 128 
 
 17 133 
 
 82867 
 
 9 
 
 22 
 
 80615 
 
 80615 
 
 19385 
 
 38 
 
 52 
 
 17971 
 
 17976 
 
 82024 
 
 8 
 
 23 
 
 82545 
 
 82546 
 
 17454 
 
 37 
 
 53 
 
 18798 
 
 18804 
 
 81 196 
 
 7 
 
 24 
 
 84393 
 
 84394 
 
 15606 
 
 36 
 
 54 
 
 19 610 
 
 19 616 
 
 80384 
 
 6 
 
 25 
 
 3.86 166 
 
 3.86 167 
 
 2.13833 
 
 35 
 
 55 
 
 2.20 407 
 
 2.20413 
 
 1-79587 
 
 5 
 
 26 
 
 87870 
 
 87871 
 
 12 129 
 
 34 
 
 56 
 
 21 189 
 
 21 195 
 
 78805 
 
 4 
 
 'I 
 
 89509 
 
 89510 
 
 10490 
 
 33 
 
 57 
 
 21958 
 
 21 964 
 
 78036 
 
 3 
 
 28 
 
 91088 
 
 91089 
 
 08 91 1 
 
 32 
 
 58 
 
 22 713 
 
 22 720 
 
 77280 
 
 2 
 
 29 
 
 92 612 
 
 92613 
 
 07 387 
 
 31 
 
 59 
 
 23456 
 
 23462 
 
 76538 
 
 I 
 
 30' 
 
 3.94084 
 
 3.94 086 
 
 2.05 914 
 
 30' 
 
 60' 
 
 2.24 186 
 
 2.24 192 
 
 1.75 808 
 
 0' 
 
 
 log cos 
 
 log cot 
 
 log tan 
 
 r 
 
 
 log oos 
 
 log oot 
 
 log tan 
 
 r 
 
 89^ 
 
 (47) 
 
 ftQo LOG SIN, etc. 
 w 89° 
 
LOG SIN, etc. 1° 
 
 
 2° 
 
 
 
 / 
 
 log sin log tan log cot 
 
 log cos 
 
 log sin log tan log cot log cos 
 
 
 
 0' 
 
 2.24186 2.24192 1.75808 
 
 1-99 993 
 
 2.54282 2.54308 7.45692 7.99974 
 
 60' 
 
 
 I 
 
 24903 24910 75090 
 
 99 993 
 
 54642 54669 45331 99973 
 
 59 
 
 
 2 
 
 25 609 25 616 74 384 
 
 99 993 
 
 54 999 55027 44 973 99 973 
 
 58 
 
 
 3 
 
 26304 26312 73688 
 
 99 993 
 
 55 354 55382 44618 99972 
 
 57 
 
 
 4 
 
 26 988 26 996 73 004 
 
 99992 
 
 55705 55 734 44266 99972 
 
 56 
 
 
 5 
 
 2.27661 2.27669 7.72331 
 
 1.99992 
 
 2.56054 2.56083 1.43 917 1.99 971 
 
 55 
 
 
 6 
 
 28324 28332 71668 
 
 99992 
 
 56400 56429 43571 99971 
 
 54 
 
 
 7 
 
 28977 28986 71 014 
 
 99992 
 
 56743 56773 43227 99970 
 
 53 
 
 
 8 
 
 29621 29629 70371 
 
 99992 
 
 57084 57 114 42886 99970 
 
 52 
 
 
 9 
 
 30 255 30 263 69 737 
 
 99991 
 
 57421 57452 42548 99969 
 
 5' 
 
 
 10 
 
 230879 2.30888 1.69112 
 
 7.99 991 
 
 2-57 757 2.57788 7.42212 7.99969 
 
 50 
 
 
 II 
 
 31495 31505 68495 
 
 99991 
 
 58089 58 121 41879 99968 
 
 49 
 
 
 12 
 
 32103 32 112 67888 
 
 99990 
 
 58419 58451 41549 99968 
 
 48 
 
 
 >3 
 
 32702 32 711 67289 
 
 99990 
 
 58 747 58 779 41 221 99 967 
 
 47 
 
 
 14 
 
 33 292 33 302 66 698 
 
 99990 
 
 _ 59 072 59105 40895 99967 
 
 46 
 
 
 'S 
 
 2-33875 2.33886 1.66 114 
 
 1.99990 
 
 2-59 395 2.59428 1.40572 1.99967 
 
 45 
 
 
 i6 
 
 34450 34461 65539 
 
 99989 
 
 59715 59 749 40251 99966 
 
 44 
 
 
 '7 
 
 35 018 35 029 64 971 
 
 99989 
 
 60033 60068 39932 99966 
 
 43 
 
 
 i8 
 
 35578 35590 64410 
 
 99989 
 
 60349 60384 39616 99965 
 
 42 
 
 
 19 
 
 36 131 36143 63857 
 
 99989 
 
 60 662. 60 698 39 302 99 964 
 
 41 
 
 
 20 
 
 2.36678 2.36689 T.63311 
 
 7.99 988 
 
 2.60973 2.61009 7.38991 7.99964 
 
 40 
 
 
 21 
 
 37217 37229 62771 
 
 99988 
 
 61282 61319 38681 99963 
 
 39 
 
 
 22 
 
 37 750 37 762 62 238 
 
 99988 
 
 61 589 61 626 38 374 99 963 
 
 38 
 
 
 23 
 
 38276 38289 61 711 
 
 99987 
 
 61894 61931 38069 99962 
 
 37 
 
 
 24 
 
 38 796 38 809 61 191 
 
 99987 
 
 62 196 62 234 37 766 99 962 
 
 36 
 
 
 25 
 
 2.39310 2.39323 T.60677 
 
 1.99987 
 
 2.62497 2.62535 1-37465 T.99961 
 
 35 
 
 
 26 
 
 39818 39832 60168 
 
 99986 
 
 62795 62834 37166 99961 
 
 34 
 
 
 27 
 
 40 320 40 334 59 666 
 
 99986 
 
 63091 63131 36869 99960 
 
 33 
 
 
 28 
 
 40816 40830 59170 
 
 99 986 
 
 63385 63426 36574 99960 
 
 32 
 
 
 29 
 
 41 307 41 321 58 679 
 
 99985 
 
 63678 63718 36282 2P959 
 
 31 
 
 
 30 
 
 2.41 792 5.41 807 7.58 193 
 
 7.99 985 
 
 2.63968 2.64009 7.35991 7.99959 
 
 30 
 
 
 3' 
 
 42272 42287 57713 
 
 99985 
 
 64256 64298 35702 99958 
 
 . 29 
 
 
 32 
 
 42 746 42 762 57 238 
 
 99984 
 
 64543 64585 35415 99958 
 
 28 
 
 
 3i 
 
 43216 43232 56768 
 
 99984 
 
 64827 64870 35130 99957 
 
 27 
 
 
 34 
 
 43 680 43 696 56 304 
 
 99984 
 
 65110 65154 34846 99 956 
 
 26 
 
 
 35 
 
 2.44139 2.44156 1.55844 
 
 1.99983 
 
 2.65391 2.65435 1.34565 1-99956 
 
 25 
 
 
 36 
 
 44594 44 61 1 55389 
 
 99983 
 
 65670 65715 34285 99955 
 
 24 
 
 
 37 
 
 45044 45061 54 939 
 
 99983 
 
 65947 65993 34007 99955 
 
 23 
 
 
 38 
 
 45489 45507 54 493 
 
 99982 
 
 66223 66269 33731 99 954 
 
 22 
 
 
 39 
 
 45930 45948 54052 
 
 99982 
 
 66497 66543 33457 99954 
 
 21 
 
 
 40 
 
 2.46 366 2.46 385 T.53 615 
 
 7.99 982 
 
 2.66769 2.66816 7.33184 7.99953 
 
 20 
 
 
 4' 
 
 46799 46817 53183 
 
 99981 
 
 67039 67087 32913 99952 
 
 19 
 
 
 42 
 
 47 226 47 245 52 755 
 
 99981 
 
 67308 67356 32644 99952 
 
 18 
 
 
 43 
 
 47 650 47 669 52 331 
 
 99981 
 
 67575 67624 32376 99951 
 
 "7 
 
 
 44 
 
 48069 48089 51 911 
 
 99980 
 
 67841 67890 32110 99951 
 
 16 
 
 
 45 
 
 5.48485 2.48505 7.51495 
 
 1.99980 
 
 2.68 104 2.68 154 7.31 846 7.99 950 
 
 •15 
 
 
 46 
 
 48896 48917 51083 
 
 99 979 
 
 68367 68417 31583 99949 
 
 '4. 
 
 
 47 
 
 49 304 49 325 50 675 
 
 99 979 
 
 68627 68678 31322 99949 
 
 13 
 
 
 48 
 
 49 708 49 729 50 271 
 
 99 979 
 
 68 886 68938 31062 99948 
 
 12 
 
 
 49 
 
 50 108 50 130 49 870 
 
 99978 
 
 69 144 69 196 30 804 99 948 
 
 11 
 
 
 50 
 
 2.50504 2.50527 1.49473 
 
 1.99978 
 
 2.69400 2.69453 7.30547 7.99947 
 
 10 
 
 
 51 
 
 50 897 50 920 49 080 
 
 99 977 
 
 69654 69708 30292 99946 
 
 9 
 
 
 52 
 
 51 287 51 310 48690 
 
 99 977 
 
 69907 69962 30038 99946 
 
 8 
 
 
 53 
 
 51673 51696 48304 
 
 99 977 
 
 70159 70214 29786 99945 
 
 7 
 
 
 54 
 
 52055 52079 47921 
 
 99976 
 
 70409 70465 29535 99944 
 
 6 
 
 
 55 
 
 2.52434 2.52459 1.47541 
 
 1.99976 
 
 2.70658 2.70714 1.29286 1.99944 
 
 5 
 
 
 56 
 
 52810 52835 47165 
 
 99 975 
 
 70905 70962 29038 99943 
 
 4 
 
 
 57 
 
 53 183 53 208 46 792 
 
 99 975 
 
 71 151 71208 28792 99942" 
 
 3 
 
 
 58 
 
 53552 53578 46422 
 
 99 974 
 
 71395 71453 28547 99942 
 
 2 
 
 
 59 
 
 53919 53 945 46055 
 
 99 974 
 
 71638 71697 28303 99941 
 
 I 
 
 
 60' 
 
 2.54282 2.54308 1.45692 
 
 1.99974 
 
 2.71880 2.71940 1.28060 1.99940 
 
 0' 
 
 
 
 log 00s log cot log tan 
 
 log sin 
 
 log cos log cot log tan log sin 
 
 > 
 
 LO 
 8 
 
 G SI 
 6°-8 
 
 N, etc. 88° 
 
 go '-"-' 
 
 (4 
 
 8) Q>;fo 
 
 

 
 3° 
 
 
 
 
 
 40 
 
 10.40 
 
 LOG SIN, etc 
 
 f 
 
 log sia 
 
 log tan 
 
 log cot 
 
 log COS 
 
 log sin 
 
 log tan 
 
 log oof 
 
 log COS 
 
 
 
 
 
 2.71 880 
 
 2.71940 
 
 1.28060 
 
 1,99940 
 
 2.84 358 
 
 2.84 464 
 
 1-15536 
 
 T.99 894 
 
 60 
 
 
 I 
 
 72 120 
 
 72181 
 
 27819 
 
 99940 
 
 84539 
 
 84646 
 
 15354 
 
 99893 
 
 5g 
 
 
 2 
 
 72359 
 
 72420 
 
 27580 
 
 99 939 
 
 84718 
 
 84826 
 
 15174 
 
 99892 
 
 58 
 
 
 .3 
 
 72597 
 
 72659 
 
 27341 
 
 99938 
 
 84897 
 
 85006 
 
 14994 
 
 99891 
 
 57 
 
 
 4 
 
 72834 
 
 72896 
 
 27104 
 
 99938 
 
 85075 
 
 85185 
 
 14815 
 
 99891 
 
 56 
 
 
 5 
 
 2.73069 
 
 2-73 132 
 
 1.26 868 
 
 1-99 937 
 
 2.85 252 
 
 2.85 363 
 
 1-14637 
 
 1 .99 890 
 
 55 
 
 
 6 
 
 73303 
 
 73366 
 
 26634 
 
 99936 
 
 85429 
 
 85540 
 
 14460 
 
 99889 
 
 54 
 
 
 7 
 
 73 535 
 
 73600 
 
 26400 
 
 99936 
 
 85605 
 
 85717 
 
 14283 
 
 99888 
 
 53 
 
 
 8 
 
 73767 
 
 73832 
 
 26168 
 
 99 935 
 
 85780 
 
 ll^V' 
 
 14107 
 
 99887 
 
 52 
 
 
 9 
 
 73 997 
 
 74063 
 
 25937 
 
 99 934 
 
 85955 
 
 86069 
 
 13931 
 
 99886 
 
 51 
 
 
 10 
 
 2.74 226 
 
 2.74 292 
 
 1.25 708 
 
 7.99 934 
 
 2.86 128 
 
 2.86 243 
 
 1-13 757 
 
 r.99 88s 
 
 50 
 
 
 II 
 
 74 454 
 
 74521 
 
 25479 
 
 99 933 
 
 86301 
 
 86417 
 
 13583 
 
 99884 
 
 49 
 
 
 12 
 
 74680 
 
 74748 
 
 25252 
 
 99932 
 
 86474 
 
 86591 
 
 13409 
 
 99883 
 
 48 
 
 
 13 
 
 74906 
 
 74 974 
 
 25026 
 
 99932 
 
 86645 
 
 86763 
 
 13237 
 
 99882 
 
 47 
 
 
 H 
 
 75130 
 
 75199 
 
 24801 
 
 99931 
 
 86816 
 
 8693s 
 
 13065 
 
 99881 
 
 46 
 
 
 15 
 
 2-75 353 
 
 2.75 423 
 
 1.24577 
 
 1.99930 
 
 2.86 987 
 
 2.87 106 
 
 1. 12 894 
 
 r.99 880 
 
 45 
 
 
 i6 
 
 75 575 
 
 75645 
 
 24355 
 
 99929 
 
 87156 
 
 87277 
 
 12 723 
 
 99879 
 
 44 
 
 
 17 
 
 75 795 
 
 75867 
 
 24133 
 
 99929 
 
 87325 
 
 87447 
 
 12553 
 
 99879 
 
 43 
 
 
 18 
 
 76015 
 
 76087 
 
 23913 
 
 99928 
 
 .87 494 
 
 87616 
 
 12384 
 
 99878 
 
 4» 
 
 
 19 
 
 76234 
 
 76306 
 
 23694 
 
 99927 
 
 87661 
 
 87785 
 
 12 215 
 
 99877 
 
 41 
 
 
 20 
 
 2.76451 
 
 2.76 525 
 
 1-23 475 
 
 1.99 926 
 
 2.87 829 
 
 2-87953 
 
 1. 12 047 
 
 T.99 876 
 
 40 
 
 
 21 
 
 76667 
 
 76742 
 
 23258 
 
 99926 
 
 87995 
 
 88120 
 
 II 880 
 
 99875 
 
 39 
 
 
 22 
 
 76883 
 
 76958 
 
 23042 
 
 99925 
 
 88 161 
 
 88287 
 
 11713 
 
 99874 
 
 38 
 
 
 23 
 
 77097 
 
 77173 
 
 22 827 
 
 99924 
 
 88326 
 
 88453 
 
 "547 
 
 99873 
 
 37 
 
 
 24 
 
 77310 
 
 77387 
 
 22 613 
 
 99923 
 
 88490 
 
 88618 
 
 11382 
 
 99872 
 
 36 
 
 
 25 
 
 2.77 522 
 
 2.77 600 
 
 1.22400 
 
 1.99923 
 
 2.88 654 
 
 2.88 783 
 
 I. II 217 
 
 1-99871 
 
 35 
 
 
 26 
 
 77 733 
 
 77 81 1 
 
 22 189 
 
 99922 
 
 88817 
 
 88948 
 
 II 052 
 
 99870 
 
 34 
 
 
 27 
 
 77 943 
 
 78022 
 
 21978 
 
 99921 
 
 88980 
 
 89 in 
 
 10889 
 
 99869 
 
 33 
 
 
 28 
 
 78152 
 
 78232 
 
 21 768 
 
 99 920 
 
 89 142 
 
 89274 
 
 10 726 
 
 99868 
 
 32 
 
 
 29 
 
 78360 
 
 78441 
 
 21559 
 
 99920 
 
 89304 
 
 89437 
 
 , 10563 
 
 99867 
 
 31 
 
 
 30 
 
 2.78 568 
 
 2.78 649 
 
 1.21351 
 
 1-99919 
 
 2.89 464 
 
 2.89 598 
 
 1. 10 402 
 
 T.99 866 
 
 30 
 
 
 31 
 
 78774 
 
 78855 
 
 21 145 
 
 99918 
 
 89625 
 
 89760 
 
 10240 
 
 99865 
 
 29 
 
 
 32 
 
 78 979 
 
 79061 
 
 20939 
 
 99917 
 
 89784 
 
 89920 
 
 10080 
 
 99864 
 
 28 
 
 
 33 
 
 79183 
 
 79 266 
 
 20734 
 
 99917 
 
 89943 
 
 90080 
 
 09 920 
 
 99863 
 
 27 
 
 
 34 
 
 79386 
 
 79470 
 
 20530 
 
 99916 
 
 90 102 
 
 90240 
 
 09 760 
 
 99862 
 
 26 
 
 
 35 
 
 2.79 588 
 
 2.79 673 
 
 1.20 327 
 
 1-99915 
 
 2.90 260 
 
 2.90 399 
 
 1.09 601 
 
 T.99 861 
 
 25 
 
 
 36 
 
 79789 
 
 7987s 
 
 20 125 
 
 99914 
 
 90417 
 
 90557 
 
 09443 
 
 99860 
 
 24 
 
 
 37 
 
 79990 
 
 80076 
 
 19924 
 
 99913 
 
 90574 
 
 90715 
 
 09 285 
 
 99859 
 
 23 
 
 
 38 
 
 80189 
 
 80277 
 
 19723 
 
 99913 
 
 90730 
 
 90872 
 
 09 128 
 
 99858 
 
 22 
 
 
 39 
 
 80388 
 
 80476 
 
 19524 
 
 99912 
 
 90885 
 
 91 029 
 
 08971 
 
 99857 
 
 21 
 
 
 40 
 
 2.80 585 
 
 2.80 674 
 
 1. 19 326 
 
 T-99911 
 
 2.91 040 
 
 2.91 185 
 
 1.08815 
 
 1.99 856 
 
 20 
 
 
 41 
 
 80782 
 
 80872 
 
 19 128 
 
 99910 
 
 91 195 
 
 91340 
 
 08660 
 
 99855 
 
 19 
 
 
 42 
 
 80978 
 
 81068 
 
 18932 
 
 99909 
 
 91349 
 
 9149s 
 
 08 505 
 
 99854 
 
 18 
 
 
 43 
 
 81 173 
 
 81264 
 
 18736 
 
 99909 
 
 91502 
 
 91 650 
 
 08350 
 
 99853 
 
 17 
 
 
 44 
 
 81367 
 
 81459 
 
 18541 
 
 99908 
 
 9165s 
 
 91803 
 
 08197 
 
 99852 
 
 16 
 
 
 45 
 
 2.81 560 
 
 2.81 653 
 
 1.18347 
 
 1-99907 
 
 2.91 807 
 
 2.91 957 
 
 1.08043 
 
 1.99 851 
 
 IS 
 
 
 46 
 
 81752 
 
 81 846 
 
 18 154 
 
 99906 
 
 91959 
 
 92 no 
 
 07 890 
 
 99850 
 
 14 
 
 
 47 
 
 81944 
 
 82038 
 
 17962 
 
 99905 
 
 92 no 
 
 92 262 
 
 07738 
 
 99848 
 
 13 
 
 
 48 
 
 82134 
 
 82230 
 
 17770 
 
 99904 
 
 92261 
 
 92414 
 
 07586 
 
 99847 
 
 12 
 
 
 49 
 
 82324 
 
 82420 
 
 17580 
 
 99904 
 
 92 41 1 
 
 92565 
 
 07435 
 
 99 846 
 
 II 
 
 
 50 
 
 2.82513 
 
 2.82 610 
 
 1-17390 
 
 1.99903 
 
 2.92 561 
 
 2.92 716 
 
 1.07 284 
 
 T.99 845 
 
 10 
 
 
 51 
 
 82 701 
 
 82799 
 
 17 201 
 
 99902 
 
 92 710 
 
 92866 
 
 07134 
 
 99844 
 
 9 
 
 
 52 
 
 82888 
 
 82987 
 
 17013 
 
 95901 
 
 92859 
 
 93016 
 
 06984 
 
 99843 
 
 8 
 
 
 53 
 
 83075 
 
 83175 
 
 16825 
 
 99900 
 
 93007 
 
 93165 
 
 06835 
 
 99842 
 
 7 
 
 
 54 
 
 83261 
 
 83361 
 
 16639 
 
 99 899 , 
 
 93154 
 
 93313 
 
 06687 
 
 99841 
 
 6 
 
 
 55 
 
 2.83 446 
 
 2.83 547 
 
 1-16453 
 
 1.99898 
 
 2.93 301 
 
 2.93 462 
 
 1.06 538 
 
 1 .99 840 
 
 5 
 
 
 56 
 
 .83630 
 
 83732 
 
 16268 
 
 99898 
 
 93448 
 
 93609 
 
 06391 
 
 99839 
 
 4 
 
 
 57 
 
 83813 
 
 83916 
 
 16084 
 
 99897 
 
 93 594 
 
 93756 
 
 06244 
 
 99838 
 
 3 
 
 
 58 
 
 83996 
 
 84 100 
 
 15900 
 
 99896 
 
 93740 
 
 93903 
 
 06097 
 
 99837 
 
 2 
 
 
 59 
 
 84177 
 
 84282 
 
 15718 
 
 99895 
 
 93885 
 
 94049 
 
 05951 
 
 99836 
 
 I 
 
 
 60 
 
 2.84 358 
 
 2.84464 
 
 1-15536 
 
 1.99894 
 
 2.94 030 
 
 2.94 195 
 
 1.05 805 
 
 1 .99 834 
 
 
 
 
 
 log cos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 log oos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 f 
 
 
 
 
 m 
 
 ) 
 
 (4 
 
 9) 
 
 
 86° 
 
 LOG S 
 85 
 
 IN, e 
 °-89° 
 
 tc 
 
LOG SIN, etc. 
 
 6= 
 
 t 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log cos 
 
 log sin . 
 
 log tan 
 
 log oot 
 
 log COS 
 
 
 0' 
 
 2.94030 
 
 2.94 195 
 
 1.05 805 
 
 T.99 834 
 
 i.oi 923 
 
 T.02 162 
 
 1.97838 
 
 T.99 761 
 
 60' 
 
 I 
 
 94174 
 
 94340 
 
 05 660 
 
 99833 
 
 02043 
 
 02283 
 
 97717 
 
 99760 
 
 59 
 
 2 
 
 94317 
 
 94485 
 
 05515 
 
 99832 
 
 02 163 
 
 02404 
 
 97596 
 
 99 759 
 
 58 
 
 3 
 
 94461 
 
 94630 
 
 05370 
 
 99831 
 
 02283 
 
 02525 
 
 97475 
 
 99 757 
 
 57 
 
 4 
 
 94603 
 
 94 773 
 
 05 227 
 
 99830 
 
 02402 
 
 02645 
 
 97 355 
 
 99756 
 
 56 
 
 5 
 
 2.94 746 
 
 2:94917 
 
 1.05 083 
 
 1.99829 
 
 T.02 520 
 
 T.02 766 
 
 1.97 234- 
 
 1-99 755 
 
 55 
 
 6 
 
 94887 
 
 95060 
 
 04940 
 
 99828 
 
 02 639 
 
 02885 
 
 97115 
 
 99 753 
 
 54 
 
 7 
 
 95029 
 
 95202 
 
 04798 
 
 99827 
 
 02757 
 
 03005 
 
 96995 
 
 99752 
 
 53 
 
 8 
 
 95170 
 
 95 344 
 
 04656 
 
 99825 
 
 02874 
 
 03124 
 
 96876 
 
 99751 
 
 52 
 
 9 
 
 95 310 
 
 95486 
 
 04514 
 
 99824 
 
 02992 
 
 03242 
 
 96758 
 
 - 99 749 
 
 51 
 
 10 
 
 2.95 450 
 
 2.95 627 
 
 1-04373 
 
 T.99 823 
 
 T.03 109 
 
 T.03 361 
 
 1.96639 
 
 1.99748 
 
 50 
 
 II 
 
 95589 
 
 95767 
 
 04233 
 
 99822 
 
 03226 
 
 03479 
 
 96521 
 
 99 747 
 
 49 
 
 12 
 
 95728 
 
 95908 
 
 04092 
 
 99821 
 
 03342 
 
 03597 
 
 96403 
 
 99 745 
 
 48 
 
 13 
 
 95867 
 
 96047 
 
 03953 
 
 99 820 
 
 03458 
 
 03714 
 
 96286 
 
 99 744 
 
 47 
 
 14 
 
 96005 
 
 96187 
 
 03813 
 
 99819 
 
 03574 
 
 03832 
 
 96168 
 
 99742 
 
 46 
 
 '5 
 
 2.96 143 
 
 2.96 325 
 
 1.03 675 
 
 199817 
 
 1.03690 
 
 1.03948 
 
 1.96052 
 
 1 .99 741 
 
 45 
 44 
 
 16 
 
 96280 
 
 96464 
 
 03536 
 
 99816 
 
 03805 
 
 04065 
 
 95 935 
 
 99740 
 
 17 
 
 96417 
 
 96602 
 
 03398 
 
 99815 
 
 03920 
 
 04 181 
 
 95819 
 
 99738 
 
 43 
 
 18 
 
 96553 
 
 96739 
 
 03 261 
 
 99814 
 
 04034 
 
 04297 
 
 95703 
 
 99 737 
 
 42 
 
 19 
 
 . 96 689 
 
 96877 
 
 03123 
 
 99813 
 
 04149 
 
 04413 
 
 95587 
 
 99736 
 
 41 
 
 20 
 
 2.96 825 
 
 2.97013 
 
 1.02987 
 
 T.99 812 
 
 T.04 262 
 
 T.04 528 
 
 1-95 472 
 
 i^-99 734 
 
 40 
 
 21 
 
 96960 
 
 97150 
 
 02850 
 
 99810 
 
 04376 
 
 04643 
 
 95 357 
 
 99 733 
 
 39 
 
 22 
 
 97095 
 
 97285 
 
 02715 
 
 99809 
 
 04490 
 
 04758 
 
 95242 
 
 99731 
 
 38 
 
 23 
 
 97229 
 
 97421 
 
 02579 
 
 99808 
 
 04603 
 
 04873 
 
 95127 
 
 99730 
 
 37 
 
 24 
 
 97363 
 
 97556 
 
 02444 
 
 99807 
 
 04715 
 
 04987 
 
 95013 
 
 99728 
 
 36 
 
 25 
 
 2.97 496 
 
 2.97 691 
 
 1.02 309 
 
 1.99806 
 
 1.04828 
 
 1.05 lOI 
 
 1.94899 
 
 1.99 727 
 
 35 
 
 26 
 
 97629 
 
 97825 
 
 02175 
 
 99804 
 
 04940 
 
 05214 
 
 94786 
 
 99726 
 
 34 
 
 ^7 
 
 97762 
 
 97 959 
 
 02041 
 
 99803 
 
 05052 
 
 05328 
 
 94672 
 
 99724 
 
 33 
 
 28 
 
 97894 
 
 98092 
 
 01 908 
 
 99802 
 
 05 164 
 
 05441 
 
 94 559 
 
 99723' 
 
 32 
 
 29 
 
 98026 
 
 98 225 
 
 01775 
 
 99801 
 
 05275 
 
 05553 
 
 94 447 
 
 99721 
 
 31 
 
 30 
 
 2.98 157 
 
 2.98 358 
 
 1. 01 642 
 
 1.99800 
 
 1.05 386 
 
 1 .05 666 
 
 1-94 334 
 
 1 .99 720 
 
 30 
 
 31 
 
 98288 
 
 98490 
 
 01 510 
 
 99798 
 
 05497 
 
 05778 
 
 94222 
 
 99718 
 
 29 
 
 32 
 
 98419 
 
 98622 
 
 01378 
 
 99797 
 
 05 607 
 
 05 890 
 
 94 no 
 
 99717 
 
 28 
 
 33 
 
 98549 
 
 9f753 
 
 01247 
 
 99796 
 
 05717 
 
 06002 
 
 93998 
 
 99716 
 
 27 
 
 34 
 
 98679 
 
 98884 
 
 01 116 
 
 99 795 
 
 05827 
 
 06 113 
 
 93887 
 
 99714 
 
 26 
 
 35 
 
 2.98 808 
 
 2.99015 
 
 1.00985 
 
 1-99 793 
 
 1-05937 
 
 1.06224 
 
 1-93 776 
 
 1-99713 
 
 25 
 
 36 
 
 98937 
 
 99145 
 
 00855 
 
 99792 
 
 06046 
 
 06335 
 
 93665 
 
 99711 
 
 24 
 
 37 
 
 99066 
 
 99275 
 
 00725 
 
 99791 
 
 06155 
 
 06445 
 
 93 555 
 
 99710 
 
 23 
 
 38 
 
 99194 
 
 99405 
 
 00595 
 
 99790 
 
 06 264 
 
 06556 
 
 93 444 
 
 99708 
 
 22 
 
 39 
 
 99322 
 
 99 534 
 
 00466 
 
 99788 
 
 06372 
 
 06666 
 
 93 334 
 
 99707 
 
 21 
 
 40 
 
 2.99 450 
 
 2.99 662 
 
 1.00338 
 
 1.99787 
 
 T.06 481 
 
 T.06 775 
 
 1.93 225 
 
 T.99 705 
 
 20 
 
 41 
 
 2.99 577 
 
 2.99 791 
 
 1. 00 209 
 
 99786 
 
 06589 
 
 06885 
 
 93115 
 
 99704 
 
 19 
 
 42 
 
 2.99 704 
 
 2.99919 
 
 1. 00 081 
 
 99785 
 
 06696 
 
 06994 
 
 93006 
 
 99702 
 
 18 
 
 43 
 
 2.99 830 
 
 1 .00 046 
 
 0.99954 
 
 99783 
 
 06804 
 
 07103 
 
 92897 
 
 99701 
 
 17 
 
 44 
 
 2.99 956 
 
 T.oo 174 
 
 0.99 826 
 
 99782 
 
 06911 
 
 07 211 
 
 92789 
 
 99699 
 
 16 
 
 45 
 
 1.00082 
 
 T.oo 301 
 
 0.99 699 
 
 1-99 781 
 
 T.07 018 
 
 T.07 320 
 
 1.92680 
 
 1.99698 
 
 IS 
 
 46 
 
 00207 
 
 00427 
 
 99 573 
 
 99780 
 
 07124 
 
 07428 
 
 92572 
 
 99696 
 
 14 
 
 47 
 
 00332 
 
 00553 
 
 99 447 
 
 99778 
 
 07231 
 
 07536 
 
 92464 
 
 99695 
 
 13 
 
 48 
 
 00456 
 
 00679 
 
 99321 
 
 99777 
 
 07337 
 
 07643 
 
 92357 
 
 99693 
 
 12 
 
 49 
 
 00581 
 
 00805 
 
 99195 
 
 99776 
 
 07442 
 
 07751 
 
 92249 
 
 99692 
 
 II 
 
 50 
 
 T.oo 704 
 
 T.oo 930 
 
 0.99 070 
 
 1.99775 
 
 1.07548 
 
 1.07858 
 
 1.92 142 
 
 1.99690 
 
 10 
 
 51 
 
 00828 
 
 01055 
 
 98945 
 
 99 773 
 
 07653 
 
 07964 
 
 92036 
 
 99689 
 
 9 
 
 52 
 
 00951 
 
 01 179 
 
 98821 
 
 99772 
 
 07758 
 
 08071 
 
 91929 
 
 99687 
 
 8 
 
 53 
 
 01 074 
 
 01303 
 
 98697 
 
 99771 
 
 07863 
 
 08177 
 
 91823 
 
 99686 
 
 7 
 
 54 
 
 01 196 
 
 01427 
 
 98573 
 
 99769 
 
 07968 
 
 08283 
 
 91 717 
 
 99684 
 
 6 
 
 55 
 
 T.oi 318 
 
 1. 01 550 
 
 0.98 450 
 
 1.99 768 
 
 T.08 072 
 
 T.08 389 
 
 1.91 6n 
 
 1.99683 
 
 5 
 
 56 
 
 01 440 
 
 01673 
 
 98327 
 
 99767 
 
 08176 
 
 08495 
 
 91505 
 
 99681 
 
 4 
 
 57 
 
 01 561 
 
 01 796 
 
 98204 
 
 99765 
 
 08280 
 
 08600 
 
 91 400 
 
 99680 
 
 3 
 
 58 
 
 01682 
 
 01 918 
 
 98082 
 
 99764 
 
 08383 
 
 08705 
 
 91295 
 
 99678 
 
 2 
 
 59 
 
 01 803 
 
 02040 
 
 97960 
 
 99763 
 
 08486 
 
 08810 
 
 91 190 
 
 99677 
 
 I 
 
 60' 
 
 1. 01 923 
 
 T.02 162 
 
 0.97 838 
 
 1.99761 
 
 1.08589 
 
 1 .08 9 14 
 
 1. 9 1 086 
 
 1.99675 
 
 0' 
 
 
 log COB 
 
 log oot 
 
 log tan 
 
 log sin 
 
 log cos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 r 
 
 LOG SIN, etc. 84° 
 81°-84° 
 
 (SO) 
 
 83= 
 
8^ 
 
 5°-8° 
 LOG SIN, etc. 
 
 1 
 
 log sin 
 
 ogtan 
 
 log cot 
 
 log cos 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log cos 
 
 ■-^^^^^ 
 
 0' 
 
 1.08589 I. 
 
 08914 
 
 0.91 086 
 
 r.99 675 
 
 T.14356 T 
 
 14780 
 
 0.85 220 
 
 1-99 575 
 
 60' 
 
 I 
 
 08692 
 
 09019 
 
 90981 
 
 99674 
 
 14 445 
 
 14872 
 
 85 128 
 
 99 574 
 
 59 
 
 2 
 
 08 795 
 
 09123 
 
 90877 
 
 99672 
 
 14 535 
 
 14963 
 
 85037 
 
 99572 
 
 58 
 
 3 
 
 08 897 
 
 09227 
 
 90773 
 
 99670 
 
 14 624 
 
 15054 
 
 84946 
 
 99570 
 
 57 
 
 4 
 
 08999 
 
 39330 
 
 90670 
 
 99669 
 
 14714 
 
 15 145 
 
 84855 
 
 99568 
 
 56 
 
 5 
 
 T.09 lOI I.( 
 
 39434 
 
 0.90 566 
 
 1.99667 
 
 1.14803 1 
 
 15236 
 
 0.84 764 
 
 1.99 566 
 
 55 
 
 6 
 
 09 202 
 
 39 537 
 
 90463 
 
 99 666 
 
 14891 
 
 15327 
 
 84673 
 
 99565 
 
 54 
 
 7 
 
 09 304 
 
 09 640 
 
 90360 
 
 99 664 
 
 14 980 
 
 15417 
 
 84583 
 
 99563 
 
 53 
 
 8 
 
 09 405 ( 
 
 09742 
 
 90258 
 
 99663 
 
 15069 
 
 15508 
 
 84492 
 
 99561 
 
 52 
 
 9 
 
 09 506 ( 
 
 39845 
 
 90155 
 
 99 661 
 
 15 157 
 
 15598 
 
 84402 
 
 99 559 
 
 51 
 
 10 
 
 r.09 606 T.( 
 
 39947 
 
 0.90053 
 
 T.99 659 
 
 1.15245 I 
 
 15688 
 
 0.84312 
 
 1-99 557 
 
 50 
 
 II 
 
 09707 
 
 10049 
 
 ?9 95i 
 
 99658 
 
 IS 333 
 
 15777 
 
 84223 
 
 99556 
 
 49 
 
 12 
 
 09807 
 
 10 150 
 
 89850 
 
 99656 
 
 15421 
 
 15867 
 
 84133 
 
 99 554 
 
 48 
 
 13 
 
 09907 
 
 10252 
 
 89748 
 
 9965s 
 
 15508 
 
 15956 
 
 84044 
 
 99552 
 
 47 
 
 14 
 
 10006 
 
 10353 
 
 89647 
 
 99653 
 
 15596 
 
 16046 
 
 83954 
 
 99550 
 
 46 
 
 IS 
 
 T.io 106 T. 
 
 10454 
 
 0.89 546 
 
 1-99651 
 
 1.15683 1 
 
 16 135 
 
 0.83 865 
 
 1-99548 
 
 45 
 
 i6 
 
 10205 
 
 10 555 
 
 89445 
 
 99650 
 
 15770 
 
 16/224 
 
 83776 
 
 99546 
 
 44 
 
 17 
 
 10304 
 
 10656 
 
 89344 
 
 99648 
 
 15857 
 
 16 312 
 
 83688 
 
 99 545 
 
 43 
 
 18 
 
 10402 
 
 10 756 
 
 89244 
 
 99647 
 
 15944 
 
 16401 
 
 83599 
 
 99 543 
 
 -42 
 
 19 
 
 10 501 
 
 10856 
 
 89144 
 
 99645 
 
 16030 
 
 16489 
 
 835" 
 
 99 541 
 
 41 
 
 20 
 
 T.IO 599 I. 
 
 10956 
 
 0.89 044 
 
 T.99 643 
 
 T.16116 T 
 
 16577 
 
 0.83423 
 
 1-99 539 
 
 40 
 
 21 
 
 10697 
 
 II 056 
 
 88944 
 
 99642 
 
 16203 
 
 16665 
 
 83335 
 
 99 537 
 
 39 
 
 22 
 
 10795 
 
 "155 
 
 88845 
 
 99640 
 
 16289 
 
 16753 
 
 83247 
 
 99 535 
 
 38 
 
 23 
 
 10893 
 
 II 254 
 
 88746 
 
 99638 
 
 16374 
 
 16841 
 
 83159 
 
 99 533 
 
 37 
 
 24 
 
 10990 
 
 "353 
 
 88647 
 
 99637 
 
 16460 
 
 16928 
 
 83072 
 
 99 532 
 
 36 
 
 25 
 
 T.I I 087 T. 
 
 11452 
 
 0.88 548 
 
 1.99635 
 
 T.16545 T 
 
 17016 
 
 0.82 984 
 
 1.99530 
 
 35 
 
 26 
 
 II 184 
 
 "551 
 
 88449 
 
 99 633 
 
 16631 
 
 17103 
 
 82897 
 
 99528 
 
 34 
 
 27 
 
 II 281 
 
 1 1 649 
 
 88351 
 
 99632 
 
 16 716 
 
 17 190 
 
 82810 
 
 99526 
 
 33 
 
 28 
 
 "377 
 
 "747 
 
 88253 
 
 99630 
 
 16801 
 
 17277 
 
 82723 
 
 99524 
 
 32 
 
 29 
 
 1 1 474 
 
 11845 
 
 881SS 
 
 99629 
 
 16886 
 
 17363 
 
 82637 
 
 99522 
 
 31 
 
 30 
 
 T.11570 I. 
 
 "943 
 
 0.88057 
 
 1.99627 
 
 T.16970 T 
 
 17450 
 
 0.82 550 
 
 T.99 520 
 
 30 
 
 31 
 
 II 666 
 
 12040 
 
 87960 
 
 99625 
 
 17055 
 
 17536 
 
 82464 
 
 99518 
 
 29 
 
 32 
 
 II 761 
 
 12 138 
 
 87862 
 
 99624 
 
 17 139 
 
 17 622 
 
 82378 
 
 99517 
 
 28 
 
 33 
 
 "857 . 
 
 12235 
 
 87765 
 
 99622 
 
 17223 
 
 17708 
 
 82292 
 
 99515 
 
 27 
 
 34 
 
 11952 
 
 12332 
 
 87668 
 
 99620 
 
 17307 
 
 17794 
 
 82206 
 
 99513 
 
 26 
 
 35 
 
 1. 12 047 I. 
 
 12428 
 
 0.87 572 
 
 T.99 618 
 
 1-17391 I 
 
 17880 
 
 0.82 120 
 
 1-99 5" 
 
 25 
 
 36 
 
 12 142 
 
 12525 
 
 87475 
 
 99617 
 
 17474 
 
 17965 
 
 82035 
 
 99509 
 
 24 
 
 3r 
 
 12236 
 
 12621 
 
 87379 
 
 99615 
 
 17558 
 
 18 051 
 
 81949 
 
 99507 
 
 23 
 
 38 
 
 12 331 
 
 [2 717 
 
 ^7283 
 
 99613 
 
 17641 
 
 18136 
 
 81864 
 
 99505 
 
 22 
 
 39 
 
 12425 
 
 [2813 
 
 87187 
 
 99612 
 
 17724 
 
 18221 
 
 81779 
 
 99503 
 
 21 
 
 40 
 
 1.12519 I. 
 
 12909 
 
 0.87091 
 
 T.99 610 
 
 1.17807 I 
 
 18306 
 
 0.81 694 
 
 1-99 501 
 
 20 
 
 41 
 
 12 612 
 
 13004 
 
 86996 
 
 99608 
 
 17890 
 
 18 391 
 
 81609 
 
 99 499 
 
 19 
 
 42 
 
 12 706 
 
 13099 
 
 86901 
 
 99607 
 
 17973 
 
 18475 
 
 81525 
 
 99 497 
 
 18 
 
 43 
 
 12799 
 
 13194 
 
 86806 
 
 99605 
 
 18055 
 
 18560 
 
 81 440 
 
 99 495 
 
 17 
 
 44 
 
 12892 
 
 13289 
 
 86711 
 
 99603 
 
 18 137 
 
 18644 
 
 81356 
 
 99 494 
 
 16 
 
 45 
 
 T.I 2 985 T. 
 
 13384 
 
 0.86 616 
 
 1.99 601 
 
 1. 18 220 I 
 
 18728 
 
 0.81 272 
 
 1.99492 
 
 15 
 
 46 
 
 13078 
 
 13478 
 
 86522 
 
 99600 
 
 18 302 
 
 18 812 
 
 81 188 
 
 99490 
 
 14 
 
 47 
 
 13 171 
 
 13573 
 
 86427 
 
 99598 
 
 18383 
 
 18896 
 
 81 104 
 
 99488 
 
 13 
 
 48 
 
 13263 
 
 13667 
 
 86333 
 
 99596 
 
 18465 
 
 18979 
 
 81 021 
 
 99486 
 
 12 
 
 49 
 
 13355 
 
 13761 
 
 86239 
 
 99 595 
 
 18547 
 
 19063 
 
 80937 
 
 99484 
 
 II 
 
 50 
 
 113447 I- 
 
 13854 
 
 0.86 146 
 
 I-99 593 
 
 1. 18 628 1 
 
 19 146 
 
 0.80 854 
 
 T.99 482 
 
 10 
 
 51 
 
 13 539 
 
 13948 
 
 86052 
 
 99 591 
 
 18709 
 
 19 229 
 
 80771. 
 
 99480 
 
 9 
 
 52 
 
 13630 
 
 14041 
 
 85959 
 
 99589 
 
 18 790 
 
 19312 
 
 80688 
 
 99478 
 
 8 
 
 53 
 
 13722 
 
 14134 
 
 85866 
 
 99588 
 
 18871 
 
 19395 
 
 80605 
 
 99476 
 
 7 
 
 54 
 
 13 813 
 
 14227 
 
 85773 
 
 99586 
 
 18952 
 
 19478 
 
 80522 
 
 99 474 
 
 6 
 
 55 
 
 1. 13 904 I. 
 
 14320 
 
 0.85 680 
 
 1.99584 
 
 1.19033 I 
 
 19 561 
 
 0.80 439 
 
 1-99472 
 
 5 
 
 56 
 
 13994 
 
 14 412 
 
 85588 
 
 99582 
 
 19 113 
 
 19643 
 
 80357 
 
 99470 
 
 4 
 
 57 
 
 14085 
 
 14504 
 
 85496 
 
 99581 
 
 19 193 
 
 19725 
 
 80275 
 
 99468 
 
 3 
 
 S8 
 
 1417s 
 
 14597 
 
 85403 
 
 99 579 
 
 19273 
 
 19807 
 
 80193 
 
 99 466 
 
 2 
 
 59 
 
 14 266 
 
 14688 
 
 85312 
 
 99 577 
 
 19353 
 
 19889 
 
 80 HI 
 
 99464 
 
 1 
 
 60' 
 
 1.14356 I. 
 
 14 780 
 
 0.85 220 
 
 1-99 575 
 
 I.I9 433 I 
 
 19971 
 
 0.80 029 
 
 1.99 462 
 
 0' 
 
 
 log cos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 log 00s 
 
 log cot 
 
 log tan 
 
 log sin 
 
 t 
 
 82° 
 
 (sO 
 
 QI0 LOG SIN, etc. 
 
 wj. 8r-84° 
 
LOG SIN, etc. 
 
 9= 
 
 10= 
 
 / 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log ooa 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log cos 
 
 
 0' 
 
 1-19 433 
 
 1. 19971 
 
 3.80029 
 
 [.99462 
 
 T.23 967 
 
 1.24 632 
 
 0.75 368 
 
 1-99 335 
 
 60' 
 
 I 
 
 19513 
 
 20053 
 
 79 947 
 
 99460 
 
 24039 
 
 24706 
 
 75294 
 
 99 333 
 
 59 
 
 2 
 
 19592 
 
 20134 
 
 79866 
 
 99458 
 
 24 110 
 
 24779 
 
 75221 
 
 99331 
 
 58 
 
 3 
 
 19672 
 
 20 216 
 
 79784 
 
 99456 
 
 24 181 
 
 24853 
 
 75147 
 
 99328 
 
 57 
 
 4 
 
 19751 
 
 20297 
 
 79703 
 
 99 454 
 
 24253 
 
 24926 
 
 75074 
 
 99326 
 
 56 
 
 5 
 
 1.19830 
 
 1.20378 
 
 0.79 622 
 
 1.99452 
 
 1.24324 
 
 T.25000 
 
 0.75000 
 
 1-99324 
 
 55 
 
 6 
 
 19909 
 
 20459 
 
 79541 
 
 99450 
 
 24395 
 
 25073 
 
 74927 
 
 99322 
 
 54 
 
 7 
 
 19988 
 
 20 540 
 
 79460 
 
 99448 
 
 24466 
 
 25 146 
 
 74854 
 
 99319 
 
 53 
 
 8 
 
 20067 
 
 20 621 
 
 79 379 
 
 99446 
 
 24536 
 
 25 219 
 
 74781 
 
 99317 
 
 52 
 
 9 
 
 20145 
 
 20 701 
 
 79299 
 
 99 444 
 
 24607 
 
 25292 
 
 74708 
 
 99315 
 
 51 
 
 10 
 
 T.20 223 
 
 T.20 782 
 
 0.79 218 
 
 7.99442 
 
 1.24677 
 
 T.25 365 
 
 0.74635 
 
 1-99313 
 
 50 
 
 II 
 
 20302 
 
 20862 
 
 79138 
 
 99440 
 
 24748 
 
 25 437 
 
 74563 
 
 99310 
 
 49 
 
 12 
 
 20380 
 
 20942 
 
 79058 
 
 99438 
 
 24818 
 
 25510 
 
 74490 
 
 99308 
 
 48 
 
 13 
 
 20458 
 
 21 022 
 
 78978 
 
 99436 
 
 24888 
 
 25582 
 
 74418 
 
 99306 
 
 47 
 
 14 
 
 20535 
 
 21 102 
 
 78898 
 
 99 434 
 
 24958 
 
 25655 
 
 74 345 
 
 99304 
 
 46 
 
 15 
 
 1.20613 
 
 7.21 182 
 
 0.78818 
 
 1.99432 
 
 1.25028 
 
 1.25 727 
 
 0.74 273 
 
 1-99301 
 
 45 
 
 i6 
 
 20691 
 
 21 261 
 
 78739 
 
 99429 
 
 25098 
 
 25799 
 
 74201 
 
 99299 
 
 44 
 
 17 
 
 20768 
 
 21341 
 
 78659 
 
 99427 
 
 25 168 
 
 25871 
 
 74129 
 
 99297 
 
 43 
 
 i8 
 
 20845 
 
 21 420 
 
 78580 
 
 99425 
 
 25237 
 
 25943 
 
 74057 
 
 99294 
 
 42 
 
 19 
 
 20922 
 
 21499 
 
 78501 
 
 99423 
 
 25307 
 
 26015 
 
 73985 
 
 99292 
 
 41 
 
 20 
 
 T.20 999 
 
 7,21 578 
 
 0.78 422 
 
 1-99 421 
 
 1-25376 
 
 T.26086 
 
 0-73914 
 
 T99 290 
 
 40 
 
 21 
 
 21 076 
 
 21657 
 
 78343 
 
 99419 
 
 25 445 
 
 26158 
 
 73842 
 
 99288 
 
 39 
 
 22 
 
 21153 
 
 21736 
 
 78264 
 
 99417 
 
 25514 
 
 26229 
 
 73771 
 
 99285 
 
 38 
 
 23 
 
 21 229 
 
 21 814 
 
 78186 
 
 99415 
 
 25583 
 
 26301 
 
 73699 
 
 99283 
 
 37 
 
 24 
 
 21 306 
 
 21893 
 
 78107 
 
 99413 
 
 25652 
 
 26372 
 
 73628 
 
 99281 
 
 36 
 
 25 
 
 1.21 382 
 
 1.21 971 
 
 0.78 029 
 
 1-99411 
 
 1.25 721 
 
 T.26 443 
 
 0-73 557 
 
 1.99278 
 
 35 
 
 26 
 
 21458 
 
 22049 
 
 77951 
 
 99409 
 
 25790 
 
 26514 
 
 73486 
 
 99276 
 
 34 
 
 27 
 
 21534 
 
 22 127 
 
 77873 
 
 99407 
 
 25858 
 
 26585 
 
 73415 
 
 99274 
 
 33 
 
 28 
 
 21 610 
 
 22205 
 
 77 795 
 
 99404 
 
 25927 
 
 26655 
 
 73 345 
 
 99271 
 
 32 
 
 29 
 
 21 685 
 
 22283 
 
 77717 
 
 99402 
 
 25995 
 
 26726 
 
 73274 
 
 99269 
 
 31 
 
 30 
 
 7.21 761 
 
 7.22 361 
 
 0.77 639 
 
 1 .99 400 
 
 1.26063 
 
 T.26 797 
 
 0.73 203 
 
 T.99 267 
 
 30 
 
 31 
 
 21836 
 
 22438 
 
 77562 
 
 99398 
 
 26 131 
 
 26867 
 
 73133 
 
 99264 
 
 29 
 
 32 
 
 21 912 
 
 22516 
 
 77484 
 
 99396 
 
 26199 
 
 26937 
 
 73063 
 
 99262 
 
 28 
 
 33 
 
 21987 
 
 22593 
 
 77407 
 
 99 394 
 
 26267 
 
 27008 
 
 72 992 . 
 
 99260 
 
 27 
 
 34 
 
 22062 
 
 22670 
 
 77330 
 
 99392 
 
 26335 
 
 27078 
 
 72922 
 
 99257 
 
 26 
 
 35 
 
 7.22 137 
 
 7.22 747 
 
 0.77253 
 
 1.99390 
 
 1.26403 
 
 1.27 148 
 
 0.72 852 
 
 1-99255 
 
 25 
 
 36 
 
 22 211 
 
 22824 
 
 77176 
 
 99388 
 
 26470 
 
 27 218 
 
 72782 
 
 99252 
 
 24 
 
 37 
 
 22286 
 
 22901 
 
 77099 
 
 99385 
 
 26538 
 
 27288 
 
 72712 
 
 99250 
 
 23 
 
 38 
 
 22361 
 
 22977 
 
 77023 
 
 99383 
 
 26605 
 
 27357 
 
 72643 
 
 99248 
 
 22 
 
 39 
 
 22435 
 
 23054 
 
 76946 
 
 99381 
 
 26672 
 
 27427 
 
 72573 
 
 99245 
 
 21 
 
 40 
 
 7.22 509 
 
 1.23 130 
 
 0.76 870 
 
 1-99 379 
 
 7.26 739 
 
 1.27496 
 
 0.72 504 
 
 T.99 243 
 
 20 
 
 41 
 
 22583 
 
 23206 
 
 76794 
 
 99 377 
 
 26806 
 
 27 566 
 
 72434 
 
 99241 
 
 'i 
 
 42 
 
 22657 
 
 23283 
 
 76717 
 
 99 375 
 
 26873 
 
 27635 
 
 72365 
 
 99238 
 
 18 
 
 43 
 
 22731 
 
 23359 
 
 76641 
 
 99372 
 
 26940 
 
 27704 
 
 72296 
 
 99236 
 
 17 
 
 44 
 
 22805 
 
 23435 
 
 76565 
 
 99370 
 
 27007 
 
 27773 
 
 72227 
 
 99233 
 
 16 
 
 45 
 
 7.22 878 
 
 1.23 510 
 
 0.7.6 490 
 
 1.99368 
 
 1.27073 
 
 1.27842 
 
 0.72 158 
 
 1.99231 
 
 IS 
 
 46 
 
 22952 
 
 23586 
 
 76414 
 
 99366 
 
 27140 
 
 27 911 
 
 72089 
 
 99229 
 
 14 
 
 47 
 
 23025 
 
 23661 
 
 76339 
 
 99364 
 
 27206 
 
 27980 
 
 72020 
 
 99226 
 
 13 
 
 48 
 
 23098 
 
 23737 
 
 76263 
 
 99362 
 
 27273 
 
 28049 
 
 71 951 
 
 99224 
 
 12 
 
 49 
 
 23171 
 
 23812 
 
 76188 
 
 99 359 
 
 27339 
 
 28117 
 
 71883 
 
 99221 
 
 II 
 
 50 
 
 1.23244 
 
 7.23 887 
 
 0.76 113 
 
 i'-99 357 
 
 7.27 405 
 
 T.28 186 
 
 0.71 814 
 
 T.99 219 
 
 10 
 
 51 
 
 23317 
 
 . 23 962 
 
 76038 
 
 99 355 
 
 27471 
 
 28254 
 
 71746 
 
 99217 
 
 9 
 
 52 
 
 23390 
 
 24037 
 
 75963 
 
 99 353 
 
 27537 
 
 28323 
 
 71677 
 
 99214 
 
 8 
 
 53 
 
 23462 
 
 24 112 
 
 75888 
 
 99351 
 
 27602 
 
 28391 
 
 71 609 
 
 99212 
 
 7 
 
 54 
 
 23535 
 
 24186 
 
 75814 
 
 99348 
 
 27668 
 
 28459 
 
 71541 
 
 99209 
 
 6 
 
 55 
 
 1.23607 
 
 7.24 261 
 
 0.75 739 
 
 1.99346 
 
 1-27734 
 
 1.28 527 
 
 0.71 473 
 
 1 .99 207 
 
 5 
 
 56 
 
 23679 
 
 24335 
 
 75665 
 
 99 344 
 
 27799 
 
 28595 
 
 71405 
 
 99204 
 
 4 
 
 57 
 
 23752 
 
 24410 
 
 75590 
 
 99342 
 
 27864 
 
 28662 
 
 71338 
 
 99 202 
 
 3 
 
 58 
 
 23823 
 
 24484 
 
 75516 
 
 99340 
 
 27 930 
 
 28730 
 
 71270 
 
 99200 
 
 2 
 
 59 
 
 23895 
 
 24558 
 
 75442 
 
 99 337 
 
 27995 
 
 28798 
 
 71 202 
 
 99197 
 
 I 
 
 60' 
 
 1.23967 
 
 1.24632 
 
 0.75 368 
 
 1-99 335 
 
 1.28060 
 
 T.28 865 
 
 0.71 13s 
 
 199195 
 
 0' 
 
 
 log G03 
 
 log cot 
 
 log tan 
 
 log sin 
 
 log 003 
 
 log oot 
 
 log tan 
 
 log sin 
 
 r 
 
 LOG SIN, etc. 80^ 
 
 77°-80° 
 
 (52) 
 
 79= 
 

 
 ir 
 
 100 ^°-12 
 12 LOG SIN, 
 
 !° 
 etc 
 
 
 f 
 
 log sin log tan log cot log 00a 
 
 log sin log tan log cot log cos 
 
 1 
 
 
 0' 
 
 ¥ 
 
 1.28060 1.28865 0-71135 1-99 195 
 28 125 28 933 71 067 99 192 
 28190 29000 71000 99190 
 28254 29067 70933 99187 
 28319 29134 70866 99185 
 
 1.31788 1.32747 0.67253 T.99040 
 
 60' 
 
 1 
 
 
 A 
 
 31 847 32 810 67 190 99 038 
 
 59 1 
 
 
 2 
 
 3 
 
 31907 32872 67128 99035 
 31966 32933 67067 99032 
 
 58 
 57 
 
 
 
 4 
 
 _ 32 025 32995 67005 99030 
 
 56 
 
 
 
 s 
 
 1.28384 1.29 201 0.70799 T.99182 
 
 1.32084 1.33057 0.66943 1.99027 
 
 55 
 54 
 53 
 52 
 
 
 
 6 
 
 28448 29268 70732 99180 
 
 32143 33 119 66881 99024 
 
 
 
 7 
 
 28512 2933s 70665 99177 
 
 32 202 33 180 66 820 99 022 
 
 
 
 8 
 
 28577 29402 70598 99175 
 
 32261 33242 66758 99019 
 
 
 
 9 
 
 28641 29468 70532 99172 
 
 32319 33303 66697 99016 
 
 51 
 
 
 
 10 
 
 1.28705 1.29535 0.70465 T.99170 
 
 1.32378 T.33365 0.66635 1-99013 
 
 50 
 
 
 
 II 
 
 28769 29601 70399 99167 
 
 32437 33426 66574 99 on 
 
 49 
 
 
 
 12 
 
 28833 29668 70332 99165 
 
 32495 33487 66513 99008 
 
 48 
 
 
 
 13 
 
 28896 29734 70266 99162 
 
 32553 33548 66452 99005 
 
 47 
 
 
 
 14 
 
 28960 29800 70200 99160 
 
 _ 32612 33609 66391 99002 
 
 46 
 
 
 
 '5 
 
 1.29024 T.29 866 0.70134 T-99 157 
 
 1.32670 1.33670 0.66330 1.99000 
 
 45 
 
 
 
 i6 
 
 29087 29932 70068 99155 
 
 32728 33 731 66269 98997 
 
 44 
 
 
 
 17 
 
 29150 29998 70002 99152 
 
 32786 33792 66208 98994 
 
 43 
 
 
 
 18 
 
 29214 30064 69936 99150 
 
 32844 33853 66147 98991 
 
 42 
 
 
 
 19 
 
 29277 30130 69870 99147 
 
 32902 33913 66087 98989 
 
 41 
 
 
 
 20 
 
 1.29340 1.30195 0.69805 T.99145 
 
 1.32960 T.33974 0.66026 T.98986 
 
 40 
 
 
 
 21 
 
 29403 30261 69739 99142 
 
 33018 34034 65966 98983 
 
 39 
 
 
 
 22 
 
 29 466 30 326 69 674 99 140 
 
 33075 34095 65905 98980 
 
 38 
 
 
 
 23 
 
 29529 30391 69609 99137 
 
 33133 34155 65845 98978 
 
 37 
 
 
 
 24 
 
 29591 30457 69543 99135 
 
 33190 34215 65785 98975 
 
 36 
 
 
 
 25 
 
 1.29654 1.30522 0.69478 1.99 132 
 
 1-33248 1-34,276 0.65724 1.98972 
 
 35 
 
 
 
 26 
 
 29716 30587 69413 99130 
 
 33305 34336 65664 98969 
 
 34 
 
 
 
 ^? 
 
 29779 '30652 69348 99127 
 
 33362 34396 65604 98967 
 
 33 
 
 
 
 28 
 
 29841 30717 69283 99124 
 
 33420 34456 65544 98964 
 
 32 
 
 
 
 29 
 
 29 903 30 782 69 218 99 122 
 
 33 477 34516 65484 98961 
 
 31 
 
 
 
 30 
 
 r.29966 r. 30 846 0.69154 Y.99119 
 
 1-33 534 T-34576 0.65424 T.98958 
 
 30 
 
 
 
 31 
 
 30028 30911 69089 99 117 
 
 33591 34635 65365 98955 
 
 29 
 
 
 
 32 
 
 30090 30975 69025 99 114 
 
 33647 34695 65305 98953 
 
 28 
 
 
 
 33 
 
 30151 31040 68960 99 112 
 
 33704 34 755 65245 98950 
 
 27 
 
 
 
 34 
 
 30 213 31 104 68 896 99 109 
 
 33761 34814 65186 98947 
 
 26 
 
 
 
 35 
 
 1.30275 1.31 168 0.68832 T.99106 
 
 1.33818 1..34874 0.65126 7.98944 
 
 25 
 
 
 
 36 
 
 30336 31233 68767 99104 
 
 33874 34 933 65067 98941 
 
 24 
 
 
 
 37 
 
 30 398 31 297 68 703 99 loi 
 
 33931 34992 65008 98938 
 
 23 
 
 
 
 38 
 
 30459 31 361 68639 99099 
 
 33987 35051 64949 98936 
 
 22 
 
 
 
 39 
 
 30521 31425 68575 99096 
 
 34043 35 III 64889 98933 
 
 21 
 
 
 
 40 
 
 1.30582 T.31489 0.68 511 1.99093 
 
 T.34 100 1.35 170 0.64 830 1.98 930 
 
 20 
 
 
 
 41 
 
 30643 31552 68448 99091 
 
 34156 35229 64771 98927 
 
 19 
 
 
 
 42 
 
 30704 31 616 68384 99088 
 
 34212 35288 64712 98924 
 
 18 
 
 
 
 43 
 
 30765 31679 68321 99086 
 
 34268 35 347 64653 98921 
 
 17 
 
 
 
 44 
 
 30826 31743 68257 99083 
 
 34324 35405 64595 98919 
 
 16 
 
 
 
 '^l 
 
 1.30887 1. 3 1 806 0.68194 1.99080 
 
 1.34380 1.35464 0.64536 1.98916 
 
 15 
 
 
 
 46 
 
 30947 31870 68130 99078 
 
 34436 35523 64477 98913 
 
 14 
 
 
 
 H 
 
 31008 31933 68067 99075 
 
 34491 35581 64419 98910 
 
 13 
 
 
 
 48 
 
 31068 31996 68004 99072 
 
 34 547 35640 64360 98907 
 
 12 
 
 
 
 49 
 
 31 129 32 059 67 941 99 070 
 
 34602 35698 64302 98904 
 
 II 
 
 
 
 50 
 
 1.3 1 189 1.32 122 0.67878 T.99067 
 
 T.34 658 1.35757 0.64243 T.98901 
 
 10 
 
 
 
 SI 
 
 31250 32185 67815 99064 
 
 34713 35815 64185 98898 
 
 9 
 
 
 
 52 
 
 31310 32248 67752 99062 
 
 34769 35873 64127 98896 
 
 8 
 
 
 
 53 
 
 31370 32 311 67689 99059 
 
 34824 35931 64069 98893 
 
 7 
 
 
 
 54 
 
 _ 31 430 32373 67627 99056 
 
 34879 35989 64011 98890 
 
 5 
 
 
 
 55 
 
 1.31490 1.32436 0.67564 1.99054 
 
 1.34934 1-36047 0.63953 1.98887 
 
 5 
 
 
 
 56 
 
 31549 32498 67502 99051 
 
 34989 36105 63895 98884 
 
 4 
 
 
 
 57 
 
 31609 32561 67439 99048 
 
 35 044 36 163 63 837 98 881 
 
 3 
 
 
 
 58 
 
 31 669 32 623 67 377 99 046 
 
 35099 36221 63779 98878 
 
 2 
 
 
 
 ^1, 
 
 31728 32685 67315 99-043 
 
 _ 35 154 _ 36 279 63721 98875 
 
 I 
 
 
 . 
 
 60' 
 
 1.31788 1.32747 0.67253 1.99040 
 
 1.35209 1.36336 0.63664 1.98872 
 
 0' 
 
 
 r 1 
 
 log 00a log cot log tan log sin 
 
 log 003 log cot log tan log sin 
 
 r 
 
 
 
 
 78° (5: 
 
 ) 77° LOG SI 
 
 N, e1 
 -80° 
 
 tc. 
 
i3^-ie? 
 
 LOG SIP), etc. 
 
 13° 
 
 14° 
 
 
 
 t 
 
 log sin 
 
 log tan log cot log cos 
 
 log sin log tan log cot log oob 
 
 
 
 0' 
 
 1.35209 
 
 1.36336 0.63664 1.98872 
 
 1.38368 1.39677 0.60323 T.98 690 
 
 60' 
 
 
 I 
 
 35263 
 
 36 394 63 606 98 869 
 
 38418 39731 60269 98687 
 
 59 
 
 
 2 
 
 35318 
 
 36452 63548 98867 
 
 38469 39785 60215 986S4 
 
 58 
 
 
 •3 
 
 35 373 
 
 36509 63491 98864 
 
 38519 39838 60162 98681 
 
 57 
 
 
 4 
 
 35427 
 
 36 566 63 434 9-8 861 
 
 38570 39892 60108 98678 
 
 56 
 
 
 s 
 
 1-35481 
 
 1.36624 0.63376 1.98858 
 
 1.38620 1.39945 0.60055 1-98675 
 
 55 
 54 
 53 
 52 
 51 
 
 
 6 
 
 35536 
 
 36681 63319 98855 
 
 38670 39999 60001 98671 
 
 
 7 
 
 35590 
 
 36 738 63 262 98 852 
 
 38721 40052 59948 98668 
 
 
 8 
 
 35644 
 
 36 795 63 205 98 849 
 
 38771 40106 59894 98665 
 
 
 9 
 
 35698 
 
 36 852 63 148 98 846 
 
 38821 40159 59841 98662 
 
 
 10 
 
 1 '35 752 
 
 T.36 909 0.63091 1.98843 
 
 1.38871 T.40212 0.59788 T.98 659 
 
 50 
 
 4Q 
 
 
 II 
 
 35806 
 
 36 966 63 034 98 840 
 
 38921 40266 59 734 98656 
 
 
 12 
 
 35860 
 
 37023 62977 98837 
 
 38971 40319 59.681-— TfS^ya- 
 
 t7 
 
 -48 
 
 
 13 
 
 35914 
 
 37 080 62 920 98 834 
 
 39021 40372 59628 98649_ 
 
 47 
 46 
 
 
 14 
 
 35968 
 
 37137 62863 98831 
 
 39071 40425 59575 98646 
 
 
 IS 
 
 1.36022 
 
 1-37193 0.62807 1-98828 
 
 1.39121 1.40478 0.59522 1.98643 
 
 45 
 44 
 43 
 42 
 
 
 16 
 
 36075 
 
 37 250 62 750 98 825 
 
 39170 40531 59469 98640 
 
 
 17 
 
 36129 
 
 37 306 62 694 98 822 
 
 39220 40584 59416 98636 
 
 
 18 
 
 36182 
 
 37 363 62 637 98 819 
 
 39270 40636 59364 98633 
 
 
 19 
 
 36236 
 
 37419 62581 98816 
 
 39319 40689 59311 98630 
 
 41 
 
 
 20 
 
 T.36 289 
 
 T.37476 0.62524 T.98813 
 
 1-39369 T.40742 0.59258 T.98 627 
 
 40 
 
 
 21 
 
 36342 
 
 37532 62468 98810 
 
 39418 40795 59205 98623 
 
 39 
 
 
 22 
 
 36395 
 
 37588 62412 98807 
 
 39467 40847 59153 98620 
 
 ^8 
 
 
 23 
 
 36449 
 
 37 644 62 356 98 804 
 
 39517 40900 59100 98617 
 
 36 
 
 
 24 
 
 36502 
 
 37 700 62 300 98 8oi 
 
 39566 40952 59048 98614 
 
 
 25 
 
 1-36555 
 
 1-37756 0.62244 1.98798 
 
 1-39 615 I-4J005 0.58995 T.98 610 
 
 35 
 34 
 
 
 26 
 
 36608 
 
 37 812 62 188 98 795 
 
 39664 41057 58943 98607 
 
 
 27 
 
 36660 
 
 37 868 62 132 98 792 
 
 39 7«3 41109 58891 98604 
 
 33 
 
 
 28 
 
 ^Vll 
 
 37 924 62 076 98 789 
 
 39 762 41 161 58 839 98 601 
 
 32 
 
 
 29 
 
 36766 
 
 37 980 62 020 98 786 
 
 39811 41214 58786 98597 
 
 31 
 
 
 30 
 
 r.36 819 
 
 T.38035 0.61965 r.98783 
 
 T.39 860 T.41 266 0.58 734 T.98 594 
 
 30 
 
 
 31 
 
 36871 
 
 38 091 61 909 98 780 
 
 39909 41 318 58682 98591 
 
 29 
 
 
 32 
 
 36924 
 
 38 147 61 853 98 777 
 
 39958 41370 58630 98588 
 
 28 
 
 
 33 
 
 36976 
 
 38 202 61 798 98 774 
 
 40006 41422 58578 98584 
 
 27 
 
 
 34 
 
 37028 
 
 38 257 61 743 98 771 
 
 40055 41474 58526 98581 
 
 26 
 
 
 35 
 
 T.37081 
 
 1.38 313 0.61687 1-98768 
 
 1.40103 1.41526 0.58474 1.98578 
 
 25 
 
 
 36 
 
 37133 
 
 38 368 61 632 98 765 
 
 40152 41578 58422 98574 
 
 24 
 
 
 37 
 
 37185 
 
 38423 61577 98762 
 
 40200 41629 58371 98571 
 
 23 
 
 
 38 
 
 37237 
 
 38479 61 521 98759 
 
 40 249 41 681 58 319 98 568 
 
 22 
 
 
 39 
 
 37289 
 
 38 534 6i 466 98 756 
 
 40 297 41 733 58 267 98 565 
 
 21 
 
 
 40 
 
 1-37 341 
 
 1.38589 0.61 411 T.98753 
 
 T.40346 T.41 784 0.58216 T.98 561 
 
 20 
 
 
 41 
 
 37 393 
 
 38 644 61 356 98 750 
 
 40394 41836 58164 98558 
 
 19 
 
 
 42 
 
 37 445 
 
 38 699 ^61 301 98 746 
 
 40442 41887 58113 98555 
 
 18 
 
 
 43 
 
 37 497 
 
 38 754 61 246 98 743 
 
 40490 41939 58061 98551 
 
 17 
 
 
 44 
 
 37 549 
 
 38 808 61 192 98 740 
 
 40538 41990 58010 98548 
 
 16 
 
 
 45 
 
 1.37600 
 
 T.38 863 0.61 137 T.98 737 
 
 T.40586 T.42041 0.57959 T.98 545 
 
 15 
 
 
 46 
 
 37652 
 
 38918 61082 98734 
 
 40634 42093 57907 98541 
 
 14 
 
 
 47 
 
 37703 
 
 38972 61028 98731 
 
 40 682 42 144 57 856 98 538 
 
 13 
 
 
 48 
 
 37 755 
 
 39027 60973 98728 
 
 40730 42195 57805 98535 
 
 12 
 
 
 49 
 
 37806 
 
 39 082 60 918 98 725 
 
 40778 42246 57754 98531 
 
 11 
 
 
 50 
 
 7-37 858 
 
 T.39 136 0.60864 1.98722 
 
 1.40825 1.42297 0.57703 1.98528 
 
 10 
 
 
 51 
 
 37909 
 
 39 190 60 810 98 719 
 
 40873 42348 57652 98525 
 
 9 
 
 
 52 
 
 37960 
 
 39 245 60 755 98 715 
 
 40921 42399 57601 98521 
 
 8 
 
 
 53 
 
 38 01 1 
 
 39299 60701 98712 
 
 40968 42450 57550 98518 
 
 7 
 
 
 54 
 
 38062 
 
 39 353 60 647 98 709 
 
 41016 42501 57499 98515 
 
 6 
 
 
 55 
 
 T-38113 
 
 1.39407 0.60593 1.98706 
 
 1.41063 1.42552 0.57448 1.98511 
 
 5 
 
 
 56 
 
 38164 
 
 39 461 60 539 98 703 
 
 41111 42603 57397 98508 
 
 4 
 
 
 57 
 
 38215 
 
 39515 60485 98700 
 
 41 158 42 653 57 347 98 505 
 
 3 
 
 
 58 
 
 38266 
 
 39569 60431 98697 
 
 41 205 42 704 57 296 98 501 
 
 2 
 
 
 59 
 
 38317 
 
 39 623 60 377 98 694 
 
 41252 42755 57245 98498 
 
 1 
 
 
 60 
 
 1.38368 
 
 1-39677 0.60323 1.98690 
 
 1.41300 1.42805 0.57195 1.98494 
 
 0' 
 
 
 
 log cos 
 
 log cot log tan log sin 
 
 log cos log cot log tan log sin 
 
 1 
 
 LOG SIN. etc. 76= 
 
 (54) 
 
 76= 
 

 15° 
 
 ^^0 13°-16° 
 lb LOG SIN, etc 
 
 t 
 
 log Bin log tan logoot log 00a 
 
 log sin log tan logoot logoos 
 
 
 
 0' 
 
 I 
 
 2 
 
 1.41300 1.42805 0.57195 1.98494 
 41347 42856 57144 98491 
 41394 42906 57094 98488 
 
 1.44034 1.45750 0.54250 1.98284 
 44 078 45 797 54 203 98 281 
 44122 45845 54155 98277 
 
 60' 
 
 59 
 58 
 
 
 3 
 
 41441 42957 57043 98484 
 
 44 166 45 892 54 108 98 273 
 
 % 
 
 
 4 
 
 41488 43007 56993 98481 
 
 44210 45940 54060 98270 
 
 
 5 
 
 141 535 1-43057 0.56943 1.98477 
 
 1-44253 1.45987 0.54013 T.98 266 
 
 55 
 54 
 
 
 6 
 
 41582 43108 56892 98474 
 41628 43158 56842 98471 
 
 44297 46035 53965 98262 
 
 
 7 
 
 44341 46082 53918 98259 
 
 S3 
 52 
 
 
 8 
 
 41675 43208 56792 98467 
 
 44385 46130 53870 98255 
 
 
 9 
 
 41 722 43 258 56 742 98 464 
 
 44428 46177 53823 98251 
 
 51 
 
 
 10 
 
 1.41 768 T.43 308 0.56 692 T.98 460 
 
 1.44472 1.46224 0.53776 T.98 248 
 
 50 
 
 
 II 
 
 41 815 43358 56642 98457 
 
 4451& 46271 53729 982^^ 
 
 49 
 
 
 12 
 
 41861 43408 56592 98453 
 
 44 559 46319 53681 98240 
 
 48 
 
 
 13 
 
 41908 43458 56542 98450 
 
 44602 46366 53634 98237 
 
 47 
 
 
 14 
 
 41954 43508 56492 98447 
 
 44646 46413 53587 98233 
 
 46 
 
 
 'S 
 
 1.42 001 1.43558 0.56442 1.98443 
 
 1.44689 1.46460 0.53540 1.98229 
 
 45 
 
 
 i6 
 
 42047 43607 56393 98440 
 
 44 733 46507 53 493 98226 
 
 44 
 
 
 17 
 
 ,42093 43657 56343 98436 
 
 44776 46554 53446 98222 
 
 43 
 
 
 18 
 
 42140 43707 56293 98433 
 
 44819 46601 53399 98218 
 
 42 
 
 
 19 
 
 42186 43756 56244 98429 
 
 44862 46648 53352 98215 
 
 41 
 
 
 20 
 
 1.42232 T.43 806 0.56194 T.98 426 
 
 T.44905 T.46694 0.53306 T.98 211 
 
 40 
 
 
 21 
 
 42278 43855 56145 98422 
 
 44948 46741 53259 98207 
 
 39 
 
 
 22 
 
 42324 43905 56095 98419 
 
 44992 46788 53212 98204 
 
 38 
 
 
 23 
 
 42370 43954 56046 98415 
 
 45035 46835 53165 98200 
 
 37 
 
 
 24 
 
 42416 44004 55996 98412 
 
 _ 45 077 46881 53 119 98196 
 
 36 
 
 
 ^5 
 
 1.42 461 T.44053 0.55947 T.98 409 
 
 1.45 120 1.46928 0.53072 1.98192 
 
 35 
 
 
 26 
 
 42507 44102 55898 98405 
 
 45163 46975 53025 98189 
 
 34 
 
 
 27 
 
 42553 44 151 55849 98402 
 
 45206 47021 52979 98185 
 
 33 
 
 
 28 
 
 42599 44 20I 55 799 98398 
 
 45249 47068 52932 98 181 
 
 32 
 
 
 29 
 
 42644 44250 55750 98395 
 
 45292 47 114 52886 98177 
 
 31 
 
 
 30 
 
 1.42690 T.44299 0.55701 T.98 391 
 
 1-45 334 T.47160 0.52840 T.98 174 
 
 30 
 
 
 31 
 
 42735 44348 55652 98388 
 
 45 377 47207 52793 98170 
 
 29 
 
 
 32 
 
 • 42781 44 397 55603 98384 
 
 45419 47253 52747 98166 
 
 28 
 
 
 33 
 
 42826 44446 55554 98381 
 
 45 462 47 299 52 701 98 162 
 
 27 
 
 
 34 
 
 42872 44495 55505 98377 
 
 45504 47346 52654 98159 
 
 26 
 
 
 3| 
 
 1.42 917 1-44 544 0.55456 1.98373 
 
 1.45547 1.47392 0.52608 1.98 155 
 
 25 
 
 
 36 
 
 42962 44592 55408 98370 
 
 45589 47438 52562 98151 
 
 24 
 
 
 37 
 
 43008 44641 55359 98366 
 
 45632 47484 52516 98147 
 
 23 
 
 
 38 
 
 43053 44690 55310 98363 
 
 45674 47530 52470 98144 
 
 22 
 
 
 39 
 
 43098 44738 55262 98359 
 
 45716 47576 52424 98140 
 
 21 
 
 
 40 
 
 1-43143 7-44787 0.55213 T.98 356 
 
 1-45758 T.47622 0.52378 T.98 136 
 
 20 
 
 
 41 
 
 43188 44836 55164 98352 
 
 45801 47668 52332 98132 
 
 19 
 
 
 42 
 
 43233 44884 55 "6 98349 
 
 45843 47714 52286 98129 
 
 18 
 
 
 43 
 
 43278 44 933 55067 98345 
 
 45885 47760 52240 98125 
 
 17 
 
 
 44 
 
 43323 44981 55019 98342 
 
 _ 45 927 47806 52194 98121 
 
 16 
 
 
 45 
 
 1.43367 1.45029 0.54971 1.98338 
 
 1.45969 1.47852 0.52148 1.98 117 
 
 15 
 
 
 46 
 
 43 4*2 45078 54922 98334 
 
 46 01 1 47897 52103 98 113 
 
 14 
 
 
 47 
 
 43 457 45126 54874 98331 
 
 46053 47943 52057 98 no 
 
 13 
 
 
 48 
 
 43502 45174 54826 98327 
 
 46095 47989 52 01 1 98106 
 
 12 
 
 
 49 
 
 43546-- 45222 54778 98324 
 
 46136 48035 51965 98102 
 
 II 
 
 
 50 
 
 1.43591 1.45 271 0.54729 T.98 320 
 
 T.46178 T.48080 0.51920 T.98 098 
 
 10 
 
 
 51 
 
 43635 45319 54681 98317 
 
 46220 48126 51874 98094 
 
 9 
 
 
 52 
 
 43680 45367 54633 98313 
 
 46262 48 171 51829 98090 
 
 8 
 
 
 S3 
 
 43 724 45 415 54 585 • 98 309 
 
 46303 48217 51783 98087 
 
 7 
 
 
 54 
 
 43769 45463 54 537 98306 
 
 46345 48262 51738 98083 
 
 6 
 
 
 ^\ 
 
 1-43813 1.45 5" 0.54489 1.98302 
 
 T.46386 T.48307 0.51693 T.98 079 
 
 5 
 
 
 56 
 
 43857 45 559 54441 98299 
 
 46428 48353 51647 98075 
 
 4 
 
 
 5^ 
 
 43901 45606 54 394 98295 
 
 46469 48398 51602 98071 
 
 3 
 
 
 58 
 
 43946 45654 54346 98291 
 
 46511 48443 51557 98067 
 
 2 
 
 
 59 
 
 43 990 45 702 54 298 98 288 
 
 46552 48489 51511 98063 
 
 I 
 
 
 60' 
 
 1.44034 1.45750 0.54250 1.98284 
 
 1.46594 1.48534 0.51466 1.98060 
 
 0' 
 
 
 
 log cos log cot log tan log sin 
 
 log COS log cot log tan log sin 
 
 t 
 
 
 
 74 (5- 
 
 730 LOG^Sl 
 
 N, e1 
 '-76° 
 
 tc. 
 

 1 7°-20° 
 
 
 
 
 LOG SIN, etc. 
 
 17° 
 
 18° 
 
 
 
 r 
 
 log sin 
 
 log tan log cot log ooa 
 
 log sin log tan log cot log cos 
 
 
 
 0' 
 
 1.46 594 
 
 1.48534 0.51466 1.98060 
 
 1.48998 1.5 1 178 0.48822 7.97821 
 
 60' 
 
 
 I 
 
 46635 
 
 48579 51 421 98056 
 
 49037 51221 48779 97817 
 
 59 
 
 
 2 
 
 46 676 
 
 48624 51376 98052 
 
 49076 51264 48736 97812 
 
 58 
 
 
 3 
 
 46717 
 
 48669 51 331 98048 
 
 49 115 51306 48694 97808 
 
 57 
 
 
 4 
 
 46758 
 
 48 714 51 286 98044 
 
 49153 51349 48651 97804 
 
 56 
 
 
 s 
 
 1.46800 
 
 7.48759 0.51 241 7.98040 
 
 1.49 192 1.51392 0.48608 1.97800 
 
 55 
 54 
 53 
 52 
 51 
 
 
 6 
 
 46841 
 
 48804 51 196 98036 
 
 49231 51435 48565 97796 
 
 
 7 
 
 46882 
 
 48849 51151 98032 
 
 49269 51478 48522 97792 
 
 
 8 
 
 46923 
 
 48894 51 106 98029 
 
 49308 51520 48480 97788 
 
 
 9 
 
 46964 
 
 48939 51061 98025 
 
 49 347 51563 48437 97784 
 
 
 10 
 
 7.47 005 
 
 7.48984 0.51 016 7.98021 
 
 1.49385 1.51606 0.48394 7.97779 
 
 50 
 
 
 II 
 
 47045 
 
 49029 50971 98017 
 
 49424 51648 48352 97775 
 
 49 
 
 
 12 
 
 47086 
 
 49073 50927 98013 
 
 49462 51 691 48309 97771 
 
 48 
 
 
 '3 
 
 47127 
 
 49 "8 50882 98009 
 
 49500 51734 48266 97767 
 
 47 
 46 
 
 
 H 
 
 47168 
 
 49163 50837 98005 
 
 49 539 51776 48224 97763 
 
 
 '5 
 
 1.47209 
 
 1.49207 0.50793 1.98001 
 
 '•49 577 1.51819 0.48181 7.97759 
 
 45 
 44 
 
 
 i6 
 
 47249 
 
 49 252 50 748 97 997 
 
 49615 51 861 48139 97754 
 
 
 17 
 
 47290 
 
 49 296 50 704 97 993 
 
 49654 51903 48097 97750 
 
 
 18 
 
 47330 
 
 49 341 50 659 97 989 
 
 49692 51946 48054 97746 
 
 42 
 
 
 19 
 
 47371 
 
 49385 50615 97986 
 
 49730 51988 48012 97742 
 
 41 
 
 
 20 
 
 1.47 41 1 
 
 7.49430 0.50570 7.97982 
 
 T.49768 7.52031 0.47969 7.97738 
 
 40 
 
 
 21 
 
 47452 
 
 49 474 50 526 97 978 
 
 49806 52073 47927 97734 
 
 39 
 
 
 22 
 
 47492 
 
 49519 50481 97 974 
 
 49844 52115 47885 97729 
 
 38 
 
 
 23 
 
 47 533 
 
 49563 50437 97970 
 
 49882 52157 47843 97725 
 
 37 
 
 
 24 
 
 47 573 
 
 49 607 50 393 97 966 
 
 49920 52200 47800 97721 
 
 36 
 
 
 ^1 
 
 1-47613 
 
 1.49652 0.50348 1.97962 
 
 1.49958 1.52242 0.47758 1.97 717 
 
 35 
 34 
 
 
 26 
 
 47654 
 
 49 696 50 304 97 958 
 
 49996 52284 47716 97713 
 
 
 27 
 
 47694 
 
 49 740 50 260 97 954 
 
 50034 52326 47674 97708 
 
 33 
 
 
 28 
 
 47 734 
 
 49 784 50 216 97 950 
 
 50072 52368 47632 97704 
 
 32 
 
 
 29 
 
 47 774 
 
 49828 50172 97946 
 
 50110 52410 47590 97700 
 
 31 
 
 
 30 
 
 T.47814 
 
 7.49872 0.50128 1.97942 
 
 7.50148 1.52452 0.47548 7.97696 
 
 30 
 
 ' 
 
 3> 
 
 47854 
 
 49916 50084 97938 
 
 50185 52494 47506 97691 
 
 29 
 
 
 32 
 
 47894 
 
 49 960 50 040 97 934 
 
 50223 52536 47464 97687 
 
 28 • 
 
 
 33 
 
 47 934 
 
 50004 49996 97930 
 
 50261 52578 47422 97683 
 
 27 
 
 
 34 
 
 47 974 
 
 50 048 49 952 97 926 
 
 50298 52620 47380 97679 
 
 26 
 
 
 35 
 
 1.48 014 
 
 7.50092 0.49908 7.97922 
 
 1.50336 1.52 661 0.47339 1.97674 
 
 25 
 
 
 36 
 
 48054 
 
 50 136 49 864 97 918 
 
 50374 52703 47297 97670 
 
 24 
 
 
 ^2 
 
 48094 
 
 50 180 49 820 97 914 
 
 50411 52745 4725s 97666 
 
 23 
 
 
 38 
 
 48133 
 
 50 223 49 777 97 910 
 
 50449 52787 47213 97662 
 
 22 
 
 
 39 
 
 48173 
 
 50 267 49 733 97 906 
 
 50486 52829 47 171 97657 
 
 21 
 
 
 40 
 
 T.48 213 
 
 7.50 31 1 0.49689 7.97902 
 
 7.50523 7.52870 0.47130 7.97653 
 
 20 
 
 
 41 
 
 48252 
 
 50 355 49 645 97 898 
 
 50561 52912 47088 97649 
 
 19 
 
 
 42 
 
 48292 
 
 50 398 49 602 97 894 
 
 50598 52953 47047 97645 
 
 18 
 
 
 43 
 
 48332 
 
 50442 49558 97890 
 
 50635 52995 47005 97640 
 
 "7 
 
 
 44 
 
 48371 
 
 50485 49 5 '5 97886 
 
 50673 53037 46963 97636 
 
 16 
 
 
 45 
 
 1.48 41 1 
 
 1.50529 0.49471 1.97882 
 
 1.50 7 10 1.53078 0.46922 1.97632 
 
 IS 
 
 
 46 
 
 48450 
 
 50572 49428 97878 
 
 50 747 53 120 46 880 97 628 
 
 14 
 
 
 47 
 
 48490 
 
 50616 49384 97874 
 
 50784 53 161 46839 97623 
 
 13 
 
 
 48 
 
 48529 
 
 50659 49341 97870 
 
 50821 53202 46798 97619 
 
 12 
 
 
 49 
 
 48568 
 
 50 703 49 297 97 866 
 
 50858 53244 46756 97615 
 
 . II 
 
 
 50 
 
 7.48 607 
 
 7.50 746" 0.49 254 7.97 861 
 
 7.50896 1.53285 0.46715 1.97 610 
 
 10 
 
 
 5« 
 
 48647 
 
 50789 49 21 1 97857 
 
 50933 53327 46673 97606 
 
 9 
 
 
 52 
 
 48686 
 
 50833 49167 97853 
 
 50 970 53 368 46 632 97 602 
 
 8 
 
 
 53 
 
 48725 
 
 50876 49 124 97849 
 
 51007 -53409 46591 97 597 
 
 7 
 
 
 54 
 
 48764 
 
 50919 49081 97845 
 
 51043 53450 46550 97593 
 
 6 
 
 
 55 
 
 1.48803 
 
 7.50 962 0.49 038 7.97 841 
 
 1. 5 1 080 1.53492 0.46508 1.97589 
 
 5 
 
 
 56 
 
 48842 
 
 51005 48995 97837 
 
 5H17 53 533 46467 97584 
 
 4 
 
 
 57 
 
 48881 
 
 51048 48952 97833 
 
 5« 154 53 574 46426 97580 
 
 3 
 
 
 58 
 
 48 920 
 
 51092 48908 97829 
 
 51 191 53615 46385 97576 
 
 2 
 
 59 1 
 
 48959 
 
 51 135 48 865 97 825 
 
 51227 53656 46344 97571 
 
 I 
 
 LO 
 6 
 
 60' 
 
 1.48998 
 
 [.51 178 0.48822 1.97 821 
 
 1-51264 1.53697 0.46303 1.97567 
 
 0' 
 
 
 log cos 
 
 log cot log tan log sin 
 
 log cos log oot log tan log sin 
 
 > 
 
 G SI 
 9°-7: 
 
 M, etc. 
 
 1° 
 
 72° (5^ 
 
 710 
 
 

 
 19° 
 
 
 »U LOG SIN, etc 
 
 f 
 
 logsm log tan log cot log 00s 
 
 log sin 
 
 log tan log oot log 00a 
 
 
 
 0' 
 
 1.51264 1.53697 0.46303 1.97567 
 
 1-53405 
 
 1.56 107 0.43893 r.97299 
 
 60' 
 
 
 I 
 
 5' 301 53738 46262 97563 
 51338 53 779 46221 97558. 
 
 53440 
 
 56 146 43 854 97 294 
 
 59 
 
 
 2 
 
 53 475 
 
 56185 43815 97289 
 
 58 
 
 
 3 
 
 51374 53820 46180 97 554 
 SI 411 53861 46139 97550 
 
 53509 
 
 56224 43776 97285 
 
 57 
 
 
 4 
 
 53 544 
 
 56 264 43 736 97 280 
 
 56 
 
 
 6 
 
 1-51447 1-53 902 0.46098 1.97545 
 51484 53943 46057 97541 
 
 1-53578 
 
 1.56303 0.43697 1.97276 
 
 55 
 
 
 S3 613 
 
 56 342 43 658 97 271 
 
 ';4 
 
 
 7 
 
 51520 53984 46016 97536 
 
 53647 
 
 56381 43619 97266 
 
 S3 
 
 
 8 
 
 51557 54025 45975 97532 
 
 53682 
 
 56 420 43 580 97 262 
 
 52 
 
 
 9 
 
 5' 593 54065 45935 97528 
 
 53716 
 
 56459 43541 97257 
 
 51 
 
 
 10 
 
 1.51629 T.54106 0.45894 T.97523 
 
 1-53 751 
 
 1.56498 0.43502 1.97252 
 
 50 
 
 
 II 
 
 51666 54147 45853 97519 
 
 53785 
 
 56 537 43 463 97 248 
 
 49 
 
 
 12 
 
 51702 54187 45813 97515 
 
 53819 
 
 56576 43424 97243 
 
 48 
 
 
 13 
 
 51738 54228 45772 97510 
 
 53854 
 
 56 615 43 385 97 238 
 
 47 
 
 
 14 
 
 51774 54269 45731 97506 
 
 53888 
 
 56 654 43 346 97 234 
 
 46 
 
 
 '1 
 
 1.51811 1.54309 0.45691 1.97 501 
 
 1-53922 
 
 1.56693 0.43307 1.97229 
 
 45 
 
 
 16 
 
 51847 54350 45650 97 497 
 
 S3 957 
 
 56 732 43 268 97 224 
 
 44 
 
 
 17 
 
 51883 54390 45610 97492 
 
 53991 
 
 56 771 43 229 97 220 
 
 43 
 
 
 18 
 
 51919 54431 45569 97488 
 
 . 54025 
 
 56810 43190 97215 
 
 42 
 
 
 19 
 
 51955 54471 45529 97484 
 
 54059 
 
 56849 43 151 97210 
 
 41 
 
 
 20 
 
 T.51991 T.54512 0.45488 T.97479 
 
 1-54093 
 
 T.56887 0.43113 T.97206 
 
 40 
 
 
 21 
 
 52027 54552 45448 97475 
 
 54127 
 
 56 926 43 074 97 201 
 
 39 
 
 
 22 
 
 52063 54593 45407 97470 
 
 54161 
 
 56965 43035 97196 
 
 38 
 
 
 23 
 
 52099 54633 45367 97466 
 
 54195 
 
 57 004 42 996 97 192 
 
 37 
 
 
 24 
 
 52135 54673 45327 97461 
 
 54229 
 
 _ 57 042 42958 97187 
 
 36 
 
 
 25 
 
 1.52 171 1.54714 0.45286 1.97457 
 
 1-54263 
 
 1.57081 0.42919 1.97182 
 
 35 
 
 
 26 
 
 52207 54754 45246 97453 
 
 54297 
 
 57120 42880 97178 
 
 34 
 
 
 27 
 
 52242 54794 45206 97448 
 
 54 331 
 
 57158 42842 97173 
 
 33 
 
 
 28 
 
 52278 54835 45165 97444 
 
 54365 
 
 57197 42803 97168 
 
 32 
 
 
 29 
 
 52314 5487s 45125 97439 
 
 54 399 
 
 57 23s 42 765 97 163 
 
 31 
 
 
 30 
 
 1-52350 1-54915 0.45085 T.97435 
 
 1-54 433 
 
 1.57274 0.42726 1.97159 
 
 30 
 
 
 31 
 
 52385 54955 45045 97430 
 
 54466 
 
 57312 42688 97154 
 
 29 
 
 
 32 
 
 52421 54 995 45005 97426 
 
 54500 
 
 57351 42649 97149 
 
 28 
 
 
 33 
 
 52456 55035 44965 97421 
 
 54 534 
 
 57389 42611 97145 
 
 27 
 
 
 34 
 
 52492 55075 44925 97417 
 
 54567 
 
 57428 42572 97140 
 
 26 
 
 
 ^l 
 
 1.52527 1.55 115 0.44885 1.97412 
 
 1.54601 
 
 1.57466 0.42534 1.97 135 
 
 25 
 
 
 36 
 
 52563 55155 44845 97408 
 
 54635 
 
 57504 42496 97130 
 
 24 
 
 
 37 
 
 52598 55195 44805 97403 
 
 54668 
 
 57 543 42457 97126 
 
 23 
 
 
 38 
 
 52634 55235 44765 97 399 
 
 54702 
 
 57581 42419 97121 
 
 22 
 
 
 39 
 
 52669 55275 44725 97394 
 
 54 735 
 
 57619 42381 97116 
 
 21 
 
 
 40 
 
 1.52705 1.55315 0.44685 T.97390 
 
 1.54 769 
 
 T.57658 0.42342 T.97111 
 
 20 
 
 
 41 
 
 52740 55 355 44645 97385 
 
 54802 
 
 57 696 42 304 97 107 
 
 19 
 
 
 42 
 
 52775 55 395 44605 973S1 
 
 54836 
 
 57 734 42 266 97 102 
 
 18 
 
 
 43 
 
 52811 55434 44566 97376 
 
 54869 
 
 57772- 42228 97097 
 
 17 
 
 
 44 
 
 52846 55474 44526 97372 
 
 54903 
 
 57810 42190 97092 
 
 16 
 
 
 45 
 
 1.52 881 1.55514 0.44486 1.97367 
 
 1-54936 
 
 r.57849 0.42151 T.97087 
 
 15 
 
 
 46 
 
 52916 55554 44446 97363 
 
 54969 
 
 57887 42113 97083 
 
 14 
 
 
 47 
 
 52951 55 593 44407 97358 
 
 55003 
 
 57925 42075 97078 
 
 13 
 
 
 48 
 
 52986 55633 44367 97 353 
 
 55036 
 
 57963 42037 97073 
 
 12 
 
 
 49 
 
 53021 55673 44327 97349 
 
 55069 
 
 58 001 41 999 97 068 
 
 II 
 
 
 50 
 
 1.53056 7.55712 0.44288 T.97344 
 
 1.55 102 
 
 T.58039 0.41961 1.97063 
 
 10 
 
 
 SI 
 
 53092 55752 44248 97340 
 
 55136 
 
 58077 41923 97059 
 
 9 
 
 
 52 
 
 53126 55 791 44209 97335 
 
 55169 
 
 58115 41885 97054 
 
 8 
 
 
 53 
 
 53161 55831 44169 97331 
 
 55202 
 
 58 153 41 847 97 049 
 
 7 
 
 
 54 
 
 53196 55870 44130 97326 
 
 _ 55 23s 
 
 58 191 41 809 97044 
 
 6 
 
 
 55 
 
 1-53 231 1.55910 0.44090 1.97322 
 
 1.55 268 
 
 1.58229 0.41 771 1.97039 
 
 5 
 
 
 56 
 
 53266 55949 44051 97317 
 
 55 301 
 
 58 267 41 733 97 035 
 
 4 
 
 
 H 
 
 53301 55989 44 01 1 97312 
 
 55 334 
 
 58 304 41 696 97030 
 
 3 
 
 
 58 
 
 53336 56028 43972 97308 
 
 55367 
 
 58 342 41 658 97 025 
 
 2 
 
 
 59 
 
 _ 53 370 56067 43933 97303 
 
 55400 
 
 58 380 41 620 97 020 
 
 1 
 
 
 60 
 
 1-53405 1-56107 0.43893 1.97299 
 
 I -55 433 
 
 1.58418 0.41582 1.97015 
 
 0' 
 
 
 
 log 00s log oot log tan log sin 
 
 log 00s 
 
 log oot log tan log sin 
 
 1 
 
 
 
 70° (s 
 
 ?) 
 
 69° LOG s 
 " 69 
 
 N, el 
 °-72° 
 
 tc. 
 
2 1 °-24° 
 LOG SIN, etc. 2r 
 
 22° 
 
 t 
 
 log aiu 
 
 log tan 
 
 log oot 
 
 log COS 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log cos 
 
 
 0' 
 
 > -55 433 
 
 f. 58 418 
 
 0.41 582 
 
 1-97015 
 
 1-57 358 
 
 T.60 641 
 
 0.39 359 
 
 T.96 717 
 
 60' 
 
 I 
 
 55466 
 
 58 455 
 
 41545 
 
 97010 
 
 57389 
 
 60 677 
 
 39323 
 
 96 711 
 
 59 
 
 2 
 
 55 499 
 
 58493 
 
 41507 
 
 97005 
 
 57420 
 
 60714 
 
 39286 
 
 96 706 
 
 58 
 
 3 
 
 55532 
 
 58531 
 
 41469 
 
 97001 
 
 57451 
 
 60 750 
 
 39250 
 
 96 701 
 
 57 
 
 4 
 
 55564 
 
 58569 
 
 41431 
 
 96996 
 
 57482 
 
 60 786 
 
 39214 
 
 96696 
 
 56 
 
 s 
 
 1-55 597 
 
 1.58606 
 
 0.41 394 
 
 T.96 991 
 
 1-57 514 
 
 T.60 823 
 
 0.39 177 
 
 T.96 691 
 
 55- 
 
 6 
 
 55630 
 
 58644 
 
 41356 
 
 96986 
 
 57 545 
 
 60859 
 
 39 141 
 
 96686 
 
 54 
 
 7 
 
 55663 
 
 58681 
 
 41 319 
 
 96981 
 
 57576 
 
 60895 
 
 39105 
 
 96681 
 
 53 
 
 8 
 
 55695 
 
 58719 
 
 41 281 
 
 96976 
 
 57607 
 
 60931 
 
 39069 
 
 96676 
 
 52 
 
 9 
 
 55728 
 
 58757 
 
 41243 
 
 96971 
 
 57638 
 
 60967 
 
 39033 
 
 96670 
 
 5J 
 
 10 
 
 1.55761 
 
 1-58794 
 
 0.41 206 
 
 T.96 966 
 
 1.57669 
 
 T.61 004 
 
 0.38 996 
 
 T.96 665 
 
 50 
 
 II 
 
 55 793 
 
 58832 
 
 41 168 
 
 96962 
 
 57700 
 
 61 040 
 
 38960 
 
 96660 
 
 49 
 
 12 
 
 "f^^ 
 
 58869 
 
 41 131 
 
 96957 
 
 57731 
 
 61 076 
 
 38924 
 
 96655 
 
 48 
 
 13 
 
 55858 
 
 58907 
 
 41093 
 
 96952 
 
 57762 
 
 61 112 
 
 38888 
 
 96650 
 
 47 
 
 14 
 
 55891 
 
 58944 
 
 41 056 
 
 _ 96 947 
 
 57 793 
 
 61 148 
 
 38852 
 
 96645 
 
 46 
 
 '5 
 
 1-55923 
 
 1.58 981 
 
 0.41 019 
 
 1 .96 942 
 
 1.57824 
 
 T.61 184 
 
 0.38816 
 
 1.96640 
 
 45 
 
 i6 
 
 55956 
 
 59019 
 
 40981 
 
 96937 
 
 57855 
 
 61 220 
 
 38780 
 
 96634 
 
 44 
 
 17 
 
 55988 
 
 59056 
 
 40944 
 
 96932 
 
 57885 
 
 61 256 
 
 38744 
 
 96629 
 
 43 
 
 18 
 
 56021 
 
 59094 
 
 40906 
 
 96927 
 
 57916 
 
 61 292 
 
 38708 
 
 96 624 
 
 42 
 
 19 
 
 56053 
 
 59 131 
 
 40869 
 
 96922 
 
 57 947 
 
 61328 
 
 38672 
 
 96619 
 
 41 
 
 20 
 
 1.56085 
 
 1.59 168 
 
 0.40 832 
 
 T.96 917 
 
 1-57978 
 
 T.61 364 
 
 0.38 636 
 
 T.96 614 
 
 40 
 
 21 
 
 56 118 
 
 59205 
 
 40795 
 
 96912 
 
 58008 
 
 61 400 
 
 38600 
 
 96608 
 
 39 
 
 22 
 
 56150 
 
 59243 
 
 40757 
 
 96907 
 
 58039 
 
 61436 
 
 38564 
 
 96603 
 
 38 
 
 23 
 
 56 182 
 
 59 280 
 
 40720 
 
 96903 
 
 58070 
 
 61472 
 
 38528 
 
 96598 
 
 37 
 
 24 
 
 56215 
 
 59317 
 
 40683 
 
 96898 
 
 58101 
 
 61508 
 
 38492 
 
 96593 
 
 36 
 
 ^1 
 
 1.56247 
 
 1-59 354 
 
 0.40 646 
 
 1.96893 
 
 T.58 131 
 
 T.61 544 
 
 0.38 456 
 
 1.96588 
 
 35 
 
 26 
 
 56279 
 
 59391 
 
 40609 
 
 96888 
 
 58162 
 
 61579 
 
 38421 
 
 96582 
 
 34 
 
 27 
 
 563" 
 
 59429 
 
 40571 
 
 96883 
 
 58192 
 
 61 615 
 
 38385 
 
 96577 
 
 33 
 
 28 
 
 56343 
 
 59466 
 
 40534 
 
 96878 
 
 58223 
 
 61651 
 
 38349 
 
 96572 
 
 32 
 
 29 
 
 56375 
 
 59503 
 
 40497 
 
 96873 
 
 58253 
 
 61687 
 
 38313 
 
 96567 
 
 31 
 
 30 
 
 1.56408 
 
 1.59540 
 
 0.40 460 
 
 1.96868 
 
 1.58284 
 
 T.6i 722 
 
 0.38 278 
 
 T.96 562 
 
 30 
 
 31 
 
 56440 
 
 59 577 
 
 40423 
 
 96863 
 
 58314 
 
 61758 
 
 38242 
 
 96556 
 
 29 
 
 32 
 
 56472 
 
 59614 
 
 40386 
 
 96858 
 
 58345 
 
 61794 
 
 38206 
 
 96551 
 
 28 
 
 33 
 
 56504 
 
 59651 
 
 40349 
 
 96853 
 
 58375 
 
 61830 
 
 38170 
 
 96546 
 
 27 
 
 ■ 34 
 
 56536 
 
 59688 
 
 40312 
 
 96848 
 
 58406 
 
 61865 
 
 38135 
 
 96541 
 
 26 
 
 35 
 
 T.56 568 
 
 1-59725 
 
 0.40 275 
 
 T.96 843 
 
 T.58 436 
 
 1.61 901 
 
 0.38099 
 
 1.96535 
 
 25 
 
 36 
 
 56599 
 
 59762 
 
 40238 
 
 96838 
 
 58467 
 
 61 936 
 
 38064 
 
 96530 
 
 24 
 
 37 
 
 56631 
 
 59 799 
 
 40 201 
 
 96833 
 
 58497 
 
 61972 
 
 38028 
 
 96525 
 
 23 
 
 38 
 
 56663 
 
 59835 
 
 40 165 
 
 96828 
 
 58527 
 
 62008 
 
 37992 
 
 96520 
 
 22 
 
 39 
 
 56695 
 
 59872 
 
 40 128 
 
 96823 
 
 58557 
 
 62043 
 
 37 957 
 
 96514 
 
 21 
 
 40 
 
 1.56727 
 
 1.59 909 
 
 0.40091 
 
 T.96 818 
 
 1.58588 
 
 T.62 079 
 
 0.37 921 
 
 T.96 509 
 
 20 
 
 41 
 
 56759 
 
 59946 
 
 40054 
 
 96813 
 
 58618 
 
 62114 
 
 37886 
 
 96504 
 
 19 
 
 42 
 
 56790 
 
 59983 
 
 40017 
 
 96808 
 
 58648 
 
 62 150 
 
 37850 
 
 96498 
 
 18 
 
 43 
 
 56822 
 
 60019 
 
 39981 
 
 96803 
 
 58678 
 
 62 185 
 
 37815 
 
 96493 
 
 17 
 
 44 
 
 56854 
 
 60056 
 
 39 944 
 
 96798 
 
 58709 
 
 62 221 
 
 37 779 
 
 96488 
 
 16 
 
 45 
 
 T.56 886 
 
 T.60 093 
 
 0.39 907 
 
 1.96793 
 
 1-58739 
 
 T.62 256 
 
 0-37 744 
 
 T.96 483 
 
 '5 
 
 46 
 
 56917 
 
 60 130 
 
 39870 
 
 96788 
 
 58769 
 
 62 292 
 
 37708 
 
 96477 
 
 14 
 
 47 
 
 56949 
 
 60 166 
 
 39834 
 
 96783 
 
 58799 
 
 62327 
 
 37673 
 
 96472 
 
 '3 
 
 48 
 
 56980 
 
 60203 
 
 39 797 
 
 96778 
 
 58 829 
 
 62 362 
 
 37638 
 
 96467 
 
 12 
 
 49 
 
 57012 
 
 60240 
 
 39760 
 
 96772 
 
 58859 
 
 62398 
 
 37602 
 
 96461 
 
 II 
 
 50 
 
 1.57044 
 
 1.60 276 
 
 0.39 724 
 
 1.96767 
 
 T.58 889 
 
 1.62433 
 
 0.37 567 
 
 T.96 456 
 
 10 
 
 51 
 
 57075 
 
 60313 
 
 39687 
 
 96 762 
 
 58919 
 
 62468 
 
 37532 
 
 96451 
 
 9 
 
 52 
 
 57107 
 
 60349 
 
 39651 
 
 96757 
 
 58949 
 
 62504 
 
 37496 
 
 96445 
 
 8 
 
 53 
 
 57138 
 
 60386 
 
 39614 
 
 96752 
 
 58979 
 
 62539 
 
 37461 
 
 96440 
 
 7 
 
 54 
 
 57169 
 
 60422 
 
 39578 
 
 96747 
 
 59009 
 
 62574 
 
 37426 
 
 96435 
 
 6 
 
 55 
 
 1.57 201 
 
 T.60 459 
 
 0.39 54« 
 
 T.96 742 
 
 1.59039 
 
 1.62 609 
 
 0.37 391 
 
 1.96429 
 
 5 
 
 56 
 
 57232 
 
 60495 
 
 39505 
 
 96737 
 
 59069 
 
 62645 
 
 37 355 
 
 96424 
 
 4 
 
 57 
 
 57264 
 
 60532 
 
 39468 
 
 96732 
 
 59098 
 
 62680 
 
 37320 
 
 96419 
 
 3 
 
 58 
 
 57295 
 
 60568 
 
 39432 
 
 96727 
 
 59128 
 
 62715 
 
 37285 
 
 96413 
 
 2 
 
 59 
 
 57326 
 
 60605 
 
 39 395 
 
 96 722 
 
 59158 
 
 62 750 
 
 37250 
 
 96408 
 
 I 
 
 60' 
 
 1-57358 
 
 1.60 641 
 
 0.39 359 
 
 1.96717 
 
 1.59188 
 
 1.62 785 
 
 0.37215 
 
 1 .96 403 
 
 0' 
 
 
 log 00s 
 
 log oot 
 
 log tan 
 
 log sin 
 
 log cos 
 
 log oot 
 
 log tan 
 
 log sin 
 
 t 
 
 LOG SIN, etc. 68<= 
 
 66°-68° 
 
 (58) 
 
 67^ 
 
23= 
 
 21°-24° 
 24° LOG SIN, etc 
 
 log sin log tan log cot log ops 
 
 1-59 188 
 59 2i» 
 
 59247 
 59277 
 
 _ 59 307 
 
 1-59336 
 
 59366 
 
 59396 
 
 59425 
 
 _ 59 455 
 
 T.59 484 
 
 59514 
 
 59 543 
 
 59 573 
 
 59602 
 
 7.59 632 
 59661 
 59690 
 
 59720 
 59 749 
 
 1-59 778 
 59808 
 
 59837 
 59866 
 
 _ 59 895 
 
 1-59924 
 
 59 954 
 59983 
 60012 
 60041 
 
 Y.60 070 
 60099 
 60128 
 
 60 157 
 60186 
 
 7.60 215 
 60244 
 60273 
 60302 
 60331 
 
 T.60 359 
 60388 
 60417 
 60446 
 
 _ 60 474 
 
 1.60503 
 60532 
 60561 
 60589 
 60618 
 
 7.60 646 
 60675 
 60704 
 60732 
 60761 
 
 T.60 789 
 60818 
 60846 
 60875 
 
 _ 60 903 
 
 1.60931 
 
 1.62 785 
 62820 
 6285s 
 62890 
 62926 
 
 T.62 961 
 62996 
 63031 
 63066 
 63101 
 
 7-63 13s 
 63170 
 63 205 
 63240 
 _ 63 275 
 1-63310 
 63345 
 63379 
 63414 
 63449 
 
 7.63 484 
 63519 
 63553 
 63588 
 63623 
 
 7.63 657 
 63692 
 
 63 726 
 63761 
 63796 
 
 7.63 830 
 63865 
 63899 
 63934 
 
 _ 63 968 
 1.64003 
 
 64037. 
 
 64072 
 
 64 106 
 64 140 
 
 7.6417s 
 64209 
 
 64243 
 
 64278 
 
 _ 64 312 
 
 1 .64 346 
 64381 
 64415 
 64449 
 
 _ 64 483 
 1.64517 
 64552 
 64586 
 64620 
 64654 
 1 .64 688 
 64 722 
 
 64756 
 
 64790 
 
 64824 
 
 7.64 858 
 
 0.37 215 
 37180 
 
 3714s 
 37 no 
 
 37074 
 
 0.37 039 
 
 37004 
 
 36969 
 
 36934 
 -36 899 
 
 0.36 865 
 36830 
 
 36795 
 36 760 
 
 36725 
 0.36 690 
 36655 
 36621 
 36586 
 36551 
 0.36516 
 36481 
 
 36447 
 36412 
 
 36377 
 0.36 343 
 36308 
 36274 
 36239 
 36204 
 
 0.36 170 
 
 36135 
 36101 
 36066 
 36032 
 
 0-35 997 
 35963 
 35928 
 35894 
 35860 
 
 0.35 825 
 35791 
 
 ■ 35 757 
 35722 
 35688 
 
 0.35 654 
 35619 
 35585 
 35551 
 35517 
 
 0.35 483 
 35448 
 35414 
 35380 
 35346 
 
 0.35 312 
 35278 
 35244 
 35210 
 
 35 176 
 0.3s '42 
 
 1.96403 
 
 96397 
 96392 
 
 96387 
 _ 96 381 
 1.96376 
 
 96370 
 
 96365 
 96360 
 
 96354 
 
 7.96 349 
 
 96343 
 
 96338 
 
 96333 
 
 _ 96 327 
 
 1.96322 
 
 96316 
 
 96311 
 
 96305 
 
 96300 
 
 7.96 294 
 96289 
 96284 
 96278 
 96273 
 
 1.96 267 
 96262 
 96256 
 96251 
 9624s 
 
 T.96 240 
 96234 
 96229 
 96223 
 96218 
 
 7.96212 
 96207 
 96 201 
 96 196 
 96 190 
 
 7.96 185 
 96179 
 96174 
 96168 
 96 162 
 
 1.96 157 
 96151 
 96 146 
 96 140 
 
 _ 96 135 
 
 1.96 129 
 96 123 
 96118 
 96 112 
 96 107 
 
 7.96 lOI 
 96095 
 96090 
 96084 
 
 _ 96 079 
 
 1.96073 
 
 log sis log tan log oot log cos 
 
 1.60 931 
 60960 
 60988 
 61 016 
 
 _ 61 045 ' 
 
 1. 61 073 
 61 loi 
 6i 129 
 61 158 
 61 186 
 
 7.61 214 
 61 242 
 61 270 
 61298 
 61 326 
 
 T-6i 354 
 61382 
 61 411 
 
 61438 
 61 466 
 
 7.61 494 
 61 522. 
 
 61550 
 61578 
 61 606 
 
 7.61 634 
 61 662 
 61689 
 61 717 
 61745 
 
 7.61 773 
 61 800 
 61828 
 61856 
 61883 
 
 7.61 911 
 
 61939 
 
 61 966 
 61994 
 62021 
 
 7.62 049 
 62076 
 
 62 104 
 62 131 
 62 159 
 
 7.62 186 
 
 62 214 
 
 62241 
 
 62268 
 
 62 296 
 
 7.62 323 
 
 62 350 
 
 62377 
 
 62405 
 
 _ 62 432 
 
 1.62459 
 
 62486 
 
 62513 
 
 62 541 
 
 _ 62 568 
 
 1-62595 
 
 1.64 858 
 64892 
 
 64 926 
 64960 
 
 •_ 64 994 
 
 1.65 028 
 
 65 062 
 65 096 
 65130 
 65 164 
 
 7.6s 197 
 65231 
 65 265 
 65299 
 
 _ 65 333 
 
 1.65 366 
 65 400 
 65434 
 65467 
 
 _ 65 501 
 
 165535 
 65568 
 
 65 602 
 65636 
 
 _ 65 669 
 
 1.65 703 
 
 65736 
 
 65770 
 
 65803 
 
 _ 65 837 
 
 1.65 870 
 65904 
 65937 
 65971 
 66004 
 
 7.66 038 
 66071 
 
 66 104 
 66138 
 66 171 
 
 7.66 204 
 66238 
 66 271 
 66304 
 _ 66 337 
 1.66371 
 66404 
 
 66437 
 
 66470 
 
 _ 66 503 
 
 1.66537 
 
 66 570 
 
 66603 
 
 66636 
 
 66669 
 
 7.66 702 
 
 66735 
 66768 
 66801 
 66834 
 7.66 867 
 
 0.35 142 
 35108 
 35074 
 35040 
 35006 
 
 0.34 972 
 34938 
 34904 
 34870 
 34836 
 
 0.34 803 
 34769 
 34 735 
 34701 
 34667 
 
 0.34 634 
 34600 
 
 34566 
 34 533 
 34499 
 
 0.34 465 
 34432 
 34398 
 34364 
 34331 
 
 0.34 297 
 34264 
 34230 
 34197 
 34163 
 
 0.34 130 
 34096 
 34063 
 34029 
 33996 
 
 0.33 962 
 33929 
 33896 
 33862 
 33829 
 
 1.96073 
 96067 
 96062 
 96056 
 96050 
 
 7.96 045 
 96039 
 96034 
 96028 
 96022 
 
 7.96017 
 96 on 
 96005 
 96000 
 95 994 
 
 7.95 988 
 95982 
 95 977 
 95971 
 95965 
 
 T-95 960 
 95 954 
 95948 
 95942 
 _ 95 937 
 1-95931 
 95925 
 95920 
 
 95914 
 95908 
 
 7.95 902 
 
 95897 
 95891 
 
 95885 
 _ 95 879 
 1-95873 
 95868 
 95 862 
 95856 
 95850 
 
 0.33 796 
 
 1-95844 
 
 33762 
 
 95839 
 
 33729 
 
 95833 
 
 33696 
 
 95827 
 
 33663 
 
 95821 
 
 0.33 629 
 
 1-95 815 
 
 33596 
 
 95 810 
 
 33563 
 
 95804 
 
 33530 
 
 • 95 798 
 
 33 497 
 
 95792 
 
 0.33463 
 
 1.95786 
 
 33430 
 
 95780 
 
 33 397 
 
 95 775 
 
 33364 
 
 95769 
 
 33331 
 
 95763 
 
 0.33 298 
 
 1-95 757 
 
 33265 
 
 95751 
 
 33232 
 
 95 745 
 
 33199 
 
 95 739 
 
 33166 
 
 95 733 
 
 0.33 133 
 
 1.95728 
 
 log COS 
 
 log cot log tan log sin | log cos log cot log tan log sin 
 
 60' 
 
 59 
 
 58 
 57 
 56 
 55 
 54 
 53 
 52 
 51 
 
 50 
 
 49 
 48 
 47 
 46 
 
 45 
 44 
 43 
 42 
 
 41 
 
 40 
 
 39 
 38 
 37 
 36 
 
 35 
 34 
 33 
 32 
 3' 
 
 30 
 
 29 
 
 28 
 
 27 
 26 
 
 25 
 24 
 23 
 
 22 
 21 
 
 20 
 
 19 
 18 
 
 17 
 16 
 
 «S 
 14 
 13 
 12 
 11 
 
 10 
 
 9 
 
 8 
 
 7 
 6 
 
 5 
 4 
 3 
 2 
 
 66° 
 
 (59) 
 
 Afio LOG SIN, etc. 
 
25°-28^ 
 LOG SIN, etc. 26*^ 
 
 26^ 
 
 t 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log cos 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log cos 
 
 ^^^" 
 
 0' 
 
 T.62 595 
 
 r.66 867 
 
 0-33 133 
 
 7.95 728 
 
 T.64 184 
 
 7.68818 
 
 0.31 182 
 
 7-95 366 
 
 60' 
 
 I 
 
 62622 
 
 66900 
 
 33100 
 
 95722 
 
 64210 
 
 68850 
 
 31 150 
 
 95 360 
 
 59 
 
 2 
 
 62649 
 
 66933 
 
 33067 
 
 95716 
 
 64 236 
 
 68882 
 
 31 118 
 
 95 354 
 
 - -58- 
 
 3 
 
 62676 
 
 66966 
 
 33034 
 
 95710 
 
 64262 
 
 68914 
 
 31086 
 
 95348 
 
 57 
 
 4 
 
 62703 
 
 66999 
 
 33 001- 
 
 95704 
 
 64288 
 
 68946 
 
 3' 054 
 
 95341 
 
 56 
 
 5 
 
 1.62730 
 
 T.67 032 
 
 0.32 968 
 
 1.95 698 
 
 7.64313 
 
 7.68 978 
 
 0.31 022 
 
 1-95 335 
 
 55 
 
 6 
 
 62757 
 
 67065 
 
 32935 
 
 95692 
 
 64339 
 
 69010 
 
 30990 
 
 95329 
 
 54 
 
 7 
 
 62784 
 
 67098 
 
 32902 
 
 95686 
 
 64365 
 
 69042 
 
 30958 
 
 95323 
 
 53 
 
 8 
 
 62 8u 
 
 67 131 
 
 32869 
 
 95680 
 
 64391 
 
 69074 
 
 30926 
 
 95317 
 
 52 
 
 9 
 
 62838 
 
 67163 
 
 32837 
 
 95674 
 
 64417 
 
 69 ie6 
 
 30894 
 
 95310 
 
 51 
 
 10 
 
 r.62 865 
 
 1.67 196 
 
 0.32 804 
 
 7.95 668 
 
 T.64 442 
 
 7.69 138 
 
 0.30 862 
 
 7.95 304 
 
 50 
 
 n 
 
 62892 
 
 67229 
 
 32771 
 
 95663 
 
 64468 
 
 69 170 
 
 30830 
 
 95298 
 
 49 
 
 12 
 
 62918 
 
 67 262 
 
 32738 
 
 95657 
 
 64494 
 
 69 202 
 
 30798 
 
 95292 
 
 48 
 
 '3 
 
 62945 
 
 67295 
 
 32705 
 
 95651 
 
 64519 
 
 69234 
 
 30766 
 
 95286 
 
 47 
 
 14 
 
 62972 
 
 67327 
 
 32 673 
 
 95645 
 
 64545 
 
 69266 
 
 30734 
 
 95279 
 
 46 
 
 IS 
 
 Y.62 999 
 
 1.67360 
 
 0.32 640 
 
 1.95639 
 
 1.64 571 
 
 1.69 298 
 
 0.30 702 
 
 1-95273 
 
 45 
 
 i6 
 
 63026 
 
 67393 
 
 32607 
 
 95633 
 
 64596 
 
 69329 
 
 30671 
 
 95267 
 
 44 
 
 17 
 
 63052 
 
 67426 
 
 32574 
 
 95627 
 
 64622 
 
 69361 
 
 30639 
 
 95261 
 
 43 
 
 18 
 
 63079 
 
 67458 
 
 32542 
 
 95621 
 
 64647 
 
 69393 
 
 30607 
 
 95254 
 
 42 
 
 19 
 
 63 1 06 
 
 67491 
 
 32509 
 
 95615 
 
 64673 
 
 69425 
 
 3057s 
 
 95248 
 
 41 
 
 20 
 
 7.63 133 
 
 T.67 524 
 
 0.32476 
 
 1.95609 
 
 T.64 698 
 
 7.69457 
 
 0-30 543 
 
 7.95 242 
 
 40 
 
 21 
 
 63159 
 
 67556 
 
 32444 
 
 95603 
 
 64724 
 
 69488 
 
 30512 
 
 95236 
 
 39 
 
 22 
 
 63186 
 
 67589 
 
 32 411 
 
 95 597 
 
 64749 
 
 69 520 
 
 30480 
 
 95229 
 
 38 
 
 23 
 
 63213 
 
 67 622 
 
 32378 
 
 95591 
 
 64775 
 
 69552 
 
 30448 
 
 95223 
 
 37 
 
 24 
 
 63239 
 
 67654 
 
 32346 
 
 95585 
 
 64800 
 
 69584 
 
 30416 
 
 95217 
 
 36 
 
 25 
 
 1.63 266 
 
 1.67687 
 
 0.32313 
 
 1-95 579 
 
 T.64 826 
 
 1.69 615 
 
 0.30 385 
 
 1.95211 
 
 35 
 
 26 
 
 63292 
 
 67719 
 
 32281 
 
 95 573 
 
 64851 
 
 69647 
 
 30353 
 
 95204 
 
 34 
 
 27 
 
 63319 
 
 67752 
 
 32248 
 
 95567 
 
 64877 
 
 69679 
 
 30321 
 
 95198 
 
 33 
 
 28 
 
 63345 
 
 67 785 . 
 
 32215 
 
 95561 
 
 64902 
 
 69 710 
 
 30290 
 
 95192 
 
 32 
 
 29 
 
 63372 
 
 67817 
 
 32183 
 
 95 555 
 
 64927 
 
 69742 
 
 30258 
 
 95185 
 
 31 
 
 30 
 
 1-63398 
 
 1.67850 
 
 0.32 150 
 
 1-95 549 
 
 7.64 953 
 
 T.69 774 
 
 0.30 226 
 
 1-95 179 
 
 30 
 
 31 
 
 63425 
 
 67882 
 
 32 118 
 
 95 543 
 
 64978 
 
 69805 
 
 30195 
 
 95173 
 
 29 
 
 32 
 
 63451 
 
 67915 
 
 32085 
 
 95 537 
 
 65003 
 
 69837 
 
 30163 
 
 95167 
 
 28 
 
 2i 
 
 63478 
 
 67947 
 
 32053 
 
 95531 
 
 65029 
 
 69868 
 
 30132 
 
 95 160 
 
 27 
 
 34 
 
 63504 
 
 67980 
 
 32020 
 
 95525 
 
 65054 
 
 69900 
 
 30100 
 
 95154 
 
 26 . 
 
 35 
 
 1-63531 
 
 T.68012 
 
 0.31 988 
 
 1-95 5'9 
 
 1.65079 
 
 7.69 932 
 
 0.30 068 
 
 1.95 148 
 
 25 
 
 36 
 
 63557 
 
 68044 
 
 31956 
 
 95513 
 
 65 104 
 
 69963 
 
 30037 
 
 95141 
 
 24 
 
 37 
 
 63583 
 
 68077 
 
 31923 
 
 95507 
 
 65130 
 
 69995 
 
 30005 
 
 95135 
 
 23 
 
 38 
 
 63 610 
 
 68109 
 
 31 891 
 
 95500 
 
 65155 
 
 70026 
 
 29974 
 
 95129 
 
 22 
 
 39 
 
 63636 
 
 68142 
 
 31858 
 
 95 494 
 
 65 180 
 
 70058 
 
 29942 
 
 95 122 
 
 21 
 
 40 
 
 T.63 662 
 
 T.68174 
 
 0.31 826 . 
 
 7.95 488 
 
 7.65 205 
 
 7.70 089 
 
 0.29911 
 
 7.95 116 
 
 20 
 
 41 
 
 63689 
 
 68206 
 
 31 794 
 
 95482 
 
 65 230 
 
 70 121 
 
 29879 
 
 -95 no 
 
 19 
 
 42 
 
 63715 
 
 68239 
 
 31761 
 
 95476 
 
 6525s 
 
 70152 
 
 29848 
 
 95 103 
 
 18 
 
 43 
 
 63741 
 
 68271 
 
 31729 
 
 95470 
 
 65281 
 
 70 184 
 
 29816 
 
 95097 
 
 17 
 
 44 
 
 63767 
 
 68303 
 
 31697 
 
 95464 
 
 65306 
 
 70215 
 
 29785 
 
 95090 
 
 16 
 
 45 
 
 1-63794 
 
 7.68 336 
 
 0.31 664 
 
 1-95458 
 
 1-65331 
 
 1.70247 
 
 0.29 753 
 
 1.95084 
 
 '5 
 
 46 
 
 63820 
 
 68368 
 
 3' 632 
 
 95452 
 
 65 356 
 
 70278 
 
 29722 
 
 95078 
 
 «4 
 
 47 
 
 63846 
 
 68400 
 
 31 600 
 
 95446 
 
 65381 
 
 70309 
 
 29691 
 
 95071 
 
 13 
 
 48 
 
 63873. 
 
 68432 
 
 31568 
 
 95440 
 
 65 406 
 
 70341 
 
 29659 
 
 95065 
 
 12 
 
 49 
 
 63898 
 
 68465 
 
 31535 
 
 95 434 
 
 65431 
 
 70372 
 
 29628 
 
 95059 
 
 11 
 
 50 
 
 T.63 924 
 
 T.68 497 
 
 0-31 503 
 
 1-95427 
 
 1.65456 
 
 1.70404 
 
 0.29 596 
 
 7.95 052 
 
 10 
 
 51 
 
 63950 
 
 68529 
 
 3' 47' 
 
 95421 
 
 65481 
 
 70435 
 
 29565 
 
 95046 
 
 9 
 
 52 
 
 63976 
 
 68561 
 
 31439 
 
 95415 
 
 65 506 
 
 70466 
 
 29534 
 
 95039 
 
 8 
 
 S3 
 
 64002 
 
 68593 
 
 3t4<?7 
 
 95409 
 
 65531 
 
 70498 
 
 29502 
 
 95033 
 
 7 
 
 54 
 
 64028 
 
 68626 
 
 3«374 
 
 95403 
 
 65556 
 
 70529 
 
 29471 
 
 95027 
 
 6 
 
 55 
 
 T.64 054 
 
 T.68 658 
 
 0.31 342 
 
 1-95 397 
 
 1.65 580 
 
 1.70560 
 
 0.29440 
 
 1.95020 
 
 5 
 
 56 
 
 64080 
 
 68690 
 
 3I3JO 
 
 95 391 
 
 65605 
 
 70592 
 
 29408 
 
 95014 
 
 4 
 
 57 
 
 64 106 
 
 68722 
 
 31278 
 
 95384 
 
 65630 
 
 70623 
 
 29377 
 
 95007 
 
 3 
 
 S8 
 
 64132 
 
 68754 
 
 31246 
 
 95378 
 
 ^5^55 
 
 70654 
 
 29346 
 
 95001 
 
 2 
 
 59 
 
 64158 
 
 68786 
 
 31 214 
 
 95372 
 
 65680 
 
 70685 
 
 29315 
 
 94 995 
 
 1 
 
 60' 
 
 1.64 184 
 
 7.68818 
 
 0.31 182 
 
 1.95366 
 
 1.65 70s 
 
 1.70 717 
 
 0.29 283 
 
 1.94988 
 
 0' 
 
 
 log COB 
 
 log oot 
 
 log tan 
 
 log sin , 
 
 log cos 
 
 log oot 
 
 log tan 
 
 log sin 
 
 1 
 
 LOG SIN, etc. 64° 
 61°-64° 
 
 (60) 
 
 63= 
 
27° 
 
 0' 
 
 I 
 
 2 
 
 3 
 4 
 
 S 
 6 
 
 7 
 8 
 
 9 
 10 
 
 13 
 H 
 
 «S 
 i6 
 
 '7 
 i8 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 24 
 
 25 
 26 
 
 27 
 28 
 29 
 
 30 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 40 
 
 41 
 42 
 
 43 
 44 
 
 45 
 46 
 
 47 
 48 
 
 49 
 
 50 
 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 60' 
 
 log sin log tan logoot log cos I log sin 
 
 26°-28° 
 28° LOG SIN, etc 
 
 1.65 705 
 65 729 
 65754 
 65779 
 65 804 
 
 T.65 828 
 
 65853 
 65878 
 
 65 902 
 65927 
 
 if -65 952 
 65976 
 66001 
 66025 
 66050 
 
 T.66 075 
 66099 
 
 66 124 
 66148 
 66173 
 
 T.66 197 
 
 66221 
 
 66246 
 
 66270 
 
 _ 66 295 
 
 1.66319 
 
 66343 
 66368 
 66392 
 66416 
 
 1.66 441 
 66465 
 66489 
 66513 
 
 _ 66 537 
 1.66562 
 66586 
 66610 
 66634 
 66658 
 
 T.66 682 
 66 706 
 66 731 
 66755 
 
 66 779 
 T.66 803 
 
 66827 
 66851 
 66875 
 $6899 
 
 T.66 922 
 66946 
 66970 
 66994 
 67018 
 
 T.67 042 
 67066 
 67090 
 
 67 113 
 
 _ 67 137 
 
 1.67 161 
 
 log cos 
 
 1.70 717 
 
 70748 
 70779 
 
 70810 
 70841 
 
 T.70 873 
 70904 
 70935 
 
 70966 
 
 70997 
 
 T.7I 028 
 
 71059 
 
 71 090 
 
 71 T2I 
 
 _7ii53 
 
 1. 71 184 
 
 71 215 
 
 71 246 
 
 71277 
 
 _ 71 308 
 
 1-71339 
 71370 
 71401 
 
 71431 
 71 462 
 
 7.71 493 
 7«524 
 71555 
 71586 
 
 71 617 
 
 T.71 648 
 
 71679 
 
 71709 
 
 71740 
 
 _ 71 771 
 
 1. 71 802 
 
 71833 
 71863 
 71894 
 71925 
 
 I-7I 955 
 71986 
 72017 
 72048 
 72078 
 
 T.72 109 
 
 72 140 
 72170 
 72201 
 72231 
 
 T.72 262 
 72293 
 72323 
 72354 
 _ 72 384 
 1-72415 
 72445 
 72476 
 72 506 
 
 _ 72 537 
 
 1-72567 
 
 log cot 
 
 0.29 283 
 29 252 
 
 29 221 
 29 190 
 29159 
 0.29 127 
 29096 
 29065 
 29034 
 29003 
 
 0.28 972 
 28941 
 28910 
 28879 
 28847 
 
 0.28816 
 28785 
 28754 
 28 723 
 28 692 
 
 0.28 661 
 28 630 
 
 28599 
 28569 
 28538 
 0.28 507 
 28476 
 
 28445 
 28414 
 28383 
 
 0.28 352 
 28 321 
 28291 
 28 260 
 28229 
 
 0.28 198 
 28167 
 28137 
 28106 
 28075 
 
 0.28 045 
 28014 
 
 27983 
 27952 
 27922 
 0.27 891 
 27860 
 27 830 
 27799 
 27 769 
 
 0.27 738 
 
 27707 
 27677 
 27 646 
 27 616 
 0.27 585 
 
 27555 
 27524 
 
 27494 
 
 27463 
 
 027433 
 
 log tan 
 
 1 .94 988 
 94982 
 
 94 975 
 94969 
 94962 
 
 1.94956 
 94 949 
 94 943 
 94936 
 94930 
 
 T.94 923 
 94917 
 
 94 9" 
 94904 
 94898 
 T.94 891 
 94885 
 94878 
 94871 
 94865 
 
 T.94 858 
 94852 
 94845 
 94839 
 _ 94 832 
 1.94826 
 94819 
 
 94813 
 94806 
 
 94 799 
 
 7.94 793 
 
 94786 
 
 94780 
 
 94 773 
 
 _ 94 767 
 
 1.94760 
 
 94 753 
 
 94 747 
 
 94740 
 
 94 734 
 
 T.94 727 
 
 94720 
 
 94714 
 
 94707 
 
 _ 94 700 
 
 1.94694 
 
 94687 
 
 94680 
 
 94674 
 
 94667 
 
 T.94 660 
 94654 
 94647 
 94640 
 
 _ 94 634 
 
 1.94627 
 94620 
 94614 
 94607 
 94600 
 
 T.94 593 
 log sin 
 
 log tan log cot log ooa 
 
 1.67 161 
 
 67 185 
 
 67 208 
 
 67232 
 
 _ 67 256 
 
 1.67 280 
 
 67303 
 
 67327 
 
 67350 
 
 _ 67 374 
 
 T.67 398 
 
 67 421 
 
 67445 
 67468 
 
 _ 67 492 
 
 1-67515 
 67539 
 67562 
 67586 
 67 609 
 
 i"-67 633 
 67 656 
 67680 
 67703 
 67 726 
 
 T.67 750 
 
 67773 
 67 796 
 67 820 
 67843 
 T.67 866 
 
 67 890 
 
 67913 
 67936 
 
 _ 67 959 
 1.67982 
 68006 
 68029 
 68052 
 68075 
 
 T.68 098 
 
 68 121 
 68 144 
 68167 
 68 190 
 
 T.68 213 
 68237 
 68260 
 68283 
 68305 
 
 T.68 328 
 68351 
 68374 
 68397 
 68420 
 
 T.68 443 
 • 68466 
 68489 
 68512 
 68534 
 1-68557 
 log cos 
 
 1.72567 
 72598 
 72628 
 72659 
 72 689 
 
 T.72 720 
 
 72750 
 
 72 780 
 72 811 
 
 72 841 
 
 T.72 872 
 72902 
 
 72932 
 72963 
 
 _ 72 993 
 1.73023 
 
 73054 
 73084 
 
 73 "4 
 73144 
 
 1-73175 
 73205 
 
 73235 
 73265 
 
 _ 73 295 
 
 1-73326 
 
 73356 
 
 73386 
 
 73416 
 
 73446 
 
 T.73 476 
 
 73507 
 
 73 537 
 
 73567 
 
 _ 73 597 
 
 1.73627 
 
 73657 
 73687 
 
 73717 
 _ 73 747 
 
 1-73 777 
 73807 
 
 73837 
 73867 
 
 _ 73 897 
 1.73927 
 
 73 957 
 73987 
 74017 
 74047 
 
 1-74077 
 74107 
 
 74137 
 
 74 166 
 
 _ 74 196 
 
 1.74226 
 
 74256 
 
 74286 
 
 74316 
 
 _ 74 345 
 
 1-74 375 
 
 0-27 433 
 27402 
 27372 
 
 27341 
 27 311 
 
 0.27 280 
 27 250 
 27 220 
 27 189 
 27159 
 
 0.27 128 
 27098 
 27068 
 27037 
 27007 
 
 0.26977 
 26946 
 26916 
 26 886 
 26856 
 
 0.26 825 
 
 26795 
 26 765 
 
 26735 
 26705 
 
 0.26 674 
 26644 
 26614 
 26584 
 26554 
 
 0.26 524 
 
 26493 
 26463 
 
 26433 
 26403 
 
 0.26 373 
 
 26343 
 26313 
 26283 
 26253 
 
 0.26 223 
 26193 
 26 163 
 26 133 
 26 103 
 
 0.26 073 
 26 043 
 26013 
 25983 
 25953 
 
 0.25 923 
 
 25893 
 25863 
 
 25834 
 25 804 
 
 0.25 774 
 
 25744 
 25714 
 25 684 
 
 2565s 
 0.25 625 
 
 1-94 593 
 94587 
 94580 
 
 94 573 
 _ 94 567 
 1.94560 
 
 94 553 
 
 94546 
 
 94540 
 
 _ 94 533 
 
 1.94526 
 
 94519 
 
 94513 
 
 94506 
 
 _ 94 499 
 
 1.94492 
 
 .94485 
 94479 
 
 94472 
 
 _ 94 465 
 
 T.94 458 
 
 94451 
 
 94 445 
 
 94438 
 
 _ 94 431 
 
 1.94424 
 
 94417 
 94410 
 
 94404 
 
 94 397 
 
 T.94 390 
 94383 
 94376 
 94369 
 
 _ 94 362 
 
 1-94 355 
 94 349 
 94342 
 94 335 
 94328 
 
 T.94 321 
 94314 
 94307 
 94300 
 
 _ 94 293 
 1 .94 286 
 94279 
 94273 
 94266 
 94259 
 T.94 252 
 
 94245 
 
 94238 
 
 94231 
 
 94224 
 
 1.94217 
 
 94 210 
 
 94203 
 
 94196 
 
 _94i89 
 
 1.94 182 
 
 log cot log tan log sin 
 
 62^^ 
 
 (61) 
 
 AI0 LOG SIN, etc. 
 • 6r-64° 
 
29°-32° 
 LOG SIN, etc. »9 
 
 30° 
 
 / 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log oos 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log 008 
 
 
 0' 
 
 '•^f557 
 
 1-74 375 
 
 0.25 625 
 
 r.94 182 
 
 7.69 897 
 
 7.76 144 
 
 0.23 856 
 
 T.93 753 
 
 60' 
 
 I 
 
 68580 
 
 74405 
 
 25595 
 
 94175 
 
 69919 
 
 76173 
 
 23827 
 
 93746 
 
 59 
 
 2 
 
 68603 
 
 74 435 
 
 25565 
 
 94168 
 
 69941 
 
 76202 
 
 23798 
 
 93738 
 
 58 
 
 3 
 
 68625 
 
 74465 
 
 25 535 
 
 94 161 
 
 69963 
 
 76231 
 
 23769 
 
 93731 
 
 57 
 
 4 
 
 68648 
 
 74 494 
 
 25 506 
 
 94154 
 
 69984 
 
 76261 
 
 23739 
 
 93724 
 
 56 
 
 S 
 
 7.68671 
 
 1.74524 
 
 0.25 476 
 
 1.94147 
 
 7.70 006 
 
 7.76 290 
 
 0.23 710 
 
 1-93717 
 
 55 
 
 6 
 
 68694 
 
 74 554 
 
 25446 
 
 94140 
 
 70028 
 
 76319 
 
 23681 
 
 93709 
 
 54 
 
 7 
 
 68 716 
 
 74583 
 
 25417 
 
 94133 
 
 70050 
 
 76348 
 
 23652 
 
 93702 
 
 53 
 
 8 
 
 68739 
 
 74613 
 
 25387 
 
 94126 
 
 70072 
 
 76377 
 
 23623 
 
 93695 
 
 52 
 
 9 
 
 68762 
 
 74643 
 
 25357 
 
 94119 
 
 70093 
 
 76406 
 
 23594 
 
 93687 
 
 51 
 
 10 
 
 T.68 784 
 
 ^■74673 
 
 0.25 327 
 
 T.94 112 
 
 7.70 115 
 
 7.76435 
 
 0,23 565 
 
 1.93680 
 
 50 
 
 II 
 
 68807 
 
 74702 
 
 25 298 
 
 94105 
 
 70137 
 
 76464 
 
 23536 
 
 93673 
 
 49 
 
 12 
 
 68829 
 
 74732 
 
 25268 
 
 94098 
 
 70159 
 
 76493 
 
 23507 
 
 93665 
 
 48 
 
 13 
 
 68852 
 
 74762 
 
 25238 
 
 94090 
 
 70 180 
 
 76522 
 
 23478 
 
 93658 
 
 47 
 
 14 
 
 68875 
 
 74791 
 
 25209 
 
 94083 
 
 70202 
 
 76551 
 
 23449 
 
 93650 
 
 46 
 
 '5 
 
 1.68897 
 
 1.74 821 
 
 0.25 179 
 
 1.94076 
 
 7.70 224 
 
 1.76580 
 
 0.23 420 
 
 1-93643 
 
 45 
 
 i6 
 
 68920 
 
 74851 
 
 25149 
 
 94069 
 
 70245 
 
 76609 
 
 23391 
 
 93636 
 
 44 
 
 17 
 
 68942 
 
 74880 
 
 25 120 
 
 94062 
 
 70267 
 
 76639 
 
 23361 
 
 93628 
 
 43 
 
 18 
 
 68965 
 
 74910 
 
 25090 
 
 9405s 
 
 70288 
 
 76668 
 
 23332 
 
 93621 
 
 42 
 
 19 
 
 68987 
 
 74 939 
 
 25061 
 
 94048 
 
 70310 
 
 76697 
 
 23303 
 
 93614 
 
 41 
 
 20 
 
 T.69010 
 
 1.74969 
 
 0.25 031 
 
 T.94 041 
 
 7.70 332 
 
 1.76725 
 
 0.23 275 
 
 7.93 606 
 
 40 
 
 21 
 
 69032 
 
 74998 
 
 25002 
 
 94034 
 
 70353 
 
 76754 
 
 23246 
 
 93 599 
 
 39 
 
 22 
 
 69055 
 
 75028 
 
 24972 
 
 94027 
 
 70375 
 
 76783 
 
 23217 
 
 93 591 
 
 38 
 
 23 
 
 69077 
 
 75058 
 
 24942 
 
 94020 
 
 70396 
 
 76812 
 
 23188 
 
 93584 
 
 37 
 
 24 
 
 69 100 
 
 75087 
 
 24913 
 
 94012 
 
 70418 
 
 76841 
 
 23159 
 
 93 577 
 
 36 
 
 ^1 
 
 T.69 122 
 
 1.75 117 
 
 0.24 883 
 
 7.94 005 
 
 7.70439 
 
 7.76 870 
 
 0.23 130 
 
 1-93569 
 
 35 
 
 26 
 
 69144 
 
 75146 
 
 24854 
 
 93998 
 
 70461 
 
 76899 
 
 23IOI 
 
 93562 
 
 34 
 
 27 
 
 69 167 
 
 75176 
 
 24824 
 
 93991 
 
 70482 
 
 76928 
 
 23072 
 
 93 554 
 
 33 
 
 28 
 
 69 189 
 
 75205 
 
 24795 
 
 93984 
 
 70504 
 
 76957 
 
 23043 
 
 93 547 
 
 32 
 
 29 
 
 69212 
 
 75235 
 
 24765 
 
 93 977 
 
 70525 
 
 76986 
 
 23014 
 
 93 539 
 
 31 
 
 30 
 
 T.69 234 
 
 1.75264 
 
 0.24 736 
 
 1.93970 
 
 1-70547 
 
 7.77015 
 
 0.22 985 
 
 1-93532 
 
 30 
 
 31 
 
 69 256 
 
 75294 
 
 24 706 
 
 93963 
 
 70568 
 
 77044 
 
 22956 
 
 93525 
 
 29 
 
 32 
 
 69279 
 
 75323 
 
 24677 
 
 93 955 
 
 70590 
 
 77073 
 
 22927 
 
 93517 
 
 28 
 
 33 
 
 69301 
 
 75 353 
 
 24647 
 
 93948 
 
 70 61 1 
 
 77101 
 
 22899 
 
 93510 
 
 27 
 
 34 
 
 69323 
 
 75382 
 
 24618 
 
 93941 
 
 70633 
 
 77130 
 
 22870 
 
 93502 
 
 26 
 
 35 
 
 1.69345 
 
 1.75411 
 
 0.24 589 
 
 ■•93 934 
 
 1.70654 
 
 1.77159 
 
 0.22 841 
 
 1-93 495 
 
 25 
 
 36 
 
 69368 
 
 75441 
 
 24559 
 
 93927 
 
 70675 
 
 77188 
 
 22812 
 
 93487 
 
 24 
 
 37 
 
 69390 
 
 75470 
 
 24530 
 
 93920 
 
 70697 
 
 77217 
 
 22783 
 
 93480 
 
 23 
 
 38 
 
 69412 
 
 75500 
 
 24500 
 
 93912 
 
 70718 
 
 77246 
 
 22754 
 
 93472 
 
 22 
 
 39 
 
 69434 
 
 75529 
 
 24471 
 
 93905 
 
 70739 
 
 77274 
 
 22 726 
 
 93465 
 
 21 
 
 40 
 
 T.69 456 
 
 1-75558 
 
 0.24 i\i\?. 
 
 7.93 898 
 
 7.70 761 
 
 1-77303 
 
 0.22 697 
 
 7-93 457 
 
 20 
 
 41 
 
 69479 
 
 75588 
 
 24412 
 
 93891 
 
 70 782 
 
 77332 
 
 22668 
 
 93450 
 
 'R 
 
 42 
 
 69 501 
 
 75617 
 
 24383 
 
 93884 
 
 70803 
 
 77361 
 
 22639 
 
 93442 
 
 18 
 
 43 
 
 69523 
 
 75647 
 
 24353 
 
 93876 
 
 70824 
 
 77390 
 
 22610 
 
 93435 
 
 17 
 
 44 
 
 69545 
 
 75676 
 
 24324 
 
 93869 
 
 70846 
 
 77418 
 
 22582 
 
 93427 
 
 16 
 
 45 
 
 1.69567 
 
 1-75 70s 
 
 0.24 295 
 
 1.93 862 
 
 7.70 867 
 
 1-77 447 
 
 0.22 553 
 
 1.93420 
 
 15 
 
 46 
 
 69589 
 
 75 735 
 
 24265 
 
 93855 
 
 70888 
 
 77476 
 
 22524 
 
 93412 
 
 14 
 
 47 
 
 69 611 
 
 75764 
 
 24236 
 
 93847 
 
 70909 
 
 77505 
 
 22495 
 
 93405 
 
 13 
 
 48 
 
 69633 
 
 75 793 
 
 24207 
 
 93840 
 
 70931 
 
 77 533 
 
 22467 
 
 93 397 
 
 12 
 
 49 
 
 69655 
 
 75822 
 
 24178 
 
 93833 
 
 70952 
 
 77562 
 
 22438 
 
 93390 
 
 II 
 
 50 
 
 1.69677 
 
 1-75852 
 
 0.24 148 
 
 1.93826 
 
 1-70973 
 
 1-77 591 
 
 0.22 409 
 
 1.93382 
 
 10 
 
 SI 
 
 69699 
 
 75881 
 
 24119 
 
 93819 
 
 70994 
 
 77619 
 
 22381 
 
 93 375 
 
 9 
 
 52 
 
 69721 
 
 75910 
 
 24090 
 
 93 811 
 
 71 015 
 
 77648 
 
 22352 
 
 93367 
 
 8 
 
 53 
 
 69743 
 
 75 939 
 
 24061 
 
 93804 
 
 71036 
 
 77677 
 
 22323 
 
 93360 
 
 7 
 
 54 
 
 69765 
 
 75969 
 
 24031 
 
 93 797 
 
 71058 
 
 77706 
 
 22294 
 
 93352 
 
 6 
 
 55 
 
 7.69 787 
 
 1.75998 
 
 0.24 002 
 
 1-93789 
 
 1.71 079 
 
 1-77 734 
 
 0.22 266 
 
 1-93 344 
 
 5 
 
 56 
 
 69809 
 
 76027 
 
 23973 
 
 93782 
 
 71 100 
 
 77763 
 
 22 237 
 
 93 337 
 
 4 
 
 57 
 
 69831 
 
 76056 
 
 23944 
 
 93 775 
 
 71 121 
 
 77791 
 
 22 209 
 
 93329 
 
 3 
 
 58 
 
 69853 
 
 76086 
 
 23914 
 
 93768 
 
 71 142 
 
 77 820 
 
 22 180 
 
 93322 
 
 2 
 
 59 
 
 69875 
 
 76 115 
 
 23885 
 
 93760 
 
 71 163 
 
 77849 
 
 22 151 
 
 93314 
 
 1 
 
 60' 
 
 1.69897 
 
 1.76144 
 
 0.23 856 
 
 1-93 753 
 
 1. 71 184 
 
 1-77877 
 
 0.22 123 
 
 1-93307 
 
 0' 
 
 
 log cos 
 
 log oot 
 
 log tan 
 
 log sin 
 
 log oos 
 
 log oot 
 
 log tan 
 
 log sin 
 
 t 
 
 LOG SIN, etc. 60*^ 
 
 67°-60° 
 
 (62) 
 
 59° 
 
t 
 
 31° 
 
 loff sin loff tan ^no• nn¥ Tftm »»« 
 
 32° log"in!^ 
 
 
 
 9tC 
 
 0' 
 
 I 
 
 2 
 
 3 
 
 4 
 
 ea *" iug uoiu iO^ oOii ■'Off COS 
 
 1.71184 1.77 S77 0.22123 I.93 307 
 71205 77906 22094 93299 
 71226 77935 22065 93291 
 71247 77963 22037 93284 
 
 _ 71 268 _ 77 992 22008 93276 
 
 log sin log tan log cot log cos 
 1.72421 1.79579 0.20421 T.92842 
 72 441 79 607 20 393 92 834 
 72461 79635 20365 92826 
 72482 79663 20337 92818 
 72502 79691 20309 92810 
 
 60' 
 
 59 
 58 
 57 
 56 
 
 55 
 54 
 SZ 
 52 
 51 
 
 
 I 
 
 1. 71 289 1.78020 0.21980 T.93 269 
 71 310 78049 21 951 93261 
 71 331 78077 21923 93253 
 71 352 78 106 21 894 93 246 
 
 1.72522 1.79719 0.20281 7.92803 
 72542 79747 20253 92795 
 72562 79776 20224 92787 
 72 582 79 804 20 196 92 779 
 72 602 79 832 20 168 92 771 
 
 
 9 
 
 71373 7813s 21865 93238 
 
 
 10 
 
 1-71393 1-78 163 0.21837 1.93230 
 
 T.72 622 r.79 860 0.20 140 r.92 763 
 
 50 
 
 
 II 
 
 71 414 78 192 21 808 93 223 
 
 72643 79888 20112 92755 
 
 49 
 
 
 12 
 
 71 435 78 220 21 780 93 215 
 
 72663 79916 20084 92747 
 
 48 
 
 
 '3 
 
 71456 78249 21 751 93207 
 
 72683 79944 20056 92739 
 
 . 47 
 
 
 «4 
 
 71477 78277 21723 93200 
 
 _ 72 7°3 79 972 20 028 92 731 
 
 46 
 
 
 '5 
 
 1.71498 1.78306 0.21694 1-93192 
 
 1.72723 1.80000 0.20000 r.92 723 
 
 45 
 
 
 l6 
 
 71 519 78334 21666 93184 
 
 72743 80028 19972 92715 
 
 44 
 
 
 •'2 
 
 71539 78363 21637 93177 
 
 72763 80056 19944 92707 
 
 43 
 
 
 i8 
 
 71 560 78 391 21 609 93 169 
 
 72783 80084 19916 92699 
 
 42 
 
 
 19 
 
 71581 78419 21 581 93 161 
 
 72 803 80 1 12 19 888 92 691 
 
 41 
 
 
 20 
 
 1. 71 602 T. 78 448 0.21552 T.93 154 
 
 1.72823 r.80140 0.19860 T.92683 
 
 40 
 
 
 21 
 
 71622 78476 21524 93146 
 
 72 843 80 168 19 832 92 675 
 
 39 
 
 
 22 
 
 71643 78505 21495 93138 
 
 72 863 80 195 19 805 92 667 
 
 38 
 
 
 23 
 
 71664 78533 21467 93 131 
 
 72883 80223 19777 92659 
 
 37 
 
 
 24 
 
 71685 78562 21438 93123 
 
 72902 80251 19749 92651 
 
 36 
 
 
 25 
 
 1.71705 1.78590 0.21 410 1.93 115 
 
 1.72922 1.80279 0.19 721 r.92 643 
 
 35 
 
 
 26 
 
 71 726 78 618 21 382 g^ 108 
 
 72942 80307 19693 92635 
 
 34 
 
 
 27 
 
 71 747 78 647 21 353 93 100 
 
 72962 80335 19665 92627 
 
 33 
 
 
 28 
 
 71767 78675 21325 93092 
 
 72982 80363 19637 92619 
 
 32 
 
 
 29 
 
 71 788 78 704 21 296 93 084 
 
 73002 80391 19609 92611 
 
 31 
 
 
 30 
 
 T.71809 1.78732 0.21268 r.93077 
 
 1.73022 T.80419 0.19 581 T.92603 
 
 30 
 
 
 31 
 
 71829 78760 21240 93069 
 
 73041 80447 19553 92595 
 
 29 
 
 
 32 
 
 71850 78789 21 211 93061 
 
 73061 80474 19526 92587 
 
 28 
 
 
 33 
 
 71870 78817 21 183 93053 
 
 73081 80502 19498 92579 
 
 27 
 
 
 34 
 
 71 891 78845 21 155 93046 
 
 73101 80530 19470 92571 
 
 26 
 
 
 ^i 
 
 1.71911 1.78874 0.21 126 1.93038 
 
 T. 73 121 1.80558 0.19442 1.92563 
 
 25 
 
 
 36 
 
 71932 78902 21098 93030 
 
 73140 80586 19414 92555 
 
 24 
 
 
 37 
 
 71952 78930 21070 93022 
 
 73 160 80 614 19 386 92 546 
 
 23 
 
 
 38 
 
 7' 973 78959 21 041 93014 
 
 73180 80642 19358 92538 
 
 22 
 
 
 39 
 
 71994 78987 21 013 93007 
 
 73200 80669 19331 92530 
 
 21 
 
 
 40 
 
 T.72014 T. 79 015 0.20985 T.92999 
 
 T. 73 219 T.80697 0.19303 T.92522 
 
 20 
 
 
 41 
 
 72034 79043 20957 92991 
 
 73239 80725 19275 92514 
 
 19 
 
 
 42 
 
 7205s 79072 20928 92983 
 
 73259 80753 19247 92506 
 
 18 
 
 
 43 
 
 72075 79100 20900 92976 
 
 73278 80781 19 219 92498 
 
 17 
 
 
 44 
 
 72096 79128 20872 92968 
 
 73 298 80 808 19 192 92 490 
 
 16 
 
 
 1^ 
 
 1.72 116 1.79 156 0.20844 1.92960 
 
 1.73318 1.80836 0.19 164 T.92482 
 
 15 
 
 
 46 
 
 72137 79185 20815 92952 
 
 73 337 80864 19 136 92473 
 
 14 
 
 
 47 
 48 
 
 72157 79213 20787 92944 
 
 73357 80892 19 108 92465 
 
 13 
 
 
 72177 79241 20759 92936 
 
 73 377 80919 19081 92457 
 
 12 
 
 
 49 
 
 _ 72 198 79269 20731 "92929 
 
 73396 80947 19053 92449 
 
 II 
 
 
 50 
 
 1.72 218 T.79297 0.20703 T.92921 
 
 1.73 416 1.80975 0.19025 1.92441 
 
 10 
 
 
 SI 
 
 72238 79326 20674 92913 
 
 73435 81003 18997 92433 
 
 9 
 
 
 52 
 
 72259 79 354 20646 92905 
 
 73455 81030 18970 92425 
 
 8 
 
 
 S3 
 
 72279 79382 20618 92897 
 
 73474 81058 18942 92416 
 
 7 
 
 
 54 
 
 72299 79 410 20590 92889 
 
 73 494 81 086 18 914 92 408 
 
 6 
 
 
 55 
 
 1.72320 1.79438 0.20562 T.92881 
 
 T.73513 T.81 113 0.18887 1.92400 
 
 s 
 
 
 56 
 
 72340 79466 20534 92874 
 
 73533 81141 18859 92392 
 
 4 
 
 
 57 
 
 72360 79495 20505 92866 
 
 73 552 81 169 18 831 92 384 
 
 3 
 
 
 58 
 
 72381 79523 20477 92858 
 
 73572 81 196 18804 92376 
 
 2 
 
 
 kl, 
 
 72401 79551 20449 92850 
 
 73591 81224 18776 92367 
 
 I 
 
 
 60' 
 
 1.72 421 1.79579 0.20421 1.92842 
 
 1.73611 1.81252 0.18748 1.92359 
 
 0' 
 
 
 
 log cos log cot log tan log sin 
 
 log 003 log oot log tan log sin 
 
 t 
 
 
 
 68° (6 
 
 3) 570 LOG S 
 
 0/ 
 
 N, e 
 
 tc. 
 
33°-36^ 
 LOG SIN, etc. 
 
 33° 
 
 
 
 
 34° 
 
 
 
 
 f 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log cos 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log 003 
 
 
 
 0' 
 
 1-73611 
 
 1.81 252 
 
 18748 
 
 1-92359 
 
 7-74 756 
 
 7.82 899 
 
 0.17 101 
 
 7-91 857 
 
 60' 
 
 
 I 
 
 73630 
 
 81279 
 
 18721 
 
 92351 
 
 74 775 
 
 82926 
 
 17074 
 
 91849 
 
 59 
 
 
 2 
 
 73650 
 
 81307 
 
 18693 
 
 92343 
 
 74 794 
 
 82953 
 
 17047 
 
 91 840 
 
 58 
 
 
 3 
 
 73669 
 
 81335 
 
 18665 
 
 92335 
 
 74812 
 
 82980 
 
 17020 
 
 91832- 
 
 57 
 
 
 4 
 
 73689 
 
 81362 
 
 18638 
 
 92326 
 
 74831 
 
 83008 
 
 16992 
 
 91823 
 
 56 
 
 
 S 
 
 1.73708 
 
 T.81 390 
 
 18610 
 
 1.92318 
 
 1.74850 
 
 ^-83035 
 
 0.16 965 
 
 1.91 815 
 
 55 
 
 
 6 
 
 73727 
 
 81 418 
 
 18582 
 
 92 310 
 
 74868 
 
 83062 
 
 16938 
 
 91 806 
 
 54 
 
 
 7 
 
 73 747 
 
 81445 
 
 1855s 
 
 92302 
 
 74887 
 
 83089 
 
 I69I1 
 
 91798 
 
 53 
 
 
 8 
 
 73766 
 
 81473 
 
 18527 
 
 92293 
 
 74906 
 
 83117 
 
 16883 
 
 91789 
 
 52 
 
 
 9 
 
 73785 
 
 81 500 
 
 18500 
 
 92285 
 
 74924 
 
 83144 
 
 16856 
 
 91 781 
 
 51 
 
 
 10 
 
 1.73805 
 
 T.8i 528 
 
 18472 
 
 7.92 277 
 
 1-74 943 
 
 7.83171 
 
 0.16829 
 
 7.91 772 
 
 50 
 
 
 II 
 
 73824 
 
 81556 
 
 18444 
 
 92 269 
 
 74961 
 
 83198 
 
 16802 
 
 91763 
 
 49 
 
 
 12 
 
 73843 
 
 81583 
 
 18417 
 
 92 260 
 
 74980 
 
 83225 
 
 16775 
 
 9175s 
 
 48 
 
 
 13 
 
 "f^3 
 
 81 611 
 
 18389 
 
 92 252 
 
 74 999 
 
 83252 
 
 16748 
 
 91746 
 
 47 
 
 
 H 
 
 73882 
 
 81638 
 
 18362 
 
 92244 
 
 75017 
 
 83280 
 
 16 720 
 
 91738 
 
 46 
 
 
 15 
 
 1.73901 
 
 T.81 666 
 
 18334 
 
 1.92235 
 
 1.75036 
 
 T-83 307 
 
 0.16 693 
 
 1-91729 
 
 45 
 
 
 16 
 
 73921 
 
 81693 
 
 18307 
 
 92 227 
 
 75054 
 
 83334 
 
 16666 
 
 91720 
 
 44 
 
 
 17 
 
 73940 
 
 81 721 
 
 18279 
 
 92219 
 
 75073 
 
 83361 
 
 16639 
 
 91712 
 
 43 
 
 
 18 
 
 73 959 
 
 81 748 
 
 18 252 
 
 92211 
 
 75091 
 
 83388 
 
 16612 
 
 91703 
 
 42 
 
 
 19 
 
 73978 
 
 81776 
 
 18224 
 
 92202 
 
 75 no 
 
 83415 
 
 16585 
 
 91695 
 
 41 
 
 
 20 
 
 1-73 997 
 
 1. 81 803 
 
 18197 
 
 7.92 194 
 
 1.75 128 
 
 7.83 442 
 
 0.16558 
 
 7.91 686 
 
 40 
 
 
 21 
 
 74017 
 
 81831 
 
 18169 
 
 92186 
 
 75147 
 
 83470 
 
 16530 
 
 91677 
 
 39 
 
 
 22 
 
 74036 
 
 81858 
 
 18 142 
 
 92177 
 
 75 '65 
 
 83497 
 
 16503 
 
 91 669 
 
 38 
 
 
 23 
 
 74055 
 
 81886 
 
 18 114 
 
 92 169 
 
 75184 
 
 83524 
 
 16476 
 
 91 660 
 
 37 
 
 
 24 
 
 74074 
 
 81913 
 
 18087 
 
 92 161 
 
 75202 
 
 83551 
 
 16449 
 
 91651 
 
 36 
 
 
 ^5 
 
 1-74093 
 
 1. 81 941 
 
 18059 
 
 7.92 152 
 
 1-75221 
 
 1.83578 
 
 0.16422 
 
 1-91 643 
 
 35 
 
 
 26 
 
 74 113 
 
 81968 
 
 18032 
 
 92144 
 
 75239 
 
 83605 
 
 16395 
 
 91634 
 
 34 
 
 
 27 
 
 74132 
 
 81 996 
 
 18004 
 
 92136 
 
 75258 
 
 83632 
 
 16368 
 
 91625 
 
 33 
 
 
 28 
 
 74 151 
 
 82023 
 
 17977 
 
 92 127 
 
 75276 
 
 l^^M 
 
 16341 
 
 91617 
 
 32 
 
 
 29 
 
 74170 
 
 82051 
 
 17949 
 
 92119 
 
 75294 
 
 83686 
 
 16314 
 
 91608 
 
 31 
 
 
 30 
 
 1.74 189 
 
 T.82078 
 
 17922 
 
 1.92 III 
 
 1-75313 
 
 T.83 713 
 
 0.16287 
 
 7.91 599 
 
 30 
 
 
 31 
 
 74208 
 
 82106 
 
 17894 
 
 92 102 
 
 75331 
 
 83740 
 
 16260 
 
 91591 
 
 29 
 
 
 32 
 
 74227 
 
 82133 
 
 17867 
 
 92094 
 
 75350 
 
 83768 
 
 16232 
 
 91582 
 
 28 
 
 
 33 
 
 74246 
 
 82161 
 
 17839 
 
 92086 
 
 75368 
 
 8379s 
 
 16205 
 
 91573 
 
 27 
 
 
 34 
 
 74265 
 
 82188 
 
 17812 
 
 92077 
 
 75386 
 
 83822 
 
 16 178 
 
 91565 
 
 26 
 
 
 35 
 
 1.74284 
 
 1.82 215 
 
 17785 
 
 1.92069 
 
 1-75405 
 
 7.83 849 
 
 0.16 151 
 
 1-91556 
 
 25 
 
 
 36 
 
 74303 
 
 82243 
 
 17757 
 
 92060 
 
 75423 
 
 83876 
 
 16 124 
 
 91547 
 
 24 
 
 
 37 
 
 74322 
 
 82 270 
 
 17730 
 
 92052 
 
 75441 
 
 83903 
 
 16097 
 
 91538 
 
 23 
 
 
 38 
 
 74341 
 
 82298 
 
 17702 
 
 92044 
 
 75 459 
 
 83930 
 
 16070 
 
 91530 
 
 22 
 
 
 39 
 
 74360 
 
 82325 
 
 1767s 
 
 92035 
 
 75478 
 
 83957 
 
 16043 
 
 91 521 
 
 21 
 
 
 40 
 
 1-74 379 
 
 1.82352 
 
 17648 
 
 7.92 027 
 
 1-75496 
 
 1.83 984 
 
 0.16016 
 
 1.91 512 
 
 20 
 
 
 41 
 
 74398 
 
 82380 
 
 17 620 
 
 92018 
 
 75514 
 
 84011 
 
 15989 
 
 91504 
 
 19 
 
 
 42 
 
 74417 
 
 82407 
 
 17593 
 
 92010 
 
 75 533 
 
 84038 
 
 15962 
 
 91495 
 
 18 
 
 
 43 
 
 74436 
 
 82435 
 
 17565 
 
 92002 
 
 75551 
 
 84065 
 
 15935 
 
 91 486 
 
 17 
 
 
 44 
 
 74 455 
 
 82462 
 
 17538 
 
 91993 
 
 75569 
 
 84092 
 
 15908 
 
 91477 
 
 16 
 
 
 45 
 
 1.74474 
 
 7.82489 
 
 17511 
 
 1.91 985 
 
 1-75 587 
 
 7.84 119 
 
 0.15881 
 
 1.91 469 
 
 15 
 
 
 46 
 
 74 493 
 
 82517 
 
 17483 
 
 91976 
 
 75605 
 
 84 146 
 
 15854 
 
 91 460 
 
 14 
 
 
 47 
 
 74512 
 
 82544 
 
 17456 
 
 91 968 
 
 75624 
 
 84173 
 
 15827 
 
 91451 
 
 13 
 
 
 48 
 
 74531 
 
 82571 
 
 17429 
 
 91959 
 
 75642 
 
 84200 
 
 15800 
 
 91442 
 
 12 
 
 
 49 
 
 74 549 
 
 82599 
 
 17401 
 
 91951 
 
 75660 
 
 84227 
 
 15773 
 
 91433 
 
 II 
 
 
 50 
 
 T-74 568 
 
 7.82 626 
 
 17374 
 
 7.91 942 
 
 1.75678 
 
 7.84 254 
 
 0.15 746 
 
 7.91 425 
 
 10 
 
 
 51 
 
 74587 
 
 82653 
 
 17347 
 
 91934 
 
 75696 
 
 84280 
 
 15720 
 
 91 416 
 
 9 
 
 
 52 
 
 74606 
 
 82681 
 
 17319 
 
 91925 
 
 75714 
 
 84307 
 
 15693 
 
 91407 
 
 8 
 
 
 S3 
 
 74625 
 
 82708 
 
 17292 
 
 91917 
 
 75 733 
 
 84334 
 
 15666 
 
 91398 
 
 7 
 
 
 54 
 
 74644 
 
 8273s 
 
 17265 
 
 91 908 
 
 75751 
 
 84361 
 
 15639 
 
 91389 
 
 6 
 
 
 55 
 
 1.74662 
 
 1.82762 0. 
 
 17238 
 
 7.91 900 
 
 1.75 769 
 
 7.84 388 
 
 0.15 612 
 
 1.91381 
 
 5 
 
 
 56 
 
 74681 
 
 82790 
 
 17 210 
 
 91 891 
 
 75787 
 
 84415 
 
 15585 
 
 91372 
 
 4 
 
 
 57 
 
 74700 
 
 82817 
 
 17183 
 
 91883 
 
 75805 
 
 84442 
 
 15558 
 
 91363 
 
 3 
 
 
 58 
 
 74719 
 
 82844 
 
 17156 
 
 91874 
 
 75823 
 
 84469 
 
 15531 
 
 91354 
 
 2 
 
 
 59 
 
 74 737 
 
 82871 
 
 17129 
 
 91866 
 
 75841 
 
 84496 
 
 15504 
 
 91345 
 
 I 
 
 
 60' 
 
 1-74756 
 
 1.82899 0. 
 
 17 101 
 
 1-91 857 
 
 1.75 859 
 
 1.84523 
 
 0-15477 
 
 1.91336 
 
 0' 
 
 
 
 log cos 
 
 log cot 
 
 'og tan 
 
 log sin 
 
 log COS 
 
 log OOt 
 
 log tan 
 
 log sin 
 
 1 
 
 LC 
 i 
 
 G SI 
 J3°-5 
 
 N, etc. 
 6° 
 
 66° 
 
 
 (6 
 
 4) 
 
 66"" 
 
 
 

 
 33 
 
 °-36° 
 
 
 
 35° 
 
 36° LOG SIN, etc. 
 
 t 
 
 log sin log tan log cot log 00s 
 
 log sin log tan log cot log cos 
 
 
 
 0' 
 
 1.75859 1.84523 0.15477 1.91336 
 
 T.76 922 T.86 126 0.13874 T.90 796 
 
 60' 
 
 
 I 
 
 75877 84550 15450 91328 
 
 76939 86153 13847 90787 
 
 59 
 
 
 2 
 
 75895 84576 15424 91319 
 
 76957 86179 13 821 90777 
 
 58 
 
 
 3 
 
 75913 84603 15397 91 310 
 
 76 974 86 206 13 794 90 768 
 
 57 
 
 
 4 
 
 75931 84630 15370 91 301 
 
 76991 86232 13768 90759 
 
 56 
 
 
 s 
 
 1.75949 1.84657 0.15343 1.91 292 
 
 1.77009 1.86259 0.13741 1.90750 
 
 55 
 
 
 6 
 
 75967 84684 15316 91283 
 
 77026 86285 13715 90741 
 
 54 
 
 
 7 
 
 75985 84 71 1 15289 91274 
 
 77043 86312 13688 90731 
 
 53 
 
 
 8 
 
 76003 84738 15262 91266 
 
 77061 86338 13662 90722 
 
 52 
 
 
 9 
 
 76021 84764 15236 91257 
 
 77078 86365 13635 90713 
 
 51 
 
 
 10 
 
 T.76039 T.84791 0.15209 1.9 1 248 
 
 T.7709S T.86 392 0.13608 T.90 704 
 
 50 
 
 
 II 
 
 76057 84818 15 182 91239 
 
 77112 86418 13582 90694 
 
 49 
 
 
 12 
 
 7607s 8484s 15155 91230 
 
 77130 86445 13555 90685 
 
 48 
 
 
 13 
 
 76093 84872 15128 91221 
 
 77147 86471 13529 90676 
 
 47 
 
 
 14 
 
 76 III 84899 IS 101 91 212 
 
 77164 86498 13502 90667 
 
 46 
 
 
 IS 
 
 T.76129 1.84925 0.15075 1.91203 
 
 T.77i8i T.86 524 0.13476 1.90657 
 
 45 
 
 
 16 
 
 76146 84952 15048 91 194 
 
 77199 86551 13449 90648 
 
 44 
 
 
 17 
 
 76164 84979 15021 91185 
 
 77216 86577 13423 90639 
 
 43 
 
 
 18 
 
 76182 85006 14994 91 176 
 
 77233 86603 13397 90630 
 
 42 
 
 
 19 
 
 76200 85033 14967 91 167 
 
 77250 86630 13370 90620 
 
 41 
 
 
 20 
 
 T.76218 T.85059 0.14 941 r.91 158 
 
 T.77268 T.86 656 0.13344 T.90611 
 
 40 
 
 
 21 
 
 76236 85086 14914 91149 
 
 77285 86683 13 317 90602 
 
 39 
 38 
 
 
 22 
 
 76253 85113 14887 91141 
 
 77302 86709 13 291 90592 
 
 
 23 
 
 76 271 85 140 14 860 91 132 
 
 77319 86736 13264 90583 
 
 ^l 
 
 
 24 
 
 76 289 85 166 14 834 91 123 
 
 77336 86762 13238 90574 
 
 36 
 
 
 25 
 
 T.76307 1.85193 0.14807 1.91 114 
 
 T.77353 1-86789 0.13211 1.90565 
 
 35 
 
 
 26 
 
 76 324 85 220 14 780 91 105 
 
 77370 86815 13185 90555 
 
 34 
 
 
 27 
 
 76342 85247 14753 91096 
 
 77387 86842 13158 90546 
 
 33 
 
 
 28 
 
 76360 85273 14727 91087 
 
 77405 86 868 13132 90537 
 
 32 
 
 
 29 
 
 76378 85300 14700 91078 
 
 77422 86894 13106 90527 
 
 31 
 
 
 30 
 
 T.7639S 1.85327 0.14673 T.91069 
 
 7.77439 T.86 921 0.13079 T.90 518 
 
 30 
 
 
 31 
 
 76413 85354 14646 91060 
 
 77456 86947 13053 90509 
 
 29 
 
 
 32 
 
 76431 85380 14620 91051 
 
 77 473 86974 13026 90499 
 
 28 
 
 
 33 
 
 76448 85407 14593 91042 
 
 77490 87000 13000 90490 
 
 27 
 
 
 34 
 
 76466 85434 14566 91033 
 
 77507 87027 12973 90480 
 
 26 
 
 
 35 
 
 1.76484 1.85460 0.14540 1.91023 
 
 T.77S24 T.87053 0.12947 1.90471 
 
 25 
 
 
 36 
 
 76501 85487 14513 91014 
 
 77541 87079 12921 90462 
 
 24 
 
 
 37 
 
 76519 85514 14486 91005 
 
 77558 87106 12894 90452 
 
 23 
 
 
 38 
 
 76537 85540 14460 90996 
 
 77 575 87132 12868 90443 
 
 22 
 
 
 39 
 
 76554 85567 14433 90987 
 
 77592 87158 12842 90434 
 
 21 
 
 
 40 
 
 T.76 572 1.85 594 0.14 406 1 .90 978 
 
 T.77609 T.8718S 0.12815 T.90 424 
 
 20 
 
 
 41 
 
 76 590 85 620 14 380 90 969 
 
 77626 87211 12789 90415 
 
 19 
 
 
 42 
 
 76607 85647 14353 90960 
 
 77643 87238 12762 90405 
 
 18 
 
 
 43 
 
 76625 85674 14326 90951 
 
 77660 87264 12736 90396 
 
 ^l 
 
 
 44 
 
 76 642 85 700 14 300 90 942 
 
 77677 87290 12710 90386 
 
 16 
 
 
 45 
 
 T.76 660 T.85727 0.14273 1.90933 
 
 T.77694 T.87317 0.12683 T.90 377 
 
 15 
 
 
 46 
 
 76677 85754 14246 90924 
 
 77711 87343 12657 90368 
 
 14 
 
 
 47 
 
 76695 85780 14220 90915 
 
 77728 87369 12631 90358 
 
 13 
 
 
 48 
 
 76712 85807 14 193 90906 
 
 77744 87396 12604 90349 
 
 12 
 
 
 49 
 
 76730 85834 14166 90896 
 
 77761 87422 12578 90339 
 
 11 
 
 
 50 
 
 7.76 747 7.85 860 0.14 140 T.90 887 
 
 T.77778 T.87448 0.12552 T.90 330 
 
 10 
 
 
 51 
 
 76765 85887- 14 113 90878 
 
 77 795 87475 12525 90320 
 
 9 
 8 
 
 
 52 
 
 76782 85913 14087 90869 
 
 77812 87501 12499 90311 
 
 
 S3 
 
 76 800 85 940 14 060 90 860 
 
 77829 87527 12473 90301 
 
 7 
 6 
 
 
 54 
 
 76817 85967 14033 90851 
 
 77846 87554 12446 90292 
 
 
 55 
 
 1.7683s 1.85993 0.14007 1.90842 
 
 T.77862 1.87580 0.12420 1.90282 
 
 5 
 
 
 56 
 
 76852 86020 13980 90832 
 
 77879 87606 12394 90273 
 
 4 
 
 
 57 
 
 76870 86046 13954 90823 
 
 77896 87633 12367 90263 
 
 3 
 
 
 58 
 
 76887 86073 13927 90814 
 
 77913 87659 12341 90254 
 
 2 
 
 
 ^g' 
 
 76904 86100 13900 90805 
 T.76 922 1.86 126 0.13874 1.90796 
 
 77930 87685 12 315 90244 
 
 0' 
 
 t 
 
 
 T.77946 1.87711 0.12289 1.90235 
 
 Incp nn<i loff cot loff tan loff sin 
 
 
 
 log 003 log oot log tan log sin 
 
 64° C 
 
 5) 63° "-""g' 
 
 51N, 
 3°-66 
 
 etc 
 
 ° 
 
37°-40° 
 LOG SIN, etc. 37° 
 
 38° 
 
 / 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log 003 
 
 log sin 
 
 log tan 
 
 log oot 
 
 log oos 
 
 
 0' 
 
 1.77 946 
 
 T.87711 0. 
 
 12289 
 
 1.90 235 
 
 T.78 934 
 
 T.89 281 
 
 o.io 719 
 
 T.89 653 
 
 60 
 
 I 
 
 77963 
 
 87738 
 
 12 262 
 
 90225 
 
 78950 
 
 89307 
 
 10693 
 
 89643 
 
 59 
 
 2 
 
 77980 
 
 87764 
 
 12236 
 
 90216 
 
 78967 
 
 89333 
 
 10667 
 
 89633 
 
 58 
 
 3 
 
 77 997 
 
 87 790 
 
 12 210 
 
 90206 
 
 78983 
 
 89359 
 
 10 641 
 
 89624 
 
 57 
 
 4 
 
 78013 
 
 87817 
 
 12 183 
 
 90197 
 
 78999 
 
 89385 
 
 10615 
 
 89614 
 
 S6 
 
 5 
 
 1.78030 
 
 1.87843 0. 
 
 12 157 
 
 1.90 187 
 
 1-79015 
 
 1-89 41 1 
 
 0.10589 
 
 T.89 604 
 
 55 
 
 6 
 
 78047 
 
 87869 
 
 12 131 
 
 90178 
 
 79031 
 
 89437 
 
 10563 
 
 89594 
 
 54 
 
 7 
 
 .78 063 
 
 87895 
 
 12 105 
 
 90168 
 
 79047 
 
 89463 
 
 10537 
 
 89584 
 
 S3 
 
 8 
 
 78080 
 
 87922 
 
 12078 
 
 90159 
 
 79063 
 
 89489 
 
 10511 
 
 89574 
 
 52 
 
 9 
 
 78097 
 
 87948 
 
 12052 
 
 90149 
 
 79079 
 
 89515 
 
 10485 
 
 89564 
 
 SI 
 
 10 
 
 1-78113 
 
 1.87974 0. 
 
 [2026 
 
 T.90 139 
 
 1.79095 
 
 1.89 541 
 
 0.10459 
 
 1.89554 
 
 50 
 
 II 
 
 •78 130 
 
 88000 
 
 t2O0O 
 
 90 130 
 
 79 III 
 
 89567 
 
 10433 
 
 89544 
 
 49 
 
 12 
 
 78147 
 
 88027 
 
 11973 
 
 90 120 
 
 79 128 
 
 89593 
 
 10407 
 
 89534 
 
 48 
 
 13 
 
 78163 
 
 88053 
 
 II 947 
 
 90 III 
 
 79144 
 
 89 619 
 
 10381 
 
 89524 
 
 47 
 
 14 
 
 78180 
 
 88079 
 
 II 921 
 
 90 lOI 
 
 79 160 
 
 89645 
 
 1035s 
 
 89514 
 
 46 
 
 IS 
 
 r.78 197 
 
 T.88 105 0. 
 
 11895 
 
 T.90 091 
 
 T.79 176 
 
 1.89 671 
 
 0.10329 
 
 1.89504 
 
 45 
 
 i6 
 
 78213 
 
 88 131 
 
 II 869 
 
 90082 
 
 79192 
 
 89697 
 
 10303 
 
 89495 
 
 44 
 
 17 
 
 78 230 
 
 88158 
 
 [1 842 
 
 90072 
 
 79208 
 
 89723 
 
 10277 
 
 89485 
 
 43 
 
 18 
 
 78246 
 
 88184 
 
 II 816 
 
 90063 
 
 79224 
 
 89749 
 
 10 251 
 
 8947s 
 
 42 
 
 19 
 
 78263 
 
 88210 
 
 [1 790 
 
 90053 
 
 79240 
 
 89775 
 
 10225 
 
 89465 
 
 41 
 
 20 
 
 T.78 280 
 
 T.88 236 0. 
 
 II 764 
 
 T.90 043 
 
 T.79 256 
 
 1.89 801 
 
 0.10 199 
 
 1-89455 
 
 40 
 
 21 
 
 78296 
 
 88262 
 
 ■1738 
 
 90034 
 
 79272 
 
 89827 
 
 10 173 
 
 89445 
 
 39 
 
 22 
 
 78313 
 
 88289 
 
 .1711 
 
 90024 
 
 79288 
 
 89853 
 
 10 147 
 
 8943s 
 
 38 
 
 23 
 
 78329 
 
 88315 
 
 II 685 
 
 90014 
 
 79304 
 
 89879 
 
 10 121 
 
 89425 
 
 37 
 
 24 
 
 78346 
 
 88341 
 
 [1 659 
 
 90005 
 
 79319 
 
 89905 
 
 10095 
 
 89415 
 
 36 
 
 25 
 
 1.78362 
 
 1.88367 0. 
 
 "633 
 
 T.89 995 
 
 1-79 335 
 
 1-89931 
 
 0.10069 
 
 1.89405 
 
 35 
 
 26 
 
 78379 
 
 f!393 
 
 [I 607 
 
 89985 
 
 79351 
 
 89957 
 
 10043 
 
 8939s 
 
 34 
 
 27 
 
 78395 
 
 88420 
 
 [1 580 
 
 89976 
 
 79367 
 
 89983 
 
 10 01 7 
 
 89385 
 
 33 
 
 28 
 
 ^^'^"S 
 
 88446 
 
 "554 
 
 89966 
 
 79383 
 
 90009 
 
 09991 
 
 89375 
 
 32 
 
 29 
 
 78428 
 
 88472 
 
 [I 528 
 
 89956 
 
 79 399 
 
 90035 
 
 09965 
 
 89364 
 
 31 
 
 30 
 
 7.78445 
 
 T.88 498 0. 
 
 [I 502 
 
 T.89 947 
 
 1-79 41S 
 
 T.90 061 
 
 0.09 939 
 
 1-89354 
 
 30 
 
 31 
 
 78461 
 
 88524 
 
 [I 476 
 
 89937 
 
 79 431 
 
 90086 
 
 09914 
 
 89344 
 
 29 
 
 32 
 
 78478 
 
 88550 
 
 [I 450 
 
 89927 
 
 79447 
 
 90 H2 
 
 09888 
 
 89334 
 
 28 
 
 33 
 
 78494 
 
 f!577 
 
 [I 423 
 
 89918 
 
 79463 
 
 90138 
 
 09862 
 
 •89 324 
 
 27 
 
 34 
 
 78510 
 
 88603 
 
 ■1397 
 
 89908 
 
 79478 
 
 90 164 
 
 09836 
 
 89314 
 
 26 
 
 35 
 
 1.78527 
 
 T.88 629 0. 
 
 «37i 
 
 1.89898 
 
 1.79494 
 
 T.90 190 
 
 0.09 810 
 
 1.89304 
 
 25 
 
 36 
 
 78543 
 
 88655 
 
 II 345 
 
 89888 
 
 79510 
 
 90 216 
 
 09784 
 
 89294 
 
 24 
 
 37 
 
 78560 
 
 8»68i 
 
 I 319 
 
 89879 
 
 79526 
 
 90242 
 
 09758 
 
 89284 
 
 23 
 
 38 
 
 78576 
 
 88707 
 
 1293 
 
 89869 
 
 79542 
 
 90268 
 
 09732 
 
 89274 
 
 22 
 
 39 
 
 78592 
 
 88733 
 
 I 267 
 
 89859 
 
 79558 
 
 90294 
 
 09706 
 
 89264 
 
 21 
 
 40 
 
 1.78609 
 
 1.88759 0. 
 
 I 241 
 
 1.89849 
 
 1-79 573 
 
 T.90 320 
 
 0.09 680 
 
 T.89 254 
 
 20 
 
 41 
 
 78625 
 
 88 786 1 
 
 I 214 
 
 89840 
 
 79589 
 
 90346 
 
 09654 
 
 89244 
 
 19 
 
 42 
 
 78642 
 
 88812 1 
 
 I 188 
 
 89830 
 
 79605 
 
 90371 
 
 09 629 
 
 89233 
 
 18 
 
 43 
 
 78658 
 
 88 838 1 
 
 I 162 
 
 89820 
 
 79621 
 
 90397 
 
 09603 
 
 89223 
 
 17 
 
 44 
 
 78674 
 
 88 864 1 
 
 I 136 
 
 89810 
 
 79636 
 
 90423 
 
 09 577 
 
 89213 
 
 16 
 
 45 
 
 1.78 691 
 
 T.88 890 0. 
 
 I no 
 
 T.89 8oi 
 
 1.79652 
 
 1-90449 
 
 0.09551 
 
 1.89 203 
 
 15 
 
 46 
 
 78707 
 
 88916 1 
 
 1084 
 
 89791 
 
 79668 
 
 90475 
 
 09525 
 
 89193 
 
 14 
 
 47 
 
 78723 
 
 88 942 ] 
 
 1058 
 
 89781 
 
 79684 
 
 90501 
 
 09499 
 
 89183 
 
 13 
 
 48- 
 
 78739 
 
 88 968 1 
 
 I 032 
 
 89771 
 
 79699 
 
 90527 
 
 09473 
 
 89173 
 
 12 
 
 49 
 
 78756 
 
 88 994 J 
 
 I 006 
 
 89761 
 
 79715 
 
 90553 
 
 09447 
 
 89162 
 
 II 
 
 50 
 
 1.78772 
 
 T.89 020 0.1 
 
 0980 
 
 T.89 752 
 
 1-79 731 
 
 1.90578 
 
 0.09 422 
 
 T.89 152 
 
 10 
 
 51 
 
 78788 
 
 89 046 1 
 
 0954 
 
 89742 
 
 79746 
 
 90604 
 
 09396 
 
 89142 
 
 9 
 
 52 
 
 78805 
 
 89073 1 
 
 0927 
 
 89732 
 
 79762 
 
 90630 
 
 09370 
 
 89132 
 
 8 
 
 S3 
 
 78821 
 
 89 099 1 
 
 0901 
 
 89722 
 
 79778 
 
 90656 
 
 09344 
 
 89 122 
 
 7 
 
 54 
 
 78837 
 
 89 125 I 
 
 0875 
 
 89712 
 
 79 793 
 
 90682 
 
 09318 
 
 89 112 
 
 6 
 
 55 
 
 1.78853- 
 
 '.89151 0.1 
 
 0849 
 
 1.89 702 
 
 1.79809 
 
 T.90 708 
 
 0.09 292 
 
 T.89 101 
 
 5 
 
 56 
 
 78869 
 
 89 "77 I 
 
 0823 
 
 89693 
 
 79 825 
 
 90734 
 
 09 266 
 
 89091 
 
 4 
 
 57 
 
 78886 
 
 89 203 1 
 
 0797 
 
 89683 
 
 79840 
 
 90759 
 
 09241 
 
 89081 
 
 3 
 
 58 
 
 78902 
 
 89 229 I 
 
 0771 
 
 89673 
 
 79856 
 
 90785 
 
 09215 
 
 89071 
 
 2 
 
 59 
 
 78918 
 
 89 255 I 
 
 °745 
 
 89663 
 
 79872 
 
 90 81 1 
 
 09189 
 
 89060 
 
 1 
 
 60' 
 
 1-78934 " 
 
 ". 89 281 0.1 
 
 0719 
 
 1.89653 
 
 1.79887 
 
 1.90837 
 
 0.09 163 
 
 1.89050 
 
 0' 
 
 
 log 00s 
 
 log cot ] 
 
 og tan 
 
 log sin 
 
 log 003 
 
 log oot 
 
 log tan 
 
 log sin 
 
 t 
 
 LOG SIN, etc. fiO° 
 
 49°-62° 
 
 (66) 
 
 6r 
 
^^__ 
 
 39° 
 
 4U LOG SIN. etc 
 
 " fir 
 
 log sin log tan log cot log 00s 
 
 log sin log tan log oot log 003 
 
 
 
 0' 
 
 I 
 
 2 
 
 1.79887 1-90837 0.09163 1.89050 
 79903 90863 09137 89040 
 79918 90889 09 I II 89030 
 
 1.80807 1.92381 0.07619 7.88425 
 80822 92407 07593 88415 
 80837 92433 07567 88404 
 80852 92458 07542 88394 
 
 _ 80 867 92484 07516 88383 
 
 60' 
 
 It 
 
 11 
 55 
 54 
 53 
 52 
 51 
 
 
 3 
 
 79 934 90914 09086 89020 
 
 
 4 
 
 79950 90940 09060 89009 
 
 
 S 
 
 1.79965 1.90966 0.09034 1.88999 
 
 1.80882 1.92 5 10 0.07490 1.88372 
 80897 92535 07465 88362 
 80912 92561 07439 88351 
 80927 92587 07413 88340 
 
 
 6 
 
 79981 90992 09008 88989 
 
 
 7 
 
 79996 91 018 08982 88978 
 
 
 8 
 
 80012 91043 08957 88968 
 
 
 9 
 
 80027 91069 08931 88958 
 
 80942 92612 07388 88330 
 
 
 10 
 
 T.80043 T.9109S 0.08905 T.88948 
 
 7.80957 7.92638 0.07362 7.88319 
 
 50 
 
 
 II 
 
 80058 91 121 08879 88937 
 
 80972 92663 07337 88308 
 
 49 
 
 
 12 
 
 80074 91 147 08853 88927 
 
 80987 92689 07311 88298 
 
 48 
 
 
 13 
 
 80089 91 172 08828 88917 
 
 81002 92715 07285 88287 
 
 47 
 
 
 14 
 
 80105 91 198 08802 88906 
 
 81 017 92740 07260 88276 
 
 46 
 
 
 ij 
 
 T.So 120 r.91 224 0.08776 T.88896 
 
 1. 8 1 032 1.92766 0.07234 7.88266 
 
 45 
 
 
 i6 
 
 80136 91250 08750 88 886 
 
 81047 92792 07208 88255 
 
 44 
 
 
 17 
 
 80 151 91 276 08 724 88 87s 
 
 81 061 92817 07183 88244 
 
 43 
 
 
 18 
 
 80 166 91 301 08 699 88 865 
 
 81076 92843 07157 88234 
 
 42 
 
 
 «9 
 
 80182 91327 08673 8885s 
 
 81 091 92 868 07 132 88 223 
 
 41 
 
 
 20 
 
 T.80197 T.91353 0.08647 T.88844 
 
 7.81 106 7.92 894 0.07 106 7.88 212 
 
 40 
 
 
 21 
 
 80 213 91 379 08 621 88 834 
 
 81 121 92920 07080 88201 
 
 39 
 
 
 22 
 
 80228 91404 08596 88824 
 
 81 136 92945 07055 88 191 
 
 38 
 
 
 23 
 
 80244 91430 08570 88813 
 
 81 151 92971 07029 88180 
 
 37 
 
 
 24 
 
 80259 91456 08544 88803 
 
 81 166 92996 07004 88169- 
 
 36 
 
 
 25 
 
 7.80274 T.91482 0.08518 1.88793 
 
 1.81 180 7.93022 0.06978 7.88158 
 
 35 
 
 
 26 
 
 80290 91507- 08493 88782 
 
 81 195 93 048 06 952 88 148 
 
 34 
 
 
 ''^ 
 
 80305 91533 08467 88772 
 
 81 210 93073 06927 88137 
 
 33 
 
 
 28 
 
 80320 91559 08441 88761 
 
 81225 93099 06901 88126 
 
 32 
 
 
 29 
 
 80336 91585 08415 88751 
 
 81240 93124 06876 88 115 
 
 31 
 
 
 30 
 
 1.80351 1.91610 0.08390 1.88 741 
 
 7.81254 7.93150 0.06850 7.88105 
 
 30 
 
 
 31 
 
 80366 91636 08364 88730 
 
 81269 93175 06825 88094 
 
 29 
 
 > 
 
 32 
 
 80 382 91 662 08 338 88 720 
 
 81 284 93 201 06 799 88 083 
 
 28 
 
 
 33 
 
 80 397 91 688 08 312 88 709 
 
 81299 93227 06773 88072 
 
 27 
 
 
 34 
 
 80 412 91 713 08 287 88 699 
 
 81314 93252 06748 88061 
 
 26 
 
 
 35 
 
 T.80428 T.91 739 0.08261 T.88 688, 
 
 1. 8 1 328 1.93278 0.06722 7.88051 
 
 25 
 
 
 36 
 
 80443 91765 08235 88678 
 
 81343 93303 06697 88040 
 
 24 
 
 
 27 
 
 80458 91791 08209 88 668 
 
 81358 93329 06671 88029 
 
 23 
 
 
 38 
 
 80473 91 816 08184 88657 
 
 81372 93 354 06646 88018 
 
 22 
 
 
 39 
 
 80489 91842 08158 88647 
 
 81387 93380 06620 88007 
 
 21 
 
 
 40 
 
 T.80504 T.91868 0.08132 T.88636 
 
 7.81402 7.93406 0.06594 7.87996 
 
 20 
 
 
 4J 
 
 80519 91893 08107 88626 
 
 81417 93431 06569 87985 
 
 19 
 
 
 42 
 
 80534 91919 08081 88615 
 
 81 431 93 457 06543 87975 
 
 18 
 
 
 43 
 
 80 550 91 945 08 055 88 605 
 
 81446 931^82 06518 87964 
 
 17 
 
 
 44 
 
 80565 91 971 08029 88594 
 
 81 461 93508 06492 87953 
 
 16 
 
 
 4| 
 
 1.80580 1. 91 996 0.08004 T.88584 
 
 1.81475 1-93 533 0.06467 7.87942 
 
 15 
 
 
 46 
 
 80595 92022 07978 88573 
 
 81490 93 559 06441 87931 
 
 14 
 
 
 '^l 
 
 80610 92048 07952 88563 
 
 81505 93584 06416 87920 
 
 13 
 
 
 48 
 
 80625 92073 07927 88552 
 
 81 519 93610 06390 87909 
 
 12 
 
 
 49 
 
 80641 92099 07901 88542 
 
 81 534 93 636 06 364 87 898 . 
 
 II 
 
 
 50 
 
 T.80656 T.92125 0.07875 7.88531 
 
 7.81 549 7.93 661 0.06 339 7.87 887 
 
 10 
 
 
 SI 
 
 80671 92150 07850 88521 
 
 81563 93687 06313 87877 
 
 9 
 
 
 52 
 
 80686 92176 07824 88510 
 
 81578 93712 06288 87866 
 
 8 
 
 
 53 
 
 80701 92202 07798 88499 
 
 81 592 93 738 06 262 87 855 
 
 7 
 
 
 54 
 
 80716 92227 07773 88489 
 
 81 607 93 763 06 237 87 844 
 
 6 
 
 
 5| 
 
 1.80 731 1.92253 0.07747 7.88478 
 
 1.81622 1.93789 0.06211 1.87833 
 
 5 
 
 
 56 
 
 80746 92279 07721 88468 
 
 81 636 93 814 06 186 87 822 
 
 4 
 
 
 57 
 
 .80762 92304 07696 88457 
 
 81651 93840 06160 8y8ii 
 
 3 
 
 
 58 
 
 80777 92330 07670 88447 
 
 81665 93865 06135 87800 
 
 2 
 
 
 59 
 
 80 792 92 356 07 644 88 436 
 
 81 680 93 891 06 109 87 789 
 
 I 
 
 
 60' 
 
 1.80807 1.92 381 0.07619 1.88425 
 
 1.81694 1.93 916 0.06084 1-87778 
 
 0' 
 
 
 
 log cos log cot log tan log sin 
 
 log 00s log oot log tan log sin 
 
 r 
 
 
 - - ■ 
 
 ao° ^^ 
 
 7) 49° LOG 1 
 
 N, e 
 °-62° 
 
 tc. 
 
41°-44° 
 LOG SIN, etc. 4r 
 
 42° 
 
 / 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log 00s 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log cos 
 
 
 0' 
 
 1. 81 694 
 
 r.93916 
 
 0.06 084 
 
 T.87 778 
 
 T.82 551 
 
 1-95 444 
 
 0.04 556 
 
 T.87 107 
 
 60' 
 
 I 
 
 81709 
 
 93942 
 
 06058 
 
 87767 
 
 82565 
 
 95469 
 
 04531 
 
 87096 
 
 59 
 
 2 
 
 81 723 
 
 93967 
 
 06033 
 
 87756 
 
 82579 
 
 95 495 
 
 04505 
 
 87085 
 
 58 
 
 3 
 
 81738 
 
 93 993 
 
 06007 
 
 8774s 
 
 82593 
 
 95520 
 
 04480 
 
 87073 
 
 57 
 
 4 
 
 81752 
 
 94018 
 
 05 982 
 
 87734 
 
 82607 
 
 95 545 
 
 04455 
 
 87062 
 
 56 
 
 S 
 
 1. 81 767 
 
 T.94 044 
 
 0.05 956 
 
 1.87 723 
 
 T.82 621 
 
 1-95571 
 
 0.04 429 
 
 T.87 050 
 
 55 
 
 6 
 
 81 781 
 
 94069 
 
 05931 
 
 87712 
 
 82635 
 
 95596 
 
 04404 
 
 87039 
 
 54 
 
 7 
 
 81 796 
 
 94095 
 
 05905 
 
 87701 
 
 82649 
 
 95622 
 
 04378 
 
 87028 
 
 53 
 
 S 
 
 81 810 
 
 94 120 
 
 05880 
 
 87 690 
 
 82663 
 
 95647 
 
 04353 
 
 87016 
 
 52 
 
 9 
 
 81825 
 
 94146 
 
 05854 
 
 87679 . 
 
 82677 
 
 95672 
 
 04328 
 
 87005 
 
 51 
 
 10 
 
 T.81 839 
 
 T.94 171 
 
 0.05 829 
 
 T.87 668 
 
 1.82 691 
 
 T.95 698 
 
 0.04 302 
 
 1.86993 
 
 50 
 
 II 
 
 81854 
 
 ■94197 
 
 05803 
 
 87657 
 
 82705 
 
 95723 
 
 04277 
 
 86982 
 
 49 
 
 12 
 
 81868 
 
 94222 
 
 05778 
 
 87646 
 
 82719 
 
 95748 
 
 04252 
 
 86970 
 
 48 
 
 13 
 
 81882 
 
 94248 
 
 05752 
 
 87635 
 
 82733 
 
 95 774 
 
 04226 
 
 86959 
 
 47 
 
 14 
 
 81897 
 
 94273 
 
 05727 
 
 87624 
 
 82747 
 
 95 799 
 
 04201 
 
 86947 
 
 46 
 
 'S 
 
 1. 81 911 
 
 1.94299 
 
 0.05 701 
 
 1.87 613 
 
 1.82 761 
 
 1-95 825 
 
 0.04175 
 
 1.86936 
 
 45 
 
 i6 
 
 81926 
 
 94324 
 
 05 676 
 
 87601 
 
 82775 
 
 95850 
 
 04 150 
 
 86924 
 
 44 
 
 17 
 
 81 940 
 
 94350 
 
 05 650 
 
 87590 
 
 82788 
 
 95875 
 
 04125 
 
 86913 
 
 43 
 
 18 
 
 81955 
 
 94 375 
 
 05625 
 
 87579 
 
 82802 
 
 95901 
 
 04099 
 
 86902 
 
 42 
 
 19 
 
 81969 
 
 94401 
 
 05599 
 
 87568 
 
 82816 
 
 95926 
 
 04074 
 
 86890 
 
 41 
 
 20 
 
 T.81 983 
 
 T.94 426 
 
 0.05 574 
 
 1-87 557 
 
 T.82 830 
 
 1-95952 
 
 0.04 048 
 
 T.86 879 
 
 40 
 
 21 
 
 81998 
 
 94452 
 
 05548 
 
 87546 
 
 82844 
 
 95 977 
 
 04023 
 
 86867 
 
 39 
 
 22 
 
 82012 
 
 94 477 
 
 05523 
 
 87535 
 
 82858 
 
 96002 
 
 03998 
 
 86855 
 
 38 
 
 23 
 
 82026 
 
 94503 
 
 05497 
 
 87524 
 
 l^lV 
 
 96028 
 
 03972 
 
 86844 
 
 37 
 
 24 
 
 82041 
 
 94528 
 
 05472 
 
 87513 
 
 82885 
 
 96053 
 
 03947 
 
 86832 
 
 36 
 
 25 
 
 T.82 055 
 
 1.94 554 
 
 0.05 446 
 
 1.87 501 
 
 1.82899 
 
 1.96078 
 
 0.03 922 
 
 1.86821 
 
 35 
 
 26 
 
 82069 
 
 94 579 
 
 05421 
 
 87490 
 
 82913 
 
 96 104 
 
 03896 
 
 86809 
 
 34 
 
 27 
 
 82084 
 
 94604 
 
 05396 
 
 87479 
 
 82927 
 
 96 129 
 
 03871 
 
 86798 
 
 33 
 
 28 
 
 82098 
 
 94630 
 
 05370 
 
 87468 
 
 82941 
 
 96155 
 
 03845 
 
 86786 
 
 32 
 
 29 
 
 82 112 
 
 9465s 
 
 05345 
 
 87457 
 
 82955 
 
 96180 
 
 03820 
 
 86775 
 
 31 
 
 30 
 
 T.82 126 
 
 T.94 681 
 
 0.05 319 
 
 1.87446 
 
 1.82968 
 
 T.96 205 
 
 0.03 795 
 
 1.86763 
 
 30 
 
 31 
 
 82 141 
 
 94706 
 
 05294 
 
 87434 
 
 82982 
 
 96231 
 
 03769 
 
 86752 
 
 29 
 
 32 
 
 8215s 
 
 94732 
 
 05268 
 
 87423 
 
 82996 
 
 96256 
 
 03744 
 
 86740 
 
 28 
 
 33 
 
 82169 
 
 94 757 
 
 05243 
 
 87412 
 
 83010 
 
 96 281 
 
 03719 
 
 86728 
 
 27 
 
 34 
 
 82184 
 
 94783 
 
 05217 
 
 87401 
 
 83023 
 
 96307 
 
 03693 
 
 86717 
 
 26 
 
 35 
 
 1.82 198 
 
 T.94 808 
 
 0.05 192 
 
 T.87 390 
 
 .1.83037 
 
 1.96332 
 
 0.03 668 
 
 T.86 705 
 
 25 
 
 36 
 
 82212 
 
 94834 
 
 05 1 66 
 
 87378 
 
 83051 
 
 96357 
 
 03643 
 
 86694 
 
 24 
 
 37 
 
 82226 
 
 94859 
 
 05141 
 
 87367 
 
 83065 
 
 96383 
 
 03617 
 
 86682 
 
 23 
 
 38 
 
 82240 
 
 94884 
 
 05 116 
 
 87356 
 
 83078 
 
 96408 
 
 03592 
 
 86670 
 
 22 
 
 39 
 
 8225s 
 
 94910 
 
 05090 
 
 87345 
 
 83092 
 
 96433 
 
 03567 
 
 86659 
 
 21 
 
 40 
 
 1.82 269 
 
 T-94 935 
 
 0.05 065 
 
 1.87334 
 
 T.83 106 
 
 1-96459 
 
 0.03 541 
 
 T.86 647 
 
 20 
 
 41 
 
 82283 
 
 94961 
 
 05039 
 
 87322 
 
 83 120 
 
 96484 
 
 03516 
 
 86635 
 
 19 
 
 42 
 
 82297 
 
 94986 
 
 05014 
 
 87311 
 
 83133 
 
 96510 
 
 03490 
 
 86624 
 
 18 
 
 43 
 
 82 311 
 
 95 012 
 
 04988 
 
 87300 
 
 83J47 
 
 96535 
 
 03465 
 
 86612 
 
 '? 
 
 44 
 
 82326 
 
 95037 
 
 04963 
 
 87288 
 
 83161 
 
 96560 
 
 03440 
 
 86600 
 
 l6 
 
 45 
 
 1.82340 
 
 1.9s 062 
 
 0.04 938 
 
 1.87277 
 
 T.83 174 
 
 T.96 586 
 
 0.03 414 
 
 1.86589 
 
 15 
 
 46 
 
 82354 
 
 95088 
 
 04912 
 
 87266 
 
 83188 
 
 96 611 
 
 03389 
 
 86577 
 
 14 
 
 47 
 
 82368 
 
 95 "3 
 
 04887 
 
 87255 
 
 83 202 
 
 96636 
 
 03364 
 
 86565 
 
 13 
 
 48 
 
 82382 
 
 95139 
 
 04861 
 
 87243 
 
 83 215 
 
 96662 
 
 03338 
 
 86554 
 
 12 
 
 49 
 
 82396 
 
 95164 
 
 04836 
 
 87232 
 
 83229 
 
 96687 
 
 03313 
 
 86542 
 
 II 
 
 50 
 
 1.82 410 
 
 T.95 190 
 
 0.04 810 
 
 T.87 221 
 
 T.83 242 
 
 T.96 712 
 
 0.03 288 
 
 T.86 530 
 
 10 
 
 51 
 
 82424 
 
 95 215 
 
 04785 
 
 87 209 
 
 83256 
 
 96738 
 
 03 262 
 
 86518 
 
 9 
 
 52 
 
 82439 
 
 95240 
 
 04 760 
 
 87198 
 
 83270 
 
 96763 
 
 03 237 
 
 86507 
 
 8 
 
 53 
 
 82453 
 
 95 266 
 
 04734 
 
 87187 
 
 83283 
 
 96788 
 
 03 212 
 
 86495 
 
 7 
 
 54 
 
 82467 
 
 95291 
 
 04709 
 
 87>7S 
 
 83297 
 
 96 814 
 
 03186 
 
 86483 
 
 6 
 
 55 
 
 1.82 481 
 
 1-95317 
 
 0.04 683 
 
 1.87 164 
 
 1.83 310 
 
 T.96 839 
 
 0.03 161 
 
 1.86472 
 
 5 
 
 56 
 
 82495 
 
 95342 
 
 04658 
 
 87153 
 
 83324 
 
 96864 
 
 03136 
 
 86460 
 
 4 
 
 57 
 
 82509 
 
 95368 
 
 04632 
 
 87 141 
 
 83338 
 
 96890 
 
 03 no 
 
 86448 
 
 •3 
 
 58 
 
 82523 
 
 95 393 
 
 04607 
 
 87130 
 
 83351 
 
 96915 
 
 03085 
 
 86436 
 
 2 
 
 59 
 
 82537 
 
 95418 
 
 04582 
 
 87119 
 
 83365 
 
 96940 
 
 03060 
 
 86425 
 
 1 
 
 60' 
 
 1.82 551 
 
 1.95444 
 
 0.04 556 
 
 1.87 107 
 
 1-83378 
 
 1.96966 
 
 0.03 034 
 
 1.86413 
 
 0' 
 
 
 log cos 
 
 log cot 
 
 log tan 
 
 logain 
 
 log cos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 t 
 
 LOG SIN, etc. ILK" 
 
 45°-48° 
 
 (68) 
 
 47° 
 
43^^ 
 
 41°-44° 
 44° LOG SIN, etc. 
 
 9 
 
 log sin 
 
 log tan 
 
 log cot 
 
 log cos 
 
 log sin 
 
 log tan log cot log cos 
 
 
 0' 
 
 7.83 378 
 
 T.96 966 
 
 0.03 034 
 
 T.86413 
 
 T.84 177 
 
 1.98484 0.01 516 T.85 693 
 
 60' 
 
 I 
 
 83392 
 
 96991 
 
 03009 
 
 86401 
 
 84190 
 
 98 509 01 491 85 681 
 
 59 
 
 2 
 
 83405 
 
 97016 
 
 02984 
 
 86389 
 
 84203 
 
 98 534 01 466 85 669 
 
 58 
 
 3 
 
 83419 
 
 97042 
 
 02958 
 
 86377 
 
 84216 
 
 98 560 01 440 85 657 
 
 57 
 
 4 
 
 83432 
 
 97067 
 
 02933 
 
 86366 
 
 84229 
 
 98585 01415 85645 
 
 56 
 
 5 
 
 1.83446 
 
 1.97092 
 
 0.02 908 
 
 1.86354 
 
 T.84 242 
 
 1.98 610 O.OI 390 1.85632 
 
 55 
 
 6 
 
 83459 
 
 97118 
 
 02882 
 
 86342 
 
 84255 
 
 98 635 oi 365 85 620 
 
 54 
 
 7 
 
 83473 
 
 97143 
 
 02857 
 
 86330 
 
 84269 
 
 98 66i 01 339 85 608 
 
 53 
 
 8 
 
 83486 
 
 97168 
 
 02832 
 
 86318 
 
 84282 
 
 98686 01 314 85596 
 
 52 
 
 9 
 
 83500 
 
 97193 
 
 02807 
 
 86306 
 
 84295 
 
 98711 01289 85583 
 
 51 
 
 10 
 
 1-83513 
 
 ^.97 219 
 
 0.02 781 
 
 T.86 295 
 
 T.84 308 
 
 T.98 737 0.01 263 T.85 571 
 
 50 
 
 II 
 
 83527 
 
 97244 
 
 - 02756 
 
 86283 
 
 84321 
 
 98 762 01 238 85 559 
 
 49 
 
 12 
 
 83540 
 
 97269 
 
 02731 
 
 86271 
 
 84334 
 
 98 787 01 213 85 547 
 
 48 
 
 13 
 
 83554 
 
 97295 
 
 02 705 
 
 86259 
 
 84347 
 
 98812 01 i88 85 534 
 
 47 
 
 14 
 
 83567 
 
 97320 
 
 02 680 ■ 
 
 86247 
 
 84 360 
 
 98838 01162 85522 
 
 46 
 
 15 
 
 1.83581 
 
 1-97 345 
 
 0.02 655 
 
 T.86 235 
 
 1-84 373 
 
 1.98863 0.01 137 T.85 510 
 
 45 
 
 16 
 
 f3 594 
 
 97371 
 
 02629 
 
 86223 
 
 84385 
 
 98888 01112 85497 
 
 44 
 
 17 
 
 83608 
 
 97396 
 
 02604 
 
 86211 
 
 84398 
 
 98 913 01 087 85 485 
 
 43 
 
 18 
 
 83621 
 
 97421 
 
 02579 
 
 86 200 
 
 84411 
 
 98 939 01 061 85 473 
 
 42 
 
 19 
 
 83634 
 
 97 447 
 
 02553 
 
 86188 
 
 84424 
 
 98 964 01 036 85 460 
 
 41 
 
 20 
 
 1.83648 
 
 T.97 472 
 
 0.02 528 
 
 T.86 176 
 
 T.84 437 
 
 T.98 989 o.oioii T.85 448 
 
 40 
 
 21 
 
 83661 
 
 97 497 
 
 02503 
 
 86164 
 
 84450 
 
 99015 00985 85436 
 
 39 
 
 22 
 
 83674 
 
 97523 
 
 02477 
 
 86152 
 
 84463 
 
 99 040 00 960 85 423 
 
 38 
 
 23 
 
 83688 
 
 97548 
 
 02452 
 
 86 140 
 
 84476 
 
 99065 00935 85411 
 
 37 
 
 24 
 
 83701 
 
 97 573 
 
 02427 
 
 86128 
 
 84489 
 
 99090 00910 85399 
 
 36 
 
 ^1 
 
 'o^ 7'S 
 
 1.97598 
 
 0.02 402 
 
 1.86116 
 
 1 .84 502 
 
 1.99116 0.00884 T.85 386 
 
 35 
 
 26 
 
 83728 
 
 97624 
 
 02376 
 
 86 104 
 
 84515 
 
 99 141 00 859 85 374 
 
 34 
 
 27 
 
 83741 
 
 97649 
 
 02351 
 
 86092 
 
 84528 
 
 99166 00834 85361 
 
 a 
 
 28 
 
 i3 7SS 
 
 97674 
 
 02326 
 
 86080 
 
 84540 
 
 99 191 00809 85349 
 
 32 
 
 29 
 
 8-3768 
 
 97700 
 
 02 300 
 
 86068 
 
 84553 
 
 99217 00783 85337 
 
 31 
 
 30 
 
 1.83 781 
 
 T.97 725 
 
 0.02 275 
 
 T.86 056 
 
 1.84566 
 
 1.99242 0.00758 T.85 324 
 
 30 
 
 3" 
 
 83795 
 
 97750 
 
 02250 
 
 86044 
 
 84579 
 
 99267 00733 85312 
 
 29 
 
 32 
 
 83808 
 
 97776 
 
 02 224 
 
 86032 
 
 84592 
 
 99 293 00 707 85 299 
 
 28 
 
 33 
 
 83821 
 
 97 801 
 
 02 199 
 
 86020 
 
 84605 
 
 99 318 00 682 85 287 
 
 27 
 
 34 
 
 83834 
 
 97826 
 
 02 174 
 
 86008 
 
 84618 
 
 99 343 00 657 85 274 
 
 26 
 
 35 
 
 T.83 848 
 
 7.97851 
 
 0.02 149 
 
 T.85 996 
 
 T.84 630 
 
 1.99368 0.00632 1.85262 
 
 25 
 
 36 
 
 83861 
 
 97877 
 
 02 123 
 
 85984 
 
 84643 
 
 99 394 00 606 85 250 
 
 24 
 
 37 
 
 83874 
 
 97902 
 
 02098 
 
 85972 
 
 84656 
 
 99419 00581 85237 
 
 23 
 
 38 
 
 83887 
 
 97927 
 
 02073 
 
 85960 
 
 84669 
 
 99 444 00 556 85 225 
 
 22 
 
 39 
 
 83901 
 
 97 953 
 
 02047 
 
 85948 
 
 84682 
 
 99469 00531 85212 
 
 21 
 
 40 
 
 1.83914 
 
 T.97 978 
 
 0.02 022 
 
 1-85936 
 
 T.84 694 
 
 1^-99 495 0.00 505 T.85 200 
 
 20 
 
 41 
 
 83927 
 
 98003 
 
 01997 
 
 85924 
 
 84707 
 
 99520 00480 85187 
 
 19 " 
 
 42 
 
 83940 
 
 98029 
 
 01971 
 
 85912 
 
 84 720 
 
 99 545 00455 85175 
 
 18 
 
 43 
 
 83954 
 
 98054 
 
 01 946 
 
 85 900 
 
 84733 
 
 99 570 00430 85 162 
 
 «7 
 
 44 
 
 83967 
 
 98079 
 
 01 921 
 
 85888 
 
 84745 
 
 99 596 00404 85 150 
 
 16 
 
 45 
 
 1.83980 
 
 1.98 104 
 
 o.oi 896 
 
 T.85 876 
 
 T.84 758 
 
 T.99 621 0.00 379 T.85 137 
 
 15 
 
 46 
 47 
 
 83993 
 
 98130 
 
 01 870 
 
 85864 
 
 84771 
 
 99 646 00 354 85 125 
 
 14 
 
 . 84006 
 
 98155 
 
 01 845 
 
 85851 
 
 84784 
 
 99 672 00328 85 112 
 
 13 
 
 48 
 
 84020 
 
 98180 
 
 01 820 
 
 85839 
 
 84796 
 
 99 697 00 303 85 100 
 
 12 
 
 49 
 
 84033 
 
 98206 
 
 01794 
 
 85827 
 
 84809 
 
 99 722 00 278 • 85 087 
 
 11 
 
 50 
 
 1.84046 
 
 T.98 231 
 
 0.01 769 
 
 1.85815 . 
 
 T.84 822 
 
 T.99 747 0.00253 T.85 074 
 
 10 
 
 51 
 
 84059 
 
 98256 
 
 01 744 
 
 85 803 
 
 84835 
 
 99 773 00 227 85 062 
 
 9 
 
 52 
 
 84072 
 
 98281 
 
 oi 719 
 
 85791 
 
 84847 
 
 99 798 00 202 85 049 
 
 8 
 
 53 
 
 84085 
 
 98307 
 
 01693 
 
 85779 
 
 84860 
 
 99823 00177 85037 
 
 7 
 
 54 
 
 84098 
 
 98332 
 
 01668 
 
 85766 
 
 84873 
 
 99848 00152 85024 
 
 6 
 
 55 
 
 T.84 112 
 
 1-98357 
 
 0.01 643 
 
 1.85754 
 
 1.84885 
 
 T.99 874 0.00126 T.85 012 
 
 5 
 
 56 
 
 84125 
 
 98383 
 
 01 617 
 
 85742 
 
 84898 
 
 99 899 00 101 84 999 
 
 4 
 
 57 
 
 84138 
 
 98408 
 
 01 592 
 
 85730 
 
 84911 
 
 99 924 00 076 84 986 
 
 3 
 
 58 
 
 84 151 
 
 98433 
 
 01567 
 
 85718 
 
 84923 
 
 99949 00051 84974 
 
 2 
 
 59 
 
 84 164 
 
 98458 
 
 01542 
 
 85706 
 
 84936 
 
 1-99 975 00025 84961 
 
 I 
 
 60' 
 
 1.84177 
 
 1 .98 484 
 
 0.01 516 
 
 1.85693 
 
 1.84949 
 
 0.00000 0.00000 1.84949 
 
 0' 
 
 
 log cos 
 
 log cot 
 
 log tan 
 
 log sin 
 
 log cos 
 
 log cot log tan log sin 
 
 t 
 
 w 
 
 (69) 
 
 450 LOG SIN, etc. 
 45°-48° 
 
CONSTANTS. 
 
 CONSTANTS. 
 
 MATHEMATICAL CONSTANTS. 
 
 Quantity. 
 
 Numerical 
 
 
 Common 
 
 
 Talue. 
 
 
 LOGABITHM. 
 
 
 2.71 828 18 
 
 Base of Napierian, natural, or hyperbolic 
 logarithms. 
 
 0.43 429 45 
 
 l/lOgl0£ 
 
 2.30 258 5 
 
 Factor to multiply into comTnon logs to 
 convert into Napierian logs. 
 
 0.36 221 57 
 
 lOgioe 
 
 0434294s 
 
 Factor to multiply into Napierian logs to 
 convert into common logs. 
 
 7.6377843 
 
 ic 
 
 3.14 159 26s 
 
 Ratio of circumference to diameter. 
 
 0.4971499 
 
 ir! 
 
 9.86 960 44 
 
 Square of ir. 
 
 0.99 429 97 
 
 I radian 
 
 57° 17' 45" 
 
 57.° 29 58 = 206265." = arc equal to 
 radius. 
 
 
 
 UNITED STA1 
 
 •ES, BRITISH, AND METRIC UNITS. 
 
 
 Note. — Th 
 
 e foUowingr ratios are 
 
 given on the authority of the U. S. Coast and Geodetic Surrey, | 
 
 "Tables of W 
 
 sights and Measures. 
 
 Washington, D. C, 1890." 
 
 
 I metre 
 
 39.37 inches. 
 
 This is the legalized ratio for the U. S. 
 The U. S. and the British inch are equal. 
 By comparisons to date (July, 1895), it 
 appears probable that this value is smal- 
 ler than the real ratio of the "Metre des 
 
 1-5951654 
 
 
 
 Archives ' ' to the thirty-sixth part of the 
 
 
 
 
 "Imperial Standard Yard" by one or 
 
 
 
 
 two parts in one million. 
 
 
 I metre 
 
 1.09 361 I yard. 
 
 The U. S. and the British yard are 
 
 0.03 886 29 
 
 
 
 equal. 
 
 • 
 
 I metre 
 
 3.28 08 33 feet. 
 
 
 0.5159842 
 
 I kilometer 
 
 0.62 13 70 mile 
 
 of 5280 feet. 
 
 1-7933503 
 
 I mile 
 
 1.60 934 7 kilom. 
 
 
 0.20 664 97 
 
 I yard 
 
 0.91 440 2 metre. 
 
 
 T.9611371 
 
 I foot 
 
 0.30 480 I metre. 
 
 
 7.48 401 58 
 
 I inch 
 
 25.40 005 mm. 
 
 Deduced from above legalized ratio of 
 yard and metre in TJ. S. 
 
 1.4048346 
 
 zinch 
 
 25.40 000 mm. 
 
 is more convenient besides being proba- 
 bly more exact. It is probably about 
 one part in one million too small, as 
 
 1.4048337 
 
 
 
 the reciprocal of 0.0254 is 39.37 008. 
 
 
 CONSTANTS. 
 
 (70) 
 
CONSTANTS. 
 
 QUASTITT. 
 
 I pound Av. 
 
 I pound Av. 
 1 ounce Av. 
 I ounce Troy 
 I grain 
 
 I kilogramme 
 I gramme 
 I litre 
 
 I litre 
 I litre 
 
 I quart, XJ. S. 
 I gallon, U. S. 
 I fluid ounce 
 I bushel, U. S. 
 I British gallon 
 I British bushel 
 
 numekioal 
 Talhe. 
 
 7000 grains. 
 
 453-59 242 77 grammes. 
 28.34 953 grammes. 
 31.10348 grammes. 
 0.06 479 892 gramme. 
 
 2.20 462 2 pounds Av. 
 1543 235 639 grains. 
 1.05 668 U. S. quarts. 
 
 0.26417 U. S. gallon. 
 33.814 U. S. fluid oz. 
 0.94 636 litre. 
 3.78 544 litres. 
 0.02 957 3 litre. 
 231 cu. inches. 
 4.54 346 litres. 
 36.34 77 litres. 
 
 CONSTANTS. 
 
 The pound avoirdupois is the 
 same in Great Britain and the 
 
 U.S. 
 
 Avoirdupois and Troy grains are 
 the same. 
 
 By original definition one litre 
 was the volume of one cubic 
 decimetre, but at present the 
 accepted definition is that pro- 
 visionally adopted by the Inter- 
 national Bureau of Weights and 
 Measures in 1880, viz. ; the 
 volume of one kilogramme of 
 water at its maximum density. 
 The experimental determina- 
 tion with high accuracy of the 
 relation between this volume 
 and the cubic decimetre is still 
 unfinished. The following val- 
 ues assume this ratio to be 
 unity. 
 
 ZZ 
 
 7 
 
 Common 
 
 LOGAllITHM. 
 
 3.84 509 80 
 
 2.65 666 58 
 1.45 254 59 
 1.49 280 91 
 2.81 156 78 
 
 0-34 333 42 
 1. 18 843 22 
 0.023944 
 
 1.42 1884 
 1.52 910 
 T.97 605 6 
 0.57 811 6 
 2.47 090 
 2.36 361 20 
 0-65 738 67 
 1.5604769 
 
 MECHANICAL OR DYNAMICAL EQUIVALENT OF HEAT. 
 
 The best values of this quantity (usually denoted by J') at present attainable (Novem- 
 ber, 1895) are the following. The values are uncertain by only about ± one twentieth 
 of one per cent. 
 427.3 kilogrammetres of work or energy are required at latitude 45°, sea-level 
 
 {g = 980.6 c.g.s.), to raise i kilogramme of water through 1° C. at 15° C. 
 778.8 ft. lbs. of work or energy are required at latitude 45"-", sea-level {g = 980.6 c.g.s.), 
 
 to raise i lb. of water through i" Tahr. at 59° Fahr. (= 15° C). For most 
 
 engineering purposes 779 ft. lbs. would be near enough. 
 
 (70 
 
 CONSTANTS. 
 
CONSTANTS. 
 
 CONSTANTS. 
 
 140a ft. lbs. of work or energy are required at latitude 45°, sea-level (g = 980.6), to 
 raise i lb. of water througb 1° Cent, at 15° C. For most engineering purposes 
 1400 ft. lbs. would be near enough. 
 4.i90"io' ergs of work or energy are required to raise i gramme of water through 1° C. 
 at 15° C. 
 To reduce these values to any given locality, multiply by the ratio gu '■ Ci where gis is 
 the value (980.6) of the acceleration of gravity at latitude 45°, sea-level, and g is the 
 value at the given place. The latter may be obtained from the latitude and altitude of 
 the place by the formula given upon the next page, unless otherwise better known. The 
 altitude correction is but six one-thousandths of one per cent (0.00 006) for each 1000 ft. 
 of elevation, and therefore quite negligible. Within the limits of uncertainty of the 
 quantities involved the latitude correction for places between 30° and 60° may be 
 applied thus : — 
 
 778.8 
 
 For each degree of latitude north of 45° subtract 
 For each degree of latitude south of 45" add 
 
 427-3 
 
 0.04 kgm. 
 
 0.04 kgm. 
 
 0.07 ft. lbs. 
 0.07 ft. lbs. 
 
 1402 
 
 0.13 ft. lbs. 
 
 0.13 ft. lbs. 
 
 Note. — The persistence with ■which the time-honored values, 772 ft. lbs. and 424 fegm., of this most impor- 
 tant constant are adhered to in practice, although known to be nearly one per cent too small, is due largely to 
 the flagrant negligence of the authors of text-books of both physics and engineering. No attention is paid to 
 the fact that Joule's original data have been amended acceptaMy to Mm, and that his work has been supple- 
 mented by the elaborate researches of at least three other independent observers with radically diverse 
 methods. How remarkably these new results check each other and confirm Joule's amended results may be 
 seen from the following table, which is given to indicate the source of the foregoing values. 
 
 
 OEiapjAL Data. 
 
 Reduced 
 TO Lat. 
 45° Sea- 
 Level. 
 
 D1FF8. 
 
 FROM 
 
 Mean. 
 
 Bate. 
 
 
 ATTTHOErrv. 
 
 J. 
 kgm. 
 
 ff- 
 
 t°.C. 
 
 Refeeehoe. 
 
 JoTJLE (as correclied and 
 
 
 
 
 
 
 
 See quotations in the 
 
 reduced to Baltimore by 
 
 
 
 
 
 
 
 Rowland and GrifSths 
 
 Rowland.) [Assigning eq. 
 
 
 
 
 
 
 
 referenceSo 
 
 wts. to all methods.] 
 
 427.99 
 
 980.05 
 
 iS-° 
 
 
 
 
 
 [Assigning Rowland's arbi- 
 
 
 
 
 
 
 
 
 trary wts.] 
 
 426.66 
 
 980.05 
 
 iS-° 
 
 
 
 
 
 Mean of both. 
 
 427-33 
 
 980.05 
 
 i5-° 
 
 427.08 
 
 -.16 
 
 1847-7B 
 
 
 Rowland [at Baltimore]. 
 
 427.4 
 
 980.05 
 
 15-° 
 
 427.16 
 
 -.08 
 
 1879 
 
 Proc. Am. Acad. A. 
 and S. XV. 75 (1880). 
 
 Gbutiths [at Greenwichl. 
 
 4.194.10' 
 
 981.17 
 
 l5-° 
 
 427.70 
 
 -I-.46 
 
 1892 
 
 Phil. Transac. cbcxxiv. 
 
 (In ergs.) 
 
 
 
 
 
 
 
 496 (1893). 
 
 MiOFLESOlJ [at Paris]. 
 
 426.84 
 
 981.00 
 
 15-° 
 
 427.01 
 
 -23 
 
 1892 
 
 Ann. de Ch. et de Ph. 
 
 - 
 
 
 
 
 
 
 
 xxvii. 237 (1892). 
 
 Mean of all. 
 
 
 
 
 427.24 
 
 ±.23 
 
 
 
 Mean omitting Joule. 
 
 427.29 
 
 
 
 
 
 
 The specific heat of water, and therefore the value of J, diminishes slightly with rise 
 of temperature. The rate of this diminution is not yet satisfactorily determined, but 
 about as nearly as it is now known the true specific heat St at any temperature t° not far 
 from 15° C, may be expressed in terms of true specific heat su at 15° C. by 
 
 St = S16 [i. - 0.00 030 (S - 15)]. 
 Hence Jt, the number of kgm. or ergs necessary to raise i kgr. of water from t° to 
 t° + 1°, will be 
 
 J, = Ju [I. - 0.00 030 (t - 15)] [Range 13° - 20°], 
 
 CONSTANTS. 
 
 (72) 
 
CONSTANTS. 
 
 CONSTANTS. 
 
 or for I lb. of water i° Fahr. 
 
 Jt=Jaali- o.ooo3o(t - 59)] [Range 56° - 68°]. 
 
 _ The values of Ji^ and J^a are given on pages 71 and 72. For further discussion of this 
 subject consult Griffiths, Phil. Mag. xi. 431 (1895). 
 
 The scale of temperature in which these results are expressed is the hydrogen scale 
 of the International Bureau of Weights and Measures, which represents, as nearly as it is 
 known, the Thomson absolute scale. 
 
 VALUE OF g AT DIFFERENT LATITUDES AND ELEVATIONS. 
 
 9 = 9iS 0(1 — 0.00 259 cos 2 X — 0.00 000 020 S). 
 
 gufi =■ 980.6 — - approx. This is the approximate average value of g at latitude 45°, 
 sec^ 
 
 sea-level. The experimental values vary widely in the next place of figures. 
 
 X = latitude of place. 
 
 H = altitude of place above sear level in metres. 
 
 Note. — Very recent observations render it probable that near the earth's surface the coefficient of R is 
 more nearly 0.00 000 030. 
 
 BROWN AND SHARPE WIRE GAUGE. 
 
 The diameter corresponding to any gauge number above zero (i.e. of any size less 
 than that of a No. o wire) may be found to within one hundred-thousandth of an inch 
 (five decimal places) by the expression 
 
 Diam. in inches of i „. „ 
 
 } = 0.32 486 X 0.89 052 5", 
 gauge number m J 
 
 or, Log of diam. in inches =7.51 170 -|- 1.94 964 5 w, 
 
 or, " " " " " — 9.51 170 — 10. -1- (9.94 9645 — io.)n. 
 
 The diameter corresponding to any gauge numbers o, 00, 000, and so on, may simi- 
 larly be computed by the following expressions in which N is the number of zeros. 
 
 Diam. in inches = 0.28 930 x 1.12 293^, 
 or, Log of diam. in inches = T.46 1348 -|- 0.05 035 3 N. 
 
 The two primary sizes on which the gauge is based are No. 0000, diameter 0.46 inch 
 exactly, and No. 36, diameter 0.005 ^^'^^ exactly. 
 
 PHYSICAL AND CHEMICAL CONSTANTS. 
 
 For very reliable and extended tables consult Landolt und Bornstein, Physikalisch — 
 Chemische Tabellen. 
 
 (73) CONSTANTS. 
 
A HISTORY OF 
 
 MATHEMATICS. 
 
 BY 
 
 FLORIAN CAJORI, PH.D. 
 
 Formerly Professor of Applied Mathematics in the Tulane University of Louisiana ; 
 now Professor of Physics in Colorado College. 
 
 8vo. Cloth. $3.50, net. 
 
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 development of mathematics. The work throughout has been written 
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 pen. Every mathematician should procure a copy of this book. The 
 book is written in a clear and pleasing style." — Dr. Halsted, in 
 American Mathematical Monthly. 
 
 "A scholarship both wide and deep is manifest." — Journal of Edu- 
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 " A clear, concise, and critical account. Its style is so clear, concise, 
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 The School Review. 
 
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ARITHMETIC 
 
 FOR SCHOOLS. 
 BY Rewritten and revised by 
 
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 Cambridge, Boys^ New York. 
 
 l6mo. Cloth. 90 cents, neU 
 
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 ELEMENTARY ALGEBRA 
 
 FOR THE USE OF PREPARATORY SCHOOLS. 
 
 BY Revised and adapted to American Schools 
 
 CHARLES SMITH, M.A., By IRVING STRINGHAM, Ph.D., 
 
 Author of*^A Treatise on Algebra" "An Professor of Mathematics and Dean of the 
 
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 versity, University of Missouri, etc., etc. 
 
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 By H. S. HALL, B.A., and S. R. KNIGHT, B.A. 
 
 Revised and Enlarged, for Use of American Scliools, 
 
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