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A PRACTICAL TREATISE 
 
 ON 
 
 COMPRESSED AIR 
 
 AND 
 
 PNEUMATIC 
 MACHINERY 
 
 BY 
 
 EDWARD A. R1X AND A. E. CHODZKO 
 
 PNEUMATIC ENGINEERS 
 
 FOR THE 
 
 X -FULTON 
 
 Engineering ^ Shipbuilding Works 
 
 SAN FRANCISCO 
 
 MANUFACTURERS OF 
 
 MINING, MILLING, SMELTING AND 
 ELECTRICAL MACHINERY 
 
 ENGINES, BOILERS, HEATERS, PUMPS, ETC. 
 
 Main Office and Branch Works, 213 First St. 
 Main Works, Harbor View 
 
 SAN FRANCISCO, CALIFORNIA 
 
L9373 
 
 Curves, Tables and Engineering Data in the body 
 
 of this Treatise are original and were 
 
 prepared by 
 
 EDWARD A. R1X AND A. E. CHODZKO 
 
 PNEUMATIC ENGINEERS 
 
 San Francisco, - California 
 
 Entered according- to Act of Congress, in the year 1896, 
 
 by 
 
 THE FULTON ENGINEERING AND SHIPBUILDING WORKS 
 
 AND 
 
 EDWARD A. RIX 
 
 In the Office of the Librarian of Congress, 
 
 at Washington, D. C 
 
COMPRESSED AIR. 
 
 It is a noteworthy fact that, while compressed air has been 
 
 ;wn and been used at a time when dynamic electricity was 
 even in its infancy, its properties and possibilities are still, 
 he minds of many practical people, an object shrouded with 
 confusion and mystery, and considered by them as a convenient 
 topic for the scientist's investigation, but altogether too intri- 
 cate and obscure to be readily grasped by a man possessed of a 
 common and average knowledge of motive machinery. 
 
 This same man, strange to say, will find no apparent mys- 
 tery in handling a first-class Compound Condensing Steam 
 Engine, whose thorough comprehension, however, involves a 
 more imposing array of natural phenomena than does the 
 action of an air motor. 
 
 Mention to him this latter machine, and he will tell you at 
 once that it is useless; he has a vague recollection that com- 
 pressed air will not yield over 15 to 20 per cent of the power 
 expended to produce it, while an electric motor utilizes 60 or 
 80 per cent of this power, and that is the end of it. 
 
 The fact is, however, without in any way disparaging the 
 wonderful strides made by electricity, that, in a great many 
 circumstances, a compressed air power transmission will be 
 found fully as much, and often more effective than an electrical 
 transmission. 
 
 Within a radius of 10 to 20 miles or more, it is not a matter 
 of theoretical speculation, but a result of actual facts, extend- 
 ing over a period of many years' experience, that compressed 
 air can be economically produced, conveyed, and utilized as a 
 motive power; and if this power is to be distributed through- 
 out a number of buildings or factories, or in the interior of a 
 mine, the absolute safety consistent with the use of compressed 
 air is an element of superiority to which the electrical trans- 
 mission has no possible claim. 
 
 However well insulated thexonductors may be, the vicinity 
 of a dynamo is always dangerous, either on the ground of fire 
 or of bodily injury. 
 
 In a large power station, manned by a picked staff of attend- 
 ants, this danger is small indeed; but the conditions are alto- 
 gether different if the motor is under the care of a miner or of 
 an ordinary workman. 
 
 Again, the location of an air motor is privileged with a con- 
 stantly renewed and wholesome atmosphere, whose tempera- 
 ture can be, at will, regulated to suit the local exigencies. 
 
 Accidental circumstances which may occur in the vicinity 
 of an electric wire under high potential are generally fraught 
 with peril. The only accident to which an air pipe is liable is 
 
4 COMPRESSED AIR. 
 
 a leak, which will cause a loss of power, but which cau be re- 
 paired and approached at no risk whatever. 
 
 But now conies another point. 
 
 Referring more especially to the mines which, in California, 
 should represent a large percentage of the users of compressed 
 air, an example will well illustrate the comparative merits of 
 the two modes of power transmission, especially for mines. 
 
 Take a mine which was equipped some years ago; ample 
 water power exists several miles away, but the configuration 
 of the ground did not permit of conveying the water to the 
 mine; a telodynamic transmission would not have been practi- 
 cal, so the owners concluded to put up a first-class steam plant 
 for hoisting, pumping, and milling purposes, and also for run- 
 ning compressors supplying air to the rock drills, and perhaps 
 to one or more underground pumps and fans. 
 
 In the course of time, however, timber has grown scarce in 
 the surrounding sections, and now they have to haul their fire- 
 wood at the rate of $5.00 or $6.00 a cord; as there is quite an 
 amount of power used at the mine, this represents a rather 
 burdensome item, so the owners begin to investigate some pos- 
 sible way out of it. 
 
 An electrical transmission is forthwith proposed to them, 
 with tangential wheels and generators near the waterfall, con- 
 ductors readily spanning all the intervening ridges and can- 
 yons, and a number of dynamos to replace the steam engines. 
 
 It is a practical, feasible, and satisfactory proposition, but 
 there is one black cloud in this bright sky: what shall become 
 of the steam engines and boilers.? They have to be torn down, 
 of course, to make room for the dynamos. This whole plant 
 is still, however, in perfect condition; it has been bought, 
 hauled, and erected at great cost, and would bring, at a sale, 
 about as much as its equivalent of scrap iron, supposing it 
 could be sold at all. The proposed plant will assuredly be 
 more economical, but this is a dead loss which it will take some 
 time to make up for. 
 
 Here comes the opportunity of the compressed-air man; he 
 proposes to put up an air-compressing plant at the water-fall; 
 the iron-pipe that carries the air will span ridges and canyons 
 as easily, for all practical purposes, as did the wires, but after 
 it reaches the mine, the list of new material closes, or nearly 
 so; for neither the engines nor the boilers will have to be 
 touched. The former will v/ork with air as they did before 
 with steam, the boilers being used for heaters or air receivers. 
 
 The compressor that used to work at the mine will not even 
 have to be discarded, as it may serve either as a reserve or as a 
 pressure transformer; in other words, there will have been an 
 addition to the mine's possessions, in the shape of the com- 
 pressors at the power-house and of the pipes, but the old plant 
 will remain just as it was, and give full value for what it did 
 cost; it will simply be necessary to find a new job for the fire- 
 men and woodchoppers. 
 
 Another very important point: suppose the power plant at 
 
COMPRESSED AIR. 5 
 
 the water-fall met with accident, or the conductors to be tem- 
 porarily crippled; with the electric plant it means a stoppage of 
 the whole mine; with the compressed air proposition it would 
 only be necessary to fill the boilers, start up the fires, and run 
 by steam again. Here, there is no possible competition between 
 the two systems. The advocates for electricity claim a superior 
 economy, but a few developments on the production and the 
 utilization of compressed air will, it is hoped, prove to the con- 
 trary, and we will try to illustrate the laws and properties 
 of air and compressed air in a simple manner, and with the 
 constant remembrance that practical men want plain facts and 
 have no use for mathematical discussions. 
 
 It is a common feature with gaseous substances that heat 
 has a tendency to increase their volume, or, as the term goes, 
 to expand them. Referring more particularly to atmospheric 
 air, it will suffice to recall the classical experiment of the cork 
 shutting hermetically a bottle full of air, and blown out, if the 
 bottle be dipped in hot water. 
 
 Therefore, if a certain amount of air is confined within a 
 closed cylinder, at the outside temperature, and then exposed to 
 a source of heat, this air will have a tendency to expand, the 
 result of which may be twofold. 
 
 If the cylinder is closed, for instance, by two covers tightly 
 bolted on, and if its walls and covers are strong enough to 
 resist deformation under this expansive tendency, the volume 
 of air will remain constant, and its pressure will increase. 
 
 But if we suppose that one of the covers be removed, and 
 replaced by a tight-fitting piston free to move in the cylin- 
 der, and loaded with a certain weight, when the air is at the 
 outside temperature, the piston will descend in the cylinder 
 until it is balanced by the pressure of the confined cushion of 
 air. 
 
 If now the cylinder is heated, the piston will start slowly 
 upward, and then stop when the expansion wall have ceased; 
 in this case, the load of the piston, and consequently the pres- 
 sure of the air, have remained the same as before heating, but 
 the volume of air has increased. 
 
 Summing up these simple facts, we will say, therefore, that 
 the effect of heat upon this mass of air is, in the first cfse, to 
 increase its pressure under constant volume; and in the second case, 
 to increase its volume under constant pressure. The reverse w 7 ould 
 happen in both cases; i. e., if we take the closed cylinder full 
 of hot air, and if we allow it to cool down to the outside tem- 
 perature, the volume of this air will, of course, remain the 
 same, but its pressure will fall gradually, until it becomes the 
 same as it was before heating. 
 
 In a similar way, if we allow the cylinder with its piston to 
 cool down to the outside temperature, the volume of air con- 
 fined under the piston will shrink, and the piston will grad- 
 ually drop down to the point where it was before the cylinder 
 was heated, the pressure, of course, remaining constant. 
 
 Now, following this line of reasoning, we may conceive 
 
6 COMPRESSED AIR. 
 
 that, if the temperature arouud the cylinder was made colder 
 and colder, the pressure of the constant volume of air of the 
 first case would keep dropping, and the volume of the mass of 
 air at constant pressure, in the second case, would also keep 
 shrinking, until, if such a process was carried on far enough, 
 the mass of air which we have been considering would be con- 
 densed in volume to nothing, and have no pressure at all. 
 
 A simple calculation shows that such a result would occur 
 at the temperature of 461 degrees below o Fahr., or 493 degrees 
 below the freezing point of water. 
 
 This temperature, which has been approached, but never 
 yet reached by any contrivance at present at our command, is, 
 so far, a matter of mental conception, but we may, however, 
 conceive its existence. It is called the absolute zero, and plays 
 an important part in the study of the properties of gases. 
 
 The absolute zero is, therefore, the temperature at which a mass of 
 air would have neither volume nor pressure. 
 
 Passing now to a seemingly different subject, although its 
 close connection to the preceding facts will soon appear, a few 
 words may be said about the fundamental principle which 
 forms the basis of all questions relating to the mechanics of 
 gases, the Principle of Equivalence of Heat and Work. 
 
 This principle, formulated in plain language, means that 
 whenever work is performed, it develops heat; and conversely, that 
 -whenever heat is generated, it can be traneformed into work. 
 
 The scope of this principle is exceedingly broad. 
 
 The elementary conception of work involves two distinct 
 elements: a force and a motion, and the measure of the 
 amount of work developed by a certain force is the product of 
 this force, multiplied by its displacement. 
 
 Thus, if we exert a pull of 1 lb., and if we move 1 foot in 
 the direction of this pull, the work that we have developed 
 amounts to i-foot pound. 
 
 But, while this definition is true in all cases, work, in nat- 
 ural phenomena, can assume a very great variety of forms, 
 which, moreover, it is not necessary to enumerate here. 
 
 Our daily experience shows us some applications of this 
 principle of equivalence, or correspondence, between heat and 
 work. 
 
 That work develops heat, we can see in hammering a cold bar 
 of iron, which soon becomes hot; we see it in the result of 
 human exertion, in the heating of a shaft journal when the 
 work of friction becomes too great; in the sparks showing at 
 the contact of a revolving wheel, and of a brake-shoe, or at the 
 periphery of a grindstone, etc. 
 
 That heat can be transformed into work has been shown in the 
 preceding explanations, when we saw a weighted piston lifted 
 by heating the air confined beneath it. ' 
 
 The steam engine is another indirect demonstration ot the 
 same fact; when the heat developed in the combustion of coal 
 generates steam, which accomplishes some work on the piston 
 of an engine. 
 
COMPRESSKD AIR. 7 
 
 It would be useless to multiply examples of this capital 
 principle; suffice it to say, that whenever work is performed, 
 there is a production of heat. This will not always be sensible, 
 especially if the work is slow and gradual, because the heat is 
 lost by radiation, by absorption in surrounding bodies, etc., as 
 soon as it is developed. 
 
 This subject of the equivalence between heat and work has 
 been exhaustively studied and verified, and it is now accepted 
 as a fundamental axiom in mechanics. 
 
 One British Thermal Unit (B. T. U.) of heat, i. e., the quan- 
 tity of heat required to raise by 1 degree Fahr. the tempera- 
 ture of I lb. of water, corresponds to 77 8-foot lbs. of work. 
 
 In other words, 778-foot lbs. of work applied to a certain 
 mass of air, for instance, will develop in it 1 B. T. U. of heat; and 
 conversely, an amount of heat of 1 B. T. U. stored up in this 
 air can develop 778-foot lbs, of work. 
 
 The number 778, or coefficient of correspondence between 
 heat and work, is known as the Joule's Equivalent, from the 
 name of the physicist who first set precise rules in this respect. 
 Joule had fixed the figure at 772-foot lbs., which was for years 
 adopted as correct. Subsequent investigation led to make it 
 778, and the most recent developments put it at 779. In this 
 treatise it has been taken as 778. 
 
 But it is now expedient to clearly explain how a certain 
 mass of air, which has been subjected to work, and which has 
 therefore accumulated a certain amount of heat, can conversely 
 develop work corresponding to that heat. 
 
 Let us take a cylinder full of air at atmospheric pressure, 
 and closed at one end, and then let us insert at the other end a 
 piston in this cylinder, and exert an effort upon the piston; 
 the air confined within the cylinder will be gradually com- 
 pressed, and occupy a smaller volume. At the same time, its 
 pressure will have increased, and this compression has absorbed 
 a certain amount of work, which will be measured by the mean 
 pressure which the piston has had to overcome, multiplied by 
 the amount of its displacement. 
 
 The pressure on the piston represents a certain number of 
 lbs.; the displacement represents a certain number of feet, 
 and their product represents a certain number of foot-lbs., 
 which measure the work of compression. 
 
 Suppose now that we release the piston; the air confined in 
 the cylinder, and whose pressure was solely owing to the effort 
 exerted on this piston, will immediately expand and push it 
 back, and if there was no friction between it and the cylinder 
 walls, it would resume its former position, when the air-cushion 
 would be at atmospheric pressure again. In other words, 
 every amount of work spent in compressing the air, would be 
 entirely returned by the expansion of this air, or, to any work of 
 compression corresponds an equal ivork of expansion, if these efforts 
 follow each other instantly. 
 
 Here, we did not make any assumption as to the tempera- 
 ture of the confined air, which has been supposed to remain 
 
8 COMPRESSED AIR. 
 
 stationary. But now let us confine, with a piston, a certain 
 amount of free air in a cylinder, and let us fix the piston in 
 this position so as to prevent it from backing out; and, then, let 
 us apply to the cylinder some source of heat. 
 
 The confined air will have a tendency to expand, and as the 
 piston cannot move, the pressure will rise; if then we let the 
 piston free, the confined air will push it out in expanding, 
 until it resumes the atmospheric pressure, and the outside tem- 
 perature, and with the same restriction as regards frictional 
 resistances. 
 
 We see that in both instances there has been some expan- 
 sive work done, and the force that produced it was supplied in 
 the first case by the work of compression, and in the second 
 case, by the heating of the air. We see also that in this latter 
 instance, the pressure of air in the cylinder depended upon the 
 amount of heat supplied to it, or, in other words, upon its tem- 
 perature, and so did the expansion work. 
 
 Returning now to the definition of the absolute zero, as 
 given, which marks, so to say, the ideal limit of existence of a 
 gas so far as volume and pressure are concerned, we can 
 readily conceive that I lb. of atmospheric air, at 60 degrees 
 Fahr., for instance, is the outcome of 1 lb. of air at the tempera- 
 ture of absolute zero, to which a sufficient amount of heat has 
 been supplied to raise its temperature by 461 +60=521 degrees 
 Fahr., and its pressure to 14.7 lbs. per square inch, above a 
 vacuum, wliich is the pressure at the absolute zero. 
 
 This pound of air is confined within the atmosphere, as was 
 the mass of air of the last example within a cylinder; but 
 should it be allowed to expand against a perfect vacuum, it 
 would produce an amount of expansion work corresponding to 
 the amount of heat which it had received to become atmos- 
 pheric air. 
 
 This capacity of producing expansion work is what is 
 termed the Intrinsic energy of this pound of air, and its exist- 
 ence is, as we see, intimately connected with the conception of 
 the absolute zero. 
 
 The amount of work that measures this intrinsic energy can 
 be determined from the law of the equivalence of heat and 
 work, since we know that by storing up a certain quantity of 
 heat in a mass of air, we give it the property of returning a 
 corresponding quantity of work. 
 
 The temperature to which a given amount of heat will raise 
 1 lb. of different substances is not the same for all of them. 
 
 The specific heat of a substance is the number of B. T. U. 
 that will raise by 1 degree Fahr. the temperature of 1 lb. 
 of this substance, the specific heat of water being taken as 
 unit. We have seen already that the specific heat of water was 1 ; 
 i. e., that it takes 1 B. T. U. to raise by 1 degree Fahrenheit the 
 temperature of 1 lb. of water. 
 
 The specific heat of air which we have to use in the subse- 
 quent developments is 0.2377. 
 
 In other words, it takes 0.2377 of a B. T. U. to raise by 1 
 
COMPRESSED AIR. 9 
 
 degree the temperature of 1 lb. of air, that is to say, the 
 amount of heat that would raise by 1 degree Fahr. the tem- 
 perature of 1 lb. of water, will raise by 1 degree Fahr. the 
 temperature of 4.2 lbs. of air. 
 
 The quantity of heat necessary to raise by 521 degrees Fahr. 
 the temperature of 1 lb. of air is, therefore: 
 
 0-2377X521=123.8412 B. T. U., 
 and the corresponding amount of work is, 
 
 123.8412x778=96,348.52 foot lbs., 
 which represents the Intrinsic energy of 1 lb. of air at 60 de 
 grees Fahr. 
 
 This, of course, presumes that no heat would be either lost 
 or gained, by radiation or otherwise, during the expansion of 
 air, and this sort of expansion is called Aiiabatic expansion. 
 
 Now, while any one will readily understand that the expan- 
 sion of air can be utilized to do useful work on a piston, it is 
 also obvious, for practical reasons, that this expansion cannot 
 be carried below atmospheric pressure, since creating a vacuum 
 would require additional work. 
 
 Consequently, we cannot expect to avail ourselves of any 
 portion of the intrinsic energy stored up in atmospheric air, 
 under ordinary circumstances. 
 
 With a steam engine wecan obtain a vacuum, or at least a 
 pressure inferior to the atmosphere, by condensing the steam, 
 but there is no such thing in the air machine. 
 
 Let us observe, moreover, that the intrinsic energy pos- 
 sessed by 1 lb. of air is entirely independent of its pressure, so 
 long as its temperature remains the same, the work of expan- 
 sion being exclusively controlled by the extreme temperatures 
 between which the air expands; so that 1 lb. of air at 100 lbs. 
 gauge pressure, and 1 lb. of air at 10 lbs. gauge pressure, and 
 both at 60 degrees Fahr., possess the same total intrinsic 
 energy as 1 lb. of atmospheric air. 
 
 But there is a vast difference between them at a practical 
 standpoint, inasmuch as air at 100 lbs., and even at to lbs., can 
 do some useful work by expanding down to atmospheric pres- 
 sure; part of their intrinsic energy can, therefore, be utilized to 
 do some actual work. 
 
 Taking, for instance, 1 lb. of air at 100 lbs. gauge, and at 60 
 degrees Fahr. — if allowed to expand adiabatically to atmos- 
 pheric pressure, it will produce work, and consequently lose 
 part of its heat, and we find that its temperature, after the 
 expansion has taken place, is: — 173.95 degrees Fahr. 
 
 The drop of temperature is: 
 
 173-9^+60=233 95 degrees, 
 and as 778x0.2377=184 93, the work of adiabatic expansion is: 
 184.93x233-95= 43,264.37 ft. lbs. 
 
 this being the useful work, 
 
 The adiabatic work of expansion from 173. 95 
 degrees Fahrenheit to the absolute o would 
 be: 18493X287.05= 53,084.15 " " 
 
 Total, 96,348.52 " ' 
 
COMPRESSED AIR. 
 
COMPRESSED AIR. II 
 
 which is the total intrinsic energy — that is to say, we have 
 utilized 45 per cent of the total intrinsic energy. 
 
 Next, taking air at 10 lbs. gauge, the temperature after adia- 
 batic expansion to atmospheric pressure is — 12.9 degrees Fahr. , 
 and the useful work of expansion is: 
 
 184.93x72.9= 13,481.39 ft. lbs. 
 
 The adiabatic expansion from — 12.9 degrees 
 to absolute zero would give: 
 
 184.93x448.1= 82,867.13 " " 
 
 Total, 96,348.52 " <( 
 i. e., the total intrinsic energy, and the useful work is here 14 
 per cent of the total intrinsic energy. 
 
 It is hardly necessary to say that these figures are theoreti- 
 cal, because, in practise, part of the work of expansion, and 
 consequently part of the heat, is absorbed by the friction of 
 the piston in the cylinder, and lost by radiation from the vari- 
 ous pieces of the machines. 
 
 We see, therefore, that the only portion of the intrinsic 
 energy of air that is practically obtainable is the expansion 
 work which it does above atmospheric pressure; i. e., that the 
 pressure of this air must be raised above the pressure of the 
 atmosphere. 
 
 From the preceding developments we might rightly con- 
 clude that this result would be reached by heating the air, 
 previously confined within a closed vessel, to a proper temper- 
 ature. But in practise, such a process would prove unaccept- 
 able. 
 
 Compressed air is slow in taking up heat, because its con- 
 ductivity is small ; i. e. , because the heat is slow to penetrate the 
 whole mass of air, and its low specific heat causes it to cool 
 down rapidly. 
 
 Then, again, the whole amount of expansive work above 
 atmospheric pressure could not, as said before, be obtained in 
 practise; so that raising the pressure of air by mere heating is 
 not a practical proposition, and it is necessary, in order to 
 meet the requirements of its industrial applications, to operate 
 this rise of pressure by direct compression; i. e., by acting upon 
 the air, confined in a cylinder, through a piston to which an 
 adequate amount of power is applied. 
 
 This compression, in whichever way the rise of pressure 
 occurs during its process, is always affected on the following 
 general lines: 
 
 A cylinder A (Fig. 1), closed at both ends by covers, con- 
 tains a piston B, which can move back and forth therein, and 
 whose rod C is connected, either to the piston of a steam 
 engine, or, through a connecting-rod and a crank, to a revolv- 
 ing shaft. 
 
 Kach one of the cylinder covers carries one or more inlet 
 valves a, a f , through which the atmospheric air can penetrate 
 into the cylinder; each valve, of course, opening inward, and 
 being maintained tightly pressed upon its seat by a spring. 
 
12 COMPRESSED AIR. 
 
 The covers also carry one or more discharge valves C 67, 
 similarly kept closed by a spring, and opening outward into 
 closed chambers g, k, connected by a common conduit c, 
 which leads to a closed receiver r, whence a pipe attached to 
 the nozzle s, conveys the air to the place where it is proposed 
 to use it. 
 
 All the valves being closed, and the piston B at one end of 
 its stroke, as shown, if it is set in motion from the left to the 
 right, a partial and increasing fall of air pressure will occur 
 behind it, and soon overcome the tension of the spring which 
 keeps the inlet valve a closed; this valve opens, and atmos- 
 pheric air rushes into the cylinder, behind the receding piston. 
 
 On the right side of this latter, we have, at the beginning of 
 the stroke, a cylinder full of atmospheric, or, as generally 
 called, of free air; the inlet valve a, and discharge valve b, are 
 both closed, and so remain as the piston moves from left to 
 right, because the air pressure in the cylinder has a tendency 
 to close the inlet valve a\ whilst its pressure is not sufficient to 
 lift the discharge valve b' '. 
 
 The piston continuing to move, the air pressure constantly 
 increases, until, at a certain point n, of the stroke it reaches, or 
 slightly surpasses, the receiver pressure. 
 
 The action of this latter on the outerside of the discharge 
 valve b' , and also the tension of its spring are now balanced, 
 and the smallest subsequent move of the piston opens this 
 valve, and the compressed air is forced through it into the 
 receiver, until the piston reaches the end of its stroke, when 
 the discharge valve is closed by its spring. 
 
 An inverse series of operations will occur during the reverse 
 stroke, and so on. 
 
 An analysis of these operations shows that during any one 
 stroke of the piston there are three distinct classes of work per- 
 formed: on one side of the piston, a work of suction; on the 
 other side, first a work of compression, under variable piston 
 load, and then a work of delivery, under constant piston load. 
 
 This is quite similar, only in the reverse order, to what 
 occurs in the cylinder of a steam engine, wherein a certain 
 volume of steam is admitted under full pressure, and then, 
 after cutting off its ingress, is allowed to expand during the 
 remainder of the stroke. 
 
 The work of suction, which overcomes the inertia of the in- 
 let valves, the tension of their springs, and the resistance of 
 air in its passage through the valve apertures, is always small, 
 and can be reduced by properly proportioning and constructing 
 the inlet valves. 
 
 It is, therefore, a matter of correct design, which has nothing 
 to do in the present developments, and no further mention of 
 it will hereafter be made. 
 
 Of the two other qualities of work, the peiiod of delivery 
 does not either offer any peculiar feature to investigation 
 besides its relative proportion to the whole stroke, inasmuch as 
 it is symbolized by a constant load acting against the piston, 
 
COMPRESSED AIR. 13 
 
 along a certain distance, which corresponds to the elementary 
 definition of work as previously given. 
 
 We are thus left to concentrate our attention upon the 
 period of compression. 
 
 The variations of volume and of pressure of air, which occur 
 gradually during the process of compression, do not follow the 
 same law in all cases; that is to say, this variation is different, 
 whether the compression takes place at a constant temperature 
 (isothermal compression) without any loss or gain of heat, or 
 by allowing the increasing heat developed during the com- 
 pression to remain integrally in the air; in other words, if the 
 compression is done at variable temperature (adiabatic com- 
 pression). 
 
 There is no intention to develop here the laws governing 
 the pressure and volume of air in those two sorts of compression . 
 
 This would necessarily involve the use of mathematical 
 formulae, which we wish to avoid. Suffice it to say that, if the 
 temperature of the air remained constant throughout the compression, 
 the volume which it occupies at any moment would vary in- 
 versely as the pressure. 
 
 Taking, for instance, 1 cubic foot of free air at 60 degrees 
 Fahr. , its pressure is, therefore, 1 atmosphere, or 14.7 lbs. per 
 square inch above a vacuum, or also zero gauge pressure. 
 Suppose that this air is confined under the piston of a 
 closed cylinder, and that, driving this piston forward, we 
 reduce the volume occupied by the air to }i cubic foot only, at 
 the same time maintaining always its temperature at 60 degrees 
 Fahr. Then the pressure of this air would be 29.4 lbs. per 
 square inch above a vacuum (or 14.7 lbs. gauge), that is, twice 
 what it was before. 
 
 If the volume was reduced to )/$ of a cubic foot, its pressure 
 would become 3x14.7, or 44.1 lbs. per square inch above a 
 vacuum or 29.4 lbs. gauge, always upon the condition that the 
 temperature remains, throughout this process, at 60 degrees 
 Fahr. 
 
 In other words, if the volume of air becomes 4, 5, 6, 10, 20 
 times smaller, its pressure becomes 4, 5, 6, 10, 20 times greater, 
 always taking the pressure of the atmosphere (or the gauge pressure 
 plus 14 7 lbs. per square inch) as unit, and not the gauge pres- 
 sure, which would lead to absurd conclusions. 
 
 These pressures counted above a vacuum are called absolute 
 pressures; the pressures indicated by the pressure gauge of a 
 boiler are termed effective or gauge pressures. The absolute pres- 
 sure is obtained by adding 14.7 lbs. to the corresponding gauge 
 pressure; and conversely, the gauge pressure is obtained by 
 subtracting 14.7 lbs. from the corresponding absolute pressure. 
 
 Let us take a cylinder open at one end (Fig. 2) and a piston 
 moving in it. Suppose that the piston is at 48 inches from the 
 cylinder head, that this space has been filled with free air 
 through the inlet valve, and that the pipe leading from the 
 discharge valve casing communicates with a receiver wherein 
 the pressure is 73.5 lbs. gauge per square inch. 
 
COMPRESSED AIR. 1 5 
 
 We will assume, also, that the compression is isothermal; 
 i. e., that the temperature in the interior of the cylinder re- 
 mains the same as in the open air. 
 
 If we move the piston 12 inches, the volume occupied by 
 the air is 36 inches, or % of its former length, 4^ inches. The 
 pressure must, therefore, be the reverse, or % of the atmos- 
 pheric pressure; i. e., 19.6 lbs. absolute, or 4.9 lbs. gauge. 
 
 Similarly, when the piston has successively covered 
 24, 32, 36, 38.4 46 inches of its stroke, the absolute 
 
 pressures are respectively: 
 29.4, 44.1, 58.8, 73.5, 82.2 lbs., and the gauge pressures 
 14.7, 29.4, 44.1, 58.8, 73 5 lbs., per square inch, 
 which are marked on the sketch. 
 
 If the piston moves further on, as the pressure in the cylin- 
 der is the same as in the receiver, the discharge valve opens; 
 there is no more compression, and the remaining 8 inches of 
 stroke are completed by the piston against a constant gauge 
 pressure of 73.5 lbs. per square inch. 
 
 Let us now draw a line, A D, which, at any scale, repre- 
 sents 48 inches, and mark on this line some points at 12, 24, 32, 
 36, 38.4, and 40 inches from its left end; then draw at those 
 points some lines 12-2, 24-3, 32-4, 36-5, 38 4-6, 40-7, perpendic- 
 ular to A D. 
 
 Now, on these lines, let us carry, at any other scale, the 
 gauge pressure at the corresponding point of the stroke; this 
 will give us a succession of points 2-3-4-5-6-7, and, if we join 
 them by a continuous line, a curve A B, that represents the 
 variations of air pressure during the compression. 
 
 This curve starts from the point A, where the gauge pres- 
 sure is zero. 
 
 If we took any number of intermediate points between 40 
 and 48 inches of the stroke, the pressure would always be 73.5 
 lbs. gauge, and consequently the curve of compression A B is 
 followed by a line B C, parallel to A D, and representing the 
 delivery under constant pressure: so the diagram A B CD gives 
 us a graphic representation of the isothermal compression and 
 delivery of air during one stroke of the piston, and its area 
 represents the work performed during that stroke, for each 
 square inch of piston area. 
 
 The law of isothermal variation of the pressures and vol- 
 umes applies to decreasing pressures as well as to increasing 
 ones; thus, if we cause one cubic foot of air at 73.5 lbs. gauge 
 (88.2 absolute) to occupv 6 cubic feet, its pressure will become 
 14.7 lbs. absolute per square inch or o gauge pressure. 
 
 In other words, the curve of isothermal compression is also 
 the curve of isothermal expansion, and the diagram A B C D' 
 represents either the work of compression and delivery of a 
 volume of free air, to 73.5 lbs. gauge, or the expansive work of 
 the same body of air at 73.5 lbs, gauge pressure, and expanded 
 from that pressure to the atmosphere, when it resumes its prim- 
 itive volume. 
 
 The practical meaning of this is, that if we compress a 
 
1 6 COMPRESSED AIR. 
 
 certain mass of air in a closed cylinder, by pushing the piston 
 forward by a certain number of inches, and then, if we let the 
 piston free, the air will expand and push it. back; and should 
 there be no friction between the cylinder and the piston, this 
 latter would return exactly to its starting-point, performing 
 during its reverse stroke exactly as much work as has been 
 required to push it forward. 
 
 Quite a similar course of reasoning leads us to conclude that 
 if we compress air isothermall} 7 in a cylinder, and if its discharge 
 valve chamber (this valve being loaded to receive pressure) 
 communicates through a pipe of any length, with another 
 cylinder exactly alike, located at some distance from the com- 
 pressing cylinder, we can obtain isothermally (neglecting 
 resistances) from the second cylinder the same amount of 
 work that has been developed in the distant first cylinder. 
 The first cylinder is the compressor, the second is the motor, 
 connected by the air main to the compressor; the whole is a 
 perfect compressed air transmission, wherein a given amount of 
 work is integrally conveyed to any distance from its point of 
 production. 
 
 But were we to establish such a system we would find that 
 in practise the work recovered from the motor would not be 
 equal to the work developed in the compressor. 
 
 To reduce this difference (which is the keynote of economy 
 in this system of power transmission) to be as small as 
 possible, constitutes, in a nutshell, the whole scope of pneu- 
 matic engineering; and as the first condition to fight a 
 difficulty is to locate it, and to size it up, these remarks will be 
 concluded by a few explanations showing what are the causes 
 of discrepancy between the work expended in the compressor, 
 and the work recovered from the motor, and how they can be 
 partly eliminated; their total disappearance^ or rather counter- 
 acting, being a purely practical matter, which has no absolute 
 limitations. 
 
 The fact of compressing air in a cylinder is always accom- 
 panied by a production of heat. What causes this heat lo 
 develop in the case of air is a question the precise answer to 
 which would carry us too far into theory. It may be said 
 however, that modern science considers air as formed of 
 minute particles in a constant state of vibration, and that com- 
 pressing a volume of air which contains a certain number of 
 these particles causes them to increase the rapidity of their 
 vibratory motions, hence friction, impact, and heat. 
 
 Direct experiment, made from the freezing to the boiling 
 point of water, has shown that the pressure of air remaining 
 the same, its volume at 32 degrees Fahr. increases by X?3 f° r 
 each increase of 1 degree Fahr. in the temperature of this air. 
 
 From this we see that air at the temperature of boiling 
 water has increased in volume by l8 % 93 =o.366, or 36.6 per 
 cent, whilst this same air, at 493 degrees below -the freezing 
 point of water, or 461 degrees below zero Fahr. has shrunken: 
 by 49 X9 3 of its volume, or by that volume itself. This is how 
 the temperature of absolute zero was ascertained. 
 
COMPRESSED AIR. 17 
 
 Compression will generate heat, and only should it be pos- 
 sible to eliminate it as soon as produced, would isothermal 
 compression be obtainable. It might probably be done by a 
 very slow and gradual compression, combined with copious 
 means of cooling the air in the compressing cylinder. 
 
 But these conditions correspond to a practical impossibility, 
 and there is in consequence a considerable amount of heat dis- 
 engaged during the compression. The following table gives 
 the temperatures Fahr. of dry air at the end of its compression, 
 to different gauge pressures iu adiabatic compression; i. e., 
 supposing that no portion of the heat developing is lost in the 
 course of compression. 
 
 \bsolute Pressure. 
 
 Gauge Pressure. 
 
 Fahr. temperature at 
 
 (Lbs. per sq. in.) 
 
 (I,bs. per sq. in.) 
 
 end of compression. 
 
 14.7 
 
 O 
 
 6o° 
 
 16.17 
 
 1.47 
 
 74-6° 
 
 18.37 
 
 3-67 
 
 94-8° 
 
 22.05 
 
 7-35 
 
 124.9 
 
 25-8r 
 
 11. n 
 
 151-6° 
 
 29.4 
 
 14.7 
 
 175.8 
 
 36.7 
 
 22 
 
 218.3 
 
 44-1 
 
 29.4 
 
 255-1° 
 
 5i-4 
 
 36.7 
 
 287.8 
 
 58.8 
 
 44-1 
 
 3'7 4° 
 
 73-5 
 
 58.8 
 
 369.4° 
 
 88.2 
 
 73-5 
 
 414-5° 
 
 102.9 
 
 88.2 
 
 454-5° 
 
 117.6 
 
 102.9 
 
 490. 6° 
 
 132.3 
 
 117. 6 
 
 523-7° 
 
 147 
 
 132.3 
 
 554° 
 
 220.5 
 
 205.8 
 
 68i° 
 
 294 
 
 279.3 
 
 781 
 
 367.5 
 
 352.8 
 
 864 
 
 We see that as the pressure increases so does the tem- 
 perature, and that when, for instance, the pressure has reached 
 73.5 lbs. gauge per square inch, the temperature is 414.5 
 degrees Fahr., instead of 60 degrees, as was the case in 
 isothermal compression. 
 
 The result is, that if we take the same cylinder which was 
 used in that case, i. e., if we act on the same weight of free air,, 
 this air, when at 73.5 lbs. gauge, will be 354.5 degrees Fahr. 
 warmer in adiabatic compression than it would in isothermal 
 compression. Its volume must therefore be necessarily greater 
 in the former case, since the pressure is supposed to be the same. 
 
 The practical meaning of it is that in adiabatic work the 
 period of compression is shorter and the period of delivery is 
 longer than in isothermal work; as the work at full pressure is 
 naturally greater than at any time during compression, when 
 the pressure is smaller, the adiabatic work is greater than the 
 isothermal work, to raise the same weight of air to the same 
 pressure. 
 
 For 73.5 lbs. gauge, and atmosphere at 60 degrees Fahr., 
 
l8 COMPRESSED AIR. 
 
 the adiabatic work is 1.31 times the isothermal work. But if 
 the work done by the motor is correspondingly greater, what 
 harm does the heat do ? There would be none but for the fact 
 that the motor is always at some distance from the compressor 
 (otherwise there would be no reason to transmit power), and 
 the air parting easily with its heat, its passage through the 
 receiver and the main will reduce the air to the temperature of 
 the atmosphere; i. e., after compressing a volume of hot air 
 EC D (7 (Fig. 3), we shall introduce in the motor a volume 
 B C D E of cold air of the same weight and pressure. 
 
 Now, this volume will expand in the motor either isother- 
 mally or adiabatically. 
 
 As we saw that the work of compression disengages heat, 
 similarly, but conversely, does the work of expansion absorb 
 heat from the surrounding bodies, and as the isothermal com- 
 pression would require a slow process with copious cooling, so 
 would the isothermal expansion require a slow process with 
 copious heating. Unless this is done, the expansion will be 
 rather adiabatic. 
 
 Rather, because if isothermal conditions never strictly 
 obtain in practise, the same is true with adiabatic work. 
 
 If we expand adiabatically the volume of air B C D E, at 
 60 degrees Fahr. and 73.5 gauge, to atmospheric pressure, the 
 work of expansion represented by the diagram B C D K, will 
 only be 0.595 of the work of adiabatic compression. 
 
 A compressed air transmission seems, therefore, to be an 
 inferior system, the more so as the above figures do not take 
 into account all the losses incurred, but only the thermic 
 losses; i.e., such as are due to loss of heat. 
 
 Several means are resorted to in order to reduce this loss. 
 
 Suppose that the volume of cold air, B C D E, when it 
 arrives at the motor, be reheated at constant pressure (73.5 
 lbs. g. ) until it becomes equal to F C D G; then we shall be 
 able to develop in the motor by the expansion of this volume 
 of hot air the same work that was used to compress it 
 adiabatically. 
 
 So if there was no other loss, the motor would utilize 100 per 
 cent of the work of compression. Indeed, should the air arriv- 
 ing at the motor be reheated to a higher temperature than that 
 reached in the compressor, the work recovered would be 
 greater than the work expended; and there is no absurdity in 
 this statement, for such a result is easily attained at the cost of 
 a certain quantity of fuel, which must be taken into account 
 and deducted in figuring up the actual efficiency of the motor. 
 
 Reheating the air upon its arrival at the motor is, indeed, 
 the bise of the superiority of compressed air as a medium of 
 power transmission. 
 
 No corresponding feature exists with electricity to the pos- 
 sibility of increasing at any time the intrinsic energy of the 
 motive agency in an easy and inexpensive manner. 
 
 There are, however — at least at present — some practical 
 limitations to this reheating ; compressed air cannot conve- 
 
COMPRESSKD AIR. 
 
 19 
 
20 COMPRESSED AIR. 
 
 niently be admitted into a cylinder at a temperature much above 
 350 degrees Fahr. ; while we have seen that in adiabatic com- 
 pression, the temperature corresponding to 73.5 lbs. gauge is 
 414.5 degrees, and this illustration points out one reason why 
 low pressure air is more economical, for power purposes, and also 
 the use of compound compression where the rise of adiabatic 
 temperature is small in comparison to single stage machines. 
 
 No lubricants of the ordinary description will be fully active 
 beyond this temperature: special oils, however, are made 
 which are not decomposed belore 500 to 600 Fahr. But it is 
 evident that, could the compressor and motor cylinders, pis- 
 tons, and packings be made of a substance that would with- 
 stand great heat without injury or the usual lubricants, the 
 reheating could be carried far enough to compensate for all 
 other losses, a feature exclusively characteristic of air; and 
 there is no apparent reason why such a substance could not be 
 discovered, and it will reward undoubtedly its discoverer in a 
 day not far distant. 
 
 Without entering into many particulars, it may be stated 
 that when the compression from atmospheric to receiver pres- 
 sure is effected in one cylinder, the air is cooled either by sur- 
 rounding the walls of the cylinder with a jacket, and providing 
 in the heads some hollow chambers, through which a continu- 
 ous stream of cold water is rapidly circulated: this is called 
 " dry cooling," because no water comes in contact with the 
 air, and represents, without exception, the best American 
 practise. 
 
 Or else, a spray of finely divided cold water is injected in 
 the body of air under compression. 
 
 Here, the contact is direct between air and water, so this 
 system is more effective than the dry cooling; and if the jacket 
 arrangement is used in connection with the spray, a marked 
 improvement occurs in the cooling of air. 
 
 This wet cooling has, however, some practical disadvantages, 
 which led to discarding it in this country, while in Europe i, 
 is still found in recent high-class compressing plants. 
 
 Another effective means of cooling consists in compounding 
 the compressor; i. e.,in effecting the total compression through 
 a series of successive cylinders, in each one of which only a 
 partial compression is effected, generating little heat, which is 
 more easily dealt with; besides, the air in passing from a cylin- 
 der to the next one in the series is discharged through a 
 cooler, where it resumes the outside temperature. 
 
 For high pressures, compounding is a necessity, and the 
 efficiency of the compression is thereby increased. 
 
 The ideal compression is, of course, the isothermal; and its 
 efficiency being 1, we have the following relative efficiencies 
 for other systems, when air is compressed to 6 atm. effective, 
 namely, 
 
 Adiabatic, without cooling 0.744 
 
 Adiabatic, with jackets .80 
 
 Adiabatic with spray 0.85 
 
COMPRESSED AIR. 21 
 
 Adiabatic compound (2-stage), jacketed, with 
 
 intercooler but no spray 0.863 
 
 3-Stage compound, with intercoolers and with • 
 
 spray 0.955 
 
 The effect of cooling is first to improve the efficiency of the 
 compression; i. e., to use less work in producing it; and then, 
 at the same time, the amount of heating is proportionally 
 reduced. 
 
 A mere mention will be made of the loss incurred by the 
 air pressure on its passage through the main connecting the 
 compressor and the motor. 
 
 Tables will be found in this book giving the loss of pressure 
 through mains of different lengths and sizes, and for different 
 velocities of circulation of air. 
 
 In a general way, and especially in a long transmission, 
 there is a conflict between the first cost of the plant and its 
 efficiency, which both increase with the size of the main. 
 
 In a properly built line, the loss can be made very small, 
 and its value will generally be assumed to suit local conve- 
 nience, according to whether the first outlay or the cost of power 
 is to have more weight in arriving at a decision. 
 
 It is hoped that the preceding remarks will enable any in- 
 telligent reader to form a correct idea of the elements to be 
 taken into consideration in installing a compressed air plant or 
 compressed air transmission, and briefly they may be enu- 
 merated: 
 
 1. An economical prime motor. 
 
 2. A compressor, which, while having a high mechanical 
 efficiency, has also means for reducing the heat of compression 
 to a minimum during and between the periods of compression. 
 
 3. A pipe line involving the least loss by friction consist- 
 ent with the finances at command. 
 
 4. Motors, which, beside possessing a high mechanical 
 efficiency, have means to expand the air to the atmospheric 
 pressure, which must be done by reheating to as great a tem- 
 perature as possible, both before and during the expansion of 
 the air in the cylinders or upon the motor wheel. 
 
 TABLES FOR THE LOSS OF PRESSURE OF 
 AIR IN PIPES. 
 
 In calculating tables for the loss of pressure in pipes, it has 
 been found necessary to take a wide departure from the form 
 of the tables usually given in catalogues on Compressed Air, 
 and whose simplicity unfortunately does not agree with more 
 recent experimental results touching upon the subject. 
 
 The formulce from which such tables are generally estab- 
 lished are the outcome of experiments made at the Mount 
 Cenis Tunnel, and of Stockalper's more recent investigations 
 at the St. Gothard Tunnel. 
 
22 COMPRESSED AIR. 
 
 Similar formulae have been used, with some modifications 
 of detail, bj 7 Professor Riedler, who conducted extensive tests 
 upon the. compressed air system in Paris, and they are based 
 on the assumption that the loss of pressure varies directly as the 
 length of the pipe, and inversely as its diameter. 
 
 Professor Unwin took up the subject, availing himself of 
 the results formerly obtained, and his investigation of the laws 
 governing the motion of air in long pipes does not support the 
 above-quoted conclusions. 
 
 Taking, for instance, three pipes, each 5 inches in diameter, 
 wherein air enters at a pressure of 70 lbs. gauge, and at a 
 velocity of 20 feet per second, if one of these pipes be one mile 
 long, the second 2 miles, and the third 5 miles long, the loss 
 of pressure according to Unwin 's formula is: 
 
 4.6 lbs. for the i-mile pipe, 
 
 9.4 lbs. for the 2-mile pipe, 
 
 26.3 lbs. for the 5-mile pipe. 
 
 In other words, the lengths being as: 1 - 2 - 5, 
 
 the drop of pressure varies as: 1 - 2.043 - 5-7 2 ! 
 
 and while the discrepancy is unimportant for short lengths, it 
 
 becomes 14.4 per cent at 5 miles, and would be still greater for 
 
 longer pipes. 
 
 As the logical tendency is toward increasing the practical 
 length of power transmissions, a saving of a few pounds of 
 loss is important; consequently, in working out a compressed 
 air transmission, more precise data are needed. To meet this re- 
 quirement, the following tables were calculated from Un win's 
 formula. 
 
 From the preceding example we notice that the loss of 
 pressure increases more rapidly than the ratio of the lengths; 
 besides, this loss does not vary inversely as the diameter of the 
 pipe. 
 
 Taking a 4-inch pipe, 2000 feet long, into which air at 60 
 lbs. gauge enters with a velocity of 15 feet per second, the loss 
 at the lower end will be 1.19s lbs.; according to the old rule, 
 the loss in an 8-inch pipe of same length, and at the same 
 pressure and velocity of air, would be one-half this amount, or 
 °>5975 ^s.; yet Unwin's rule makes it 0.52 lbs. 
 
 In the same way the loss in a 12-inch pipe should be 0.398 
 lbs., while its actual value is o.j lbs. Here the loss of pres- 
 sure decreases more rapidly than the diameter increases. 
 
 And if we accept the theory that recent rules, when ema- 
 nating from a reliable source, are the best, we must conclude 
 that no satisfactory approximation to exact results can be ob- 
 tained with the proportional formulae. 
 
 In the annexed tables, the air pressure at the entrance to 
 the main has been assumed to be 70, 80, 90, and 100 lbs. gauge, 
 which figures cover the working pressures at which air will 
 generally be admitted to the motors. 
 
 The use of the tables involves a few elementary operations, 
 which we have clearly defined in several numerical examples, 
 
COMPRESSED AIR. 23 
 
 selected to suggest a ready method of solving any ordinary 
 problems. 
 
 Some little calculation must of necessity be done, inasmuch 
 as to construct a series of tables, which would take into consid- 
 eration every element which influences all cases of transmission, 
 would necessitate too much elaboration, and would not be de- 
 sirable in a treatise of this character. 
 
 EXAMPLE 1. 
 
 500 cubic feet of free air is compressed per minute to 80 lbs. gauge, 
 and conveyed through a 6% -inch pipe, 2 miles long. What will be the 
 air pressure at the lower end of the pipe? 
 
 Referring to Table Fig. 5, which deals with air compressed 
 to 80 lbs. gauge, and starting down column 3 (size of pipe in 
 inches) we stop at 6-% ins. On the left side (Col. I) we find 
 for the ratio of absolute air pressures at lower and upper ends of 
 main : 
 
 -j fi — 0.00000003709 v t 3 1 
 
 (z/, is the velocity of air at entrance to main, in feet per second, 
 and / is the length of pipe in feet.) 
 
 Following now the horizontal line to the right until it 
 meets the vertical column headed 500, we find 36.5 which is the 
 value of v t 2 . 
 
 So z/, 2 1=36.5x5280X2=385,440 
 and the ratio of air pressures (Col. I) becomes: 
 
 / 
 
 1 — 0.00000003709X385,440=0.992 
 
 The pressure at entrance to main is 80 lbs. gauge or 94.7 
 lbs. absolute; the pressure at the lower end will be: 
 94.7X0.992=93.9 lbs. absolute 
 
 14.7 
 
 Or 79.2 lbs. gauge. 
 The loss is: 80 — 79.2=0.8 lbs. 
 
 EXAMPLE 2. 
 
 How many cubic feet of free air per minute, compressed to 90 lbs. 
 gauge, can be conveyed in a 9-^6 inch pipe^ 5 miles long, the loss of 
 pressure to be 3 lbs.? 
 
 The absolute pressure at entrance to main is: 104.7 l° s - 
 The absolute pressure at lower end is: 101.7 " 
 
 Their ratio is: — = 0.971 
 
 104.7 
 
 Referring to Table Fig. 6 (90 lbs. gauge) and following Col. 
 3 down to 9-^$ inch, we find on the left of this figure (Col. 1) 
 
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28 COMPRESSED AIR. 
 
 that the ratio of absolute pressures at lower and upper eud of 
 main is: 
 
 1 f i — 0.00000002075 z\ 2 / 
 
 and as we know that this ratio is equal to 0.971, we may write: 
 
 0.971=1/ I — 0.C00C0002C 75 z/, 
 
 Or, squaring both members of this equation: 
 
 0.9428=1 — 0.00000002075 v x 2 X528oX5 
 Or: 0.0005478 v x *=i — 0.9428 
 
 hence: z;, '=104.4 
 which we must find in the horizontal column starting from 
 9-^ 7/ ; we see that this number is comprised between 84 (2000 
 cu. ft.) and 131. 3 (2500 cu. ft.). 
 
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 cu. ft.; it can, with sufficient accuracy, be obtained by interpo- 
 lation: 
 
 131. 3 — 84=47.3. Corresponding to a difference of 500 cu. ft. 
 of free air (from 2500 to 2000). 
 
 104.4 — 84=20.4, which, by a simple rule of three, corresponds 
 to: §QOY.~—2\$, and the required number of cubic feet of free 
 air per minute is: 
 
 2215. 
 
 EXAMPLE 3. 
 
 We desire to convey 1000 cu. ft. of free air per minute, com- 
 pressed to 70 lbs. gauge, through a pipe 3 miles long, the loss in 
 pressure not to exceed 5 lbs. What must be the diameter of the pipe 1 
 
 This diameter could be determined directly, but through 
 calculations more intricate than by the tables, which can be 
 used in the following manner: 
 
 The pressure at entrance to main is 84.7 lbs. absolute. 
 
 The permissible loss is 5. 
 
 The pressure at the lower end oi main is: 
 
 79.7 lbs. absolute, 
 and the percentage of loss is: 
 
 §3=°-94. 
 
 Referring to Table Fig. 4 (70 lbs. gauge) the right value of 
 vf 1 is somewhere in the vertical column headed 1000. 
 
 The length is 15840 feet=/. 
 
 We will try some values of z', 3 and apply them to the cor- 
 responding ratio of terminal pressures, until the result is 
 exactly or approximately 0.94. 
 
 If the result is not exactly 0.94 we will then take the 
 nearest larger commercial size of pipe, thus giving less than 
 5 lbs. loss through the main. 
 
 To facilitate these approximations we may remark that, 
 
COMPRESSED AIR. 29 
 
 using the formula of Col. I, we will have an expression of 
 this form: 
 
 -V 
 
 1 — o. 0000000 v 
 
 0.94= 
 
 in which the stars represent some numerical value to be dis- 
 covered; or, squaring both members of this equation: 
 0.0000000 * * * "* z\ 2 /=i — 0.94 2 
 =0.1164 
 Let us try v t 2 =4^g, corresponding to a 5-in. pipe, we have 
 o. 00000004972 X449 X 1 5840 =0.3536 
 which result is much too large. 
 
 We see that we have evidently to take a smaller value of 
 z', a since / remains constant, while the factor corresponding to 
 4972 diminishes with z\ 2 . 
 
 Trying v x 2 =ioo, which corresponds to a 7%-mch pipe, we 
 
 0.0000000299X100X15840=0.0474 
 which is below the value o. 1164 which we desire. 
 
 Taking i\ 2= i83, which corresponds to a 6X-i"ch pipe, we 
 0.00000003709X183X15840=0.1075. 
 
 This is the nearest value smaller than 0.1164 and will give 
 less than 5 lbs. less; and thus we conclude that the required 
 diameter of pipe is 6X ins. 
 
 A short use of the tables will render them quite convenient 
 to use: 
 
 The above three examples cover the principal question 
 liable to arise in ordinary practise, and the few calculations 
 involved are more than balanced by the greater correctness of 
 the results derived from Unwin's formulae. 
 
 We can use the tables to find the loss of pressure incurred 
 in the passage of air through a pipe of a given diameter and 
 length, and with a given velocity of ingress. But it is interest- 
 ing to know at the same time the corresponding loss of power. 
 
 With this object in view, a Table (Fig. 9) and curves (Fig. 8) 
 are here given, showing the ratio of available power at full 
 expansion and without reheating at the lower end of the main 
 to the available power at full expansion and without reheating 
 at its entrance. 
 
 These curves show that the comparative loss of power is 
 always smaller than the comparative loss of pressure, and they 
 will be found useful in estimating the total loss incurred in a 
 given transmission. 
 
 Each curve corresponds to a certain pressure at the entrance 
 to the main, these pressures being, as above, 70, 80, 90, and 
 100 lbs. gauge. 
 
 This addition to the study of the frictional losses is intended 
 to dispel the confusion frequently made between the loss of 
 pressure and the loss of power, there being a common tendency 
 to consider those two terms as equivalent. 
 
COMPRESSED AIR. 
 
COMPRKSSED AIR. 
 
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32 COMPRESSED ATR. 
 
 For instance, if air enters a pipe at ioo lbs. gauge pressure 
 =114.7 absolute, and is discharged at 80 lbs. gauge, or 94,7 lbs. 
 absolute, thus showing a reduction of 20 per cent of gauge 
 pressure, it is popularly and erroneously estimated that the air 
 has lost 20 per cent of its power. The ratio between the abso- 
 lute pressures is 9 4 Xi 4.7=^2.5 per cent. 
 
 Referring to the 100 lbs. curve, we note that the ratio of 
 pressures 0.825 lies midway between 92 and 94 per cent ratios 
 of power; i. e., corresponds to 93 per cent, showing a loss of 
 7 per cent only, instead of the so-called loss of 20 per cent of 
 power. 
 
 The explanation of this is, that, while the pressure is 
 diminished, the volume is proportionately increased, and the 
 real loss of power is the work which the air could perform in 
 expanding isothermally from the higher pressure to the lower 
 pressure, which work has been absorbed by friction. 
 
 An inspection of the curves (Fig. 8) will show that the actual 
 pressure at each point on the main becomes a constantly 
 decreasing fraction of the initial pressure as the distance of this 
 point from the entrance becomes greater, and these variations 
 of pressure are figured by a line at 45 degrees on the co-ordi- 
 nate axes. For each absolute pressure, the value of the avail- 
 able power at full expansion, as compared with the available 
 power at entrance, is carried on the corresponding ordinate, 
 and by joining the ends of these ordinates, four curves of 
 powers have been drawn, each one corresponding to one of the 
 above-named initial pressures. Although a limited range of 
 initial pressures has been considered, the following general 
 deductions are suggested by an inspection of these curves: 
 
 1. So long as the fall of pressure remains below a certain 
 value, which, in the cases considered, is about 50 per cent, the 
 loss of pressure is more rapid than the loss of power, and the 
 ratio of powers is greater than the corresponding ratio of 
 pressures. 
 
 2. When the pressure continues to fall beyond this 
 value, the loss of power becomes more rapid than the loss of 
 pressures, the ratio of powers remaining, however, greater than 
 the corresponding ratio of pressure. 
 
 3. When the absolute pressure in the main becomes — in 
 the cases considered — from 1 5 to 25 per cent of the initial absolute 
 pressure, the ratio of the powers becomes equal to the ratio of 
 the pressures. 
 
 4. The pressure continuing to fall, the loss of power 
 becomes much more rapid than the loss of pressure, until the 
 pressure is equal to the atmosphere, when the available power 
 naturally becomes o. and then negative (a case which is not to 
 be considered here), and the ratio of powers is smaller than the 
 corresponding ratio of pressures. 
 
 The inspection of the curves also shows that the relative 
 deficiency of the power, as compared with the corresponding 
 pressure, occurs more rapidly with a low initial pressure than 
 with a higher one, and incidentally confirms the foregone 
 
COMPRESSED AIR. 33 
 
 statement, that, for a given initial pressure and velocity at 
 entrance, there is a limit of length to each particular size of 
 main, beyond which neither pressure nor power would be 
 obtainable at its lower end. the whole pressure having been 
 absorbed in overcoming the friction, and the air issuing from 
 the pipe at atmospheric pressure. 
 
 And as, on the other hand, the velocity of the air varies 
 inversely with its pressure at entrance, the desirability of 
 high pressure is apparent, either as permitting the use of a 
 smaller pipe to convey a given weight of air, or as increasing 
 the distance at which a certain power can be obtained with a 
 given size of pipe. This statement refers to the conveyance 
 of the air, and is, of course, irrespective of the convenience of 
 producing a high air pressure. 
 
 LOSS OF PRESSURE IN THE PASSAGE OF 
 AIR THROUGH BENDS. 
 
 In addition to the frictional loss incurred in the passage of 
 air through a straight pipe, under given conditions of length, 
 diameter, and velocity, another cause of resistance is due to the 
 changes of direction in the flow of air. 
 
 The bends in a pipe line should be as few as possible, but 
 whenever they are absolutely necessary, as, for instance, when 
 leaving the surface of the ground to penetrate in a vertical or 
 inclined shaft, abrupt bends should be avoided. The 
 branching at right angles by means of a T, so frequently found 
 in small-sized steam, air, or water pipe, should be absolutely 
 discarded. 
 
 Iron pipes of small size can easily be bent to a larger 
 radius, and as to larger pipes, special elbows should be used 
 instead of the common fittings, whose radius is always small 
 as compared with the diameter of the pipe. 
 
 The annexed table shows that when the mean radius of 
 curvature is equal to the diameter of the pipe, the loss incurred 
 in the air pressure is nearly four times as great as when the 
 radius of curvature is equal to five diameters, so that a pipe 
 line may be established with all possible care regarding its 
 diameter and the velocity of the air, consistent with a small 
 frictional loss, and much of the benefit derived therefrom be 
 counteracted by the use of one or two short bends. 
 
 With reference to the table, it will be noticed that it 
 applies to bends at a right angle. When a smaller or larger 
 arc than 90 degrees is used, a sufficient approximation will be 
 obtained in figuring the frictional loss in proportion to the 
 length of arc of the bend, as compared with an arc of 90 
 degrees, and of same radius. 
 
 If possible, from 15 to 20 feet per second should be the 
 average entrance velocity given to air in pipes less than 12 
 inches in diameter. Above this the velocity may be increased, 
 but never to exceed 50 feet per second, for economical use. 
 
34 
 
 COMPRESSED AIR. 
 
 
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COMPRESSED AIR. 35 
 
 THE INFLUENCE OF THE DIFFERENCE OF 
 EEVEE ON THE USE OF COMPRESSED AIR. 
 
 The calculations concerning the applications of compressed 
 air are generally based upon the standard values of the at- 
 mospheric pressure at the sea level; viz., 14.7 lbs. per square 
 inch. The fact that a large number of mines are located 
 at a considerable altitude makes it necessary to investigate the 
 influence of this condition upon the use of compressed air, and 
 it will be shown herein that the differences of level are not 
 to be overlooked in designing a system for power transmis- 
 sion. The weight of one cubic foot of air, at the surface of 
 the earth, and at 32 degrees Fahr., and when the barometer 
 stands at 30 inches, is 0.0807 lbs. The position of the mercury 
 in a barometer is due to the weight of a column of air. whose 
 height would be the thickness of the atmospheric layer that 
 surrounds the earth, and as one cubic inch of mercury weighs 
 0.491 lbs., the weight of a column of mercury 1 inch square 
 and 30 inches high is 30X0.491=14.73 lbs. Hence the con- 
 clusion that a column of air 1 inch square and of the height of 
 the atmosphere weighs 14.7 lbs., and will balance the weight 
 of a column of mercury 1 inch square and 30 inches high. 
 
 The immediate consequence of this is that as we rise above 
 the level of the sea at a given place, the atmospheric pressure 
 per square inch must decrease, since the height of the column 
 of atmosphere pressing on the mercury of the barometer 
 diminishes, and we can readily calculate that if the whole at- 
 mospheric layer were of equal density, that is, if one cubic foot 
 of air had the same weight at any altitude, the thickness of 
 our atmosphere would be 26,208 feet, or 4 97 miles. 
 
 Such, however, is not the case. The weight of one cubic 
 foot of air varies with its pressure and with its temperature, 
 which both change with the altitude. 
 
 It is commonly assumed, that at the same latitude, the 
 temperature drops by 1 degree Fahr. for every 340 feet of 
 height above the sea level; but this could not be taken as any- 
 thing like a general rule, since the temperature is affected by 
 many local and variable conditions. It suffices, however, to 
 show that the density of air changes with the altitude, but as 
 the laws of this variation are imperfectly known, and only for 
 moderate altitudes, the exact thickness of the atmospheric 
 layer that surrounds our planet is a matter of speculation. It 
 is generally conceded, however, to be about 45 miles. 
 
 The variations of atmospheric pressure with the altitude 
 have been, in the annexed table, calculated from the sea level 
 to io,oco feet above it, and for equal steps of 500 feet, on the 
 assumption of a constant temperature of 60 degrees Fahr. pre- 
 vailing throughout the change of altitude. This supposition, 
 however, as we have mentioned before, is not correct, but the 
 exact influence of the temperature can easily be computed for 
 any particular instance. 
 
36 COMPRESSED AIR. 
 
 An inspection of the table of atmospheric pressures leads to 
 an immediate practical conclusion. Iyet us take, for instance, 
 a machine designed to compress at the sea level 500 cubic feet of 
 free air per minute to 80 lbs. gauge, that is, 80 lbs. above the 
 atmospheric pressure. The volume of cold compressed air de- 
 livered per minute is 
 
 500X^=77.6 cu. ft. 
 Suppose now that the same compressor be used at 5000 feet 
 altitude and run at the same number of revolutions; the piston 
 will sweep through 500 cubic feet as before, but the atmos- 
 pheric pressure being only 12.14 lbs. per square inch, the 
 volume of cold air at 80 lbs. gauge delivered per minute will be 
 
 500X^=65.85 cu. ft. 
 
 That is to say, the delivery of air at 80 lbs. gauge and at 5000 
 feet altitude will be 85 per cent of the delivery at 80 lbs. gauge 
 and at the sea level, from the same sized compressor running 
 at the same number of revolutions. 
 
 These volumetric variations, reckoned upon the volume at 
 the sea level taken as a unit, will be found recorded in four 
 columns corresponding respectively to 70, 8o, 90, and 100 lbs. 
 gauge and annexed to the pressure column. It will be noticed 
 that the volumetric efficiency, that is the ratio of the delivery 
 at any given altitude to the delivery at the same pressure and 
 at the sea level, decreases as the receiver pressure increases. 
 
 We know that in adiabatic compression (which we may 
 take as a standard of comparison) the compression to 80 lbs. 
 gauge and delivery of 500 cu. ft. of free air per minute absorbs 
 79.4 I. H. P. It may easily be calculated that for the same 
 outside temperature (60 degrees Fahr.) and the same gauge 
 pressure (80 lbs.) the compression and delivery at 5000 feet 
 altitude of the same amount of atmospheric air will absorb 
 73.7L H. P. 
 
 The ratio of these powers is ^=.928. 
 That is to say, we lose in capacity 15 per cent and we gain in 
 power 7.2 per cent, which amounts to saying that the produc- 
 tion at the same volume of air at the same effective pressure 
 will require: 
 
 1 I. H. P. at the sea level, 
 1.093 " at 5000 feet, 
 
 1. 1 90 " at 10,000 feet altitude. 
 
 It costs more, therefore, to obtain the same useful work from a 
 given compressor at high altitudes than at the sea level. 
 
 Four columns of I. H. P., referring to the compression of 
 100 cubic feet of free air per minute to 70, 80, 90, and 100 lbs. 
 respectively, are recorded alongside of the volumetric results. 
 An inspection of the table shows that if we compare the work 
 absorbed by 1 cu. ft. of air delivered at a given pressure, at 
 10,000 feet altitude for instance, and at the sea level, the ratio 
 will be practically the same within the whole range of pres- 
 sures considered. 
 
COMPRESSED AIR. 
 
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38 COMPRESSED AIR. 
 
 This is not the only effect of a difference of altitude and 
 a practical case will illustrate another side of the question: 
 
 Suppose that a mining plant is located 1500 feet above the 
 Compressor plant, and that the Compressor plant itself is 
 situated at an altitude of 3000 feet above the sea level, aud 
 that the receiver pressure at the compressor is 80 lbs. The 
 atmospheric pressure at the elevation of 3000 feet in the Com- 
 pressor room is 13. 1 lbs. per square inch. One cubic foot of 
 air at the sea level, and at 60 degrees Fahr. weighs 0.0764 lbs. 
 One cubic foot of air at 3000 feet elevation and 60 degrees 
 Fahr. will weigh 
 
 o.o764Xfj 1 7 =0.0681 lbs. 
 
 Or, 1 lb. of air will represent a volume of 14.68 cubic feet. 
 This volume represents a vertical column one inch square and 
 2113.92 feet high at the pressure of 13. 1 lbs. per square inch, 
 and at a pressure of 80 lbs. gauge or 93.1 lbs. absolute, the 
 height of this column weighing 1 lb., and 1 inch square in 
 section is 
 
 2113.92X9471=298.06 ft. 
 
 Consequently a column of air at 80 lbs. pressure, 1500 feet 
 high, represents a pressure of 5.03 lbs. per square inch. 
 
 The absolute pressure of air, which at the lower end of the 
 pipe is 93.1 lbs., is at the upper end: 
 
 93.1 — 5.03=88.07 absolute, 
 aud as the atmospheric pressure at 4500 ft. is 12.37 lbs. the ef- 
 fective pressure at the hoisting works is 88.07 — r2 -37 l° s -. or 
 75.7 lbs. So there is, regardless of the loss due to friction in 
 this respect, no loss of volume, but a loss of pressure. 
 
 A very similar course of reasoning would show that when 
 compressed air is carried down a shaft the pressure at the 
 lower end is greater than the receiver pressure, and this excess 
 of pressure, due to the weight of this column of air, will 
 generally more than balance any friction al losses there may be 
 in the pipes. 
 
 It must be remembered, in this connection, that any motors 
 operated by this compressed air will also have a larger back 
 pressure to encounter in the exhaust than they would at the 
 mouth of the shaft, but still the loss due to this back pressure 
 is only a small portion of the gain by the difference of level. 
 
 In both of these examples an exact computation would re- 
 quire a consideration of the temperature, but which may be 
 neglected in all ordinary propositions. 
 
 AIR ENGINES. 
 
 Compressed Air, like all elastic gases, can be made to oper- 
 ate a piston by its expansive force, exactly as does steam, and 
 it may be stated in a general way, that any steam engine can 
 be actuated by air without altering its arrangement. It is, 
 
COMPRESSED AIR. 39 
 
 moreover, hardly necessary to add that this statement applies 
 to the non-condensing steam engines only. 
 
 Tables are herewith given of the consumption of air per 
 minute, reduced to atmospheric pressure, in three classes of 
 engines more commonly used; viz: 
 The Slide Valve Engine, 
 
 The Automatic Cut-off Engine, Single and Compound, 
 The Corliss Engine, Single and Compound. 
 
 Air and Steam, however, while partaking of the same gen- 
 eral active property, differ widely in several respects, and a few 
 explanatory remarks are here necessary. 
 
 In the first place, the pressure of air may be independent of 
 its temperature. This valuable feature, which makes other- 
 wise the use of compressed air so convenient, is fraught, how- 
 ever, with practical consequences which in many cases, and 
 unless provided for, would render it impossible. 
 
 Air, in most cases, expands in a motor adiabatically; i. e., its 
 expansion is accompanied by a considerable fall of tempera- 
 ture. An additional table is here presented (Fig. 19), giving 
 the temperature of exhaust of air, after working expansively in 
 the various types of engines considered. This temperature is 
 found to range from +7.5 in the slide valve engine to — 143 in 
 the Compound Corliss, cutting off at }{ of stroke, the air being 
 admitted to the engine at 60 degrees Fahr., and while the for- 
 mer temperature might not prove troublesome with dry air, on 
 account of the strong exhaust blast of an engine with a late 
 cut-off, the latter is decidedly unacceptable, as any lubricant 
 introduced in the cylinder would freeze instantly, and the 
 exhaust ports be promptly clogged with ice, especially in the 
 interior of a mine where the moisture of air is more marked 
 than outside. 
 
 It will therefore be necessary for the economical use of air 
 to heat it to a certain extent, either before it enters the motor, 
 or during the process of its expansion within the cylinder. 
 We know already that this operation has also the effect of in- 
 creasing the volume of the air at constant pressure. Two 
 curves are here presented showing the increase of volume of 1 
 cubic foot of air, at 32 degrees Fahr. and at 60 degrees Fahr., 
 when heated to various temperatures up to 500 degrees Fahr. 
 
 In connection with this subject of re-heating, another dis- 
 tinctive feature of air as compared with steam must be pointed 
 out. 
 
 In all non-condensing steam engines, even with an early 
 cut-off, the proportions are such as to maintain at the end of 
 the period of expansion, a sufficient steam pressure to insure 
 a speedy exhaust of the gaseous and of the condensed steam. 
 This pressure must of course be greater in a fast moving than 
 in a slow engine, with the consequence that part of the energy 
 of the steam is thus sacrificed, not uselessly, indeed, but with- 
 out doing useful work. 
 
 But with air, there is no condensation during the expansion, 
 and also the active gas which operates the piston being the 
 
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46 COMPRESSED AIR. 
 
 same as the medium into which it is discharged, the exhaust 
 pressure may become a very insignificant quantity. 
 
 The result of this is two-fold: First, an air motor, unlike a 
 steam engine, can work practically at complete expansion, i. e. , 
 the compressed air can expand into the cylinder down to 
 atmospheric pressure; and second, this more prolonged ex- 
 pansion will be accompanied by a greater fall of temperature. 
 So that it may be said that the genuine air motor is inseparable 
 from a system of reheating, and also that the complete ex- 
 pansion of the air producing a greater variation of load on the 
 piston, and of strains on the pieces, an air motor should not 
 necessarily but preferably be a compound, rather than a single 
 machine. For similar reasons it may rationally be expected 
 that turbo-motors of the Parsons' type and DeLaval Rotary 
 Engines would be especially well adapted to show a high 
 efficiency as air motors. 
 
 It may be inferred, that while an ordinary steam engine will 
 perform satisfactory duty if operated with air, a less consump- 
 tion of it will be obtained by cutting off earlier in the stroke 
 so as to work at complete expansion. This will diminish the 
 mean effective pressure throughout the stroke, and, conse- 
 quently, the power developed by the engine, at the same time 
 extending the range of variation of the strains. 
 
 Such a state of affairs may be acceptable if the load on the 
 motor is regular, but if — as will often be the case, especially in 
 mining machinery — the load constantl} r varies or else is inter- 
 mittent, the air motor at complete expansion must have its 
 valve gear so arranged as to permit a later cut-off and, of 
 course, a greater or smaller amount of exhaust pressure, which 
 amounts to saying that it must be an ordinary steam engine 
 susceptible of an earlier cut-off than is commonly used with 
 steam. 
 
 Reverting now to the subject of reheating, several systems 
 have been suggested and used. 
 
 If the only object was to preclude the obstruction of the 
 exhaust ports by the formation of ice due to the moisture of 
 air, it would be obtained by the application to this portion of 
 the engine, of some source of heat, such as a lamp, or an 
 injection of steam, or of hot water. 
 
 This process, however, hardly deserves more than a mere 
 mention, for if such a source of heat is handy, it can be used 
 to far better advantage in heating the air, either in the cylinder 
 or before entering it. 
 
 One method consists in injecting into the cylinder a spray 
 of warm water, whose heat is absorbed by the air, while the 
 water is cooled. The annexed table gives the weight of water 
 at 75 degrees, ioo degrees, and 150 degrees Fahr. to be supplied 
 for each pound of air expanding to the atmospheric pressure 
 from 70, 80, 90, and 100 lbs. gauge, so that the final tempera- 
 ture of air will be 32 degrees Fahr., its initial temperature 
 being 60 degrees Fahr. 
 
COMPRESSED AIR. 
 
 47 
 
 Gauge 
 pressure of 
 
 B. T. U. 
 
 required per 
 lb. of air. 
 
 Pounds of water per lb. of air, the 
 temperature of water being 
 
 
 75 Fahr. ioo° Fahr. 
 
 350° Fahr. 
 
 lbs. 
 
 (A) 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 70 
 
 59- 
 
 i-37 
 
 .86 
 
 • 5 
 
 80 
 
 62.8 
 
 1.46 
 
 .92 
 
 •53 
 
 90 
 
 66.2 
 
 1-54 
 
 •97 
 
 •56 
 
 100 
 
 69.2 
 
 1.61 
 
 1.02 
 
 .6 
 
 Another and better method is to inject steam instead of 
 hot water into the C}dinder. The advantages of this system 
 are, first that steam, being in a gaseous state, mixes up with air 
 more readily than water, even finely pulverized, and besides, 
 the condensation of this steam gives up its latent heat, which 
 increases considerably the heating of air. 
 
 A comparison of this process with the previous one can 
 readily be made. Assuming that a spray of water at 212 de- 
 grees Fahr. is injected iuto the cylinder, each pound of this 
 water will give up 180 B. T. U. before it is cooled to 32 degrees 
 Fahr. 
 
 But, taking steam at atmospheric pressure, i. e., also at 212 
 degrees Fahr , 1 lb. of steam, in the process of liquefaction, 
 will abandon 966 B. T. U., its latent heat of vaporization, and 
 besides 180 B. T. U. as above, making a total of 1146 B. T. U. 
 
 The following table gives the weight of steam at 212 degrees 
 Fahr. required for each pound of air to prevent its temperature 
 from falling below 32 degrees Fahr. at complete expansion. 
 
 Lbs. of steani at 212 de- 
 grees per lb. of air. 
 
 051 
 
 055 
 
 Gauge pressure of air. 
 Ivbs. 
 
 70 
 
 B. T. U. required for 
 each lb. of air. 
 
 59.0 
 
 .... 62.8 
 
 90 
 IOO 
 
 66.2 
 69,2 
 
 •059 
 .0604 
 
 It is evident that quite similar calculations could be made 
 to maintain the exhaust temperature at any given point. Be- 
 sides, the use of steam keeps the walls of the cylinder wet, and 
 while water alone is a poor lubricant between metallic surfaces, 
 it facilitates the action of the regular lubricants, and is also 
 favorable to the tightness of the piston packing. 
 
 It will readily be seen that both these methods completely 
 preclude the formation of ice in the exhaust ports; their good 
 effect is still more pronounced if the cylinder is provided with 
 a jacket, into which hot air is circulated. 
 
4 8 
 
 COMPRESSED AIR. 
 
COMPRESSED AIR. 49 
 
 Air can also be reheated before being admitted into the 
 cylinder. Various designs of heaters are used for this purpose, 
 the air generally passing through a system of pipes heated by 
 an interior furnace, a flue being provided for the passage of the 
 hot gases on the outside of the pipes before they reach the 
 chimney. And as air, on account of its bad conductivity, does 
 not easily take up heat from the metallic sides of the pipes, it 
 is expedient to inject in the pipes a small quantity of water 
 which absorbs the heat more readily and penetrates with the 
 hot air into the cylinder. 
 
 Another method of heating is to place a lamp or gas jet 
 within the air pipe. The use of coal or wood is not advisable 
 in this case, as grit and cinders would be carried by the current 
 of air into the motor. 
 
 Reheating by the electric current is still in the experimental 
 state. 
 
 When the motor is a compound machine, the air should be 
 again reheated after it has done work in the H. P. cylinder, 
 and before it is admitted to the L. P. cylinder. 
 
 The table giving the temperatures of exhaust in cold air 
 work, also gives the temperatures at which air should be 
 reheated prior to its admission to the single engines, or to each 
 cylinder of the compound engines, in order to exhaust at 32 
 degrees Fahr. 
 
 These temperatures are moderate, and can be obtained with 
 hot water, or low pressure steam. If the heating is done by 
 passing the air through heated pipes, the fuel consumption 
 will be very small, as practise shows that 1 lb. of coal gives the 
 air from 8,000 to 10,000 B. T. U. in a properly designed 
 heater. 
 
 To utilize the full benefit of reheating, and of air expansion in 
 compound engines, an early cut-off is very desirable. This 
 can be accomplished by reheating to 350 degrees before the air 
 enters each cylinder, and Table Fig. 20 shows the amount 
 of free air required for various horse powers under this condi- 
 tion. A comparision with Table Fig. 16 will show the 
 marked advantage of this arrangement. 
 
 Fig. 20^ shows a compound direct connected Corliss 
 Hoisting Engine, built by the Fulton Engineering and Ship- 
 building Company, in conformity with the data in Fig. 20. 
 The air is twice reheated; that is to say before entering the 
 high pressure cylinder, and also before entering the low pres- 
 sure cylinder. 
 
 For convenience in estimating the power required to com- 
 press air and the amount of air which will be furnished by 
 given powers, the following tables have been constructed: 
 
 The table in Fig. 21 shows the amount of cubic feet of free 
 air at 60 degrees Fahr. and 14.7 lbs. absolute pressure per 
 square inch, that can be compressed and delivered per minute 
 per I. H. P., adiabatically, in a single stage jacketted cylinder 
 compressor, in a two-stage compound jacketted compression 
 and in isothermal compression. 
 
COMPRESSED AIR. 
 
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COMPRESSKD AIR. 
 
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COMPRESSED AIR. 55 
 
 This table is constructed from the curve represented in 
 Fig. 22. 
 
 In the table the amount of air is given for each indicated 
 horse power in the air cylinder and also for each I. H. P. in 
 the direct-acting steam cylinder which drives the compressor. 
 
 The table in Fig. 23 is practically the reverse of the pre- 
 ceding curve and the table gives the I. H. P. to compress and 
 deliver 100 cubic feet per minute of air, at 60 degrees Fahr. and 
 14.7 lbs. per square inch absolute pressure. This table is con- 
 structed from the curve (Fig. 24) and gives the I. H. P. in the 
 adiabatic compression, in single stage jacketed cylinder com- 
 pression, in two-stage compound jacketed compression and 
 also isothermal compression, and the horse powers under each 
 of the different gauge pressures read both for the I. H. P. in 
 the air cylinder and the I. H. P. in the direct-acting cylinder. 
 
 Fig. 25 is the curve of mean effective pressures per square 
 inch in adiabatic compression, for the various receiver pres- 
 sures enumerated. This will be found useful in computing 
 piston loads. 
 
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 weight of air at 60 degrees Fahr. in vertical pipes, and also the 
 weight of one cubic foot of air in pounds avoirdupois. For 
 example, if the gauge pressure at the surface of a mine is 70 
 lbs. per square inch, at the depth of one thousand feet the 
 pressure will be 73 lbs. to the square inch. Where there are 
 extreme variations in altitude in a transmission plant this 
 weight of air has to be taken into consideration. 
 
56 
 
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60 COMPRESSED AIR. 
 
 AMOUNT OF FREE AIR REQUIRED TO RUN 
 DIRECT-ACTING STEAM PUMPS. 
 
 In preparing these tables the object has been to furnish 
 information to the oft-repeated query, "How many cubic feet 
 of free air, compressed to, say 60 lbs., is required to run a 
 direct-acting pump that will raise 50 gals, per minute 200 feet 
 high, or say 8 miners' inches 150 feet nigh, or at any other 
 pressure of air ? " We have made three assumptions in these 
 calculations, which are likely to cover all possible losses of 
 efficiency in ordinary work. 
 
 First — The work absorbed by the pump has been estimated 
 by adding 20 per cent to the actual work in water raised, to 
 make up for frictional and other resistances. 
 
 Second — The actual capacity of the air cylinder, that is, the 
 volume swept by the piston, has been increased by 15 per cent 
 to take into account the clearance, leakage, etc. 
 
 Third — The working pressure of air, when entering the air 
 cylinder, has been taken at 10 lbs. per square inch lower than 
 the receiver pressure, to compensate for frictional and other 
 resistances. 
 
 We have not assumed that the air was reheated before 
 entering the cylinder, nor was any account taken of the differ- 
 ence of level between the receiver and the pump, which in 
 many cases would add several pounds per square inch to the 
 working pressure, as noted in the Table (Fig. 26). The 
 results given in these tables may therefore be referred direct to 
 the intake capacity of the compressor and the estimate of the 
 air consumption required is therefore very much simplified. 
 
 If the necessary power to produce the quantities of com- 
 pressed air indicated in these tables be compared to the cor- 
 responding work in water raised, the efficiency, which is 
 measured by the ratio of the latter to the former, will be as 
 low as 25 per cent. A direct-acting pump does not use air 
 expansively, and this is well known to be a simple but a waste- 
 ful manner of transmitting power. 
 
 Assuming the values in these tables to be one, the follow- 
 ing table will show the percentages required for the different 
 kinds of power-actuated pumps, both for cold air and air 
 delivered at 300 degrees Fahr. at the pump motor. 
 
 
 AIR. 
 
 
 Cold. (60° F.) 
 
 Reheated to 
 300 F. 
 
 Direct Acting Single 
 
 I 
 .70 to .60 
 
 .60 
 •50 
 
 •33 
 
 .69 
 
 .48 to .41 
 
 .41 
 
 .329 
 
 .226 
 
 Direct Acting Compound 
 
 ( Slide Valve Single .... 
 
 Fly Wheel -j Slide Valve Compound 
 
 / Corliss Compound 
 
COMPRESSED AIR. 
 
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COMPRESSED AIR. 63 
 
 REFRIGERATION BY COMPRESSED AIR. 
 
 This Treatise would soon grow beyond reasonable limits if 
 it had to enumerate all the applications of compressed air in 
 modern industry; in fact, a publication claiming to give an 
 exact " up to date'' account of" these applications would never 
 come to an end, as some new and unexpected uses are con- 
 stantly arising. 
 
 But a review, however cursory, of the properties of com- 
 pressed air considered as motive power, must of necessity 
 touch upon one of its most interesting uses; viz., the produc- 
 tion of cold. A rapid treatment of this question is here the 
 more justified as it does not correspond to a class of apparatus 
 intended solely for refrigerating purposes. 
 
 Every air motor is in itself, and at no additional cost, a 
 cold-producing machine, and this property, which belongs 
 exclusively to compressed air, will often be found a valuable 
 addition to its other merits, especially by the underground 
 worker. 
 
 A quotation from Prof. A. B. W. Kennedy on the Paris air 
 installations may fitly be reproduced here: 
 
 "By using air direct from the main in the motor, or by 
 heating it only very slightly, the exhaust air can be, of course, 
 so greatly reduced in temperature as to be available for freez- 
 ing purposes. 
 
 "In one Paris restaurant, for instance, which I visited, I 
 found that the exhaust was carried through a brick flue into 
 the beer cellar. In this flue the carafes were set to freeze, 
 large molds of block ice were also being made for table use, 
 while the air was still cold enough in passing away through 
 the beer cellar to render the use of ice for cooling quite un- 
 necessary even in the hottest weather. 
 
 "The nominal function of the engine in this case was the 
 charging of batteries used in the electric lighting of the 
 restaurant. 
 
 "The conjoint use of power and cold is common in Paris, 
 the power being in this case generally applied to electric 
 lighting. While in any large city, such as Paris, it is no doubt 
 a great point that by a compressed air system the handiest 
 possible cooling appliances can be brought everywhere within 
 reach, in tropical climates this is something rather of necessity 
 than of luxury. In such cases we might have the apparent 
 paradox of a motor worked essentially for its exhaust; the 
 work done would be a bye-product, the cold air would be the 
 principal thing. 
 
 " In such a case, if there were no useful work to be done, the 
 motor could even be made (as has been suggested to me) to 
 pump air back into the main, and thus to virtually halve its 
 air consumption." 
 
 From these remarks the conclusion is obvious that ice- 
 making, water-cooling, and cold-storage contrivances are of 
 easy application whenever air motors are used; and it will be 
 
64 COMPRESSED AIR. 
 
 readily understood that the exhaust temperature of air may be 
 regulated by a variation in the degree of heating. 
 
 An inexpensive and tolerably efficient arrangement consists 
 of exhausting the air from the motor at one end of a duct 
 made of insulating material, such as two or more parallel 
 courses of one-inch boards, paper-coated on the outside, and 
 secured one or two inches apart by wooden strips; or, else, in a 
 more permanent installation the duct may be a brick flue, 
 such as described in the above report. 
 
 In both cases its upper portion can be laid open, and 
 arrangements are made at the interior of it for suspending ice 
 molds, water pails, etc., which are removed at intervals 
 depending upon the exhaust temperature of the motor and its 
 activity. 
 
 Provision should be made to rid the exhaust air from all the 
 grease or oil which it might carry out of the motor before it is 
 admitted into the duct. 
 
 One noteworthy feature about air thus used for cooling 
 purposes is its wholesome nature; with its defects, adiabatic 
 compression is endowed with this beneficial property that the 
 combined heat and pressure thus generated prove too much 
 for the endurance of microbes; air thus treated becomes thor- 
 oughly sterilized, and can be safely put in contact with 
 alimentary substances at no risk of contamination. In fact, 
 fruits are wonderfully preserved during transportation by a 
 new system wherein the exhaust from the air brake cylinders 
 is the vital principle. 
 
 More elaborate ice-making or cold-storage appliances might, 
 of course, be devised, and special machinery has been con- 
 structed to that effect. 
 
 It is not here intended to treat upon the general subject of 
 ice-making machines. This cannot be done in an elementary 
 way with any degree of completeness. Referring solely to the 
 air machine, it may be stated that it is not the most economical 
 for cold production, but in many instances it remains in use 
 because of its convenience and safety. 
 
 Air is found everywhere, and in case of leakage is not apt, 
 like ammonia or sulphur dioxide, to spoil the provisions sub- 
 jected to cooling. 
 
 The developments previously expounded in this treatise 
 will facilitate the comprehension of the cold air machine, 
 which is principally used on shipboard, for the preservation of 
 provisions, and for ice-making. 
 
 Two principal types of machines are commonly used. 
 
 THE BEIvL-COLKMAN MACHINE. 
 
 A revolving shaft d, is operated either by a steam engine S, 
 and a crank c, as shown on the line drawing, or by a belt 
 transmission. 
 
 This shaft carries two flywheels IV, W, and two opposite 
 cranks e, f, actuating by connecting rods and crossheads two 
 pistons v, h. 
 
COMPRESSED AIR. 
 
 65 
 
66 COMPRESSED AIR. 
 
 The piston h travels in a cylinder g, which, for the sake of 
 simplicity, has been shown single-acting. The piston h is 
 solid, and the back head of the cylinder carries two automatic 
 valves z, K. The valve i, opening inward, is an inlet valve 
 admitting the free air into the cylinder, during one stroke of 
 the piston h; during the reverse stroke the valve i is closed, 
 the air confined in the cylinder is compressed, and escapes 
 through the outlet valve K, and the pipe /, into a tubular 
 cooler, through which a series of tubes t\ establishes a contin- 
 uous circulation of cold water. This water enters the cooler 
 through the cover m, and is discharged through the opposite 
 end n. 
 
 The air delivered by the compressing cylinder g, passes 
 around the tubes t, is cooled to, or nearly to, the outside tem- 
 perature, and passes through the pipe o y connected to the 
 backhead of another cylinder u. 
 
 This cylinder, which is also shown single-acting, has a 
 solid piston v, operated by the crank e; the backhead carries 
 two separate and closed chambers, containing one an inlet 
 valve p, and the other a discharge valve q; but instead of 
 acting automatically, these valves have their motion controlled 
 by two adjustable cams revolving within the shaft d, as shown 
 on the cut. 
 
 While the compression cylinder g delivers at each stroke 
 some compressed air into the cooler, the inlet valve p admits 
 into the cylinder q a certain volume of this air, which, as said 
 before, has been cooled on its passage around the tubes, but 
 the setting of the cam operating the valve p on tHe shaft is so 
 arranged as to close this valve long before the piston v is at 
 the outer end of its stroke; the volume of air introduced into 
 the cylinder u is then left to expand adiabatically, and its 
 temperature falls to a point which depends upon the amount of 
 expansion, i. e. upon the quantity of air admitted by the 
 valve/; besides, this work of expansion helps the motion of 
 the machine to some extent. For this reason, the cylinder u is 
 called the expansion cylinder. 
 
 When the piston v has reached the end of its stroke, the 
 discharge valve q is opened by its cam, and so remains during 
 the whole reverse stroke, the piston v driving the cold air 
 through the pipe r, to the cold storage rooms. 
 
 It will be readily understood that when the valve p closes 
 early on the stroke of the expansion piston v, the pressure in 
 the cooler increases, and the exhaust temperature in the cylin- 
 der u decreases; when, on the contrary, the closing of the 
 valve p is retarded, the pressure in the cooler drops, and the 
 exhaust temperature rises. So that, by a proper adjustment of 
 the cams, the degree of cooling air can be varied within a large 
 range. 
 
 This machine is comparatively cumbersome, if the amount of 
 cooling is important. 
 
COMPRESSED AIR. 67 
 
 THE AIvLEN DENSE-AIR MACHINE. 
 
 To obviate this defect, another class of machines has been 
 devised, known as the Aeeen Dense- Air Machine. Its gen- 
 eral arrangement being practically the same, no special draw- 
 ing of it is given. 
 
 The air penetrating into the compression cylinder has been 
 primitively raised to a certain pressure, say 40 lbs.; the com- 
 pression carries this pressure to, say 160 lbs.; then the air 
 passes through the cooler into the expansion cylinder, wherein 
 it again expands from 160 lbs. to 40 lbs. or more, according to 
 the temperature at which it is desired to discharge it through a 
 pipe like r; but instead of being allowed to diffuse freely into 
 the cold storage ducts or chambers, this air is circulated through 
 coils of closed pipe, which are finally connected to the inlet 
 valve chamber of the compression cylinder, the same air being 
 thus used over and over again. 
 
 This machine operates upon a greater weight of air under a 
 given volume, and consequently is more effective under this 
 volume, than the Bell-Coleman machine. Or else, the Allen 
 machine can produce the same cooling effect with smaller 
 dimensions than the Bell-Coleman, which is an important fea- 
 ture on shipboard. 
 
 It is interesting to form an idea of the practical results 
 which can be attained with this sort of machine, to which 
 object the following data refers: 
 
 One pound of ice at 32 degrees to be transformed into water 
 at 32 degrees, absorbs 142 B. T. U. without variation of temper- 
 ature. 
 
 This amount of heat, which disappears, without influencing 
 the thermometer's indications, is termed the latent heat of 
 fusion of ice. In the same way, if we want to transform 1 lb. 
 of water at 32 degrees Fahr., into ice at 32 degrees Fahr., we 
 must subtract 142 B. T. U. from that pound of water, without 
 changing its temperature, and these 142 B. T. U. are the latent 
 heat of solidification of water. These two terms are entirely 
 equivalent. 
 
 One ton of 2000 lbs. of ice in the process of melting into 
 water at 32 degrees Fahr., will therefore subtract from the sur- 
 rounding bodies, air, water, or whatever they may be, 2000x142 
 or 284,000 B. T. U., and the resulting effect produced on those 
 bodies is measured by 1 ton of ice melting capacity. 
 
 The refrigerating action of a machine or process of any 
 kind, producing that same effect, is estimated in the same 
 terms, and such a machine is said to have a cooling capacity 
 of 1 ton ice melting. 
 
 The annexed Table gives the numbers of negative B. T. U. 
 and of lbs. of ice melting capacity, developed in the adiabatic 
 expansion of 1 cubic foot of air from 60, 70, 80, 90, and 100 lbs. 
 gauge respectively to 14.7 lbs. absolute; these are the calculated 
 or theoretical capacities. 
 
 These figures show that there is no advantage in using a 
 high air pressure, because the refrigerating capacity does not 
 
68 
 
 COMPRESSED AIR. 
 
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COMPRESSED AIR. 69 
 
 vary proportionately with the rise of pressure; for instance, if 
 this latter passes from 60 to 70 lbs., the pressure increases by 
 16 per cent and the cooling capacity by 9 per cent; while if the 
 pressure becomes 100 lbs. the increase of pressure is 65 per 
 cent and the increase of cooling capacity is 23 per cent. In 
 other words, the percentage of pressure having increased 4.1 
 times, the percentage of cooling capacity rises only 2.5 times. 
 
 No very complete record of experiments has been published 
 showing the practical efficiency of cold air machines, one 
 reason being that, for this special object, their use is limited, 
 as compared with the ammonia machines. But whenever cold 
 air machines are adopted, it is because their efficiency is super- 
 seded by other practical reasons. Some accurate tests place it 
 at 43 per cent of the theoretical cooling capacity of the air for 
 the "Bell-Coleman, and 37 per cent for the Allen Dense-Air 
 Engine. 
 
 The former coefficient has been used to establish the column 
 of the Table headed " Practical Capacity." 
 
 But while in a large city, where ammonia can be readily ob- 
 tained a wholesale ice-making and cold-storage business would 
 not be undertaken with a compressed air plant, it is none the 
 less certain that in mining camps, or in remote localities, where 
 cheap motive power is frequently obtainable, the application of 
 air to the production of cold remains one of the most interest- 
 ing and profitable adjuncts of this valuable power agency. 
 
70 
 
 COMPRESSED AIR. 
 
COMPRKSSKD AIR. 71 
 
 POWER TRANSMISSION BY COMPRESSED 
 AIR. 
 
 The use of compressed air for transmitting power for a long 
 distance is daily gaining in importance, and this application of 
 air, which a few years ago did not receive much consideration, 
 outside of actuating rock drills and coal cutters, stands at present 
 as one of the most economical and satisfactory systems of power 
 transmission. 
 
 No fair-minded and impartial person will contend that in 
 every possible case in practise one particular system of power 
 transmission can be always preferable to all others. 
 
 The economical solution of industrial problems involves so 
 many factors of entirely independent and often contradictory 
 nature, that the strictly engineering side of the question may 
 be overcome in importance by other conditions which would 
 hardly have been thought of at a first glance. 
 
 One fact however, may be stated as general, and that is that 
 compressed air is better adapted to underground work than any 
 other agency of power transmission. Not only can it be trans- 
 ported anywhere, through crooked and narrow passages, either 
 wet or dry, and regardless of insulation or losses other than 
 leakage at the pipe joints, but its use and handling is totally 
 devoid of danger, and after its work is done it becomes the 
 most essential element to human life. This can be said of air 
 alone, although it has nothing to do with its value as a power 
 transmitter. 
 
 The principles of the production of compressed air are ex- 
 pounded in another part of this Treatise; it is therefore unnec- 
 essary to explain here, how, when air has been raised to a 
 certain pressure, with production of heat, and when on its pas- 
 sage through a long pipe, this air has cooled down to the tem- 
 perature of the atmosphere, the loss of efficiency incurred in 
 this drop of temperature can be balanced, and even exceeded, 
 by reheating the air before it is admitted to the motors. 
 
 This reheating, which can be done at a small expenditure of 
 fuel, is an important element in the total efficiency of the 
 system. 
 
 Being now in possession of all the essential elements of 
 information required in estimating the size and the cost of a 
 compressed air transmission, their application to some practi- 
 cal examples will form a fitting conclusion to the preceding 
 developments: 
 
 EXAMPLE 1. 
 
 A stamp mill is located at 3000 feet from a water wheel 
 developing 70 B. H. P. 
 
 Required a compressed air transmission to deliver 40 H. P. 
 on the line shaft. 
 
 The motor operating the mill is 500 feet higher up than the 
 air receiver, wherein the air pressure is to be 80 lbs. 
 
72 COMPRESSED AIR. 
 
 Altitude of compressor: 3500 feet above sea level. 
 Temperature at compressor and Mill, 50 degrees Fahr. 
 
 The loss from belt-slipping between the cam shaft and the 
 motor shaft, and from other causes, can be taken as 10 per 
 cent, and the I. H. P. of the motor will be: 
 
 40 
 
 7t=44-4 
 and assuming another loss of 8 per cent for clearance, wire 
 drawing, etc., the available power at the lower end of the main 
 must be: 48.3 H. P. 
 
 As there is, at first glance, an important margin between 
 the powers at the wheel and at the mill, it naturally occurs to 
 consider whether the reheating of the air at the motor cannot 
 be dispensed with. 
 
 We will use a slide-valve engine, cutting off at Yz stroke, 
 which would likely be the earliest admissible cut-off as regards 
 exhaust temperature. 
 
 The amount of air necessary to develop 48.3 H. P. is: 1.13 
 lbs. per second, or 67.8 lbs. per minute. If we were at the sea 
 level, 1 lb. of air at 60 degrees Fahr. would represent 13. 1 
 cubic feet. 
 
 Sixty-seven and eight- tenths pounds represent, therefore: 
 67.8x13.1=888.2 cubic feet. 
 
 If we use a single stage compressor, the I. H. P. required 
 for 80 lbs. gauge receiver pressure will be: 
 15.18x8.882=134.83. 
 
 But the Table of columns and powers at various altitudes 
 shows that the power required to compress and deliver the 
 same volume of air at the same pressure, but at 3500 feet alti- 
 tude, is (Cols. 5 and 6): 
 
 89xl572 =i.o67 times greater than at the sea level. 
 And as the temperature is 50 degrees Fahr., this figure should 
 be reduced in the ratio of the absolute temperature (at 60 
 degrees and 50 degrees Fahr.) and becomes 1.046. 
 
 The power actually required will therefore be: 
 
 134.83X1.046=141 I.-H. P. in the compressor. 
 And if we allow it mechanical efficiency, the brake power on 
 the wheel is: 
 
 £=155 B. H. P. 
 Whilst we have only 70 B. H. P. at our disposal. 
 
 The air cannot therefore be used cold in the motor; in other 
 words, we have not yet a sufficient margin of power between 
 the wheel and the mill to permit the use of cold air; reheating 
 must necessarily be resorted to. 
 
 We have 70 B. H. P. on the compressor shaft, and 70X0.9= 
 63 I. H. P. in the air cylinder. 
 
 From the above calculations, we know that the compression 
 and delivery of 100 cubic feet of free air per minute at 80 lbs. 
 receiver pressure, and at the given altitude and temperature, 
 require: 15.18x1.046=15.88 I. H. P. 
 
COMPRESSED AIR. 73 
 
 The available power of 63 I. H. P. will permit of compress- 
 ing iooXj5g§-=397 cubic feet of free air per minute, whose weight 
 at 3500 feet altitude and 50 degrees Fahr. is: 
 
 397X.o8o7X54i--=3o.97- 
 Giving per second a weight of air of: 
 
 30.97 c ,, 
 
 -^-=.516 lbs. 
 
 We have next to determine the air pressure at the lower end 
 or outlet of the main, for a length of 3000 feet. 
 
 The tables of frictional resistance show that 80 lbs. gauge 
 (94.7 lbs. absolute) being the pressure at entrance to the main, 
 the pressure at the lower end is: 
 
 With a 4-inch main: 77.7 lbs. gauge. 
 
 With a 3-inch main: 73. lbs. gauge. 
 
 Besides, as the outlet of the main is 500 feet above the re- 
 ceiver, we lose from this fact 1.7 lbs., which leaves as available 
 pressures at the outlet: 
 
 With a 4-inch main: 76 lbs. gauge. 
 
 With a 3-iuch main: 71.3 lbs. gauge. 
 
 We will use the 4-inch main, and as the necessary reheating 
 obviates the low temperature of exhaust caused by a long 
 expansion, we will use a motor expanding from 76 lbs. to 2 
 lbs. gauge, and find that to develop 48.3 H. P. with 516 lbs. 
 of air per second, this air must be reheated to 247 degrees Fahr. 
 
 What amount of fuel this reheating will require can be 
 easily computed. 
 
 We have to reheat 30.97 lbs. of air per minute, from 50 
 degrees to 247 degrees Fahr., or 197 degrees Fahr. 
 
 The specific heat of air being .238, this will require: 
 
 30.97 X- 238x197=1451.9 B. T. U. per minute, or: 
 
 1451.9X1440=2.090736 B. T. U. per 24 hours. 
 
 And allowing that 1 lb. of coal will yield 10,000 B. T. U. 
 209 1 lbs. of coal per 24 hours. 
 
 Or if 1 lb. of pine wood will yield 5400 B. T. U., the weight 
 consumed per 24 hours is: 309. ix -5-^5=386.84. 
 
 Or about X cord. 
 
 SIZE OF COMPRESSOR. 
 
 We found as the "useful" amount of air per minute 397 
 cubic feet, and allowing .85 volumetric efficency for the com- 
 pressor, its intake capacity must be 467 cubic feet. 
 
 With 300 feet per minute piston velocity, and referring to 
 Table (Fig. 37), the compressor will be a single 18^-inch ma- 
 chine, or a duplex 12^ -inch machine. 
 
 EFFICIENCY OF THE TRANSMISSION. 
 
 The apparent efficiency of the transmission is: 
 
 40 
 
 to 57 
 But its exact value should take into account the coal con- 
 sumed in reheating the air. 
 
74 COMPRESSED AIR. 
 
 This latter amounts to 8.70 lbs. per hour, and if we assume 
 that in a compound steam engine the coal consumption is 2 lbs. 
 per I. H. P., this quantity represents: -^- =4.35 I. H. P. on the 
 piston of a direct-acting steam engine operating the compressor, 
 or, in the present case, on the compressor shaft. 
 
 The true efficiency is therefore: 
 
 40 
 
 fi5S=-54 
 With reverse conditions, i. e., mill 500 feet below compressor, 
 the total efficiency would be 55. 
 
 This is an example of a comparatively low efficiency in 
 transmission. The power is so small that comparative losses 
 become large. This transmission, however, can be improved 
 by using a 2-stage compound compressor and motor, the calcu- 
 lations for which would be as follows: 
 
 379 cu. ft. of free air at sea level, and 50 Fahr. 4" pipe. 
 
 Absolute pressure I A J entrance 114. 7 lbs. (100 g.) 
 y \ At exit, 114 lbs. (99.3 g.) 
 
 COMPOUND MOTOR. 
 
 First reheating, 50 to 350 Fahr. 
 
 Power in H. P. cylinder 32.84 
 
 Second, 153 to 350 Fahr. 
 
 Power in L. P. cylinder 27.26 
 
 Total 60. 10 
 
 First loss, 8 per cent, as in preceding example. 
 
 6o.ix-9 2 =55-29 
 Second loss, 10 per cent 
 
 55-29X. 9 =49.76 
 
 on line shaft. 
 Coal used for reheating: 12.58 lbs. per hour, corresponding 
 to: 6.29 I. H. P. 
 
 Total efficiency: ^^= 652 
 
 65.2 per cent. 
 
 EXAMPLE 2. 
 
 A system of Power Transmission will now be considered in 
 the case of a large mine, requiring: 
 100 B. H. P. for hoisting ] 
 
 100 ?• 5' £' J° r P U f mpiUg -,i i At the surface. 
 100 B. H. P. for a stamp mill { 
 
 25 B. H. P. for lighting J 
 
 And 
 
 25 B. H. P. for hoisting ~] 
 
 25 B. H. P. for pumping j 
 
 1500 cu. ft. of free air per [- At 1500 ft. level. 
 
 minute at 60 degrees Fahr. | 
 
 for rock drills J 
 
COMPRESSED AIR. 75 
 
 Length of Transmission to surface plant: 4 miles. 
 Compressors of the 2-stage Compound type. 
 Receiver pressure 75 lbs. gauge. 
 Outside temperature 60 degrees Fahr. 
 Permissible loss of pressure: 
 
 In surface main: 1 lb. 
 
 In underground: ^ lb. 
 Required: 
 
 Size of surface and underground mains. 
 Size of Compressor. 
 B. H. P. on compressor shaft. 
 
 The power received at the mine will be divided under two 
 heads, viz: Surface and Underground. 
 
 SURFACE PEANT. 
 
 We will assume for the motors a mechanical efficiency of .9, 
 giving -^=361 H. P.; and then, another loss of 5 per cent 
 between the cylinder and the lower end of the main, for wire- 
 drawing, elbows, etc. 
 
 The available power at the end of main is: 
 
 361 
 
 ^5=380, 
 
 the total efficiency being ^X-Oo^-Sss. 
 
 The absolute pressure at upper end of main is: 89.7 
 The absolute pressure at lower end of main is: 88.7 
 and the weight of air at this pressure, reheated to 400 degrees 
 Fahr. and completely expanded is: 3.26 lbs. per second. 
 
 UNDERGROUND PEANT. 
 
 Pressure at top of main: 88.7 
 
 Pressure at bottom of main 88. 2 
 
 Additional pressure at bottom of main, 4.8, due to weight 
 of air. 
 
 Absolute pressure at 1500 level 93.0 
 
 Fifty B. H. P. with .855 efficiency give: 5S.5 H. P., which 
 require a weight of air per second of: .59 lbs. 
 
 The rock drills work practically at full pressure, and the 
 expansion of 19 lbs. (to 60 lbs. gauge) cannot be utilized. 
 
 The temperature of the compressed air at the bottom of 
 shaft column is 250 degrees, and assuming a loss of ico degrees 
 before reaching the drills, i. e., a temperature of 150 degrees at 
 the drills, the 1500 cubic feet of air will have to be reduced in the 
 ratio of: ~, and become: 1275 cu. ft, whose weight is (per 
 minute] 97.41 lbs. 
 
 The "total weight of air to be supplied per second is, there- 
 fore: 
 
 Surface: 3.26 
 
 Underground: .^,9 
 Rock Drills: 1.62 
 
 Total 5.47 lbs. 
 
76 COMPRESSED AIR. 
 
 corresponding to 4299.43 cubic feet per minute of free air at 60 
 degrees Fahr., whose compression, in a 2-stage Compound 
 Compressor, will require: 
 
 578.8 I. H. P. 
 With .9 mechanical efficiency, the B. H. P. is: 
 
 643 B. H. P. 
 The reheating will require 159.34 lbs. of coal per hour, cor- 
 responding to: 67 B. H. P., making a total B. H. P. of, 710 
 B. H. P. 
 
 The power obtainable at the lower end of main is: 
 637.3 H. P. 
 and on the shaft of the motors, with .855 efficiency: 
 545 B. H. P. 
 The total actual efficiency is, therefore: —=76.7. 
 
 SIZE OF MAINS. 
 
 The Tables of frictional resistances, of which the use has 
 been explained, give, as proper size of the pipes: 
 For the surface main: 12^ inches. 
 For the shaft column: 6% inches. 
 
 SIZE OF COMPRESSOR. 
 
 The useful capacity has been found as: 
 
 4299.42 cubic feet of free air per minute. 
 
 Taking for the compressor 85 per cent volumetric efficiency, 
 the actual capacity is: 5058 cubic feet, and with 400 feet of 
 piston velocity, we will find by referring to Fig. 37 the proper 
 size of the compressor. 
 
 It is desirable, for reasons of practical convenience, to 
 divide the compressing plant in two equal units, each formed 
 of a duplex compound machine. There will be, consequently, 
 4 intake cylinders, each having a capacity of 1264 cubic feet per 
 minute, which correspond to a diameter of 24^ inches. 
 
 For 75 lbs. gauge receiver pressure, the area of the H. P. 
 cylinder should be: 189.36 square inches, corresponding to 15^ 
 inch bore, and at the rate of 80 revolutions per minute, the 
 stroke will be 2 feet, 6 inches. So the size of cylinders is: 
 24 / ^"+i5^"X30 // . 
 
 EXAMPLE 3. 
 
 IOO H. P. DELIVERED BY WHEEL, 2 MILES, 5-INCH PIPE. 
 
 Required: Potential at lower end of line. 
 80 lbs. gauge receiver pressure. 
 
 One hundred B. H. P. will compress and deliver 598 cubic 
 feet of free air per minute, or 9.95 cubic feet of free air per 
 second, corresponding to: 1.546 cubic feet per second of cold 
 air at 80 lbs. gauge. 
 
 The velocity at entrance in a 5-inch pipe is: 11.35 feet per 
 second, and the absolute pressure at the lower end of the line 
 is 94.7X-977=92.52 absolute=77.82 gauge. 
 
COMPRESSED AIR. 77 
 
 Available work: 
 
 If air is used cold 54.6 per cent. 
 
 If air is reheated from 
 
 6o° to 300 Fahr 79.7 per cent. 
 
 If air is reheated from 
 
 6o° to 350 Fahr 84.9 per cent. 
 
 FUEL CONSUMPTION 
 
 Reheating to 300 Fahr . . .% cord of wood in 24 hours. 
 Reheating to 350 Fahr. . . . y 2 cord of wood in 24 hours. 
 
 The total efficiency, taking into account the fuel consumed, 
 is, plain expansion, single cylinder: 
 
 Cold Air 546 per cent. 
 
 Reheating to 300 75.9 per cent. 
 
 Reheating to 350 79 per cent. 
 
 The total efficiency, taking into account the fuel consumed, 
 using compound cylinders and reheating for both high and 
 low pressure cylinders is: 
 
 Reheating to 300 80.7 per cent. 
 
 Reheating to 350 83.3 per cent. 
 
 EXAMPLE 4. 
 
 PUMPING 8 MINER'S INCHES OE WATER 500 FEET HIGH 
 WITH DIRECT-ACTING PUMP. 
 
 Consumption of cold free air per minute 352 cu. ft. 
 
 If air is heated (dry) from 6o° Fahr. to 300 Fahr. 
 the consumption falls to 241 cu. ft. 
 
 FUEL consumption: 
 
 241 cu. ft.=i8 412 lbs. air per minute. 
 1 lb. of air raised in tempera- 
 ture by 240 absorbs 57-12 B. T. U. per minute. 
 
 3,427.2 B. T. U. per hour. 
 
 82,252. B. T. U. per 24 hours. 
 
 and 18.412 lbs. will require. ..1,513,452. B. T. U. per 24 hours. 
 
 Assuming 1 lb. wood to yield 5000 B. T. U., and 1 cord= 
 
 2000 lbs. the consumption is: .153 or Ye cord per 24 hours. 
 
78 COMPRESSED AIR. 
 
 AN EXAMPLE OF A COMPRESSED AIR AND AN 
 ELECTRICAL TRANSMISSION. 
 
 To be supplied at the mine: 
 
 ioo H. P. to drive motors and 
 
 500 cu. ft. free air per minute, compressed to 80 lbs. 
 The latter requires 83.5. B. II. P. Now, assuming a motor 
 efficiency of .95 there will be required at motor in the electrical 
 transmission: 
 
 ^8 7 .8H.P 87,8 
 
 100 H. P. for machinery. 
 
 ~ at motor driving machinery 105.2 
 
 Power at lower end of conductor 193-° 
 
 2 per cent loss on line. 
 
 Power at upper end of line: -7^= *97 
 
 •95 generator efficiency B. 
 
 H. P. on generator: ^ 
 
 207 
 
 AIR TRANSMISSION. 
 
 500 cu. ft. for drills. 
 675 for 100 B. H. P. 
 
 1175 
 requiring: 11.75X16,7=196.226 H. P. 
 
 
RIX AIR COMPRESSORS 
 
 MANUFACTURED BY THE 
 
 Fulton Engineering and Shipbuilding Works 
 
 SAN FRANCISCO, CAL. 
 
RIX AIR COMPRESSORS 
 
 MANUFACTURED BY THE 
 
 Fulton Engineering and Shipbuilding Works 
 
 SAN FRANCISCO, CAL. 
 
 After the preceding article on the different phenomena and 
 laws, both theoretical and practical, which enter into the sub- 
 ject of compressed air engineering, it seems right and proper 
 to set forth as plainly as possible the different styles and gen- 
 eral specifications of the air compressors manufactured espe- 
 cially on this Pacific Coast. 
 
 These compressors are all designed and built under the 
 special superintendence of Mr. Edward A. Rix, by the Fulton 
 Engineering and Shipbuilding Works, and are the result of 
 some eighteen years' experience in pneumatics on the Pacific 
 Coast. 
 
 There is no doubt that from the conditions under which 
 mining is carried on on the Pacific Coast, one would naturally 
 expect to see a different style and class of air compressor built 
 from those manufactured in the East. The facilities for trans- 
 portation are vastly different. The special requirement for 
 prospecting plants, which shall be cheap and easily operated, 
 and the tremendous heads of water which are found on the 
 Pacific Coast, necessitate a peculiar construction of compressor, 
 and the large varieties manufactured, descriptions of which 
 follow hereafter, give the intending purchaser or operator 
 ample opportunity to select machines especially fitted to his 
 character of work. 
 
 All of the Rix Compressors are of the water-jacket type; 
 that is, the partial cooling during compression is effected by 
 circulating water in a jacket around the cylinder and through- 
 out the heads of the air cylinder. Frequently, also, this cir- 
 culation is carried within the pistons of the machine, but no 
 water whatever is injected into the cylinder. This method of 
 construction has been constantly followed ever since the manu- 
 facture of these machines was begun some eighteen years ago, 
 even though during this time the principal Eastern manufac- 
 turers were still enamored of the injection system. 
 
 This jacket circulation is not a simple one, and in the small- 
 est of the machines is double, that is, there are two independent 
 water circulations for the machine, the water entering the 
 lower part of the cylinder at two openings, going thence im- 
 mediately and independently to each head and then around 
 
82 RIX AIR COMPRESSORS. 
 
 the body of the cylinder and finally escaping at two inde- 
 pendent outlets. 
 
 In all cylinders of large diameter or for high pressure, the 
 heads are often built with independent circulations. In this 
 manner cold water is assured to many parts of the cylinder at 
 the same time. 
 
 All of the Standard Rix Compressors for ordinary use have 
 inlet valves of the poppet type, that is, the valves have neither 
 nuts nor bolts nor threads, and there is nothing about them to 
 get out of order, and they cannot fall into the cylinder. They 
 are subjected, of course, to the usual wear and tear in their 
 springs, and these may be taken out in a few seconds and re- 
 placed as easily. 
 
 The outlet valves of the standard machines are of the check 
 valve type, well known to most all builders of compressed air 
 machinery. 
 
 The frames are made in two general styles, one of the Cor- 
 liss pattern, and the other of fiat bed pattern with slipper cross 
 head, one being designed for heavy and one for light duty. 
 
 All of the working parts, such as cranks, boxes, shafts, pis- 
 tons, etc., are made in conformity with the best engineering 
 practise. The crank pins specially are made unusually large, 
 so that they do not heat with the intermittent work which is 
 placed upon them. 
 
 The water jackets can be readily cleared out of any mud or 
 sediment which may form therein, inasmuch as when the heads 
 are taken off the jackets are completely exposed. This is a 
 very convenient device. 
 
 Sight feed lubricators and all necessary oilers and standard 
 fittings are furnished with every machine. 
 
 In the tables for the various compressors there have been 
 no capacities mentioned for cubic feet of free air. Inas- 
 much as the cubic feet of free air will depend entirely upon 
 the piston speed of the machine and inasmuch as the piston 
 speed of the machine depends to a great extent upon a number 
 of circumstances, it is deemed easier to use the following table 
 to determine the capacities of any of the compressors. It will 
 be noted that the left-hand column contains the cylinder 
 diameters of the various sized compressors manufactured by 
 the Fulton Engineering Company, and on the right of this 
 column, under the piston speeds mentioned, will be found the 
 various capacities for these cylinders, at the piston speeds 
 directly above. 
 
 From this table it will be easy to select the proper size of 
 compressor to do the work required, for all the tables in this 
 treatise give the number of cubic feet of air required to do the 
 various kinds of work. It will only be necessary then to find 
 the total number of cubic feet required and to select the piston 
 speed most advantageous to at once determine the proper size 
 of cylinder. For example, from the requirements if it has been 
 determined that 350 feet of piston velocity per minute is as 
 much as is desirable and that the cubic feet of air required is 
 
R1X AIR COMPRESSORS. 83 
 
 about 550 cubic feet per minute, then an 18 54 -inch cylinder 
 would be the proper size for a single compressor, or a duplex 
 14^, making somewhat less than 300 feet of piston velocity 
 per minute. 
 
 The question of determining the piston velocity is one of 
 the vital points in the selection of an air compressor. Notwith- 
 standing anything which may be said to the contrary, the most 
 economical compressor is one which moves at a slow piston 
 velocity and high piston velocities are only used to save initial 
 expenditure. Therefore, when one contemplates the install- 
 ment of a permanent air compressing plant or one which will 
 likely be operated for one or more years, it is always better to 
 select a low piston speed and pay the extra price for the larger 
 machine which this entails, than to pay the extra fuel bill 
 caused by a higher velocity. 
 
 It is to be regretted that most purchasers do not understand 
 the value of a low piston speed for an air compressor. A low 
 initial price seems to be the principal virtue. There is not 
 room enough in the ordinary cylinder diameter to give the 
 proper ingress and egress of air under economical conditions. 
 An indicator card from most compressors, running under a 
 piston speed of 400 feet per minute, shows an enormous increase 
 of pressure to force the air through the delivery valves, 
 which, of course means a corresponding loss. The ideal indi- 
 cator card is one which shows no suction pressure, and which 
 shows that the delivery valves open at, or nearly at, the receiver 
 pressure. Practically, this is not accomplished, and there are 
 few, if any , compressor-builders proud of the indicator card taken 
 from one of their compressing cylinders at such a piston speed. 
 Yet their machines are forced to such speeds, oftener constantly 
 than frequently. The writer has taken cards from various 
 machines that showed 10 per cent of power used in forcing air 
 through the delivery valves. It is not a simple matter to 
 make a practical machine that shall work economically at 
 high piston speed. It is at present far better practise to use a 
 compressor at low piston speed and avoid those losses which 
 cannot be recovered. The ideal system of compression is a 
 continuous one, and while it seems almost impossible, the 
 writer has already built one machine which gives fair promise, 
 and future experiments will probably develop the question. In 
 continuous compression there are no mechanical cylinder losses 
 that amount to much. 
 
 No compressor builder advocates high rotative or piston 
 speed, and for the advancement of compressed air practise it is 
 to be hoped that purchasers will consult operative expense 
 rather than initial expenditure. 
 
8 4 
 
 RIX AIR COMPRESSORS. 
 
 
 
 
 
 
 
 
 
 
 
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RIX AIR COMPRESSORS. 
 
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86 RIX AIR COMPRESSORS. 
 
 RIX DUPLEX STEAM ACTUATED 
 COMPRESSOR. 
 
 Cdass A, Fig. 32. 
 
 Fig. 32 is a half-tone of the Rix Duplex Steam Actuated Com- 
 pressor, of the flat bed type, having slipper cross head. 
 
 Fig. 33 is a plan of this same machine, showing arrange- 
 ments of foundation bolts and piping. 
 
 Fig. 34 is an end elevation of the same compressor. 
 
 Fig. 35 is a side elevation of the same compressor, and is at 
 the same time a side elevation of the Single steam actuated 
 compressor. 
 
 Wherever possible, it is desirable to install a Duplex Air 
 Compressor. The cranks being placed at right angles, the air 
 is discharged more continuously throughout the whole revolu- 
 tion, and the result is that the strains in the machine are more 
 evenly divided and the machine as a whole gives better satis- 
 faction . 
 
 Another reason which should prompt a Duplex machine is, 
 that should it be necessary to discontinue the use of one-half 
 of the machine for repairs, the other half is always available 
 and is a complete working compressor in itself. 
 
 The following is a table of dimensions for these compressors: 
 
 RIX DUPLEX STEAM ACTUATED COMPRESSOR. 
 
 CLASS A. 
 
 For Revolutions per minute, Cubic Feet Free Air, Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter 
 Steam Cylinder. 
 
 Diameter 
 Air Cylinder. 
 
 Stroke. 
 
 H. P. 
 Boiler. 
 
 Price. 
 
 I 
 
 IO 
 
 IO>'2 
 
 14 
 
 60 
 
 
 2 
 
 12 
 
 l2 l / 2 
 
 16 
 
 80 
 
 
 3 
 
 14 
 
 I4K 
 
 18 
 
 1IO 
 
 
 4 
 
 16 
 
 16^ 
 
 18 
 
 140 
 
 
 5 
 
 18 
 
 l8# 
 
 24 
 
 200 
 
 
 6 
 
 20 
 
 2oy 2 
 
 24 
 
 2 O 
 
 j 
 
 7 
 
 22 
 
 22}i 
 
 SO 
 
 3IO 
 
 
 8 
 
 24 
 
 24^ 
 
 30 
 
 400 
 
 
RIX AIR COMPRESSORS. 
 
 87 
 
88 
 
 RIX AIR COMPRESSORS. 
 
/ 1 
 
 RIX AIR COMPRESSORS. 
 
 8 9 
 
 Fio. 34— Class A.— Rix Duplex Steam Actuated Compressor. 
 
9 o 
 
 R1X AIR COMPRESSORS. 
 
RIX AIR COMPRESSORS. 
 
 91 
 
 RIX SINGLE STEAM ACTUATED 
 COMPRESSOR. 
 
 Class B, Fig. 36. 
 
 The following half-tone, Fig. 36, shows the general style of 
 construction of Class B, Rix Single Steam Actuated Compressor, 
 and Fig. 35 shows the side elevation of same. 
 
 This machine differs only from the Duplex Compressor in 
 the fact that it is one-half of that machine and has an outboard 
 bearing. 
 
 The following is a table of the various and proper 
 
 dimensions. 
 
 RIX SINGLE STEAM ACTUATED COMPRESSOR. 
 
 CI.ASS B. 
 
 For Revolutions per minute, Cubic Feet Free Air, and Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter. 
 Steam Cylinder 
 
 Di^meter 
 Air Cylinder. 
 
 Stroke. 
 
 H P. 
 Boiler 
 
 Price. 
 
 9 
 IO 
 II 
 12 
 13 
 14 
 15 
 16 
 
 IO 
 12 
 
 14 
 16 
 18 
 2 J 
 22 
 24 
 
 ioy 2 
 
 i6y 2 
 isy 2 
 
 2oy 2 
 22^ 
 24; 2 
 
 14 
 16 
 18 
 18 
 24 
 24 
 30 
 30 
 
 30 
 
 40 
 
 55 
 
 70 
 
 IOO 
 
 I30 
 
 155 
 
 200 
 
 
92 
 
 RIX AIR COMPRESSORS. 
 
 a m 
 
RIX AIR COMPRESSORS. 
 
 93 
 
 RIX SINGLE STEAM ACTUATED 
 COMPRESSOR, SELF-CON- 
 TAINED TYPE. 
 
 Class C, Fig. 38. 
 
 This machine is one which is offered to the mining public as 
 the least expensive andmost generallyuseful machine of the kind 
 ever constructed. It will be noted from the half tone that this 
 consists of an independent standard engine on a bed-plate con- 
 nected to an. air-compressing cylinder, the whole being tied 
 together for proper operation. The engine is self contained, 
 there being no outboard box, the fly wheel pulley being over- 
 hung, so that this machine can be placed anywhere and is 
 ready for operation at once. A belt can be placed upon the 
 fly wheel pulley and be used to operate a pump or any other 
 machine that may be desired while the compressor is not in 
 use, in which case it will only be necessary to remove one inlet 
 valve on each end of the air cylinder and the compressor end 
 of the machine becomes inactive. 
 
 This machine is especially built for prospecting, temporary 
 work and for experiments, where a permanent plant is too 
 expensive. It will' be noted, from the construction, that the 
 engine can be entirely removed and used independently should 
 occasion demand, and the whole arrangement is one which 
 gives a prospector an opportunity to easily dispose of his 
 machine should his mining venture prove a poor one. 
 
 The following is the list of sizes of the Class C Compressor. 
 
 RIX SINGLE STEAM ACTUATED COMPRESSOR, SELF- 
 CONTAINED. 
 
 For Revolutions per minute, Cubic Feet Free Air, and Rock 
 Drill Capacity, see pages 84 and 85. 
 
 17 
 18 
 
 19 
 
 23 
 24 
 25 
 26 
 
 27 
 
 Diameter Diameter 
 
 Steam Cylinder Air Cylinder 
 
 13 
 14 
 16 
 18 
 
 Stroke. 
 
 H. P. 
 
 Boiler 
 
 IO 
 
 15 
 
 IO 
 
 20 
 
 12 
 
 25 
 
 12 
 
 30 
 
 14 
 
 30 
 
 14 
 
 35 
 
 16 
 
 40 
 
 16 
 
 45 
 
 18 
 
 55 
 
 20 
 
 70 
 
 22 
 
 100 
 
94 
 
 RIX AIR COMPRESSORS. 
 
 ¥■■ 
 
 ~»45M 
 
R1X AIR COMPRESSORS. 
 
 95 
 
 COM- 
 
 RIX DUPLEX SHAFT- DRIVEN 
 PRESSOR. 
 
 Class D, Fig. 39. 
 
 This half-tone represents one of the new style Shaft-Driven 
 Rix Duplex Compressors, heavy duty style. This machine has 
 Corliss frame, extra large wrist pins, and large cross head. 
 The frame is swelled up on the front head so that the head 
 may be removed without disconnecting the cylinder. The 
 Compressor which was the subject for this half-tone was driven 
 by a twelve-foot tangential water wheel, under a head of two 
 hundred and seveuty-five feet. It may, however, be driven by 
 belt. 
 
 Fig. 40 is a side elevation of the same machine, showing 
 belt pulley. 
 
 Fig. 41 shows a sectional machine of the same class, but 
 having a fiat bed, with water wheel attached upon the shaft. 
 
 This Compressor, as all the sectional compressors herein- 
 after mentioned, is made in sections not to exceed 325 lbs. in 
 weight, so that they may be carried upon mules. 
 
 The following table gives the sizes and principal dimen- 
 sions for the Class D machines: 
 
 RIX DUPLEX SHAFT-DRIVEN COMPRESSORS. 
 
 CLASS D. 
 
 For Revolutions per minute, Cubic Feet Free Air, and Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter 
 Air Cylinder. 
 
 Stroke. 
 
 Price. 
 
 28 
 
 8 
 
 10K 
 
 13 
 
 12 
 
 14 
 16 
 
 
 29 
 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 
 
 
 16 y 2 i8 
 18^ 24 
 
 20^ 24 
 22^ 30 
 
 2A\4 "20 
 4/2 
 
 
 
 
 
 
9 6 
 
 RXI AIR COMPRESSORS. 
 
RIX AIR COMPRESSORS. 
 
9 8 
 
 RIX AIR COMPRESSORS. 
 
RIX AIR COMPRESSORS. 
 
 99 
 
 RIX DUPLEX TANDEM SECTIONAL 
 SHAFT-DRIVEN COMPRESSORS. 
 
 Class E, Fig. 42. 
 
 These Compressors are entirely similar to the Class D Ma- 
 chines as noted in Fig. 4r, with the exception that the bed 
 is extended and an additional air cylinder placed tandem to 
 the others. This makes a very convenient form of machine, 
 and one which gives a large air capacity with little additional 
 weight. These air cylinders are so connected up that any one 
 of the four cylinders, or any combination of the four cylinders, 
 may be run together. The utility of this machine will be 
 recognized at once. 
 
 Fig. 43 is a side elevation of this Class E machine. 
 
 RIX DUPLEX TANDEM SECTIONAL SHAFT-DRIVEN 
 COMPRESSORS. 
 
 For Revolutions per minute, Cubic Feet Free Air, and Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter 
 Air Cylinder. 
 
 No. of Air 
 Cylinders. 
 
 Stroke. 
 
 Price. 
 
 37 
 33 
 39 
 40 
 
 8 
 I4# 
 
 4 
 4 
 4 
 4 
 
 12 
 
 14 
 16 
 18 
 
 
 
 
 
 
RIX AIR COMPRESSORS. 
 
 y^iiJln* 
 
 | 
 
 
 J, be 
 
 '" .-»J * 
 
 ' 
 
RIX AIR COMPRESSORS. 
 
 hB>- 
 
 H&- 
 
 #o 
 
102 RIX AIR COMPRESSORS. 
 
 RIX SINGLE SHAFT-DRIVEN 
 COMPRESSOR. 
 
 Ceass F, Fig. 44. 
 
 This half-tone shows a flat bed type of compressor, but they 
 are made also with Corliss frames, as shown in the Class D 
 machines, Fig. 40, the smaller machines being made as per 
 Fig. 44. This machine has an outboard bearing and may be 
 driven either by belt, pulley, or by water wheel upon the shaft. 
 
 Fig. 45 shows a side elevation of this Class F compressor. 
 
 The following is a table of the sizes and general dimensions 
 of this style of air compressor: 
 
 RIX SINGLE SHAFT-DRIVEN COMPRESSOR. 
 
 CEASS F. 
 
 For Revolutions per minute, Cubic Feet Free Air, and Rock 
 Drill capacity, see pages 84 and 85. 
 
 4i 
 42 
 43 
 
 44 
 45 
 46 
 47 
 48 
 
 49 
 
 Diameter 
 Air Cylinder. 
 
 E3 
 14>2 
 
 i6y 2 
 
 H 
 16 
 18 
 iS 
 24 
 24 
 
KIX AIR COMPRESSORS. 
 
 I0 3 
 
io4 
 
 RIX AIR COMPRESSOR 
 
RIX AIR COMPRESSORS. 
 
 I05 
 
 RIX COMBINED DUPLEX STEAM 
 ACTUATED AND SHAFT- 
 DRIVEN COMPRESSOR. 
 
 (Xass G, Fig. 46-46^. 
 
 This is a form of compressor which is especially adapted to 
 the wants of the Pacific Coast, where there is abundance of 
 water supply during one portion of the season and an insuffi- 
 cient supply during the remainder. It becomes, therefore, 
 necessary to run the compressor with water power during a 
 portion of the year, and steam power during the balance. 
 
 It will be noted from the half tone that the air cylinders 
 are placed next to the water wheel, which water wheel has 
 been built upon the fly wheel of the machine, the steam 
 cylinders being tandem to the air cylinders, with a sleeve 
 coupling between. When it is desired to run by water power 
 it is only necessary to remove the sleeve coupling, and the 
 machine becomes a water power compressor. The couplings 
 may be replaced in an hour, at any time, and the machine 
 again converted into a duplex steam machine, using the com- 
 bined fly wheel and water wheel for a fly wheel. 
 
 These compressors are made in the following sizes: 
 
 RIX COMBINED DUPLEX STEAM ACTUATED AND 
 SHAFT-DRIVEN COMPRESSOR. 
 
 For Revolutions per minute, Cubic F'eet Free Air, and Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter 
 Steam Cylinder 
 
 Diameter 
 Air Cylinder 
 
 Stroke 
 
 H. P. 
 
 Boiler 
 
 Price 
 
 50 
 
 51 
 
 52 
 
 53 
 
 54 
 
 55 
 
 56- 
 
 57 
 
 IO 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 
 I2# 
 16% 
 
 isy 2 
 
 2oy 2 
 22 i y 2 
 24^ 
 
 14 
 16 
 18 
 18 
 24 
 24 
 30 
 30 
 
 60 
 80 
 no 
 140 
 200 
 260 
 
 310 
 
 400 
 
 
io6 
 
 RIX AIR COMPRESSORS. 
 
 
 i\ 
 
RTX AIR COMPRESSORS. 
 
 
I08 RIX AIR COMPRESSORS. 
 
 RIX STEAM ACTUATED VERTICAL 
 COMPRESSORS. 
 
 Ceass H, Fig. 47. 
 
 This style of compressor is one which has given universal 
 satisfaction in this State, a machine of similar type having run 
 continuously from 1880 to the present date with no expense 
 whatever beyond valve springs. It is single acting; the air 
 cranks being placed at 180 degrees from each other, which 
 balances the machine completely, and the cylinders being ver- 
 tical there is no internal wear of any consequence. The steam 
 engine is placed horizontally on the floor, for the double pur- 
 pose of keeping the warmth of the steam cylinder away from 
 the inlet air, and also for the purpose of making the steam 
 crank at right angles to the air cranks. 
 
 This compressor is made in only one size: 12-inch steam 
 cylinders, 12^-inch air cylinders by 16-inch stroke, and 
 catalogued No. 58. Capacity in free air per minute, see page 
 84, both cylinders being the equivalent of one double-acting 
 12^-inch cylinder, as per table. 
 
 Figs. 48, 49, and 50 show different views of this same 
 machine. 
 
RIX AIR COMPRESSORS. 
 
 I09 
 
 . 47— Class H.— Rix Steam Actuated Vertical Compressor. Manufactured 
 by Fulton Engineering and Shipbuilding Works, San Francisco. 
 
RIX AIR COMPRESSORS. 
 
 Fig. 48— Class H.— Rix Steam Actuated Vertical Compressor. Manufactured by 
 Fulton Engineering and Shipbuilding Works, San Francisco. 
 
RIX AIR COMPRESSORS. 
 
 
 Fi3. 49— Class H.—Rix Steam Actuated Vertical Compressor. Manufactured 
 by Fulton Engineering and Shipbuilding Works, San Francisco. 
 
RIX AIR COMPRESSORS. 
 
 Fig. 50— Class H.— Rix Steam Actuated Vertical Compressor. Manu- 
 factured by Fulton Engineering and Shipbuilding Works, 
 San Francisco. 
 
RIX AIR COMPRESSORS. 
 
 113 
 
 RIX SINGLE CORLISS ACTUATED 
 COMPRESSORS. 
 
 Class I, Fig 51. 
 
 These Compressors consist of a Standard Corliss engine, to 
 which there is placed tandem the air cylinder. 
 
 Fig. 52 shows a plan of the single machine. They are an 
 economical and high-class machine in every respect. 
 
 The following table shows the sizes and dimensions of the 
 Class I,;Rix Single Corliss Actuated Compressors: 
 
 RIX SINGLE CORLISS ACTUATED COMPRESSORS. 
 
 CLASS I. 
 
 For Revolutions per minute, Capacity Free Air, Rock Drill 
 Capacity, see pages 84 and 85. 
 
 59 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 
 67 
 68 
 69 
 70 
 7i 
 72 
 
 73 
 74 
 
 St'm Cylinder. 
 
 16 
 16 
 16 
 16 
 16 
 16 
 18 
 18 
 18 
 18 
 ]8 
 18 
 
 Diameter 
 Air Cylinder. 
 
 12^ 
 
 i6# 
 
 16^ 
 i8# 
 
 18K 
 16^ 
 i8# 
 i8# 
 
 20>£ 
 
 iSj4 
 2o>£ 
 18K 
 20K 
 
 30 
 30 
 30 
 30 
 30 
 30 
 36 
 36 
 42 
 42 
 36 
 36 
 42 
 42 
 48 
 
RIX AIR COMPRESSORS. 
 
RIX AIR COMPRESSORS. 
 
Il6 RIX AIR COMPRESSORS. 
 
 RIX COMPOUND CORLISS ACTUATED 
 COMPRESSORS. 
 
 Class J comprises the Rix Compound Corliss Acttiated Com- 
 pressors^ which are entirely similar to those of Class I excepting 
 that the steam cylinders are compound, the air cylinders being 
 alike. 
 
 The following is a table showing the sizes and principal 
 dimensions of the Class J Compressors: 
 
 RIX COMPOUND CORLISS ACTUATED COMPRESSORS. 
 
 CEASS J. 
 
 For Revolutions per minute, Cubic Feet Free Air, Rock 
 Drill Capacity, see pages 84 and 85. 
 
 No. 
 
 Diameter High 
 Pressure. 
 
 Diameter Eow 
 Pressure. 
 
 Diameter Air 
 Cylinder. 
 
 Stroke. 
 
 Price. 
 
 75 
 
 12 
 
 22 
 
 12^ 
 
 30 
 
 
 76 
 
 12 
 
 22 
 
 14^ 
 
 30 
 
 
 77 
 
 f4 
 
 26 
 
 14^ 
 
 30 
 
 
 78 
 
 14 
 
 26 
 
 16^ 
 
 30 
 
 
 79 
 
 16 
 
 30 
 
 l6>^ 
 
 30 
 
 
 80 
 
 16 
 
 30 
 
 l8>^ 
 
 30 
 
 
 81 
 
 16 
 
 SO 
 
 16^ 
 
 36 
 
 
 82 
 
 16 
 
 30 
 
 i8/ 2 
 
 36 
 
 
 83 
 
 16 
 
 30 
 
 16^ 
 
 42 
 
 
 84 
 
 16 
 
 30 
 
 isy 2 
 
 42 
 
 
 85 
 
 18 
 
 34 
 
 isy 2 
 
 36 
 
 
 86 
 
 18 
 
 34 
 
 20 l / 2 
 
 36 
 
 
 87 
 
 18 
 
 34 
 
 isy 2 
 
 42 
 
 
 88 
 
 18 
 
 34 
 
 20 l A 
 
 42 
 
 
 89 
 
 18 
 
 34 
 
 isy 2 
 
 48 
 
 
 90 
 
 18 
 
 34 
 
 2oy 2 
 
 48 
 
 
 Both the Compressors Class I or Class J are furnished either 
 condensing or non-condensing. 
 
RIX AIR COMPRESSORS. 
 
 RIX LIGHT DUTY COMPRESSOR OR 
 VACUUM PUMR 
 
 Ci,ass K, Fig 53. 
 
 This Compressor is adapted for very light work and is a 
 self-contained machine working from a Scotch yoke. It is 
 intended for pressures up to 25 lbs. only, and can be either 
 used as a compressor or a vacuum pump, the valves being 
 arranged for that purpose. It is single acting and the dis- 
 charge is absolutely complete, there being no clearance what- 
 ever. It is capable of creating a 2g-inch vacuum. 
 
 Made in four sizes having 4 7/ , 5 /7 , 6 // , and 7 7/ diameter of 
 cylinders, and catalogued No. 91, 92, 93, and 94 respectively. 
 
 This machine is a very inexpensive and satisfactory com- 
 pressor to have in laboratories, shops, and canneries, or for 
 blowing crude oil into furnaces. A four-inch belt is ample to 
 run any of them. The peculiar feature which is advantageous 
 as a vacuum pump is the discharge valve which covers the 
 whole end of the cylinder. The piston touches it, moves it 
 slightly from its seat, thus dispelling all the air, the valve 
 reseating as the piston begins the return stroke. 
 
RIX AIR COMPRESSORS. 
 
 Fig. 53— Class K.— Rix I^ight Duty Compressor or Vacuum Pump. 
 
 
RIX AIR COMPRESSORS. 119 
 
 RIX STEAM ACTUATED DUPLEX 
 COMPRESSORS. 
 
 Class Iv. 
 
 These compressors are designed for compressing air to not 
 exceeding twenty-five pounds per square inch, with a steam 
 pressure at from sixty to ninety pounds. They are made with 
 Scotch Yoke, as may be seen from the cut in Fig. 54, and are 
 self contained in every respect. They are especially adapted 
 for this Coast, for furnishing air for burning crude petroleum 
 or distillate. 
 
 These machines are far heavier and stronger than any 
 machine which is built in the East for the same purpose; the 
 same comparative cylinder sizes being made about twenty-five 
 per cent heavier, so that for use on shipboard they may be 
 absolutely relied upon not to break or give out when at service. 
 
 These machines are complete with all lubricators, valves, 
 and also automatic governor, which will regulate the machine 
 to within two or three pounds of the receiver pressure. 
 
 Kach one of these compressors is set up in the shop and 
 thoroughly tested before shipment, so that the machine will be 
 ready to go to work as soon as set upon its foundations. 
 
 The following are the sizes of the Rix Steam Actuated Duplex 
 Compressors, Class L ; 
 
RIX AIR COMPRESSORS. 
 
RIX AIR COMPRESSORS. 
 
 RIX STEAM ACTUATED SINGLE AIR 
 COMPRESSORS. 
 
 Cl,ASS M. 
 
 These machines are precisely like those of Class L,, except- 
 ing that they are Single instead of Duplex, and are fitted up in 
 precisely the same manner. 
 
 They are complete with governor, lubricators, oilers, and 
 wipers. 
 
 Each machine is tested before leaving the shop, so that it is 
 ready for work immediately it is erected upon its foundations. 
 
 The following are the sizes of the Rix Steam Actuated Single 
 Air Compressors, Class M : 
 
RIX AIR COMPRESSORS. 
 
 -ISAIOJ 3SJOH 
 
 •3irxnxj\[ asd 
 axy aa-itf }3<3^[ oxqn^ 
 
 10 r^ 
 
 O ro O 
 
 
 •saqoui 
 
 lit 3§-lBipSI(I J.IV 
 
 W rO 
 
 •saipui m l-snxi axy 
 
 CN O Ol <T> 
 
 •saxpixi 
 in }sixbi[Xk£ xxxBais 
 
 •saxpui 
 UT Arddng uxB3is 
 
 •saqoui 
 ux s^oa^e; jo xj.}£ii3l 
 
 vO 
 
 r-» 
 
 i>» 
 
 o> 
 
 C^ 
 
 C^ 
 
 •saipxxi ux .xapixx 
 
 •\&d JXV J313XXXBXQ 
 
 ^O 
 
 t^ 
 
 CO 
 
 On 
 
 O 
 
 ^h 
 
 •S3X|0UI xxi japux 
 -1^0 uiBaas ab^aaxBia 
 
 ^t- 
 
 to 
 
 lO 
 
 v£> 
 
 !>. 
 
 o> 
 
RIX AIR COMPRESSORS. 
 
 123 
 
 J3MOJ 3SJOH 
 
 04 ro rO IO 
 
 
 jad snopnxoAa-a 
 
 •saipui 
 in 3g.reipsia -»V 
 
 « ro 
 
 •saqoui ni ^\uj axv 
 
 OJ CN CS rO 
 
 ■S3XIDUI 
 III ^sriBuxjj xuBa;s 
 
 •S3t[0UI 
 
 ux Xjddns raB3;s 
 
 >S 
 
 •S3H0UI 
 
 MD 
 
 r^ 
 
 r^ 
 
 o\ 
 
 c^ 
 
 On 
 
 •saxpni in jap 
 -uyi^o jiy Jajauma 
 
 VD 
 
 t^ 
 
 CO 
 
 a\ 
 
 
 
 "* 
 
 •saipni in japin 
 
 "* 
 
 to 
 
 10 
 
 vo 
 
 t^ 
 
 On 
 
124 
 
 ■RIX AIR COMPRESSORS. 
 
 Class N, Fig. 54— Duplex Direct Acting Steam Actuated Compressors. 
 
 DUPLEX DIRECT ACTING STEAM 
 ACTUATED COMPRESSORS. 
 
 Ceass N. 
 
 It will be noted from the cut, Figure 54, that these com- 
 pressors are made after the style of the DIRECT ACTING 
 STEAM PUMP, and they are designed to meet certain require- 
 ments where light pressures and inexpensive or temporary 
 machinery are desired. They are the least expensive of all com- 
 pressors which are built, and while they do not have a very 
 high volumetric efficiency, they are easily installed and for cer- 
 tain classes of work are amply economical. 
 
 The AIR CYLINDERS are composition lined and the PIS- 
 TON rods are of brass. Every machine is fitted complete with 
 its PROPER LUBRICATOR and wrenches. The VALVE 
 MECHANISM is so arranged that the air pistons work against 
 a constant pressure at all times, thus obtaining quite a high 
 efficiency for this character of compressor, and insuring a uni- 
 form stroke. 
 
 There are no DEAD CENTERS on the machine, and the 
 pump is consequently always ready to start. The dispensing 
 of the crank and flywheel renders it possible to place this com- 
 pressor in an extremely small space. 
 
RIX AIR COMPRESSORS. 1 25 
 
 The VALVES in the steam end are slide valves, and in the 
 air and poppet valves of the ordinary type positively con- 
 trolled by the valve mechanism. The entire apparatus is com- 
 pact, durable, and self-contained. There are no intricate 
 working parts whatever, and it requires very little attention 
 to operate it. 
 
 As a general rule it is desirable to operate this machine in 
 connection with a PRESSURE REGULATOR, which we fur- 
 nish with the machine if desired. The PRESSURE REGU- 
 LATOR automatically controls the speed, slowing down and 
 finally stopping the pump when the desired air pressure is ob- 
 tained, and gradually starting up again when the air is ex- 
 hausted from the reservoir. This regulator practically makes 
 the machine automatic in its operation. 
 
 This Compressor is used in BREWERIES for BEER 
 RACKING, and is especially desirable for that purpose. It is 
 also used in running PNEUMATIC TOOLS for cutting mar- 
 ble or granite, or other building stone, and also for CHIPPING 
 and CALKING BOILERS; for the running of SAND BLASTS; 
 for the handling of ACIDS in refineries; for running small 
 PNEUMATIC CRANES; for use in RUBBER FACTORIES, 
 or for pumping pressures upon AUTOMATIC FIRE EXTIN- 
 GUISHERS; for CLEANING CARS where a jet of air is used 
 to dust off cushions it is especially valuable as an inexpensive 
 and cheap machine; for the running of CLIPPING MA- 
 CHINES, or for running COAL CONVEYORS, or SMALL 
 ROCK DRILLS, where pressures not exceeding fifty or sixty 
 pounds are required; for PNEUMATIC EJECTORS, or for 
 producing vacuums for FILTERING purposes; and the enum- 
 erable requirements where low pressure compressed air is 
 desired. 
 
 For RUNNING ROCK DRILLS we do not advocate it for 
 a permanent plant, but for a prospecting plant for small drills, 
 these compressors can be readily installed and will prove first- 
 class in their operation. 
 
 These Compressors are particularly adapted for furnishing 
 the compressed air to BURN PETROLEUM COMPOUNDS 
 UNDER BOILERS FOR GENERATING STEAM. 
 
126 
 
 RIX AIR COMPRESSORS. 
 
 DUPLEX DIRECT ACTING COM- 
 PRESSORS. 
 
 Class N. 
 
 Capacities calculated on piston speed of 60 feet and volu- 
 metric efficiency of 70 per cent. 
 
 No. 
 
 S s si 
 
 a-M a 
 
 g«J a 
 Q U 
 
 © 
 35 
 
 Cubic Feet 
 
 of 
 Free Air. 
 
 <U g D 
 (D.gE 
 
 w 
 
 6 
 
 CO u 
 
 < 
 
 94: g 
 
 Price. 
 
 107 
 
 4X 
 
 3 
 
 4 
 
 2.07 
 
 % 
 
 % 
 
 60 
 
 
 108 
 
 4^ 
 
 4 
 
 4 
 
 3-68 
 
 X 
 
 X 
 
 50 
 
 
 109 
 
 4K 
 
 4X 
 
 4 
 
 4-65 
 
 X 
 
 X 
 
 40 1 
 
 no 
 
 5X 
 
 3 
 
 5 
 
 2.07 
 
 X 
 
 I 
 
 60 
 
 
 III 
 
 5>4 
 
 3X 
 
 5 
 
 2.8l 
 
 X 
 
 I 
 
 50 
 
 
 112 
 
 5X 
 
 4 
 
 5 
 
 3.68 
 
 X 
 
 I 
 
 50 
 
 113 
 
 5X 
 
 4X 
 
 5 
 
 4-65 
 
 X 
 
 I 
 
 45 
 
 114 
 
 5X 
 
 4X 
 
 5 
 
 5.o6 
 
 X 
 
 I 
 
 40 
 
 115 
 
 5X 
 
 6 
 
 5 
 
 8.28 
 
 x 
 
 I 
 
 20 
 
 Il6 
 
 6 
 
 3 
 
 6 
 
 2.07 
 
 
 IX 
 
 70 
 
 117 
 
 6 
 
 3^2 
 
 6 
 
 2.8l 
 
 
 iX 
 
 60 
 
 Il8 
 
 6 
 
 4 
 
 6 
 
 3-68 
 
 
 *x 
 
 55 
 
 119 
 
 6 
 
 4X 
 
 6 
 
 4.65 
 
 
 iX 
 
 50 
 
 120 
 
 6 
 
 4X 
 
 6 
 
 5.06 
 
 
 iX 
 
 45 
 
 
 121 
 
 6 
 
 6 
 
 6 
 
 8.28 
 
 
 iX 
 
 40 
 
 
 122 
 
 6 
 
 6^ 
 
 6 
 
 9.70 
 
 
 iX 
 
 30 
 
 123 
 
 6 
 
 7 
 
 6 
 
 II.27 
 
 
 iX 
 
 25 
 
 124 
 
 6 
 
 7X 
 
 6 
 
 13. 
 
 
 iX 
 
 20 
 
 
 125 
 
 6 
 
 8 
 
 6 
 
 14.72 
 
 
 iX 
 
 15 
 
 
RIX AIR COMPRESSORS. 127 
 
 PNEUMATIC GOVERNORS. 
 
 Fig. 54/^ shows the Pneumatic Governor which the Fulton 
 Engineering Company attach to all the Corliss Compressors. 
 This Governor consists in a special attachment arranged in 
 connection with the Standard Corliss Governor, which is 
 actuated by the air pressure. When the pressure rises in the 
 air receiver the Governor balls are automatically lifted and 
 the hooks are thus tripped independently of the number of 
 revolutions which the engine is making. When the pressure 
 falls in the tank the device drops out of the way and the 
 engine is controlled by the Corliss Governor pure and simple. 
 
 For all ordinary compressors, when desired, a Governor is 
 furnished which controls the admission of steam readily as the 
 load varies. It is simple and effective in its operation. 
 
128 
 
 RIX AIR COMPRESSORS. 
 
 gfc 
 
 u.9 
 
THE RIX COMPOUND COMPRESSOR. 
 
 In speaking of the various means in practise for cooling 
 the air during its compression, reference has been made here- 
 tofore in this treatise to compounding the compressing cylin- 
 ders. The advantages of this process are so important that it 
 has come into general use and Compound Compressors nowa- 
 days are beginning to be the rule rather than the exception. 
 It is therefore interesting to give some explanation of this 
 method of compression. 
 
 The principle of Compound Compression can be described 
 as follows: Suppose that a certain volume of air at atmospheric 
 pressure and temperature is to be raised to a certain pressure 
 and delivered into a receiver; in ordinary, or single stage 
 compression, this air is introduced into a cylinder wherein a 
 piston effects the compression and delivery of that air at each 
 stroke. This compression, as we know, and especially in fast 
 moving machines, is accompanied by a considerable develop- 
 ment of heat, which causes a loss of efficiency. 
 
 In the compound machine, air is adm tted into a cylinder, as 
 before, but it is compressed and delivered into a receiver at a 
 pressure smaller than the desired final pressure. In this first 
 period or stage of compression there is a certain amount of 
 heat developed, less, however, than in the single stage ma- 
 chine. The compressed air, after it is delivered into this first 
 receiver at the intermediate pressure, is cooled by coming in 
 contact with a number of copper tubes through which cold 
 water is rapidly circulated. This receiver is quite similar to 
 the surface condenser used in marine engines and is termed 
 the Intercooler, and the compressed air leaves it after having 
 been deprived of its heat, and reduced to practically the tem- 
 perature of the water. It is then admitted into another smaller 
 cylinder wherein its pressure is raised by another piston — the 
 air being again passed through another intercooler — then ad- 
 mitted into a third cylinder, and so on until the final desired 
 pressure is reached. 
 
 The compression of air, instead of being affected all at once, 
 is therefore performed in several stages, each separated from 
 the following one by a cooling to the atmospheric temperature. 
 It may be readily conceived that the partial amounts of heat 
 developed in this series of cylinders are more effectively dealt 
 with than when the whole amount of heat is liberated in a 
 single cylinder. On this ground the Compound Compressor 
 will therefore possess a higher efficiency than the single stage 
 machine. 
 
 Another advantage is that the variation of load on the 
 piston during the stroke is less in the compound, and conse- 
 quently the strains on the crankpins are reduced, and a lighter 
 
130 
 
 THE RIX COMFOUND COMPRESSOR. 
 
THE RIX COMPOUND COMPRESSOR. I3I 
 
 flywheel will regulate the motion of the machine than is the 
 case in a single-stage compressor. For instance, if we use a 
 12-inch cylinder to compress air to 100 lbs. gauge, in the single- 
 stage compressor, the load on the piston during one stroke 
 will vary from o to 11,300 lbs., whereas in the compound ma- 
 chine this load can be made to vary from o to 5960 in all. 
 
 The principle of the Compound Compressor applies to any 
 number of successive stages, and, theoretically, the more 
 stages there are used the nearer will the compression approach 
 the isothermal. But, at a practical standpoint, the increased 
 number of cylinders is, of course, objectionable, inasmuch as 
 it makes a heavier and more intricate machine, which will cost 
 more and necessitate more expenditure for maintenance. The 
 frictional resistances also become greater with the number of 
 cylinders, and it is, therefore, readily seen that there are some 
 practical limitations in the use of this system. 
 
 It may be stated that for pressures not exceeding 200 and 
 even 300 lbs. per square inch, there should not be more than 
 two stages in the compression. Four stages is the limit which 
 has not been thus far exceeded, even with air pressure reach- 
 ing to 2000 lbs. per square inch, and even for these high pres- 
 sures three-stage compressors are deemed amply sufficient. 
 
 On the other hand, the compound system would be an 
 unnecessary improvement with low pressures. For 50 or 60 
 lbs. receiver pressure it is quite likely that the percentage of 
 extra resistances would balance if not overcome the percentage 
 of gain in cooling. 
 
 In general, the advantages of a compound system consist in 
 that less heat is developed at each stroke of the piston, while 
 the air under compression is exposed to a larger cooling sur- 
 face than in a single-stage machine. 
 
 The diagram, Fig. 56, represents the theoretical adiabatic 
 cards of a 12x16 single stage compressor and of a tandem com- 
 pound 12 and 73^x16, both compressing to 70 lbs. gauge. It 
 also shows the expansion curve in a 12x16 steam cylinder de- 
 veloping with steam at 80 lbs. gauge the same work as the 
 single stage compressor. 
 
 These cards do not show the variations of pressure of steam 
 and air, but the variations of effective load on the piston rod 
 of the three cylinders, and they will serve for a comparison of 
 two direct-acting steam compressors — one in the single stage 
 and one in the compound system. 
 
 We know already that the aggregate piston load in the com- 
 pound is less than in the single machine and as the initial 
 loads are o in both cases, the range of variation is less in the 
 compound. This allows a reduction in the size of the piston 
 rods. It will be noticed that the compound curve has a sharper 
 rise, since the maximum load H. G. is reached at the point / 
 of the stroke, while in the single cylinder this same load is 
 only reached at the pointy. The result of it is that during 
 this portion of the stroke, which precedes the point of equal 
 loads in the two compressors, i. e., the point of intersection of 
 
132 
 
 THE RIX COMPOUND COMPRESSOR. 
 
THE RIX COMPOUND COMPRESSOR. 
 
 133 
 
 the steam and air curves, the difference of the load between the 
 steam and air pistons is smaller in the compound, where it is 
 6" V for instance, than in the single cylinder compressor, 
 where at the same point T, of the stroke, the difference is 
 5 V. 
 
 The same may be said for the second portion of the stroke, 
 except in the region// 7 , but here the discrepancy is unim- 
 portant, the piston loads being but little at variance in the two 
 compressors, and this region corresponding to the maximum 
 velocities of the pistons. 
 
 As the mass of moving pieces, whose momentum is resorted 
 to for securing a regular motion, is a function of the actual dif- 
 ference between the steam air piston loads, lighter regulating 
 pieces, like flywheels, will be required in the compound than 
 in the single compressor. 
 
 The same size of steam cylinder will be found adopted in 
 practise with both kind of compressors, the point of cut off 
 being, moreover, variable. 
 
 A longer expansion of steam, combined with a less weight 
 of machine, combine to win for a compound compressor the 
 deserved claim of being a better balanced and more economi- 
 cal machine than the single stage. 
 
 It will be seen that a proper design of such machines must 
 tend to an equal division of the total work among the several 
 cylinders; that the loads are equal on each one of the pistons 
 at any point of the stroke, and that the temperature of the 
 entrance and exit of the air are the same in all the cylinders. 
 
 The following table shows the percentage of gain obtained by 
 compounding as against the single-stage system, with various 
 modes of compression: 
 
 PERCENTAGE OF GAIN OF 2-STAGE VS. I-STAGE SYSTEMS OF 
 COMPRESSION. 
 
 Ratio of Receiver pressure to atmos- 
 pheric pressure. 
 
 Gain per cent in: 
 Adiabatic Compression (no cooling). 
 Jacketed Cylinders 
 
 Jacketed Cylinders cooled by spray in- 
 jection in the most efficient way 
 possible 
 
 n-5 
 
 8-95 
 
 6.4 
 
 12.5 
 
 13-8 
 
 14.8 
 11. 8 
 
 7 5 8.2! 8.7 
 
 15.9 
 12.5 
 
 9.2 
 
 These figures show that for the usual air pressures the 
 amount of work saved by compounding varies from 9 to 12 
 per cent. This is by no means a quantity to be neglected. 
 
134 The rix compound compressor. 
 
 We also note that the advantage of compounding increases 
 with the pressure and is more marked with a poor than with an 
 improved system of cooling. 
 
 The Fulton Engineering and Shipbuilding Works do not 
 issue a list of the various sizes of their Compound Compressors, 
 for the reason that the relation between the two cylinders can 
 never be fixed, the sizes of the initial cylinders depending of 
 course upon the quantity of air required, and the size of the 
 compound cylinders depending entirely upon the pressure 
 desired. Special estimates and specifications are furnished 
 with each compound machine. The following illustrations 
 show some of the compound machines built by the Fulton 
 Engineering and Shipbuilding Works, and give an idea of 
 their general style. 
 
 The Compound Compressor, Fig. 60, shown in the preced- 
 ing cut, illustrates the general style of the Compound Com- 
 pressors built by the Fulton Engineering and Shipbuilding 
 Works. This Compressor was built for the North Star Mining 
 Company, of Grass Valley, Cal., and consists of Duplex Tan- 
 dem Compound machines. The initial cylinders are 18 inches 
 in diameter, and the high pressure cylinders are 10 inches in 
 diameter by 24-inch stroke. The piston speed of the machine 
 is 440 feet, which, while not quite as economical as one much 
 lower, was dictated by the conditions under which the water 
 wheel operated. 
 
 The air enters the initial cylinder at the temperature of the 
 power room, which is approximately 62 degrees, and is therein 
 compressed to 25 lbs. to the square inch gauge pressure. It 
 leaves the cylinder at a temperature of 200 degrees Fahr. and 
 passes through an intercooler of about 1000 running feet of 1- 
 inch copper tubes placed directly beneath the water wheel, and 
 which receives from the wheel a continual shower of water at a 
 temperature of about 58 degrees. This cools the air to such an 
 extent that it is delivered to the high pressure cylinders at a 
 temperature of about 60 degrees. In these cylinders the air is 
 compressed to 90 lbs. and is delivered from the cylinders at a 
 temperature of 204 degrees into 6-inch mains, which lead to the 
 mine. Indicator cards taken from the cylinders show that the 
 cylinders are doing equal work, and at no revolutions they 
 work smoothly and perfectly. 
 
 Notwithstanding the fact that some builders claim that 
 clearance has no detrimental effect upon the economy of their 
 air compressors, in the Rix compressors the clearance is prac- 
 tically eliminated, being not to exceed one-thirty-second of an 
 inch at each end of the stroke. The cards taken from these 
 cylinders are practically square-cornered. 
 
 The water-jacket system is quite unique, it being a duplex 
 system — that is, there is an independent circulation for each 
 end of the cylinder, the water passing longitudinally back and 
 forth on the side of the cylinder and from the center in two 
 
 I' 
 
THE RIX COMPOUND COMPRESSOR. 
 
 135 
 
 -|s 
 
 ^ssj 
 
 -i=- 
 
 # 
 
136 
 
 'The: rix compound compressor. 
 
THE RIX COMPOUND COMPRESSOR. 
 
 137 
 
138 
 
 the; rix compound compressor. 
 
THE RIX 'COMPOUND COMPRESSOR. 139 
 
 independent streams, cooling the heads at the same time. The 
 efficacy of this water jacket will be noted in the temperatures 
 above given. 
 
 In testing for volumetric efficiency, the receivers were care- 
 fully measured a number of times and found to contain 291 
 cubic feet. These were filled repeatedly, and the number of 
 revolutions of the machine accurately counted each time. All 
 of these experiments were conducted after the machine had 
 been in operation for a sufficient length of time to reach its 
 maximum temperature. 
 
 The barometer at the power house is 27.35 inches, corre- 
 sponding to an elevation of about 2400 feet. This gives an 
 atmospheric pressure of 13.32 lbs. per square inch. At 90 lbs. 
 gauge pressure the ratio of compression would be 7.7, and the 
 receiver containing 291 cubic feet represents 2240 cubic feet 
 capacity of free air. The average of a great many experiments 
 showed that the compressor took 102^ revolutions to fill the 
 receiver from 25 lbs, which is the pressure of the initial cylin- 
 der, to 90 lbs. At this pressure of 25 lbs. gauge there is 830 
 cubic feet of free air in the receiver. The difference between 
 these two capacities, or 1410 cubic feet, would represent the 
 imount of air which was forced into the receiver at the revolu- 
 tions stated. Inasmuch as the temperature of the receiver is 
 somewhat higher than the temperature of the inlet air, there 
 should be a deduction made from this sum corresponding to 
 that temperature of about two per cent, making the corrected 
 amount delivered to the receiver 1382 cubic feet. 
 
 The theoretical capacity of the compressor, deducting the 
 piston rods, and at 102^ revolutions, is 1429 cubic feet of free 
 air per minute. The ratio between 1382 cubic feet, actually 
 delivered, and 1429 cubic feet, theoretical capacity, is 96.6 per 
 cent, which represents the actual volumetric efficiency of the 
 machine at the present writing. This of course will vary pro- 
 portionately with the ratios of the absolute temperatures of the 
 inlet air, depending upon the season of the year. 
 
 One peculiarity about the Rix Compressor, as may be noted 
 from the cut, is the fact that the compressor is so arranged that 
 any cylinder may be disconnected or any end of any cylinder 
 may be disconnected without interfering with the operation of 
 the machine. This feature is very valuable in case of repairs 
 or accident to the machine. 
 
 To drive this compressor there has been placed upon the 
 main shaft a Pelton water wheel, eighteen feet in diameter, 
 which is believed to be the largest tangential water wheel ever 
 made. 
 
THE PNEUMATIC TORPEDO PLANT 
 AT THE PRESIDIO. 
 
 (Originally published in "Journal of Electricity," S. F.) 
 
 The recent tests made by the military authorities on the 
 dynamite guns at Fort Point may lend some interest to a few 
 particulars regarding the Air Compressing Plant which forms 
 the vital element of this installation. 
 
 The contract for the construction of the mechanical part of 
 it, with the exception of the guns and their immediate fixtures, 
 was awarded by the Pneumatic Torpedo and Construction Com- 
 pany of New York to the Fulton Engineering and Shipbuild- 
 ing Works of this city, upon the plans and special designs of 
 Mr. E. A. Rix, who supervised the construction of the plant. 
 
 The compression of" air is made in three stages, from the 
 atmosphere to the working pressure of 2000 lbs. effective per 
 square inch. It is performed in two sets of horizontal engines, 
 to both of which the subsequent description applies, they being 
 in all respects entirely alike. The steam is supplied by four 
 boilers of the Horizontal Tubular type, of 750 H. P. capacity, 
 arranged to work either with natural or with forced draught. 
 
 Two steam cylinders connected to the same shaft by cranks 
 at an angle of 145 degrees from each other, actuate in tandem, 
 that is, through their piston tail rods, each two air cylinders, 
 there being on one side one low pressure and the intermediate 
 or second stage cylinder, and on the other side one low pres- 
 sure and the high pressure or finishing cylinder. 
 
 This duplex set therefore comprises two steam cylinders, 
 two intake cylinders, wherein the atmospheric air is compressed 
 to about 75 lbs. effective, one intermediate cylinder, carrying 
 the air pressure from 75 to about 400 lbs. effective, and one high 
 pressure cylinder, which takes the air at 400 lbs. and com- 
 presses it to 2000 lbs. effective. 
 
 The intake or low pressure cylinders are double acting, that 
 is, they have inlet and discharge valves at each end, while the 
 intermediate and high pressure cylinders are single acting, that 
 is, provided with valves at one end only, their pistons being 
 plunger rams with spherical heads, connected to the tail rods 
 of the intake cylinders. 
 
 The special purpose which these compressors have to serve 
 made their design and construction subservient to conditions 
 at entire variance with the lines upon which an air compressing 
 plant is usually established. The main object of the designer, 
 when a large power is to be used, as in the case of the Fort 
 Point installation, is commonly to secure the greatest possible 
 economy in the production of the compressed air. In the pres- 
 ent instance, compound condensing engines of the most 
 approved type, and air cylinders working at a moderate linear 
 
THE PNEUMATIC TORPEDO PI<ANT. 
 
 141 
 
THE PNEUMATIC TORPEDO PEANT. 
 
THE PNEUMATIC TORPEDO PEANT. 
 
 143 
 
144 THE) PNEUMATIC TORPEDO PLANT. 
 
 piston speed, would present themselves to the mind as advis- 
 able. Such engines would be established in view of a regular 
 working speed, or approximately so, and everything would be 
 provided to give the economical appliances a chance to work to 
 their full advantage. 
 
 At Fort Point the primary requirement was to have a plant 
 as little liable as possible to getting out of order. Solidity 5 
 simplicity, and endurance were therefore the main points to be 
 considered, economy being a desirable but decidedly an acces- 
 sory feature. 
 
 Upon these general lines, supplemented by conditions of 
 capacity within a given time, of efficiency in the means of cool- 
 ing the air and of practical effectiveness of several important 
 parts, the present plant was designed, built, and erected. 
 
 The steam engines are non-condensing and each cylinder 
 acts independently; that is, no compounding has been adopted. 
 The valves are provided with Meyer's cut-off, regulated by 
 hand, the Governors merely acting on the throttle in case 
 of racing. The cranks are set at the angle heretofore 
 indicated, in order that the machine may be balanced as nearly 
 as possible and yet the engines be able to start in any position. 
 
 In the air cylinders the greatest care has been used to 
 secure a cooling efficiencv as high as possible. The heads and 
 the barrels of the cylinders are water-jacketed, the water dis- 
 charge pipes from the jackets being in full view and easily 
 accessible, and the supply of cooling water being regulated 
 according to its temperature at the discharge. 
 
 A very elaborate and effective system of intercoolers has 
 been established between the intake and intermediate cylinders 
 and also between the intermediate and high pressure cylinders. 
 These intercoolers consist of nests of copper pipes extending 
 under the floor in cemented trenches, where a stream of cold 
 water is constantly running. The proportions of these inter- 
 coolers have purposely been made very ample, and their effect- 
 iveness is fully demonstrated by the low temperature of the 
 air before it enters the intermediate and the high pressure 
 cylinder, which are given hereafter. 
 
 A similar cooler is provided for the air at working pressure 
 after it leaves the high pressure cylinder and before reaching 
 the 24 forged steel storage tubes, which through a complete 
 system of pipes and manifolds, and also a compact arrangement 
 of valves, can be set in communication with each particular 
 gun, or if so desired, with a supplementary storage supply 
 located in the foundation of the guns. 
 
 That the demand upon the compressors may vary during 
 action, within widely distinct limits, was exemplified by the 
 fact that while 360 feet per minute is generally considered as a 
 limit of piston velocity in water jacketed cylinders, this velocity 
 
THE PNEUMATIC TORPEDO PLANT. 
 
 145 
 
146 
 
 THE PNEUMATIC TORPEDO PLANT. 
 
THE PNEUMATIC TORPEDO PLANT. 1 47 
 
 has been, during part of the trials, carried to 568 feet, or an 
 excess of 58 per cent. At this high rate of speed no undue 
 heating could be observed in the moving parts and the absence 
 of jarring and of trepidations was the best evidence of the 
 remarkable strength and steadiness of the plant. 
 
 Of course, when working at high speed, no claim is nor 
 could be entertained to maintaining a satisfactory cooling 
 efficiency in each individual cylinder. As before stated, the 
 intercoolers are of sufficient size to deal with the heat liberated 
 during the compression even at high speed. But when the 
 period of compression, and, of course, the period of effective 
 possible cooling, lasts two-fifteenths of a second, the heat units 
 passing through the cylinder walls during that time cannot be 
 expected to be many. It might be argued that the Riedler 
 compressors in Paris work at a nominal piston velocity of 550 
 feet and occasionally 733 feet per minute, but aside from the 
 fact that the use of a spray for cooling and of mechanically 
 moved valves are both combined to reduce the rise of temper- 
 ature, the pressures in the two-stage Riedler compressor are 
 considerably lower, the air being sent into the mains at only 
 118 lbs. gauge per square inch, an insignificant pressure as 
 compared to 2000 lbs. 
 
 Another point of interest in the Fort Point plant is the 
 absence of leakage at the stuffing boxes of the intermediate and 
 high pressure rams. This point has been the cause of much 
 annoyance in similar plants built elsewhere, and the present 
 arrangement is the outcome of long and costly experiments. 
 
 The friction, in a running joint capable of holding 2000 lbs. 
 of air pressure against the atmospheric, is necessarily enor- 
 mous, and after the nature, the shape, and the size of the 
 packing had been determined upon, it became necessary to 
 keep the packing sufficiently cool to prevent its rapid wear. 
 This is effected by a special circulation of cold water inside the 
 rams, the arrangement being quite apparent on the general 
 plan, and that it is successfully effected can be easily ascer- 
 tained. This water circulation also partly contributes to cool- 
 ing the air under compression. 
 
 At the normal rate of speed of about 400 feet per minute of 
 piston velocity, the compressors supply to the storage tubes 
 460 cubic feet of air per hour at 2000 lbs. gauge. The annexed 
 abstract from trials made in view of timing the production of 
 the compressors gives interesting evidence of the effectiveness 
 of the intercoolers and of the regularity of the temperature of 
 air at its entrance to each cylinder. 
 
 For a range of final pressures comprised between 800 and 
 2000 lbs. effective, the variation of temperature was only 8 
 degrees Fahr. for the intermediate and 3 degrees Fahr. 
 for the high pressure cylinder, the temperature of the engine- 
 room being 71 degrees Fahr. 
 
148 
 
 THE PNEUMATIC TORPEDO PI,ANT. 
 
THE) PNEUMATIC TORPEDO PEANT. 
 
 149 
 
150 
 
 the; pneumatic torpedo pivANT. 
 
 Gauge pressure 
 
 Fahr. 
 
 temperature at entrance to 
 
 lbs. per sq. in. 
 
 
 
 E. P. Cylinders. 
 
 I. P. Cylinders. 
 
 H. P. Cylinders. 
 
 800 
 
 71 
 
 67 
 
 66 
 
 900 
 
 71 
 
 68 
 
 6 7 
 
 IOOO 
 
 71 
 
 69 
 
 67 
 
 I IOO 
 
 71 
 
 69 67 
 
 I200 
 
 71 
 
 70 68 
 
 1300 
 
 71 
 
 70 68 
 
 1400 
 
 71 
 
 71 68 
 
 1500 
 
 71 
 
 72 68 
 
 1600 
 
 71 
 
 72 68 
 
 1700 
 
 71 
 
 74 69 
 
 1800 
 
 71 
 
 74 
 
 69 
 
 1900 
 
 71 
 
 73 
 
 69 
 
 2000 
 
 71 
 
 72 
 
 69 
 
 The discharge temperature of the low pressure cylinders 
 gradually increased and then remained stationary at 320 degrees 
 Fahr. The intermediate cylinder discharge likewise attained 
 a temperature of 292 degrees Fahr., and the high pressure 
 cylinder, beginning at 375 lbs. per square inch, and at a tem- 
 perature of 66 degrees Fahr., delivered from the intercoolers, 
 gradually rose in temperature as the pressure increased, until 
 it reached 2000 lbs., and after running at that pressure for one 
 hour, the thermometer indicated its maximum, viz., 358 degrees 
 Fahr. 
 
 The sum total of those temperatures, viz., 970 degrees, as 
 compared to the adiabatic temperature of single stage compres- 
 sion to 2000 lbs., which is 1762 degrees Fahr., indicate the 
 work saved by the three-stage method of compression combined 
 with the jacket and ram cooling devices. 
 
 The compression throughout the whole range was practi- 
 cally regular, being as an average 115.1 lbs. for each 500 revolu- 
 tions of both machines. 
 
 The mean of many cards taken from the steam cylinders 
 showed that each compressor absorbed 342.61 I. H. P., while 
 the cards from the three air cylinders showed 293 78 I. H. P. 
 for each compressor. The work then absorbed by the friction, 
 inertia, etc., was 48.83 I. H. P. or 14.2 percent of the indicated 
 power employed, showing a mechanical efficiency for the com- 
 pressor of 85. S per cent, which is high, especially in view of 
 the facts that the engines were new and consequently stiff to 
 some extent, and also that some extra friction is developed at 
 the ram stuffing-boxes as compared with a compressor working 
 at the usual air pressures. 
 
 The resisting load of 48.83 H. P. while the compressors 
 were doing full duty may be compared with the friction load 
 on the machine without air pressure, and an interesting result 
 
THE PNEUMATIC TORPEDO PLANT. 
 
 151 
 
 Fort Point 
 
 Air Compressing Plant 
 
 «= Steam *n Air Cards = 
 
152 THE PNEUMATIC TORPEDO PEANT. 
 
 obtained. Cards taken showed that this friction load was 32.4 
 H. P., being .663 of the resisting work under load and showing 
 an increase of 50.7 per cent in the resistances between no load 
 and full load. 
 
 The combined indicator cards illustrated herewith are 
 plotted from actual cards and show a saving of 36.8 over adia- 
 batic single stage compression. 
 
 The boilers for this plant were of the Return Tubular type, 
 and manufactured by the Chandler & Taylor Co. of Indian- 
 apolis, Ind.; were 72 inches in diameter, by 16 feet long, and 
 of a nominal horse power of 500, which were increased by the 
 forced draught employed, to about 750 horse. 
 
 These boilers were tested to 150 lbs. to the square inch, and 
 fully satisfied the requirements of the Treasury Department. 
 The forced draught was employed because it was not con- 
 sidered desirable to continue the stacks above the roof, and thus 
 give an opportunity for invading forces to discover the posi- 
 tion of the plant. A short stack was therefore necessary, 
 about fifteen feet in length, which required the employment of 
 a forced draught. The forced draught was instituted b}* two 
 Sturtevant fans, with engines attached, having cylinders three 
 inches in diameter by three and a half inch stroke. These fans 
 delivered each 12,000 cubic feet per minute of free air, through 
 a 22-inch main, which, passing underneath the battery of four 
 boilers, was connected to each by a 10-inch outlet underneath 
 the grate bars. It was found during the test that these fans 
 need be run only to about 60 per cent of their capacity. 
 
 The engines exhausted their steam into two heaters of 
 the National type, of 300 H. P. each, which furnished to the 
 boilers feed water at a temperature of 200 degrees Fahr. 
 
 The Feed Pumps were of the Deane type, being Duplex and 
 two in number, the steam cylinders being six inches, the 
 water cylinders being four inches, and the stroke being six 
 inches. At a slow piston speed these pumps furnished all the 
 necessary water, which was drawn from the pits after being 
 heated by the air from the compressors. 
 
 As an auxiliary there are installed alongside of the Feed 
 Pumps two Nathan Injectors of 300 H. P. each, which are 
 amply sufficient to furnish all of the water necessary to feed 
 the boilers. 
 
 During the test for rapidity of firing, while the plant was 
 supposed to be strained to its utmost, the firemen had ample 
 time to observe the operation of the compressor plant, showing 
 that the boilers were more than sufficient to supply the steam 
 necessary for the proper operation of the compressors. 
 
 The electrical plant was furnished by the Electrical En- 
 gineering Company of this city, and consisted of one 35-kilo- 
 Watt compound wound dynamo, capable of being worked up 
 to 25 per cent of its rated capacity for thirty minutes without 
 undue heat, and operated by an Armington & Sims engine. 
 
 This dynamo was connected by about 800 feet of two-wire, 
 insulated copper cable, encased in lead covering, and capable 
 
THE PNEUMATIC TORPEDO PLANT. 
 
 153 
 
154 THE PNEUMATIC TORPEDO PI.ANT. 
 
 of carrying a current of 400 amperes, without undue heating. 
 This cable was placed in and fastened to the side of an 
 underground conduit. 
 
 This Company also placed in position, at about ten feet 
 distant from the dynamo, a switchboard of slate, and wired 
 complete, having three double-pole three hundred ampere 
 knife switches. 
 
 The compressed air, after leaving the compressors and 
 being confined in the storage tanks, was distributed to the three 
 guns independently, through a manifold of bronze, having 
 attached five gauges, two registering 2coo lbs., and three 1250 
 lbs., and so arranged with valves that any or all of the guns 
 could be operated at once. 
 
 This air is carried to the underground storage reservoirs of 
 the guns, through a pipe having an outside diameter of 2]/ 2 
 inches, and inside diameter of i)4 inches and duly tested to 
 3500 lbs. to the square inch for tightness. 
 
 From the guns to these manifolds also there are three cop- 
 per pipes, % inch inside diameter by ]/ z inch outside diameter, 
 to register the pressures at the manifolds that are contained in 
 the carriages of the guns. 
 
 This is in general the description of the air-compressing 
 plant. We now come to speak of the guns themselves, which 
 were manufactured at the West Point foundry on the Hudson, 
 each 15 inches in diameter, with a length of 50 feet; each gun 
 mounted on its carriage, weighing about 70 tons, perfectly bal- 
 ances, and these are mounted upon concrete foundations. 
 
 The tests of these guns for their mechanical efficiency, 
 which may be called their ease of operation, showed that they 
 could be traversed by the electric motors, which were situated 
 in the gun carriage, in an average of one minute, throughout 
 the entire 360 degrees, and they could be elevated from extreme 
 elevation to extreme depression, in from eight to eleven 
 seconds. Any one familiar with the length of time necessary 
 to operate ordinary powder guns by hand will appreciate the 
 fact that this facility of operation is marvelous. 
 
 For testing these guns for mechanical efficiency, the 
 requirements were, first, that 45 shots should be fired in the 
 first hour and 30 shots in the hour succeeding. Inasmuch as 
 the wastage of air would be the same whether actual projectiles 
 were fired, or whether the air was simply wasted through the 
 muzzle of the gun in "air shots," no projectiles were fired in 
 this test, and it was found for the first hour that 45 shots were 
 fired and the compressors running at their normal speed regis- 
 tered a final pressure of 1800 lbs., it being thus demonstrated 
 that the compressors were amply sufficient to maintain any 
 requirements which might be placed upon the gun. Twenty 
 air shots were fired to ascertain the utmost rapidity with which 
 
THE PNEUMATIC TORPEDO PLANT. 1 55 
 
 35 K. W. Dynamo for ranging Dynamite Gun 
 
156 THE PNEUMATIC TORPEDO PLANT. 
 
 they could be discharged, and the same were discharged in 7^ 
 minutes, though the contract did not require that these shots 
 should be discharged inside of 30 minutes, it being thus 
 demonstrated that the compressors and the guns were amply- 
 capable to maintain the test required by the Government. 
 
 The test for rapidity of firing with actual projectiles took 
 place next. The projectiles used were pieces of gas pipe 12 
 inches in diameter and 8 feet long, loaded with sand. The 
 weight was 1040 lbs. Each one of the three guns was required 
 to fire five of these projectiles within twenty minutes. The 
 test developed the fact that these projectiles were all discharged 
 from each gun within eight and one-half minutes, and they 
 were by far the most interesting feature of the whole test. 
 
 Having no means for maintaining the accuracy of their 
 flight, these projectiles were nevertheless thrown for the first 
 one-half distance of their flight perfectly accurate; that is, they 
 maintained the position of a well-directed projectile, after 
 Which they tumbled end over end and fell into the sea. With- 
 out any plain table measurements being taken upon them, they 
 apparently fell quite accurately within a small target. 
 
 The time of flight of these projectiles averaged about nine- 
 teen seconds for about 2200 yards. 
 
 The question of rapidity of firing and of loading having been 
 determined, the next test was one of accuracy, and the live 
 projectiles were discharged from these guns at a distance of 
 5000 yards. The projectiles used were of the eight-inch cali- 
 ber, the difference in diameter being made up by wooden pis- 
 tons in four sections so that the wooden pieces would fly off 
 after the projectile had left the gun, leaving it free to make its 
 flight. The first projectile flew 5000 yards and exploded; the 
 second projectile flew 5070 yards and exploded; the third pro- 
 jectile flew 5015 yards and exploded; the fourth projectile 
 flew 5040 yards and exploded; all of these projectiles being 
 plotted on a plane table in a rectangle 70 yards long by 20 
 yards wide, the time of flight being about 27^ seconds. 
 
 As a matter of experiment, two shots were fired into the 
 hills of Marin County, at a distance of 3350 yards, each with 
 the 8-inch sub-caliber shell loaded with 100 lbs. of dynamite, the 
 first shot being fired five days previous to the second shot. The 
 shots struck within 45 yards of each other and exploded in a 
 perfectly satisfactory manner; in fact, the pits caused by the 
 explosion joined each other. The larger shells, viz., the 15- 
 inch full caliber projectiles being eleven feet long and weighing 
 some 1050 lbs., loaded with 500 lbs. of nitro-gelatine, were 
 thrown into the sea at a range of an average of 2100 yards. 
 They exploded practically upon striking the water, throwing 
 into the air a column of water about 100 feet in diameter at the 
 
THE PNEUMATIC TORPEDO PI,ANT. 157 
 
 base, and, from the levels taken at the gun, about 400 feet in 
 altitude. 
 
 The tests as above enumerated were perfectly satisfactory in 
 every respect and exceeded in every way the requirements of 
 the Government. There were no mistakes made and no delays 
 whatever caused by the air-compressing plant or the gun plant, 
 which probably exceeded the Government requirements in an 
 aggregate of over one thousand per cent, if the various exceed 
 percentages of the different tests were added together, and 
 which reflected great credit upon the manufacturers of the 
 power plant, the constructing engineer, the manufacturers of 
 the guns and projectiles, and also the Pneumatic Torpedo & 
 Construction Company of New York, which contracted for and 
 thus successfully carried to completion their contract with the 
 Government. 
 
I58 ROCK DRILLS. 
 
 ROCK DRILLS. 
 
 The RIX and the GIANT ROCK DRILLS are manufactured 
 in San Francisco, Cal., and their construction is the result of a 
 study of the requirements of the Pacific Coast in rock drilling, 
 covering the last twenty years. It has been the aim of the man- 
 ufacturers of these machines to produce something which will be 
 especially satisfactory to the miners of the Pacific Coast. 
 
 Many of the improvements in these machines have been 
 suggested by the operators of the drills themselves, to suit par- 
 ticular conditions, and it has been the aim of the manufacturers 
 to construct a machine which is rapid and powerful in its 
 action. 
 
 The GIANT and the RIX DRILLS are manufactured under 
 the following patents, controlled by EDWARD A. RIX. 
 
 U. S. PATENTS AS FOLLOWS. 
 
 Re-issue 0,705 Patent No. 190,699 
 
 Patent No. 149,013 Patent No. 206,067 
 
 Patent No. 152,712 Patent No. 235,296 
 
 Patent No. 156,003 Patent No. 235,816 
 
 Patent No. 169,389 Patent No. 255,335 
 
 Patent No. 172,529 Patent No. 410,334 
 
 Patent No. 178,214 Patent No. 454,228 
 Patent No. 490,152 
 Others pending. 
 
ROCK DRILLS. 
 
 159 
 
i6q 
 
 ROCK DRIUS. 
 
ROCK DRIW^. l6l 
 
 Knowing that the average man who runs a rock drill is not 
 a skilled mechanic, in the construction of tbe RIX DRILL the 
 aim has been to produce a valve motion which could not by any 
 means whatever go wrong or fail to go together, providing no 
 piece should be omitted. To accomplish this the entire VALVE 
 MOTION is arranged symmetrical to a line perpendicular to the 
 line of motion and passing through the center of the exhaust. 
 This permits the main valve spool, the caps, plates, and buf- 
 fers, the auxiliary valve, the whole valve chest, or anything per- 
 taining to it, to be reversed in any way, and the result is a 
 proper and complete valve motion, and it also allows the ex- 
 haust to be turned in any direction by simply using an ordinary 
 street elbow. 
 
 All JOINTS on either of these drills are scraped, and there 
 are no gaskets to get out of order. 
 
 One of the most annoying faults about imported rock drills 
 is the rubber buffer, which has to be introduced into both heads 
 in order to prevent accident to the heads by the careless opera- 
 tors. Especially is this true when steam is used, for the rubber 
 rapidly disintegrates and interferes with the proper working of 
 the machine. In both the RIX and the GIANT DRILLS these 
 interior buffers are dispensed with and a SPIRAL SPRING is 
 placed on the back head of the machine which does service for 
 both heads and which never wears out. In fact, a duplicate 
 spring has never been furnished for any of these machines. A 
 flat bow-spring does not accomplish the same result, as it breaks 
 quite readily, and is generally replaced by a solid bar to avoid 
 further difficulty. 
 
 Quite a feature with the GIANT and RIX DRILLS is in the 
 use of the same sized COLUMN, CLAMP, and TRIPOD for any 
 of the machines. The result is that a mine need purchase but 
 one sized mounting, and any drill will fit thereon. A 3-inch drill 
 may be taken out of the heading if hard rock is encountered 
 and a larger machine attached to the same clamp at once, 
 without any re-setting of the column, and this is also found 
 especially valuable in upraising work. 
 
 All of the machines above the 2^-inch size use the same 
 hose and the same COUPLINGS, and any of the machines will 
 take drill steel of any size up to iX-inch, and use any shape 
 bushing. 
 
 The above-named conveniences are of great consideration, 
 and have never failed to commend themselves to intelligent 
 purchasers. It may be urged that a COLUMN which is large 
 enough in diameter to properly carry a 3-inch machine is too 
 small for a 3^ -inch drill. This may be true where the 
 machines stand away from the column to any extent and 
 where they are being racked by lost motion and where they 
 reciprocate slowly, but with the GIANT and RIX machines, 
 which hug the column closely and which have no lost motion on 
 account of the DOUBLE FEED NUT DEVICE, and which 
 
l62 
 
 ROCK DRII^S. 
 
 Fig. 63.— RIX ROTATING DEVICE. Patented. 
 
ROCK DRILLS. J 63 
 
 reciprocate fully fifteen percent faster than any other drill, it is 
 not necessary, and therefore a purchaser need not pay for that 
 which he does not require. 
 
 The ROTATING MOTION in these drills is one of the finest 
 features about them, and it fulfils perfectly every requirement. 
 From the sketch, it will be seen that it consists of an internal 
 ratchet engaging with swinging pawls carried in the head of 
 the rotating bar. A very slight spring pressure serves to 
 throw them into contact, when by the nature of the angles of 
 adjustment the pawls will be carried into a pinch that cannot 
 slip or be broken. All the angles in the ratchet and pawls are 
 right angles ; therefore the ratchet may be reversed after it is 
 worn on one side, and equal service be given to the other. 
 
 The same is true of the PAWLS, and being symmetrical, it 
 does not matter which side or end is first presented, for duty. 
 
 This feature of having nearly all of the moving parts sym- 
 metrical and reversible is quite a feature in the construction of 
 these machines and is of immense assistance in the cost of 
 operating and convenience, as well as being very useful in 
 emergency. 
 
 It is not necessary that these PAWLS SHOULD BE REVER- 
 SIBLE, — a fact which has been taken advantage of by an East- 
 ern drill manufacturer — and the owners of the patent on this 
 rotating device desire us to state for them and in their behalf 
 that the INTRODUCTION OF THIS SWINGING PAWL IN 
 A DRILL ROTATING MOTION, WHERE THE PAWL IS 
 SYMMETRICAL OR NON-SYMMETRICAL, IS AN IN- 
 FRINGEMENT UPON THEIR RIGHTS, AND ANY PAR- 
 TIES USING SAME WITHOUT PROPER LICENSE FROM 
 THESE ORIGINAL PATENTEES WILL BE ENJOINED 
 FROM USING SAME AND BE ALSO REQUIRED TO PAY 
 DAMAGES. 
 
 All rock drills, of either the RIX or the GIANT pattern, 
 which use compressed air as a motive power, are supplied with a 
 FRONT HEAD, which has no stuffing box but which is inter- 
 nally packed with a leather-cupped ring, which is absolutely per- 
 fect in its action. This is an old method of packing a drill piston 
 rod, having been used about twenty years ago, and is now used 
 by other drill makers occasionally. It has, however, never 
 given any great amount of satisfaction and never was absolutely 
 tight, for the air had always escaped through the split in the 
 ring, and the cup was not the proper shape. 
 
 The LEATHER CUPS, however, for these drills are made 
 by a machine especially constructed to shape the joints, form- 
 ing a perfect interior and exterior cylinder, one-eighth of an 
 inch apart. There is no split at all, and they remain perfectly 
 tight under any pressure and last about four months under 
 continuous wear. 
 
]64 
 
 ROCK DRILLS. 
 
 #*. 
 
ROCK DRII^S. 
 
 I6 5 
 
 Fig. 65.— GIANT DRILL, Mounted 011 Tripod. 
 
l66 ROCK DRII^S. 
 
 The FEED NUT DEVICE is another special feature of both 
 of these machines. All other rock drills are provided with a 
 single feed nut, and this together with the feed screw naturally 
 wears rapidly. After wearing so that the lost motion becomes 
 apparent, it acts materially against the cutting power of the 
 machine, as well as being noisy and a fruitful source of acci- 
 dents, for at every stroke of the ordinary rock drill it thumps 
 back and forth in its cage to the full extent of this lost motion. 
 The only remedy is a new nut and screw. 
 
 In the RIX and GIANT DRILLS, by means of the double 
 feed nut all trouble of this kind is avoided. One of the nuts 
 is secured to the cylinder of the drill in a manner similar to all 
 drills; the other has a toothed edge and may be turned to the 
 extent of a tooth at a time as the feed screw wears. This 
 allows the front edge of the feed screw thread to work on the 
 back edge of the first feed nut thread, and the back edge of 
 the feed screw thread to work on the front edge of the second 
 feed nut thread, thus furnishing the feed screw with practically 
 one perfect-fitting nut all the time, and in this manner, a feed 
 screw may be worn until its threads break away without any 
 lost motion being apparent in the drill. It needs no comment 
 to show that the drill uses FEW FEED SCREWS, in fact, the 
 life of the screw is not less than TWO YEARS in any case, 
 barring accident. 
 
 The clamp is a powerful one, very light, a perfect DROP 
 STEEL FORGING, and has but ONE BOLT, so that it is easy 
 to work, and being very light can be operated in half the time 
 that it requires for some others. This clamp has been in con- 
 tinuous use for twenty years and has proved itself to be 
 thoroughly reliable. 
 
 The PISTON of both the RIX and the GIANT DRILLS is so 
 arranged that it will receive any size bushing up to ij^ inches. 
 The drills are always fitted with an octagon bushing, unless 
 otherwise ordered, for that style receives the steel just as it is 
 manufactured and thus saves the expense of TURNING THE 
 SHANKS as well as doing away with the annoying breakage 
 which happens when the ends of the steel are turned. The full 
 size octagon is none too strong to withstand the powerful blows 
 delivered by these machines and a much lower pressure must 
 be used if the drill shanks are turned. 
 
 The COLUMN MOUNTINGS used for these machines are 
 similar to those used by other makers, excepting that only one 
 size is manufactured. Other sizes are made and kept in stock to 
 satisfy the ideas of customers who have been used to other 
 drills, but the increased size is not necessary to a satisfactory 
 working of the machines. 
 
 The TRIPOD is one furnished with universal joints to its 
 
ROCK DRT1XS. 167 
 
 Fig. 66.— 23^ -inch RIX DRIIyl, Mounted on Tripod. 
 
l68 ROCK DRIU,S. 
 
 legs and has stood the test of twenty years of good service. A 
 clamp is always used with this tripod; this enables the head of 
 the tripod to be used as a short column, so that the drill may 
 be given a lateral motion of about four inches, a feature which 
 is very useful in drilling holes in uneven rock full of cracks or 
 fissures, or which from any cause deflects the drill steel. 
 
 In the RIX DRILL the VALVE MOTION is in every way 
 superior to anything which now operates a rock drill, and one 
 of the most noticeable things about the drill when it is running 
 alongside of other makes, is the wonderful regularity of its 
 motion reciprocating as evenly as a steam engine, and deliver- 
 ing a blow with much greater velocity than any other machine, 
 and also more of them. Most of the drill makers make a claim 
 for an uncushioned blow, and that the valve does not change 
 until after the blow is struck, but these are not facts which are 
 consistent with another claim which they make; viz., that 
 their machines are the only ones which make a variable stroke. 
 None of the standard makers claim that the reversing of the 
 valve is dependent upon the striking of the rock, yet their 
 statements would lead one to that conclusion. Every one 
 knows that the drills will run at quite a speed without striking 
 even the front head, and any one who examines their valve 
 mechanism will perceive that it is practically the same for both 
 the front and back stroke, and they certainly would not like 
 the inference drawn that the piston must strike the back head 
 in order to reverse the valve. 
 
 The fact is that all the standard drills strike a cushioned 
 blow, and the valve is always reversed before the drill strikes 
 the rock, and this must necessarily be so in order to allow for 
 a variable stroke, and to provide for a sufficient number of 
 strokes. Drills have been used in Europe, and many experi- 
 mental ones made here have been so constructed that the valve 
 changed after the blow was struck. This, undoubtedly, gives 
 the heaviest blow, but the number of the strokes is so limited 
 that can be delivered in a minute, that the machine could not 
 begin to do the work an ordinary rock drill can do. The 
 more the cushion in a drill, the faster it will reciprocate, and 
 the less effective will be the blow. The less the cushion, the 
 heavier the blow and the less the number of strokes. The 
 shorter the working stroke, the greater the number of strokes 
 and the less the blow, and the less the working pressure, the 
 less the number of strokes and the less the force of the blow. 
 Therefore, in fashioning a rock drill, the result must be a 
 mean between these four relations, which shall give the best 
 results. In other words, the length of stroke, the amount of 
 cushion, the number of strokes, and the pressure used, must be 
 so adjusted with relation to each other that the best result-will 
 be produced — allowing, of course, that the diameter of the 
 cylinder has been determined. All these problems have been 
 very satisfactorily solved in both the RIX and the GIANT 
 machines. 
 
ROCK DRIIyl^S. 169 
 
 The VALVE MOTION of the GIANT DRILL is one which is 
 operated directly from the piston by mechanical contact, and 
 this drill is manufactured to satisfy the beliefs of some drill 
 users that a machine of this construction is better than a ma- 
 chine operating with the auxiliary valve motion, such as the 
 RIX. 
 
 The sizes of the GIANT DRILL are made to alternate with 
 the sizes of the RIX, so that the following Tables of sizes and 
 capacities, which represent a complete range, are offered to 
 the public: 
 
170 
 
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172 ROCK DRILLS. 
 
 DUPLICATE PARTS OF THE RIX 
 ROCK DRILLS. 
 
 i — Rotating Nut. 
 
 2 — Piston, bare. 
 
 3 — Piston Ring. 
 4-5 — Sleeve. 
 
 6 — Feed Nut (adjustable). 
 
 7 — Feed Nut (plain). 
 
 8— Yoke for Feed Nuts. 
 
 9 — Lower Head. 
 
 10 — Leather Crimp for Lower Head, 
 ir — Chuck Bolts and Nuts. 
 12 — Chuck Bushing. 
 13 — Chuck Key. 
 14 — Steam Chest, bare. 
 15 — Main Valve. 
 16 — Steam Chest Cap. 
 17— Steel Cushion Plate. 
 18 — Rubber Cushion. 
 19 — Auxiliary Valve. 
 20 — Auxiliary Valve Spring. 
 21 — Auxiliary Valve Claw. 
 22 — Oil Screw. 
 23— Yoke for Head Bolts. 
 24 — Head Spring. 
 25 — Cover for Ratchet Ring. 
 26 — Bottom Plate for Ratchet Ring. 
 27 — Rotating Bar. 
 28 — Cylinder, bare. 
 29— Guide Block. 
 30— Shell Strip. 
 31 — Cylinder Bolts. 
 32— Shell Bolt. 
 33 — Feed Screw. 
 34— Yoke for Shell Bolts. 
 35 — Feed Screw Handle (brass). 
 36 — Pawl. 
 37 — Ratchet Ring. 
 38 — Pawl Spring. 
 39 — Shell without Strips or Yoke. 
 40 — Clamp Wrench. 
 41— Steam Chest Wrench. 
 42 — Chuck Wrench. 
 
ROCK DRILLS. 
 
 173 
 
 DUPLICATE PARTS OF THF, R1X ROCK DRILL. 
 
ROCK DRILLS. 
 
 duplicate; parts of the giant DRir.r y . 
 
ROCK DRII^S. 175 
 
 DUPLICATE PARTS OF THE GIANT 
 ROCK DRILLS. 
 
 1 — Rotating Nut. 
 
 2 — Piston, bare. 
 
 3 — Piston Ring. 
 
 4 — Valve Chest. 
 
 5 — Valve Chest Cover. 
 
 6 — Feed Nut (adjustable). 
 
 7 — Feed Nut (plain). 
 
 S— Yoke for Feed Nuts. 
 
 9 — Lower Head. 
 
 10 — Leather Crimp for Lower Head. 
 11 — Chuck Bolts and Nuts. 
 12 — Chuck Bushing. 
 13 — Chuck Key. 
 14 — Valve. 
 15 — Valve Rocker. 
 16 — Piston Ring Spring. 
 17 — Rocker Pin. 
 22 — Oil Screw. 
 23 — Yoke for Head Bolts. 
 24 — Head Spring. 
 25 — Cover for Ratchet Ring. 
 26— Bottom Plate for Ratchet Ring. 
 27 — Rotating Bar. * 
 
 28 — Cylinder, bare. 
 30— Shell Strip. 
 31 — Cylinder Bolts. 
 32— Shell Bolt. 
 33 — Feed Screw, 
 34— Yoke for Shell Bolts. 
 35 — Feed Screw Handle (brass). 
 36 — Pawl. 
 37 — Ratchet Ring. 
 38— Pawl Ring. 
 
 39 — Shell without Strips or Yoke. 
 40 — Clamp Wrench. 
 41 — Steam Chest Wrench. 
 42 — Chuck Wrench. 
 
176 ROCK DRILLS. 
 
 RIX PLUG AND FEATHER DRILL. 
 
 The Rix Plug and Feather Drill, a cut of which appears in 
 Fig. 66^, is the smallest drill manufactured by this Company. 
 It has a two-inch diameter cylinder, from four to five inch 
 stroke, and makes from seven hundred to nine hundred strokes 
 per minute. It is designed for drilling small holes about one 
 inch in diameter and for depths up to twenty-four inches. 
 
 For quarry work it is mounted on a tripod, as shown in the 
 cut, and for mining purposes it has the usual column mountings. 
 The tripod is one which gives a wide range of movement. 
 
 The Drill itself weighs about 65 lbs. and is extremely con- 
 venient to handle. It is generally used with seven-inch steel 
 and the chuck is made tapering to take the end of the steel in 
 similar to the way a twist drill fits in its socket. This will be 
 found most convenient in the handling of these small drills. 
 
 This machine will tfe found very handy for many ranges of 
 work, including the driving of wooden pins in caison, scow, or 
 dry dock constructions where the pins have to be driven from 
 underneath the work being constructed. 
 
 In the use of air it is very economical, taking about twenty- 
 five cubic feet of free air per minute. 
 
ROCK DRILLS. 
 
 177 
 
 u 
 
 Fig. 65y 2 — RIX PLUG AND FEATHER DRII,!,. 
 
A FEW GENERAL HINTS. 
 
 Buy a Compressor larger than you need. 
 Buy one which is economical. 
 Run it slow. 
 
 Put in good foundations. 
 Have a spare boiler if you can afford it. 
 Have a clean, ship-shape engine-room. 
 Cover all of your steam-pipes. ' 
 Provide large air-pipes. 
 
 A generous sized receiver will come in handy. 
 Make as few short turns as possible in the air-pipe. 
 Use a good cylinder lubricant. 
 Circulate ample water in the air cylinder jackets. 
 Have some extra compressor valves, and change them fre- 
 quently. 
 Put in one or two shut-off valves in your air-pipe. 
 Keep the receiver properly drained. 
 Buy a rock drill of a size best suited to the work, and don't buy 
 
 any unless your mind is made up to do it properly. 
 Have plenty of steel, so your men are not running for drill-bits 
 
 all the time. 
 Get a good blacksmith, and have him keep both ends of the 
 
 steel properly sized. 
 Drill good-sized holes, for the powder does better work at 
 
 the bottom of a hole. 
 Have an intelligent workman to run the drill. 
 Have an extra drill always ready in the shop, and you will find 
 
 less breakages and accidents occur to those in use. 
 Oil the machine well before starting. 
 See that all the nuts are tight. 
 Be sure that no dirt is in the hose before it is attached to the 
 
 machine. 
 Keep the column well jacked up, and have blocks of wood top 
 
 and bottom. 
 Start the holes on the shortest stroke of the machine, and 
 
 gradually lengthen out the stroke as the hole deepens. 
 Feed the machine so that the piston will clear the front head. 
 
A FKW GENERAI, HINTS. 179 
 
 In soft ground, make haste slowly. 
 
 If the steel gets stuck in the hole, strike it sharply until it 
 releases. 
 
 Never strike the chuck. 
 
 Do not screw up too hard on the chuck-nuts or clamp-bolts, 
 for it is perfectly possible to break them. 
 
 Keep your bushings in good order. 
 
 A bit of cast-iron or iron borings thrown into a fissured hole 
 will help it out. 
 
 A piece of broken drill-bit will often cause a hole to run out. 
 
 Drill wet holes whenever you cau. 
 
 A leaky stuffing-box will often prevent the piston pulling out 
 from a tight hole. 
 
 Never run the drill against the head to throw the steel out. 
 
 Do not expect the drill to furnish brains to run itself. 
 
 Do not expect it to run without repairs. 
 
 Carry as high a pressure as possible when your rock is hard, 
 and calculate always that the repairs will vary, as the pres- 
 sure and also the work done. 
 
 Remember that a rock drill is an engine, after all, and the 
 fewer times it goes over the dump, or is dropped off the 
 column, or is blasted upon, the longer it will last. 
 
 Generous and faithful oiling will help a machine wonderfully. 
 
 Use a good steam-trap when using a drill in a quarry. 
 
 A tripod must be securely set to do good work. 
 
 The same kind of drill-points do not work equally well in 
 different kinds of rock. 
 
i8o 
 
 ROCK DRILLS. 
 
 Fig. 67.— Column with Arm 
 
 Fig. 68.— Plain Column. 
 
 Column Mountings for Rock Drills. Made in any length. One price for 
 all lengths under ten feet. 
 
ROCK DRII^S. 
 
 181 
 
AIR RECEIVERS. 
 
 In conjunction with an air compressor there is generally- 
 attached a reservoir called an air receiver. The purpose of this 
 is twofold: to collect the moisture which is condensed from the 
 air after it is compressed, and also to afford a sufficient volume 
 to receive the intermittent discharges from the compressor, and 
 reduce them to a continuous flow in the pipes leading from the 
 receiver. 
 
 The ordinary receiver is fitted with an air gauge, a safety 
 valve, and a valve to draw off the moisture. These are arranged 
 as shown in the cut herewith attached. 
 
 Our reservoirs are made of homogeneous steel, with bumped 
 heads, of a sufficient thickness to be tight at 125 lbs. cold 
 water pressure, for all ordinary plants. We prefer bumped 
 heads because bracers are not then necessary. We put three 
 cast iron feet on one end of the receiver for it to stand upon, 
 and sufficiently high to permit drawing off the entrained water 
 water easily, above the floor line. 
 
 We are frequently asked where is the proper place for 
 the receiver — at the compressor or in the mine ? We reply, 
 both. There never was too much receiver capacity on any 
 plant. We do not believe it essential to have a very large 
 receiver near the compressor, providing there is an oppor- 
 tunity to place one further along the pipe. About fifteen 
 times the cylinder capacity would, in all ordinary cases, keep 
 the gauge steady at the compressor. It would be a great 
 benefit to systems having medium or small size pipes to 
 have as large a receiver capacity at or near the point where 
 the air is used, and especially is this the case where hoisting 
 engines are drawing from the air pipes. It requires no engi- 
 neering knowledge to see that if air receivers could be made 
 large enough to diffuse the intermittent work into an average 
 draw on the pipe leading from the compressor, that the com 
 pressor need be only large enough for the average work, whereas 
 ordinarily it must be large enough for the maximum work, and 
 consequently uneconomical. 
 
 It is not generally practicable to have reservoirs so large, 
 however, but a reasonable approach can be made to this capa- 
 city without much expense. We have known compressors to 
 do 25 per cent more useful work by putting receivers near the 
 point where the air is to be used, and where numerous bends 
 and elbows are required in the main pipe. 
 
 When air is drawn too fast through the main pipe, causing 
 a reduction, of pressure, the increase of volume due to the loss 
 pressure causes quite a marked increase in all the frictional 
 losses through the system. We therefore advise receivers at 
 both ends of the line, the smaller ones near the compressor, and 
 this is independent of the amount of storage capacity in 
 the pipe. 
 
AIR RECEIVERS. 
 
 DIMENSIONS OF AIR RECEIVERS. 
 
 Diameter, inches 30 30 36 36 36 42 
 
 Height, feet 6 8 8 io 12 8 
 
 Thickness of Shell, inches . }( % % % % }( 
 
 Thickness of Heads, inches. Xe s At Y& Y% % % 
 
 « 
 
 Weight 700 900 1200 1400 1600 1800 
 
 No. of 3>(-i n ch Drills Re- 
 ceiver is suitable for 11 2 3 4 5 
 
 Diameter, inches 42 42 42 48 48 48 
 
 Height, feet 10 12 16 10 12 j6 
 
 Thickness of Shell, inches. % % % y it s / lt c / t 
 
 Thickness of Heads, inches Y& Y& Ys yU %e Yit 
 
 Weight 1900 2000 2100 2400 2900 3400 
 
 No. of 3X-inch Drills Re- 
 ceiver is Suitable for S 10 12 12 15 20 
 
AIR RECEIVERS. 
 
 toxccooooooo oooo o o c 
 
 (puroooooooo o o qoooooooooooqcchu 
 
 <mmxoooooooooo oooooooooocaJS 
 
 ooo ooo ooooooooc 
 
 Verticav. a»r Receiver 
 
AIR RECEIVERS. 
 
 I8 5 
 
i86 
 
 DRILL BITS AND HOSK COUPLINGS. 
 
 SPECIAL BLACKSMITH TOOLS FOR 
 DRILL BITS. 
 
 Fig. 72. Fig. 73- Kg- 74- Fig. 75- Fig- I 6 - 
 
 Sow. Dolly. Spreader. Flatter. Swedge. 
 
 RIX PATENT HOSE COUPLINGS- 
 
 This coupling 
 is the only coup- 
 ling which will 
 stay on a hose 
 under all condi- 
 tions of use. They 
 have been used 
 successfully at 600 
 lbs. per square 
 inch, and are per- 
 fectly reliable. 
 The nature of the 
 coupling is such 
 
 Fig- 77- 
 
 that it is rigidly 
 connected to the 
 hose, and nothing 
 but the tearing away 
 of the hose itself 
 will separate it from 
 the coupling. 
 
 Fig. 78. 
 
 SIZES AS FOLLOWS: 
 
 For i-inch 4 or 5 ply Hose. 
 For 3^-inch 4 or 5 ply Hose. 
 For 2-inch 4 or 5 ply Hose. 
 
LUBRICATORS AND LUBRICANTS. 187 
 
 LUBRICATORS AND LUBRICANTS. 
 
 All of our Compressors for ordinary pressures, that is, up to 
 200 lbs. per square inch, are provided with the Ellis Sight 
 Feed Lubricator for the air cylinders. This, or some similar 
 device, is the only method for certain and economical lubrica- 
 tion. The ordinary oil cup delivers its entire contents in a 
 short time, and there is no means of knowing when it requires 
 filling, except by opening it. For all of our crank pins we use 
 the Economy Oiler, which feeds only when the compressor is 
 running. We have reports stating that one filling of one of 
 these 4^2-ounce oilers on the crank of a 10-inch compressor 
 lasted four weeks of continuous run. 
 
 The ordinary cylinder lubricating oils will not suffice for 
 single stage dry compressor cylinders, where the compression 
 is almost adiabatic from 200 degrees to 400 degrees, depending 
 on the pressures. Poor oils are decomposed at these tempera- 
 tures, and form combustible gases which may explode with 
 dangerous effect. There was an explosion of this kind in the 
 Idaho Mine, Grass Valley, a number of years ago, which 
 destroyed several hundred feet of 6-inch air pipe in the shaft. 
 Oils of at least 600 degrees fire test should be used. Any oil 
 which burns on the outlet valves, leaving a hard, black, 
 rubber-like substance, is not fit to be used. 
 
 Some engineers mix kerosene or coal oil with their cylinder 
 lubricant, to cut the deposit and dirt from their valves, but it 
 is a dangerous practise and will lead to accident, because the 
 fire test of coal oil does not ordinarily exceed 175 degrees Fahr. 
 
 We carry in stock special oils for Compressors and Rock 
 Drills, known as 
 
 RIX COMPRESSOR OIL. 
 
 RIX ROCK DRILL, OIL- 
 
l88 AIR CYLINDER OIL CUP. 
 
 ELLIS AIR CYLINDER OIL CUP. 
 
 The cylinders of Air Compressors are generally lubricated 
 with a plain oil cup, and a great deal of difficulty is encoun- 
 tered in making this feed steady enough for practical purposes. 
 Hither the cup will not feed at all, or it will feed its entire 
 contents in a few minutes. The 
 lubricator which we are offer- 
 ing is a special lubricator, de- 
 signed so that the pressure of 
 air in the cylinder will force the 
 oil through a small opening, 
 which may be regulated, into 
 the cylinder. The drops may 
 be regulated as slow or as fast 
 as necessary, and are made to 
 drop in plain view, so as to 
 make it a drop sight lubricator, 
 something entirely new for air 
 compressing cylinders and 
 which we feel sure will be a 
 great relief and satisfaction to 
 ^' '9- those who have plants equipped 
 
 with this class of machinery. It goes without saying that a 
 lubricator of this kind will use about one-half of the oil that the 
 ordinary lubricators require. 
 
 Made in either brass or nickel-plated finish, in the follow- 
 ing sizes: j^-pint, ^-pint, ^-pint, i-pint, i-quart. 
 
APPENDIX. 
 
 USEFUL TABLES, 
 
 TO BE USED IN THE CALCULATION OF 
 
 COMPRESSED AIR PROBLEMS. 
 
 The following tables and data in general will be found 
 useful in the calculation of Compressed Air Problems. These 
 tables have been taken from Kent's Hand Book, from The 
 Pelton Water Wheel Company's catalogue, and from Carnegie 
 Phipps & Co.'s catalogue, and we desire to express to the 
 publishers of these volumes our thanks. 
 
USEFUL TABLES. 
 
 CIRCUMFERENCES AND AREAS OF CIRCLES 
 
 Advancing by Eighths. 
 
 191 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 1/64 
 
 .04909 
 
 .00019 
 
 2 % 
 
 7 4613 
 
 4.4301 
 
 G % 
 
 19.242 
 
 29.465 
 
 1/32 
 
 .09818 
 
 .00077 
 
 7/16 
 
 7.6576 
 
 4.6064 
 
 y 4 
 
 19.6:35 
 
 30.680 
 
 3/64 
 
 .14726 
 
 .00173 
 
 14 
 
 7.8540 
 
 4.9087 
 
 20.028 
 
 31.919 
 
 1/16 
 
 .19635 
 
 .00307 
 
 9/16 
 
 8.0503 
 
 5.1572 
 
 8 
 
 20.420 
 
 33.183 
 
 3/32 
 
 .29452 
 
 .00690 
 
 % 
 
 8.2467 
 
 5.4119 
 
 20.813 
 
 34.472 
 
 5/32 
 
 .39270 
 
 .01227 
 
 11/16 
 
 8.4430 
 
 5.0727 
 
 8 
 
 21 206 
 
 35 785 
 
 .49087 
 
 .01917 
 
 H 
 
 8.6394 
 
 5.9396 
 
 21.598 
 
 37. 122 
 
 3/16 
 
 .58905 
 
 .02761 
 
 13/16 
 
 8.8357 
 
 6.2126 
 
 7. 
 
 21.991 
 
 38.485 
 
 7/32 
 
 .C8722 
 
 .03758 
 
 % 
 
 9.0321 
 
 6.4918 
 
 % 
 
 22.384 
 
 39.871 
 
 
 
 
 15/16 
 
 9.2284 
 
 6.7771 
 
 8 
 
 22.776 
 
 41.282 
 
 H 
 
 .78540 
 
 .01909 
 
 
 
 
 23.169 
 
 42.718 
 
 9/32 
 
 .88357 
 
 .06213 
 
 3. 
 
 9.4248 
 
 7.0686 
 
 H 
 
 23.562 
 
 44.179 
 
 5/16 
 
 .98175 
 
 .07670 
 
 1/16 
 
 9 6211 
 
 7.3662 
 
 % 
 
 23.955 
 
 45.664 
 
 11/32 
 
 1.0799 
 
 .09281 
 
 % 
 
 9.8175 
 
 7.6699 
 
 8 
 
 24.347 
 
 47.173 
 
 % 
 
 1.1781 
 
 .11045 
 
 3/16 
 
 10.014 
 
 7.9798 
 
 24.740 
 
 48.707 
 
 13/32 
 
 1.2763 
 
 .12962 
 
 Ya 
 
 10.210 
 
 8.2958 
 
 8. 
 
 25.133 
 
 50.265 
 
 7/16 
 
 1.3744 
 
 .15033 
 
 5/16 
 
 10.407- 
 
 8.6179 
 
 % 
 
 25.525 
 
 51.849 
 
 15/32 
 
 1.4726 
 
 . 17257 
 
 % 
 
 10.603 
 
 8.9462 
 
 k 
 
 25.918 
 
 53.456 
 
 
 
 
 7/16 
 
 10.799 
 
 9.2806 
 
 
 26.311 
 
 55.088 
 
 H 
 
 1 5708 
 
 .19635 
 
 ¥1 
 
 10.996 
 
 9.6211 
 
 i£ 
 
 26.704^ 
 
 56.745 
 
 17/32 
 
 1.6690 
 
 .22166 
 
 9/16 
 
 11.192 
 
 9:9678 
 
 §8 
 
 27.096 
 
 58.426 
 
 9/16 
 
 1.7671 
 
 .24850 
 
 % 
 
 11.388 
 
 10.321 
 
 § 
 
 27.489 
 
 60.132 
 
 19/32 
 
 1-.8653 
 
 .27688 
 
 11/16 
 
 11.585 
 
 10.680 
 
 27.882 
 
 61.862 
 
 21/32 
 
 1.9635 
 
 .30680 
 
 ¥x 
 
 11.781 
 
 11.045 
 
 9. 
 
 28.274 
 
 63.617 
 
 2.0617 
 
 .33824- 
 
 13/16 
 
 11.977 
 
 11.416 
 
 H 
 
 28.667 
 
 65.397 
 
 11/16 
 
 2.1598 
 
 .37122 
 
 % 
 
 12.174 
 
 11.793 
 
 & 
 
 29.060 
 
 67.201 
 
 23/32 
 
 2.2580 
 
 .40574 
 
 15/16 
 
 12.370 
 
 12.177 
 
 
 29.452 
 
 69.029 
 
 
 
 
 4. 
 
 12.566 
 
 12.566 
 
 t<g 
 
 20.845 
 
 70.882 
 
 H 
 .25/32 
 
 2.3562 
 
 .44179 
 
 1/16 
 
 12.763 
 12.959 
 
 12.962 
 
 rk 
 
 . 30.238 
 
 72.760 
 
 2.4544 
 
 .47937 
 
 % 
 
 13.364 
 
 % 
 
 30.631 
 
 74.662 
 
 13/16 
 
 2.5525 
 
 .51849 
 
 3/16 
 
 13.155 
 
 13.772 
 
 vk 
 
 31.023 
 
 76.589 
 
 27/32 
 
 2.6507 
 
 .55914 
 
 M 
 
 13.352 
 
 14.186 
 
 10. 
 
 31.416 
 
 78.540 
 
 % 
 
 2.7489 
 
 .60132 
 
 5/16 
 
 13.548 
 
 14,607 
 
 ft 
 
 31.809 
 
 80.516 
 
 20/32 
 
 2.8471 
 
 .64504 
 
 % 
 
 13.744 
 
 15.033 
 
 32.201 
 
 82.516 
 
 15/16 
 
 2.9452 
 
 .69029 
 
 7/16 
 
 13.941 
 
 15.466 
 
 % 
 
 32.594 
 
 84.541 
 
 31/32 
 
 3.0434 
 
 .73708 
 
 H 
 
 14.137 
 
 15.904 
 
 
 32.987 
 
 86.590 
 
 
 
 
 9/16 
 
 14.334 
 
 16.349 
 
 % 
 
 33.379 
 
 88.664 
 
 1- 
 
 3.1416 
 
 .7854 
 
 % 
 
 14.530 
 
 16.800 
 
 8 
 
 33.772 
 
 90.763 
 
 1/16 
 
 3.3379 
 
 .8866 
 
 11/16 
 
 14.726 
 
 17.257 
 
 34.165 
 
 92.886 
 
 H 
 
 3.5343 
 
 .9940 
 
 ¥4 
 
 14.923 
 
 17.728 
 
 11. 
 
 34.558 
 
 95.033 
 
 3/16 
 
 3.7306 
 
 1.1075 
 
 13/16 
 
 15.119 
 
 18.190 
 
 % 
 
 34.950 
 
 97.205 
 
 H 
 
 3.9270 
 
 1.2272 
 
 % 
 
 15.315 
 
 18.665 
 
 H 
 
 35.343 
 
 99.402 
 
 5/16 
 
 4.1233 
 
 1.3530 
 
 15/16 
 
 15 512 
 
 19.147 
 
 % 
 
 35.736 
 
 101.62 
 
 % 
 
 4.3197 
 
 1.4849 
 
 5. 
 
 15.708 
 
 19.635 
 
 VH 
 
 36.128 
 
 103.87 
 
 7/16 
 
 4.5160 
 
 1.6230 
 
 1/16 
 
 15.904 
 
 20.129 
 
 8 
 
 36.521 
 
 106.14 
 
 Vi 
 
 4.7124 
 
 1.7671 
 
 % 
 
 16.101 
 
 20.629 
 
 36.914 
 
 108.43 
 
 9/16 
 
 4.9087 
 
 1.9175 
 
 3/16 
 
 16.297 
 
 21.135 
 
 % 
 
 37.306 
 
 110.75 
 
 % 
 
 5.1051 
 
 2.0739 
 
 M 
 
 10.. 493 
 
 21 648 
 
 12. 
 
 37.699 
 
 113.10 
 
 11/16 
 
 5.3014 
 
 2.2365 
 
 5/16 
 
 16.690 
 
 22.166 
 
 % 
 
 38.092 
 
 115.47 
 
 ■H 
 
 5.4978 
 
 2.4053 
 
 % 
 
 16.886 
 
 22.691 
 
 H 
 
 • 38.485 
 
 117.86 
 
 13/16 
 
 5.6941 
 
 2.5802 
 
 7/16 
 
 17.082 
 
 23.221 
 
 % 
 
 38.877 
 
 120.28 
 
 % 
 
 5.8905 
 
 2.7612 
 
 }4 
 
 17.279 
 
 23.758 
 
 
 39.270 
 
 122.72 
 
 15/16 
 
 6.0868 
 
 2.9483 
 
 9/16 
 
 17.475 
 
 24.301 
 
 vk 
 
 39.663 
 
 125.19 
 
 
 
 
 % 
 
 17.671 
 
 24.850 
 
 8 
 
 40.055 
 
 127.68 
 
 2. 
 
 6.2832 
 
 3.1416 
 
 11/16 
 
 17.868 
 
 25.406 
 
 40.448 
 
 130.19 
 
 1/16 
 
 6.4795 
 
 3.3410 
 
 u 
 
 18.064 
 
 25.967 
 
 13 
 
 40.841 
 
 132.73 
 
 k 
 
 6.6759 
 
 3.5466 
 
 13-16 
 
 18.261 
 
 26.535 
 
 
 41.233 
 
 135.30 
 
 3/16 
 
 6.8722 
 
 3.7583 
 
 % 
 
 18.457 
 
 27.109 
 
 M 
 
 41.626 
 
 137.89 
 
 l A 
 
 7.0686 
 
 3.9761 
 
 15-16 
 
 18.653 
 
 27.688 
 
 % 
 
 42.019 
 
 140.50 
 
 .5/16 
 
 7.2649 
 
 4.2000 
 
 e 
 
 18.850 
 
 28.274 
 
 M&i 
 
 . 42.412 
 
 143.14 
 
192 
 
 USEFUL TABLES. 
 
 Diam. 
 
 Circum . 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area.. 
 
 Diam 
 
 Cireum. 
 
 Area. 
 
 1 
 
 42.804 
 
 145.80 
 
 21% 
 
 68.722 
 
 375.83 
 
 30% 
 
 94.640 
 
 712.76 
 
 43.197 
 
 148 49 
 
 32 
 
 69.115. 
 
 380.13 
 
 
 95.083 
 
 718.69 
 
 43.590 
 
 151.20 
 
 H 
 
 69.508 
 
 384 46 
 
 78 
 
 95.426 
 
 724 64 
 
 14. 
 
 43.982 
 
 153.94 
 
 S 
 
 69.900 
 
 388.82 
 
 \& 
 
 95.819 
 
 730.62 
 
 1^ 
 
 44.375 
 
 156 70 
 
 70.293 
 
 393.20 
 
 78 
 
 96.211 
 
 736.62 
 
 J4 
 
 44.768 
 
 159.48 
 
 
 70.686 
 
 397.61 
 
 % 
 
 96.604 
 
 742.64 
 
 % 
 
 45.160 
 
 162.30 
 
 % 
 
 71.079 
 
 402.04 
 
 vi 
 
 96.997 
 
 74869 
 
 % 
 
 45.553 
 
 165.13 
 
 1 
 
 71 471 
 
 406.49 
 
 31. 
 
 97.389 
 
 754.77 
 
 78 
 
 45.946 
 
 167.99 
 
 71.864 
 
 410.97 
 
 % 
 
 97.782 
 
 760.87 
 
 % 
 
 46.338 
 
 170.87 
 
 28. 
 
 72.257 
 
 415 48 
 
 jl 
 
 98.175 
 
 766 99 
 
 46.731 
 
 173.78 
 
 ^ 
 
 72.649 
 
 420.00 
 
 H 
 
 98.567 
 
 773.14 
 
 15 
 
 47.124 
 
 176 71 
 
 H 
 
 73 042 
 
 424.56 
 
 
 98.960 
 
 779.31 
 
 1 
 
 47.517 
 
 179.67 
 
 
 73.435 
 
 429.13 
 
 7& 
 
 99.353 
 
 785 51 
 
 47.909 
 
 182.65 
 
 Lg 
 
 73.827 
 
 433.74 
 
 % 
 
 99.746 
 
 791 73 
 
 
 48.302 
 
 185.66 
 
 % 
 
 74.220 
 
 438.36 
 
 % 
 
 100.138 
 
 797 98 
 
 MB 
 
 48.695 
 
 188.69 
 
 % 
 
 74.613 
 
 443.01 
 
 32 
 
 100,531 
 
 804 25 
 
 % 
 
 49.087 
 
 191.75 
 
 % 
 
 75.006 
 
 447 69 
 
 ri 
 
 100.924 
 
 $.0.54 
 
 8 
 
 49.480 
 
 194.83 
 
 24 
 
 75 398 
 
 452.39 
 
 k 
 
 101.316 
 
 816.86 
 
 49.873 
 
 197.93 
 
 % 
 
 75.791 
 
 457.11 
 
 
 101 709 
 
 823.21 
 
 16 
 
 50.265 
 
 201.06 
 
 » 
 
 76.184 
 
 46186 
 
 14 
 
 102.102 
 
 829.58 
 
 & 
 
 50.658 
 
 204.22 
 
 76.576 
 
 466 64 
 
 7B 
 
 102.494 
 
 835.97 
 
 g 
 
 51.051 
 
 207.39 
 
 
 76.969 
 
 471.44 
 
 l 
 
 102.887 
 
 842.39 
 
 
 51.444 
 
 210.60 
 
 7» 
 
 77.362 
 
 476 26 
 
 108.280 
 
 848.83 
 
 L£ 
 
 51.836 
 
 213.82 
 
 % 
 
 77 754 
 
 481.11 
 
 33 
 
 103 673 
 
 855.30 
 
 7& 
 
 52.229 
 
 217.08 
 
 78.147 
 
 485.98 
 
 % 
 
 104.065 
 
 861.79 
 
 n 
 
 52.622 
 
 220.35 
 
 26. 
 
 78.540 
 
 490.87 
 
 I 
 
 104.458 
 
 868.31 
 
 53.014 
 
 223.65 
 
 7& 
 
 78.933 
 
 495 79 
 
 
 104.851 
 
 874.85 
 
 17 
 
 53.407 
 
 226.98 
 
 54 
 
 79.325 
 
 500.74 
 
 Ms 
 
 105.243 
 
 881.41 
 
 ^ 
 
 53.800 
 
 230.33 
 
 9s 
 
 79.718 
 
 505 71 
 
 % 
 
 105 636 
 
 88800 
 
 *4 
 
 54.192 
 
 233.71 
 
 Yi 
 
 80.111 
 
 510.71 
 
 H 
 
 106,029 
 
 894.62 
 
 % 
 
 54.585 
 
 237.10 
 
 7& 
 
 80503 
 
 515.72 
 
 % 
 
 106.421 
 
 901.26 
 
 H 
 
 54.978 
 
 24053 
 
 8 
 
 80 896 
 
 520.77 
 
 34 
 
 106.814 
 
 907.92 
 
 55.371 
 
 243.98 
 
 81.289 
 
 525.84 
 
 I 
 
 107.207 
 
 914.61 
 
 s 
 
 55.763 
 
 247.45 
 
 26. 
 
 81.681 
 
 530.93 
 
 107.600 
 
 921.32 
 
 56.156 
 
 250.95 
 
 I 
 
 82.074 
 
 536.05 
 
 
 107.992 
 
 928.06 
 
 18. 
 
 56.549 
 
 254.47 
 
 82 467 
 
 541.19 
 
 L£ 
 
 108 385 
 
 934.82 
 
 i 
 
 56.941 
 
 258.02 
 
 
 82.860 
 
 546 35 
 
 7ft 
 
 108.778 
 
 941.61 
 
 57.334 
 
 261.59 
 
 L£ 
 
 83.252 
 
 551 55 
 
 8 
 
 109.170 
 
 948.42 
 
 57.727 
 
 265.18 
 
 78 
 
 88.645 
 
 556.76 
 
 109.563 
 
 955.25 
 
 » 
 
 58. 119 
 
 268.80 
 
 3£ 
 
 84.038 
 
 562 00 
 
 35 
 
 109.956 
 
 962.11 
 
 58.512 
 
 272.45 
 
 v\ 
 
 84.430 
 
 567.27 
 
 vi 
 
 110.348 
 
 969.00 
 
 
 58.905 
 
 276.12 
 
 27. 
 
 84.823 
 
 572 56 
 
 1 
 
 110.741 
 
 975.91 
 
 59.298 
 
 279.81 
 
 vi 
 
 85.216 
 
 577.87 
 
 111.134 
 
 982.84 
 
 19 
 
 59.690 
 
 283.53 
 
 8 
 
 85.608 
 
 583.21 
 
 
 111.527 
 
 989 80 
 
 V6 
 
 60 083 
 
 28727 
 
 
 86 001 
 
 588 57 
 
 76 
 
 111.919 
 
 996 78 
 
 ^ 
 
 60.476 
 
 291 .04 
 
 v2 
 
 86.394 
 
 593.96 
 
 7& 
 
 112.312 
 
 1003 8 
 
 
 60.868 
 
 294.83 
 
 78 
 
 86 786 
 
 599.37 
 
 % 
 
 112.705 
 
 1010 8 
 
 \& 
 
 61.261 
 
 298.65 
 
 8 
 
 87.179 
 
 604.81 
 
 36 
 
 113.097 
 
 1017 9 
 
 §6 
 
 61.654 
 
 302.49 
 
 87.572 
 
 610.27 
 
 7& 
 
 113.490 
 
 1025 
 
 § 
 
 62.046 
 
 306.85 
 
 28 
 
 87.965 
 
 615.75 
 
 I 
 
 113 883 
 
 1032.1 
 
 62.439 
 
 310.24 
 
 % 
 
 88.357 
 
 62126 
 
 
 114.275 
 
 1039 2 
 
 20 
 
 62.832 
 
 814.16 
 
 H, 
 
 88.750 
 
 626.80 
 
 !Uj 
 
 114.668 
 
 1046 3 
 
 ^ 
 
 63.225 
 
 318.10 
 
 
 89.143 
 
 532.36 
 
 §6 
 
 115.061 
 
 1053.5 
 
 » 
 
 63.617 
 
 322.06 
 
 % 
 
 89 535 
 
 537.94 
 
 8 
 
 115.454 
 
 1060 7 
 
 64.010 
 
 326.05 
 
 vk 
 
 89.928 
 
 543 55 
 
 115.846 
 
 1068.0 
 
 ^6 
 
 64.403 
 
 330.06 
 
 % 
 
 90.321 
 
 549 18 
 
 37 
 
 116 239 
 
 1075 2 
 
 % 
 
 64.795 
 
 334 10 
 
 % 
 
 90'713 
 
 354.84 
 
 % 
 
 116.632 
 
 1082 5 
 
 f^ 
 
 65.188 
 
 338 16 
 
 29 
 
 91 106 
 
 560 52 
 
 8 
 
 117 024 
 
 1089.8 
 
 ».** 
 
 65.581 
 
 342 25 
 
 H 
 
 91.499 
 
 566 23 
 
 117 417 
 
 1097 1 
 
 21. 
 
 65.973 
 
 346 36 
 
 8 
 
 91 892 
 
 571 96 
 
 
 117 810 
 
 1104 5 
 
 ^ 
 
 66.366 
 
 350.50 
 
 
 92.284 
 
 377 71 
 
 78 
 
 118 202 
 
 1111.8 
 
 | 
 
 66.759 
 
 354.66 
 
 L£ 
 
 92 677 
 
 383.49 
 
 8 
 
 118.596 
 
 1119.8 
 
 67.152 
 
 358.84 
 
 5,| 
 
 93,070 689.30 
 
 118.988 
 
 1126.7 
 
 \4& 
 
 67.544 
 
 363 05 
 
 s 
 
 93 462 695 IS 
 
 38 
 
 119.381 
 
 1134.1 
 
 96 
 
 67.987 
 
 367 28 
 
 98 855 700 98 
 
 14 
 
 119 773 
 
 141.6 
 
 % 
 
 68.330 
 
 371 54 
 
 30 
 
 94 248 1 
 
 roe 86 
 
 v± 
 
 120, 166 
 
 149.1 
 
TTSKFUIy TABLES. 
 
 193 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 38 & 
 
 120.559 
 
 1156.6 
 
 46^ 
 
 146.477 
 
 1707.4 
 
 54% 
 
 172.395 
 
 2365.0 
 
 <Hs 
 
 120.951 
 
 1164.2 
 
 s 
 
 146.869 
 
 1716.5 
 
 55. 
 
 172.788 
 
 2375.8 
 
 7& 
 
 121.344 
 
 1171.7 
 
 147.262 
 
 1725.7 
 
 % 
 
 173.180 
 
 2386.6 
 
 3£ 
 
 121.737 
 
 1179.3 
 
 47. 
 
 147.655 
 
 1734.9 
 
 H 
 
 173.573 
 
 2397.5 
 
 vk 
 
 122.129 
 
 1186.9 
 
 H 
 
 148.048 
 
 1744.2 
 
 % 
 
 173.966 
 
 2408.3 
 
 39. 
 
 122.522 
 
 1194.6 
 
 % 
 
 148.440 
 
 1753.5 
 
 
 174.358 
 
 2419.2 
 
 1 
 
 122.915 
 
 "1202.3 
 
 148.833 
 
 1762.7 
 
 % 
 
 174.751 
 
 2430.1 
 
 12:5.308 
 
 1210.0 
 
 1 
 
 149.226 
 
 1772.1 
 
 M 
 
 175.144 
 
 2441.1 
 
 
 123.700 
 
 1217.7 
 
 149.618 
 
 1781.4 
 
 % 
 
 175.536 
 
 2452.0 
 
 /^ 
 
 124.093 
 
 1225^4 
 
 
 150.011 
 
 1790.8 
 
 56. 
 
 175.929 
 
 2463.0 
 
 % 
 
 124.486 
 
 1233.2 
 
 % 
 
 150.404 
 
 1800.1 
 
 % 
 
 176.322 
 
 2474.0 
 
 » 
 
 124.878 
 
 1241.0 
 
 48. 
 
 150.796 
 
 1809.6 
 
 H 
 
 176.715 
 
 2485.0 
 
 % 
 
 125.271 
 
 1248.8 
 
 % 
 
 151.189 
 
 1819.0 
 
 
 177.107 
 
 2496.1 
 
 40. 
 
 125.664 
 
 1256.6 
 
 1 
 
 151.582 
 
 1828.5 
 
 14 
 
 177.500 
 
 2507.2 
 
 % 
 
 126.056 
 
 1264.5 
 
 151.975 
 
 1837.9 
 
 7& 
 
 177.893 
 
 2518.3 
 
 y± 
 
 126.449 
 
 1272.4 
 
 
 152.367 
 
 1847.5 
 
 H 
 
 178.285 
 
 2529.4 
 
 % 
 
 126.842 
 
 1280.3 
 
 % 
 
 152.760 
 
 1857.0 
 
 % 
 
 178.678 
 
 2540.6 
 
 14 
 
 127.2:35 
 
 1288.2 
 
 1 
 
 153.153 
 
 1866.5 
 
 57. 
 
 179.071 
 
 2551.8 
 
 % 
 
 127.627 
 
 1296.2 
 
 153.545 
 
 1876.1 
 
 1 
 
 179.463 
 
 2563.0 
 
 H 
 
 128.020 
 
 1304.2 
 
 49. 
 
 153.938 
 
 1885.7 
 
 179.856 
 
 2574.2 
 
 % 
 
 128.413 
 
 1312.2 
 
 % 
 
 154.331 
 
 1895.4 
 
 180.249 
 
 2585.4 
 
 41. 
 
 128.805 
 
 1320.3 
 
 8 
 
 154.723 
 
 1905 
 
 
 180.642 
 
 2596.7 
 
 % 
 
 129.198 
 
 1328.3 
 
 155.116 
 
 1914.7 
 
 %k 
 
 181.034 
 
 2608.0 
 
 8 
 
 129.591 
 
 1336.4 
 
 P 
 
 155.509 
 
 1924.4 
 
 % 
 
 181.427 
 
 2619.4 
 
 129.983 
 
 1344.5 
 
 155.902 
 
 1934.2 
 
 181.820 
 
 2630.7 
 
 H 
 
 130.376 
 
 1352.7 
 
 
 156.294 
 
 1943.9 
 
 58. 
 
 182.212 
 
 2642.1 
 
 % 
 
 130.769 
 
 1360.8 
 
 % 
 
 156 687 
 
 1953.7 
 
 1 
 
 182.605 
 
 2653.5 
 
 % 
 
 131.161 
 
 1369.0 
 
 50. 
 
 157.080 
 
 1963.5 
 
 182.998 
 
 2664.9 
 
 % 
 
 131.554 
 
 1377.2 
 
 % 
 
 157.472 
 
 1973.3 
 
 
 183.390 
 
 2676.4 
 
 42. 
 
 131.947 
 
 1385.4 
 
 1 
 
 157.865 
 
 1983.2 
 
 14 
 
 183.783 
 
 2687.8 
 
 I 
 
 132.340 
 
 1393.7 
 
 158.258 
 
 1993.1 
 
 % 
 
 184.176 
 
 2699.3 
 
 132.732 
 
 1402.0 
 
 
 158.650 
 
 2003.0 
 
 S 
 
 184.569 
 
 2710.9 
 
 133.125 
 
 1410.3 
 
 5/| 
 
 159.043 
 
 2012.9 
 
 184.961 
 
 2722.4 
 
 
 133.518 
 
 1418.6 
 
 % 
 
 159.436 
 
 2022.8 
 
 59. 
 
 185.354 
 
 2734.0 
 
 % 
 
 133.910 
 
 1427.0 
 
 % 
 
 159.829 
 
 2032.8 
 
 1 
 
 185.747 
 
 2745.6 
 
 9£ 
 
 134.303 
 
 1435.4 
 
 51 
 
 160.221 
 
 2042.8 
 
 186.139 
 
 2757.2 
 
 % 
 
 134.696 
 
 1443.8 
 
 14 
 
 160.614 
 
 2052.8 
 
 186.532 
 
 2768.8 
 
 43 
 
 135.088 
 
 1452.2 
 
 « 
 
 161.007 
 
 2062.9 
 
 
 186.925 
 
 2780.5 
 
 H 
 
 135.481 
 
 1460.7 
 
 161.399 
 
 2073.0 
 
 % 
 
 187.317 
 
 2792.2 
 
 % 
 
 135.874 
 
 1469.1 
 
 
 161.792 
 
 2083.1 
 
 8 
 
 187.710 
 
 2803.9 
 
 % 
 
 136.267 
 
 1477.6 
 
 tS 
 
 162.185 
 
 2093.2 
 
 188.103 
 
 2815.7 
 
 14 
 
 136.659 
 
 1486.2 
 
 g 
 
 162.577 
 
 2103.3 
 
 60 
 
 188.496 
 
 2827.4 
 
 % 
 
 137.052 
 
 1494.7 
 
 162.970 
 
 2113.5 
 
 % 
 
 188.888 
 
 2839.2 
 
 ¥a 
 
 137.445 
 
 1503.3 
 
 53 
 
 163.363 
 
 2123.7 
 
 8 
 
 189.281 
 
 2851.0 
 
 % 
 
 137.837 
 
 1511.9 
 
 8 
 
 163.756 
 
 2133.9 
 
 189.674 
 
 2862.9 
 
 44 
 
 138.230 
 
 1520.5 
 
 164.148 
 
 2144.2 
 
 
 190.066 
 
 2874.8 
 
 n 
 
 138.023 
 
 1529.2 
 
 % 
 
 164.541 
 
 2154.5 
 
 76 
 
 190.459 
 
 2886.6 
 
 139.015 
 
 1537.9 
 
 14 
 
 164.934 
 
 2164.8 
 
 M 
 
 190.852 
 
 2898.6 
 
 
 139.408 
 
 1546.6 
 
 % 
 
 165.326 
 
 2175.1 
 
 % 
 
 191.244 
 
 2910.5 
 
 i2 
 
 139.801 
 
 1555.3 
 
 1 
 
 165.719 
 
 2185.4 
 
 61 
 
 191.637 
 
 2922.5 
 
 % 
 
 140.194 
 
 1564.0 
 
 166.112 
 
 2195.8 
 
 H 
 
 192.030 
 
 2934.5 
 
 % 
 
 140.586 
 
 1572.8 
 
 53 
 
 166.504 
 
 2206.2 
 
 Ya 
 
 192.423 
 
 2946.5 
 
 % 
 
 140.979 
 
 1581.6 
 
 % 
 
 166.897 
 
 2216.6 
 
 
 192.815 
 
 2958.5 
 
 45 
 
 141.372 
 
 1590.4 
 
 H 
 
 167.290 
 
 2227.0 
 
 L£ 
 
 193.208 
 
 2970.6 
 
 M 
 
 141.764 
 
 1599.3 
 
 % 
 
 167.683 
 
 2237.5 
 
 % 
 
 193.601 
 
 2982.7 
 
 
 142.157 
 
 1608.2 
 
 \i 
 
 168.075 
 
 2248.0 
 
 1 
 
 193.993 
 
 2994.8 
 
 % 
 
 142.550 
 
 •1617.0 
 
 % 
 
 168.468 
 
 2258.5 
 
 194.386 
 
 3006.9 
 
 1£ 
 
 142.942 
 
 1626.0 
 
 % 
 
 168.861 
 
 2269.1 
 
 62. 
 
 194.779 
 
 3019.1 
 
 7& 
 
 143. 3&5 
 
 1634.9 
 
 169.253 
 
 2279.6 
 
 % 
 
 195.171 
 
 3031.3 
 
 s 
 
 143.728 
 
 1643.9 
 
 54- 
 
 169.646 
 
 2290.2 
 
 H 
 
 195.564 
 
 3043.5 
 
 144.121 
 
 1652.9 
 
 M 
 
 170. 039 
 
 2300.8 
 
 
 195.957 
 
 3055.7 
 
 46 
 
 144.513 
 
 1661.9 
 
 S 
 
 170.431 
 
 2311.5 
 
 1^ 
 
 196.350 
 
 3068.0 
 
 ^ 
 
 144.906 
 
 1670.9 
 
 170.824 
 
 2322.1 
 
 vk 
 
 196.742 
 
 3080.3 
 
 I 
 
 145.299 
 
 1680.0 
 
 1 
 
 171.217 
 
 2332.8 
 
 B 
 
 197.135 
 
 3092.6 
 
 
 145.691 
 
 1689.1 
 
 171.609 
 
 2343.5 
 
 197.528 
 
 3104.9 
 
 *6 
 
 146.084 
 
 1698.2 
 
 172.002 
 
 2354.3 
 
 63 
 
 197.920 
 
 3117.2 
 
194 
 
 USEFUL TABLES. 
 
 FIFTH ROOTS AND FIFTH POWERS, 
 
 (Abridged from Trautwine.) 
 
 ° C 
 
 
 ® o 
 
 
 ® o 
 
 
 oif 
 
 
 k~ 
 
 
 IS 
 
 Power. 
 
 6 q 
 
 Power. 
 
 6 o 
 
 Power. 
 
 o o 
 
 Power. 
 
 . o 
 o o 
 
 Power, 
 
 
 £« 
 
 
 £tf 
 
 
 £« 
 
 
 Itf 
 
 
 .10 
 
 .000010 
 
 3.7 
 
 693.440 
 
 9.8 
 
 90392 
 
 21.8 
 
 4923597 
 
 40 
 
 102400000 
 
 .15 
 
 .000075 
 
 3.8 
 
 792.352 
 
 9.9 
 
 95099 
 
 22.0 
 
 5153632 
 
 41 
 
 115856^:01 
 
 .20 
 
 .000320 
 
 3.9 
 
 902.242 
 
 10.0 
 
 100000 
 
 22.2 
 
 5392186 
 
 42 
 
 130691232 
 
 .25 
 
 .000977 
 
 4.0 
 
 1024.00 
 
 10 2 
 
 110408 
 
 22.4 
 
 5639493 
 
 43 
 
 147008443 
 
 .30 
 
 .002430 
 
 4.1 
 
 1158.56 
 
 10.4 
 
 121665 
 
 22.6 
 
 5895793 
 
 44 
 
 164916224 
 
 .35 
 
 .005252 
 
 4.2 
 
 1306.91 
 
 10.6 
 
 133823 
 
 22.8 
 
 6161327 
 
 45 
 
 184528)25 
 
 .40 
 
 .010240 
 
 4.3 
 
 1470.08 
 
 10.8 
 
 146933 
 
 23.0 
 
 6436343 
 
 46 
 
 205962976 
 
 .45 
 
 .018453 
 
 4.4 
 
 1649.16 
 
 11.0 
 
 161051 
 
 23.2 
 
 6721093 
 
 47 
 
 229345007 
 
 .50 
 
 .031250 
 
 4.5 
 
 1845.28 
 
 11.2 
 
 176234 
 
 23.4 
 
 7015834 
 
 48 
 
 254803968 
 
 .55 
 
 .050328 
 
 4.6 
 
 2059.63 
 
 11.4 
 
 192541 
 
 23.6 
 
 7320825 
 
 49 
 
 282475249 
 
 .60 
 
 .077760 
 
 4.7 
 
 2293.45 
 
 11.6 
 
 210C34 
 
 23.8 
 
 7636332 
 
 50 
 
 312500000 
 
 .65 
 
 .116029 
 
 4.8 
 
 2548.04 
 
 11.8 
 
 228776 
 
 24.0 
 
 7962624 
 
 51 
 
 345025251 
 
 .70 
 
 .168070 
 
 4.9 
 
 2824.75 
 
 12.0 
 
 248832 
 
 24.2 
 
 8299976 
 
 52 
 
 380204032 
 
 .75 
 
 .237305 
 
 5.0 
 
 3125.00 
 
 12.2 
 
 270271 
 
 24.4 
 
 8648666 
 
 53 
 
 418195493 
 
 .80 
 
 .327680 
 
 5.1 
 
 3450.25 
 
 12.4 
 
 293163 
 
 24.6. 
 
 9008978 
 
 54 
 
 459165024 
 
 .85 
 
 .443705 
 
 5.2 
 
 3802.04 
 
 12.6 
 
 317580 
 
 24.8 
 
 9381200 
 
 55 
 
 503284375 
 
 .90 
 
 .590490 
 
 5.3 
 
 4181.95 
 
 12.8 
 
 343597 
 
 25.0 
 
 9765625 
 
 56 
 
 550731776 
 
 .95 
 
 .773781 
 
 5.4 
 
 4591.65 
 
 13.0 
 
 371293 
 
 25.2 
 
 10162550 
 
 57 
 
 601692057 
 
 1.00 
 
 1.00000 
 
 5.5 
 
 5032.84 
 
 13.2 
 
 400746 
 
 25.4 
 
 10572278 
 
 58 
 
 656356768 
 
 1.05 
 
 1.27628 
 
 5.6 
 
 5507.32 
 
 13.4 
 
 432040 
 
 25.6 
 
 10995116 
 
 59 
 
 714924299 
 
 1.10 
 
 1.61051 
 
 5.7 
 
 6016.92 
 
 13 6 
 
 465259 
 
 25.8 
 
 11431377 
 
 60 
 
 777600000 
 
 1.15 
 
 2.01135 
 
 5.8 
 
 6563.57 
 
 13.8 
 
 500490 
 
 26.0 
 
 11881376 
 
 61 
 
 844596301 
 
 1.20 
 
 2.48832 
 
 5.9 
 
 7149.24 
 
 14.0 
 
 537824 
 
 26.2 
 
 12345437 
 
 62 
 
 916132832 
 
 1.25 
 
 3.05176 
 
 6.0 
 
 7776.00 
 
 14.2 
 
 577353 
 
 26.4 
 
 12823886 
 
 63 
 
 992436543 
 
 1.30 
 
 3.71293 
 
 6.1 
 
 8445.96 
 
 14.4 
 
 619174 
 
 26.6 
 
 13317055 
 
 64 
 
 1073741824 
 
 1.35 
 
 4.48403 
 
 6.2 
 
 9161.33 
 
 14 6 
 
 663383 
 
 26.8 
 
 13825281 
 
 65 
 
 1160290625 
 
 1.40 
 
 5.37824 
 
 6.3 
 
 9924.37 
 
 14.8 
 
 710082 
 
 27.0 
 
 14348907 
 
 66 
 
 1252332576 
 
 1.45 
 
 6.40973 
 
 6.4 
 
 10737 
 
 15.0 
 
 759375 
 
 27.2 
 
 14888280 
 
 67 
 
 1350125107 
 
 1.50 
 
 7.59375 
 
 6.5 
 
 11603 
 
 15.2 
 
 811368 
 
 27.4 
 
 15443752 
 
 68 
 
 1453933568 
 
 1.55 
 
 8.94661 
 
 6.6 
 
 12523 
 
 15.4 
 
 866171 
 
 27»6 
 
 16015681 
 
 69 
 
 1564031349 
 
 1.60 
 
 10.4858 
 
 6.7 
 
 13501 
 
 15.6 
 
 923896 
 
 27.8 
 
 16604430 
 
 70 
 
 1680700000 
 
 1.65 
 
 12.2298 
 
 6.8 
 
 14539 
 
 15.8 
 
 984658 
 
 28.0 
 
 17210368 
 
 71 
 
 1804229351 
 
 1.70 
 
 14.1986 
 
 6.9 
 
 15640 
 
 16.0 
 
 1048576 
 
 28.2 
 
 17833868 
 
 72 
 
 1934917632 
 
 1.75 
 
 16.3141 
 
 7.0 
 
 16807 
 
 16.2 
 
 1115771 
 
 28.4 
 
 18475309 
 
 73 
 
 2073071593 
 
 1.80 
 
 18.8957 
 
 7.1 
 
 18042 
 
 16.4 
 
 1186367 
 
 28.6 
 
 19135075 
 
 74 
 
 2219006624 
 
 1.85 
 
 21.6700 
 
 7.2 
 
 19349 
 
 16.6 
 
 1260493 
 
 28.8 
 
 19813557 
 
 75 
 
 2373046875 
 
 1.90 
 
 24.7610 
 
 7.3 
 
 20731 
 
 16.8 
 
 1338278 
 
 29.0 
 
 20511149 
 
 76 
 
 2535525376 
 
 1.95 
 
 28.1951 
 
 7.4 
 
 22190 
 
 17.0 
 
 1419857 
 
 29.2 
 
 21228253 
 
 77 
 
 2706784157 
 
 2.00 
 
 32.0000 
 
 7.5 
 
 23730 
 
 17.2 
 
 1505366 
 
 29.4 
 
 21965275 
 
 78 
 
 2887174368 
 
 2.05 
 
 36.2051 
 
 7.6 
 
 25355 
 
 17.4 
 
 1594947 
 
 29.6 
 
 22722628 
 
 79 
 
 3077056399 
 
 2.10 
 
 40 8410 
 
 7.7 
 
 27068 
 
 17.6 
 
 1688742 
 
 29.8 
 
 23500728 
 
 80 
 
 3276800000 
 
 2.15 
 
 45.9101 
 
 7.8 
 
 28872 
 
 17.8 
 
 1786899 
 
 30.0 
 
 24300000 
 
 81 
 
 3486784401 
 
 2 20 
 
 51.5363 
 
 7.9 
 
 30771 
 
 18.0 
 
 1889568 
 
 30.5 
 
 26393634 
 
 82 
 
 3707398432 
 
 2.25 
 
 57.6650 
 
 8.0 
 
 32768 
 
 18.2 
 
 1996903 
 
 31.0 
 
 28629151 
 
 83 
 
 3939040643 
 
 2.30 
 
 64.3634 
 
 8.1 
 
 34868 
 
 18.4 
 
 2109061 
 
 31.5 
 
 31013642 
 
 84 
 
 4182119424 
 
 2.35 
 
 71.6703 
 
 8.2 
 
 37074 
 
 18.6 
 
 2226203 
 
 32.0 
 
 33554432 
 
 85 
 
 4437053125 
 
 2.40 
 
 79.6262 
 
 8.3 
 
 39390 
 
 18.8 
 
 2348493 
 
 32.5 
 
 36259082 
 
 86 
 
 4704270176 
 
 2.45 
 
 88.2735 
 
 8.4 
 
 41821 
 
 19.0 
 
 2476099 
 
 33.0 
 
 39135393 
 
 87 
 
 4984209207 
 
 2.50 
 
 97.6562 
 
 8.5 
 
 44371 
 
 19.2 
 
 2609193 
 
 33.5 
 
 42191410 
 
 88 
 
 5277319168 
 
 2.55 
 
 107.820 
 
 8.6 
 
 47043 
 
 19.4 
 
 2747949 
 
 34.0 
 
 45435424 
 
 89 
 
 5584059449 
 
 2.60 
 
 118.814 
 
 8.7 
 
 49842 
 
 19.6 
 
 2892547 
 
 34.5 
 
 48875980 
 
 90 
 
 5904900000 
 
 2.70 
 
 143.489 
 
 8.8 
 
 52773 
 
 19.8 
 
 3043168 
 
 35.0 
 
 52521875 
 
 91 
 
 6240321451 
 
 2.80 
 
 172.104 
 
 8.9 
 
 55841 
 
 20.0 
 
 3200000 
 
 35.5 
 
 56382167 
 
 92 
 
 6590815232 
 
 2.90 
 
 205.111 
 
 9.0 
 
 59049 
 
 20.2 
 
 3363232 
 
 36.0 
 
 60466176 
 
 93 
 
 6956883693 
 
 3.Q0 
 
 243 000 
 
 9.1 
 
 62403 
 
 20.4 
 
 3533059 
 
 36.5 
 
 64783487 
 
 94 
 
 7339040224 
 
 3.10 
 
 286.292 
 
 9.2 
 
 65908 
 
 20.6 
 
 3709677 
 
 37.0 
 
 69343957 
 
 95 
 
 7737809375 
 
 3.20 
 
 335.544 
 
 9.3 
 
 69569 
 
 20.8 
 
 3893289 
 
 37.5 
 
 74157715 
 
 96 
 
 8153726976 
 
 3.30 
 
 391.354 
 
 9.4 
 
 73390 
 
 21.0 
 
 4084101 
 
 38.0 
 
 79235168 
 
 97 
 
 8587340257 
 
 3.40 
 
 454.354 
 
 9.5 
 
 77378 
 
 21.2 
 
 4282322 
 
 38.5 
 
 84587005 
 
 98 
 
 9039207968 
 
 8.50 
 
 525.. 219 
 
 9.6 
 
 81537 
 
 21.4 
 
 4488166 
 
 39.0 
 
 90224199 
 
 99 
 
 9509900499 
 
 3.60 
 
 604.662 
 
 9.7 
 
 85873 
 
 21.6 
 
 4701850 
 
 39.5 
 
 9615801.2 
 
 
 
USEFUL TABLES. 
 
 195 
 
 
 SQTJABES, CUBES AND RECIPROCALS. 
 
 Hos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 Nos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 1 
 
 1 
 
 1 
 
 1. 000000000 
 
 51 
 
 26 01 
 
 132 651 
 
 .019607843 
 
 2 
 
 4 
 
 8 
 
 .500000000 
 
 52 
 
 27 04 
 
 140 608 
 
 .0192:0769 
 
 3 
 
 9 
 
 27 
 
 .333333333 
 
 53 
 
 28 09 
 
 148 877 
 
 .018867925 
 
 4 
 
 16 
 
 64 
 
 .250000000 
 
 64 
 
 29 16 
 
 157 464 
 
 .018518519 
 
 5 
 
 25 
 
 125 
 
 .200000000 
 
 55 
 
 30 25 
 
 166 375 
 
 .018181818 
 
 6 
 
 36 
 
 216 
 
 .166666667 
 
 56 
 
 3136 
 
 175 6f 6 
 
 .017857143 
 
 7 
 
 49 
 
 343 
 
 .142857143 
 
 57 
 
 32 49 
 
 185 193 
 
 .017543860 
 
 8 
 
 64 
 
 512 
 
 .125000000 
 
 58 
 
 33 64 
 
 195 112 
 
 .017241379 
 
 9 
 
 81 
 
 729 
 
 .111111111 
 
 59 
 
 34 81 
 
 205 379 
 
 .016949153 
 
 10 
 
 100 
 
 1000 
 
 .100000000 
 
 60 
 
 36 00 
 
 216 000 
 
 .016666667 
 
 11 
 
 121 
 
 1331 
 
 .090909091 
 
 61 
 
 37 21 
 
 226 981 
 
 .016393443 
 
 12 
 
 144 
 
 1728 
 
 .083333333 
 
 62 
 
 38 44 
 
 238 328 
 
 .016129032 
 
 13 
 
 169 
 
 2197 
 
 .0T6923077 
 
 63 
 
 39 69 
 
 250 047 
 
 .015873016 
 
 14 
 
 196 
 
 2 744 
 
 .071428571 
 
 64 
 
 40 96 
 
 262 144 
 
 .015625000 
 
 15 
 
 225 
 
 3 375 
 
 .066666667 
 
 65 
 
 42 25 
 
 274 625 
 
 .015384615 
 
 16 
 
 2 56 
 
 4 096 
 
 .062500000 
 
 66 
 
 43 56 
 
 287 496 
 
 .015151515 
 
 17 
 
 2 89 
 
 4 913 
 
 .0588-23529 
 
 67 
 
 44 89 
 
 3'.0 763 
 
 .014925373 
 
 18 
 
 324 
 
 5 832 
 
 .055555556 
 
 68 
 
 46 24 
 
 314 432 
 
 .014705882 
 
 19 
 
 361 
 
 6 859 
 
 .052631579 
 
 69 
 
 47 61 
 
 328 509 
 
 .014492754 
 
 20 
 
 400 
 
 8 000 
 
 .050000000 
 
 70 
 
 49 00 
 
 343 000 
 
 .014285714 
 
 21 
 
 4 41 
 
 9 261 
 
 .047619048 
 
 71 
 
 50 41 
 
 357 911 
 
 .014081507 
 
 22 
 
 4 84 
 
 10 618 
 
 .045451545 
 
 72 
 
 5184 
 
 373 2)8 
 
 .013888889 
 
 23 
 
 5 29 
 
 12 167 
 
 .043478^60 
 
 73 
 
 53 29 
 
 389 017 
 
 .013698630 
 
 24 
 
 5 76 
 
 13 824 
 
 .041666667 
 
 74 
 
 54 76 
 
 405 224 
 
 .01:3513514 
 
 25 
 
 625 
 
 15 625 
 
 .0400000UO 
 
 75 
 
 56 25 
 
 421 875 
 
 .013333333 
 
 26 
 
 6 76 
 
 17576 
 
 .038461538 
 
 76 
 
 57 78 
 
 438 976 
 
 .013157895 
 
 27 
 
 729 
 
 19 683 
 
 .037037037 
 
 77 
 
 59 29 
 
 456 5 !3 
 
 .012987013 
 
 28 
 
 7 84 
 
 21 952 
 
 .035714286 
 
 78 
 
 60 84 
 
 474 552 
 
 .012820513 
 
 29 
 
 8 41 
 
 24 389 
 
 .034482759 
 
 79 
 
 62 41 
 
 493 039 
 
 .012658228 
 
 SO 
 
 9 00 
 
 27 000 
 
 .033333333 
 
 80 
 
 64 00 
 
 512 000 
 
 .012500000 
 
 31 
 
 9 61 
 
 29 791 
 
 .032258065 
 
 81 
 
 65 61 
 
 531441 
 
 .012345679 
 
 32 
 
 10 24 
 
 32 768 
 
 .031250000 
 
 82 
 
 67 24 
 
 551 368 
 
 .012195122 
 
 33 
 
 10 89 
 
 35 937 
 
 .03)303030 
 
 83 
 
 68J-9 
 
 571 787 
 
 .012048193 
 
 34 
 
 1156 
 
 39 304 
 
 .029411765 
 
 84 
 
 70 56 
 
 592 704 
 
 .011904762 
 
 85 
 
 12 25 
 
 42 875 
 
 .028571429 
 
 85 
 
 72 25 
 
 614125 
 
 .011764706 
 
 36 
 
 12 96 
 
 46 656 
 
 .027777778 
 
 86 
 
 73 96 
 
 636 056 
 
 .011627907 
 
 37 
 
 13 69 
 
 50 653 
 
 .027027027 
 
 87 
 
 75 69 
 
 658 503 
 
 .011494253 
 
 38 
 
 14 44 
 
 51 872 
 
 .026315789 
 
 88 
 
 77 44 
 
 681472 
 
 .011363636 
 
 39 
 
 15 21 
 
 59 319 
 
 .025641026 
 
 89 
 
 79 21 
 
 704 969 
 
 .011235955 
 
 40 
 
 16 00 
 
 64 000 
 
 .025000000 
 
 90 
 
 8100 
 
 729 000 
 
 .011111111 
 
 41 
 
 16 81 
 
 68 921 
 
 .024390244 
 
 91 
 
 82 81 
 
 753 571 
 
 .010989011 
 
 42 
 
 17 64 
 
 74(188 
 
 .023809524 
 
 92 
 
 84 64 
 
 778 688 
 
 .010869565 
 
 43 
 
 18 49 
 
 79 507 
 
 .023255814 
 
 93 
 
 86 49 
 
 804 357 
 
 .010752(>88 
 
 44 
 
 19 86 
 
 85184 
 
 .022727273 
 
 94 
 
 88 36 
 
 830584 
 
 .010638298 
 
 45 
 
 20 25 
 
 91125 
 
 .02.4222222 
 
 95 
 
 90 25 
 
 857 375 
 
 .010526316 
 
 46 
 
 2116 
 
 97 336 
 
 .091739130 
 
 96 
 
 9216 
 
 884 736 
 
 .010416667 
 
 47 
 
 22 09 
 
 103 8*3 
 
 .021276600 
 
 97 
 
 94 09 
 
 912 673 
 
 .010309278 
 
 48 
 
 23 04 
 
 110 592 
 
 .020K33333 
 
 98 
 
 96 04 
 
 941192 
 
 .OK); 04082 
 
 49 
 
 24 01 
 
 117 649 
 
 .020408163 
 
 99 
 
 98 01 
 
 970299 
 
 .010101010 
 
 50 
 
 25 CO 
 
 125000 
 
 .020000000 
 
 100 
 
 10000 
 
 1000000 
 
 .010000000 
 
196 
 
 USEFUL TABLES. 
 
 SQUARES, CUBES AND RECIPROCALS— Continued. 
 
 Hos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 Nos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 101 
 
 102 01 
 
 1030 301 
 
 .009900990 
 
 151 
 
 2 28 01 
 
 3 442 951 
 
 .006622517 
 
 102 
 
 104 04 
 
 1 061 208 
 
 .009803922 
 
 152 
 
 2 3104 
 
 3 511808 
 
 .006578947 
 
 103 
 
 106 09 
 
 1 092 727 
 
 .009708738 
 
 153 
 
 2 34 09 
 
 3 581 577 
 
 .006535948 
 
 104 
 
 108 16 
 
 1 124 864 
 
 .009615385 
 
 154 
 
 2 37 16 
 
 3 652 264 
 
 .006493.506 
 
 105 
 
 110 25 
 
 1 157 62} 
 
 ,009523810 
 
 155 
 
 240 25 
 
 3 723 875 
 
 .006151613 
 
 106 
 
 112 36 
 
 1 191 016 
 
 .009433962 
 
 156 
 
 243 36 
 
 3 796 416 
 
 .006410256 
 
 107 
 
 114 49 
 
 1 225 043 
 
 .009345794 
 
 157 
 
 2 46 49 
 
 3 869 893 
 
 .006369427 
 
 106 
 
 116 64 
 
 1 25^ 712 
 
 .009259259 
 
 158 
 
 2 49 64 
 
 3 944312 
 
 .006329114 
 
 109 
 
 118 81 
 
 1 295 029 
 
 .009174312 
 
 159 
 
 2 52 81 
 
 4 019 679 
 
 .006289308 
 
 110 
 
 12100 
 
 1331000 
 
 .009090909 
 
 160 
 
 256 00 
 
 4 096 000 
 
 .006250000 
 
 111 
 
 1^23 21 
 
 1 367 631 
 
 .009009009 
 
 161 
 
 2 59 21 
 
 4173281 
 
 .006211180 
 
 112 
 
 125 44 
 
 1 404 928 
 
 .008928571 
 
 162 
 
 2 62 44 
 
 4 2515 8 
 
 .006172840 
 
 113 
 
 127 69 
 
 1 442 897 
 
 .008849558 
 
 163 
 
 2 65 69 
 
 4 330 747 
 
 .006134969 
 
 114 
 
 129 96 
 
 1 481 544 
 
 .008771930 
 
 164 
 
 2 68 96 
 
 4 410 944 
 
 .00609-561 
 
 115 
 
 132 25 
 
 1 520 875 
 
 .008695652 
 
 165 
 
 2 72 25 
 
 4 492125 
 
 .006060608 
 
 116 
 
 1 34 56 
 
 1 560 896 
 
 .008620690 
 
 166 
 
 2 75 56 
 
 4 574 296 
 
 .006021096 
 
 117 
 
 136 89 
 
 1601 6 L3 
 
 .008547009 
 
 167 
 
 2 78K9 
 
 4 657 463 
 
 .005988024 
 
 118 
 
 139 24 
 
 16*3 032 
 
 .008474576 
 
 168 
 
 2 82 24 
 
 4 741 632 
 
 .005952381 
 
 119 
 
 14161 
 
 1 685 159 
 
 .008403361 
 
 169 
 
 2 85 61 
 
 4 826 809 
 
 .005917160 
 
 120 
 
 144 00 
 
 1728 000 
 
 .008333333 
 
 170 
 
 2 89 00 
 
 4 913 000 
 
 .005882353 
 
 121 
 
 146 41 
 
 1 771 561 
 
 .008264463 
 
 171 
 
 2 92 41 
 
 5000211 
 
 .005847953 
 
 122 
 
 148 84 
 
 1 815 848 
 
 .008196721 
 
 172 
 
 2 95 84 
 
 5 088 448 
 
 .005813953 
 
 123 
 
 15129 
 
 1 860 867 
 
 .008130081 
 
 173 
 
 2 99 29 
 
 5 177 717 
 
 .005780347 
 
 124 
 
 153 76 
 
 1 906 624 
 
 .008064516 
 
 174 
 
 3 02 76 
 
 5 268 024 
 
 .005747126 
 
 125 
 
 156 25 
 
 1 953 125 
 
 .008000000 
 
 175 
 
 3 06 25 
 
 5 359 375 
 
 .005714286 
 
 126 
 
 1 58 76 
 
 2 000 376 
 
 .007936508 
 
 176 
 
 3 09 76 
 
 5 451 776 
 
 .005681818 
 
 127 
 
 16129 
 
 2 048 3S3 
 
 .007874016 
 
 177 
 
 3 13 29 
 
 5 545 233 
 
 ,0i 156(9718 
 
 128 
 
 163 84 
 
 2 097 152 
 
 .007812500 
 
 178 
 
 3 16 84 
 
 5 659 752 
 
 .005617978 
 
 129 
 
 166 41 
 
 2 146 6S9 
 
 .007751938 
 
 179 
 
 3 20 41 
 
 5 735 339 
 
 .005566592 
 
 130 
 
 169 00 
 
 2 197 000 
 
 .017692308 
 
 180 
 
 .3 24 00 
 
 5 832 000 
 
 .005555556 
 
 131 
 
 17161 
 
 2 248 091 
 
 .007633588 
 
 181 
 
 3 27 61 
 
 5 929741 
 
 .005524862 
 
 132 
 
 1 74 24 
 
 2 293 968 
 
 .007575758 
 
 182 
 
 3 3124 
 
 6 028 568 
 
 .005494505 
 
 133 
 
 176 89 
 
 2 352 637 
 
 .007-il8797 
 
 183 
 
 3 34 89 
 
 6 128 487 
 
 .005464481 
 
 J 34 
 
 179 56 
 
 2 406 104 
 
 .007462687 
 
 184 
 
 3 38 56 
 
 6 229 504 
 
 .005434783 
 
 135 
 
 182 25 
 
 2 460 375 
 
 ,007407407 
 
 185 
 
 3 42 25 
 
 6 331 625 
 
 .005405405 
 
 136 
 
 184 96 
 
 2 515 456 
 
 .007352941 
 
 186 
 
 3 45 96 
 
 6 434 856 
 
 .005376344 
 
 137 
 
 187 69 
 
 2 571 353 
 
 .007299270 
 
 187 
 
 3 49 69 
 
 6 539 203 
 
 .005347594 
 
 138 
 
 190 44 
 
 2 628 072 
 
 ,007246377 
 
 188 
 
 35341 
 
 6 644 672 
 
 .005319149 
 
 139 
 
 193 21 
 
 2 685 619 
 
 .007 194 '45 
 
 189 
 
 3 57 21 
 
 6 751 239 
 
 . 00529 H '05 
 
 140 
 
 196 00 
 
 2 744 000 
 
 .007142857 
 
 190 
 
 3 6100 
 
 6 859 000 
 
 .005263158 
 
 141 
 
 198 81 
 
 2 803 221 
 
 .007092199 
 
 191 
 
 3 64 81 
 
 6 967 871 
 
 .005235602 
 
 142 
 
 2 0164 
 
 2 863 288 
 
 .007042254 
 
 192 
 
 3 68*4 
 
 7 077 888 
 
 .005208333 
 
 113 
 
 2 04 49 
 
 2 924 207 
 
 .006993007 
 
 193 
 
 3 72 49 
 
 7189 057 
 
 .005181347 
 
 144 
 
 2 07 36 
 
 2 985 984 
 
 .006914144 
 
 194 
 
 3 76 36 
 
 7 301 384 
 
 .005154639 
 
 145 
 
 210 25 
 
 3 048 625 
 
 .006898552 
 
 195 
 
 380 25 
 
 7 414 875 
 
 ,005128205 
 
 146 
 
 21316 
 
 6 112 136 
 
 .006819315 
 
 196 
 
 3 84 16 
 
 7 529 536 
 
 .005102041 
 
 147 
 
 2 16 09 
 
 3 176 523 
 
 .006802721 
 
 197 
 
 388 09 
 
 7 645 373 
 
 .005076142 
 
 148 
 
 21904 
 
 3 241 792 
 
 .006756757 
 
 108 
 
 3 92 01 
 
 7 762 392 
 
 .005050505 
 
 149 
 
 2 22 01 
 
 3 307 949 
 
 .006711409 
 
 199 
 
 3 96 01 
 
 7 880 599 
 60OOOOO 
 
 .005025126 
 
 150 
 
 225 00 
 
 3 375 000 
 
 • .006666667 
 
 200 
 
 400 00 
 
 .005000000 
 
USEFUL TABIDS. 
 
 I 9 7 
 
 SQUARES, CUBES AND RECIPROCALS— Continued. 
 
 Hos, 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 Kos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 201 
 
 4 04 01 
 
 8 120 601 
 
 .004975124 
 
 251 
 
 6 30 01 
 
 15 813 251 
 
 .003934061 
 
 202 
 
 4 08 04 
 
 8 242 408 
 
 .004950495 
 
 252 
 
 635 04 
 
 16 003 008 
 
 .003968254 
 
 203 
 
 4 12 09 
 
 8 365 427 
 
 .034926108 
 
 253 
 
 6 40 09 
 
 16 194 277 
 
 .003952569 
 
 204 
 
 4 16 16 
 
 8 489 661 
 
 .004901961 
 
 254 
 
 6 45 16 
 
 16 387 064 
 
 .003937008 
 
 205 
 
 4 20 25 
 
 8 615 125 
 
 .004878049 
 
 255 
 
 6 50 25 
 
 16 581375 
 
 .003921569 
 
 206 
 
 • 4 24 36 
 
 8 741 816 
 
 .004854369 
 
 256 
 
 6 55 36 
 
 16 777 216 
 
 .003906250 
 
 207 
 
 4 28 49 
 
 8 869 743 
 
 .004830918 
 
 257 
 
 6 60 49 
 
 16 974 593 
 
 .003891051 
 
 208 
 
 4 32 64 
 
 8 998 912 
 
 .004807692 
 
 258 
 
 6 65 64 
 
 17173 512 
 
 .003875969 
 
 209 
 
 4 36 81 
 
 9 129 329 
 
 .004784689 
 
 259 
 
 6 70 81 
 
 17 373 979 
 
 .003861004 
 
 210 
 
 4 4100 
 
 9 261 000 
 
 .001761905 
 
 260 
 
 6 76 00 
 
 17 576 000 
 
 .003846154 
 
 211 
 
 4 45 21 
 
 9 393 931 
 
 .004739336 
 
 261 
 
 6 8121 
 
 17 779 581 
 
 .003831418 
 
 212 
 
 4 49 44 
 
 9 528 128 
 
 .0J4716981 
 
 262 
 
 6 86 44 
 
 17 984 728 
 
 .003816794 
 
 213 
 
 4 53 69 
 
 9 663 597 
 
 .004694836 
 
 263 
 
 6 9169 
 
 18 191 447 
 
 .003802281 
 
 214 
 
 4 57 96 
 
 9 800 344 
 
 .004672897 
 
 264 
 
 6 96 96 
 
 18 399 744 
 
 .003787879 
 
 215 
 
 4 62 25 
 
 9 938 375 
 
 .004651163 
 
 265 
 
 7 02 25 
 
 18 609 625 
 
 .003773585 
 
 216 
 
 4 66 56 
 
 10 077 696 
 
 .004629630 
 
 266 
 
 7 07 56 
 
 18 821 096 
 
 .003759398 
 
 217 
 
 4 70 89 
 
 10 218 313 
 
 .004608295 
 
 267 
 
 7 12 89 
 
 19 034 163 
 
 .003745318 
 
 218 
 
 4 75 24 
 
 10 360 232 
 
 .0045*7156 
 
 268 
 
 718 24 
 
 19 248 832 
 
 .003731343 
 
 2! 9 
 
 4 79 61 
 
 10 503 459 
 
 .004566210 
 
 269 
 
 7 23 61 
 
 19 465 109 
 
 .003717472 
 
 220 
 
 4 84 00 
 
 10 648 000 
 
 .004545155 
 
 270 
 
 7 29 00 
 
 19 683 000 
 
 .003703704 
 
 221 
 
 4 88 41 
 
 10 793 861 
 
 .004524887 
 
 271 
 
 7 34 41 
 
 19 902 511 .003690037 
 
 222 
 
 4 92 84 
 
 10 941 048 
 
 .004504505 
 
 272 
 
 7 39 84 
 
 20 123 648 
 
 .003676471 
 
 223 
 
 4 97 29 
 
 11089567 
 
 .004484305 
 
 273 
 
 7 45 29 
 
 20 346 417 
 
 .003663004 
 
 224* 
 
 5 0176 
 
 11239 424 
 
 .004464286 
 
 274 
 
 7 50 76 
 
 20 570 824 
 
 .003649635 
 
 225 
 
 506 25 
 
 11 390 625 
 
 -.004444444 
 
 275 
 
 7 56 25 
 
 20 796 875 
 
 .003366364 
 
 226 
 
 510 76 
 
 11 543 176 
 
 .004424779 
 
 276 
 
 7 6176 
 
 21 024 576 
 
 .003623188 
 
 227 
 
 515 29 
 
 11697 083 
 
 .001405286 
 
 277 
 
 7 67 29 
 
 21 253 933 
 
 .003610108 
 
 228 
 
 519 84 
 
 11 852 352 
 
 .004-385965 
 
 278 
 
 7 72 84 
 
 21 484 952 
 
 .003597122 
 
 229 
 
 52441 
 
 12 0)8 989 
 
 .004366812 
 
 279 
 
 7 78 41 
 
 21 717 639 
 
 .003584229 
 
 230 
 
 5 29 01) 
 
 12167 000 
 
 .001347826 
 
 280 
 
 7 84 00 
 
 21 952 000 
 
 003571429 
 
 231 
 
 6 33 61 
 
 12 326 391 
 
 .004329004 
 
 281 
 
 7 89 61 
 
 . 22 188 041 
 
 .U03558719 
 
 232 
 
 5?8 24 
 
 12 487 163 
 
 .004310:345 
 
 232 
 
 7 95 24 
 
 22 425 768 
 
 .003546099 
 
 233 
 
 5 42 89 
 
 12 649 337 
 
 .0)4291845 
 
 283 
 
 8 00 89 
 
 22 665 187 
 
 .003533569 
 
 234 
 
 5 47 56 
 
 12 812 904 
 
 .00427.3504 
 
 284 
 
 806 56 
 
 22 906 304 
 
 .003521127 
 
 235 
 
 .5 52 25 
 
 12 977 875 
 
 .004255319 
 
 285 
 
 812 25 
 
 23 149 125 
 
 .003508772 
 
 236 
 
 5 56 96 
 
 13 144 256 
 
 .004237288 
 
 286 
 
 817 96 
 
 23 393 656 
 
 .003496503 
 
 237 
 
 5 6169 
 
 13 312 053 
 
 .004219409 
 
 287 
 
 8 23 69 
 
 23 639 903 
 
 .003484321 
 
 238 
 
 5 66 44 
 
 13 481 272 
 
 .004-01681 
 
 288 
 
 829 44 
 
 23 887 872 
 
 .003472222 
 
 239 
 
 5 7121 
 
 13 651919 
 
 .004184100 
 
 289 
 
 8 35 21 
 
 24 137 569 
 
 .003460208 
 
 240 
 
 5 76 00 
 
 13 824 000 
 
 .004166667 
 
 290 
 
 8 4100 
 
 24 389 000 
 
 .003448276 
 
 241 
 
 5 80 81 
 
 13 997521 
 
 .004149378 
 
 291 
 
 8 46 81 
 
 24 642 171 
 
 .003436426 
 
 242 
 
 5 85 64 
 
 14172 488 
 
 .004132231 
 
 292 
 
 8 52 64 
 
 24 897 088 
 
 .003424658 
 
 243 
 
 5 90 49 
 
 14 348 907 
 
 .004115226 
 
 293 
 
 8 58 49 
 
 25 153 757 
 
 .003412969 
 
 244 
 
 5 95 86 
 
 14 526 784 
 
 .004098361 
 
 294 
 
 8 64 36 
 
 25 412 184 
 
 ,003401861 
 
 245 
 
 6 00 25 
 
 14 706 125 
 
 .004081633 
 
 295 
 
 8 70 25 
 
 25672 375 
 
 .003389831 
 
 246 
 
 6 05 16 
 
 14 886 936 
 
 .004065041 
 
 296 
 
 8 7616 
 
 25 934 336 
 
 .003378378 
 
 247 
 
 6 10 09 
 
 15 069 223 
 
 .004048583 
 
 297 
 
 8 82 09 
 
 26 19S 073 
 
 .003367003 
 
 218 
 
 615 04 
 
 15 252 992 
 
 .004032258 
 
 298 
 
 8 88 04 
 
 26463 592 
 
 .003355705 
 
 249 
 
 6 20 01 
 
 15 438 249 
 
 .004019064 
 
 299 
 
 8 94 01 
 
 26 730 899 
 
 .003344482 
 
 250 
 
 6 25 00 
 
 15 625 000 
 
 .004000000 
 
 300 
 
 900 00 
 
 27 000 000 
 
 .003333333 
 
198 
 
 USKFUIv TABLES. 
 
 SQUARES, CUBES AND RECIPROCALS— Continued. 
 
 flos. 
 
 Squares Cubes. 
 
 Reciprocals. J Nos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 801 
 
 9 06 01 
 
 27 270 901 
 
 .003322259 1 351 
 
 12 32 01 
 
 43 243 551 
 
 .002849003 
 
 802 
 
 912 04 
 
 27 543 608 
 
 .003311258 
 
 352 
 
 12 39 04 
 
 43 614 208 
 
 .002840909 
 
 803 
 
 918 09 
 
 27 818 127 
 
 .003300330 
 
 353 
 
 12 46 09 
 
 43 986 977 
 
 .002832861 
 
 304 
 
 92416 
 
 28 094 464 
 
 .003289474 
 
 354 
 
 12 53 16 
 
 44 361864 
 
 .002824859 
 
 305 
 
 93025 
 
 28372 625 
 
 .008278689 
 
 355 
 
 126025 
 
 44 738 875 
 
 .002816901 
 
 306 
 
 03*36 
 
 28652616 
 
 .003267974 
 
 356 
 
 12 6736 
 
 45118016 
 
 .002808989 
 
 307 
 
 9 42 49 
 
 28934443 
 
 .003257329 
 
 357 
 
 12 74 49 
 
 45 499 293 
 
 .002801120 
 
 303 
 
 9 48 64 
 
 29 218 112 
 
 .003246753 
 
 358 
 
 12 8164 
 
 45 882 712 
 
 .002793296 
 
 309 
 
 9 54 81 
 
 29 503 629 
 
 .003236246 
 
 359 
 
 12 88 81 
 
 46 268 279 
 
 .002785515 
 
 310 
 
 Q6100 
 
 29 791000 
 
 .003225806 
 
 860 
 
 12 96 00 
 
 46 656000 
 
 .002777778 
 
 311 
 
 96721 
 
 30080231 
 
 .003215434 
 
 361 
 
 1303 21 
 
 47 045 881 
 
 .002770083 
 
 312 
 
 97344 
 
 30 371 328 
 
 .003205128 
 
 362 
 
 13 10 44 
 
 47 437 928 
 
 .002762431 
 
 313 
 
 9 79 69 
 
 30 664 297 
 
 .0-3194888 
 
 363 
 
 13 17 69 
 
 47 832 147 
 
 .002754821 
 
 314 
 
 9 85 96 
 
 30 959 144 
 
 .003184713 
 
 364 
 
 13 24 96 
 
 48 228 544 
 
 .002747253 
 
 315 
 
 9 9225 
 
 31255 875 
 
 .003174603 
 
 365 
 
 13 3225 
 
 48 627125 
 
 .002739726 
 
 316 
 
 9 98 56 
 
 31554 496 
 
 .003164557 
 
 366 
 
 133956 
 
 49 027896 
 
 .002782240 
 
 317 
 
 10 04 89 
 
 31 855 013 
 
 .003154574 
 
 367 
 
 13 46 89 
 
 49 430 863 
 
 .002724796 
 
 318 
 
 101124 
 
 32 157 432 
 
 .003144654 
 
 368 
 
 13 54 24 
 
 49 836 032 
 
 .002717891 
 
 319 
 
 101761 
 
 32461759 
 
 .003134796 
 
 369 
 
 13 61 61 
 
 50 243 409 
 
 .002710027 
 
 320 
 
 1024 00 
 
 32 768000 
 
 .003125000 
 
 370 
 
 13 69 00 
 
 60 653 000 
 
 .002702703 
 
 821 
 
 10 3041 
 
 83 076 161 
 
 .003115265 
 
 371 
 
 13 76 41 
 
 61064 811 
 
 .002695418 
 
 
 1036 84 
 
 33 386 248 
 
 .003105590 
 
 372 
 
 13 83 84 
 
 61 478 848 
 
 ,002688172 
 
 323 
 
 10 43 29 
 
 33 698 267 
 
 .003095975 
 
 373 
 
 13 9129 
 
 51 895 117 
 
 .002680965 
 
 324 
 
 10 49 76 
 
 34 012 224 
 
 .003086420 
 
 374 
 
 13 98 76 
 
 62 313 624 
 
 .002673797 
 
 325 
 
 1056 25 
 
 34 328125 
 
 .003076923 
 
 375. 
 
 1406 25 
 
 62 734375 
 
 .002666667 
 
 326 
 
 106276 
 
 34 645976 
 
 .003067485 
 
 376 
 
 1413 76 
 
 53 157 376 
 
 .002659574 
 
 327 
 
 10 69 29 
 
 34 965 783 
 
 .003058104 
 
 377 
 
 14 2129 
 
 53 582 633 
 
 .002652520 
 
 
 10 75 84 
 
 35 287 552 
 
 .003048780 
 
 378 
 
 14 28 84 
 
 54 010 152 
 
 .002645503 
 
 329 
 
 10 82 41 
 
 35 611 289 
 
 .003039514 
 
 379 
 
 14 36 41 
 
 54 439 939 
 
 .002638522 
 
 330 
 
 10 89 00 
 
 35 937000 
 
 .003030303 
 
 380 
 
 14 44 00 
 
 64 872 000 
 
 .002631679 
 
 331 
 
 1095 61 
 
 36 264 691 
 
 .003021148 
 
 381 
 
 14 51 61 
 
 65 306 341 
 
 .002624672 
 
 332 
 
 1102 24 
 
 36 594 368 
 
 .003012048 
 
 382 
 
 14 59 24 
 
 55 742 968 
 
 .002617801 
 
 
 11 08 89 
 
 36 926 037 
 
 .003003003 
 
 383 
 
 14 66 89 
 
 66 181 887 
 
 .002610966 
 
 m 
 
 1115 56 
 
 37 259 704 
 
 .002994012 
 
 384 
 
 14 74 56 
 
 56 623 104 
 
 .002604167 
 
 335 
 
 112225 
 
 37 595 375 
 
 .002985075 
 
 385 
 
 14 82 25 
 
 67066 625 
 
 .002597403 
 
 336 
 
 1128 96 
 
 37 933056 
 
 .002976190 
 
 386 
 
 14 89 96 
 
 67 512 456 
 
 .002590674 
 
 237 
 
 1135 69 
 
 38 272 753 
 
 .002967359 
 
 387 
 
 14 97 69 
 
 67 960 603 
 
 .002583979 
 
 83S 
 
 1142 44 
 
 38 614 472 
 
 .002958580 
 
 388 
 
 15 05 44 
 
 58 411 072 
 
 .002-577320 
 
 .'(39 
 
 1149 21 
 
 38 958 219 
 
 .002949853 
 
 389 
 
 15 13 21 
 
 68 863 869 
 
 .002570694 
 
 3-10 
 
 1156 00 
 
 39 304 000 
 
 .002941176 
 
 390 
 
 15 2100 
 
 69 319 000 
 
 .002564103 
 
 341 
 
 11 62 81 
 
 39 651 821 
 
 .002932551 
 
 391 
 
 15 28 81 
 
 59 776 471 
 
 .002557645 
 
 
 11 69 64 
 
 40 001 688 
 
 .002923977 
 
 392 
 
 15 36 64 
 
 60 236 288 
 
 .002551020 
 
 343 
 
 1176 49 
 
 40 353 607 
 
 .0029 5452 
 
 303 
 
 15 44 49 
 
 60 698 457 
 
 .002544529 
 
 344 
 
 11 83 36 
 
 40 707 584 
 
 .002906977 
 
 394 
 
 15 52 36 
 
 61162 984 
 
 .002538071 
 
 345 
 
 1199 25 
 
 41063 625 
 
 .002898551 
 
 395 
 
 1560 25 
 
 61629 875 
 
 .002531646 
 
 3<6 
 
 1197 16 
 
 41 421 736 
 
 .002890173 
 
 396 
 
 15 6816 
 
 62 099 136 
 
 .002525253 
 
 347 
 
 12 04 09 
 
 41 781923 
 
 ,002881844 
 
 397 
 
 15 76 09 
 
 62 570 773 
 
 .002518892 
 
 348 
 
 121104 
 
 42144192 
 
 ,0028' 7 356i 
 
 398 
 
 15 84 04 
 
 63 044 792 
 
 .002512563 
 
 340 
 
 12 18 01 
 
 42 508 549 
 
 .002865330 
 
 309 
 
 15 92 01 
 
 63 521 199 
 
 .002.506265 
 
 350 
 
 12 25 00 
 
 42 875 000 
 
 .002857143 
 
 400 
 
 16 00 00 
 
 64 000 000 
 
 .002500000 
 
USEFUL TABIDS. 
 
 199 
 
 SQUARES, CUBES AND RECIPROCALS— Continued. 
 
 Nos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 flos. 
 
 Squares. 
 
 Cubes. 
 
 Reciprocals. 
 
 401 
 402 
 403 
 404 
 405 
 
 16 03 01 
 16 16 04 
 16 24 09 
 16 32 18 
 1640 25 
 
 61 481 201 
 
 64 964 808 
 
 65 450 827 
 
 65 939 264 
 
 66 430 125 
 
 .002493766 
 .002487562 
 .002481390 
 .002475248 
 .002469136 
 
 451 
 452 
 453 
 454 
 455 
 
 20 3101 
 20 43 04 
 
 20 52 09 
 20 6116 
 20 70 25 
 
 91 733 851 
 
 92 345 408 
 
 92 959 677 
 
 93 576 664 
 
 94 196 375 
 
 .002217295 
 .002212389 
 .002207506 
 .002202643 
 .002197802 
 
 406 
 407 
 408 
 409 
 410 
 
 1648 36 
 16 56 49 
 16 64 64 
 1672 81 
 168100 
 
 66 923 416 
 
 67 419 143 
 
 67 917 312 
 
 68 417 929 
 68 921000 
 
 .002463054 
 .002457002 
 .002450980 
 .002444988 
 .002439024 
 
 456 
 457 
 458 
 459 
 460 
 
 20 79 36 
 20 88 49 
 
 20 97 64 
 
 21 06 81 
 21 16 00 
 
 94 818 816 
 
 95 443 993 
 
 96 071 912 
 
 96 702 579 
 
 97 336 000 
 
 .002192982 
 .002188184 
 .002183406 
 .002178649 
 .002173913 
 
 411 
 
 412 
 413 
 414 
 415 
 
 16 89 21 
 
 16 97 44 
 
 17 05 69 
 17 13 96 
 17 22 25 
 
 69426 531 
 
 69 931 528 
 70444 997 
 
 70 957 944 
 71473 375 
 
 .002433090 
 .002427184 
 .002421308 
 .002415459 
 .002489639 
 
 461 
 462 
 463 
 464 
 465 
 
 2125 21 
 2134 44 
 21 43 69 
 21 52 96 
 2162 25 
 
 97 972181 
 
 98 611 128 
 
 99 252 847 
 99 897 344 
 
 100544 625 
 
 .002169197 
 .002164502 
 .002159827 
 .002155172 
 .002150538 
 
 41G 
 417 
 418 
 419 
 
 420 
 
 17 30 56 
 17 38 89 
 17 47 24 
 17 55 61 
 17 64 00 
 
 71 991 296 
 
 72 51! 713 
 
 73 034 632 
 73560 059 
 74088 000 
 
 .002403846 
 .002398082 
 .002392344 
 .002386635 
 .002380952 
 
 466 
 467 
 468 
 469 
 470 
 
 217156 
 218089 
 21 90 24 
 
 21 99 61 
 
 22 0900 
 
 101 194 696 
 101847563 
 
 102 503 232 
 
 103 161 709 
 103 823000 
 
 .002145928 
 .U02141328 
 .002136752 
 .002132196 
 .002127660 
 
 421 
 422 
 423 
 424 
 425 
 
 17 72 41 
 17 8084 
 17 89 29 
 
 17 97 76 
 
 18 0625 
 
 74 618 461 
 
 75 151 448 
 
 75 686 967 
 
 76 225 024 
 76 765 625 
 
 .002375297 
 .002369668 
 .002364066 
 .002358491 
 .002352941 
 
 471 
 
 472 
 473 
 474 
 
 475 
 
 2218 41 
 
 22 27 84 
 22 37 29 
 22 46 76 
 22 56 25 
 
 104 487 111 
 105154 048 
 
 105 823 817 
 
 106 496424 
 107 171 875 
 
 .002123142 
 .002118644 
 .002114165 
 .002109705 
 .002105263 
 
 426 
 427 
 428 
 429 
 430 
 
 1.8 14 76 
 
 18 23 29 
 18 3184 
 18 40 41 
 18 49 00 
 
 77 308776 
 
 77 854 483 
 
 78 402 752 
 
 78 953589 
 
 79 507 000 
 
 .002347418 
 .002341920 
 .002336449 
 .002331002 
 .002325581 
 
 476 
 477 
 478 
 479 
 480 
 
 22 6576 
 22 75 29 
 2284 84 
 22 94 41 
 230400 
 
 107 850176 
 
 108 531333 
 
 109 215 352 
 109902239 
 110692 000 
 
 .002100840 
 .002096436 
 .002092050 
 .002087683 
 .002083383 
 
 431 
 432 
 43} 
 434 
 435 
 
 18 57 61 
 18 63 21 
 18 74 89 
 18 83 56 
 18 92 25 
 
 80 062 991 
 
 80 621 568 
 81 182 737 
 
 81 746 504 
 
 82 312 875 
 
 .002320186 
 .002314815 
 .002309469 
 .002304147 
 .002298851 
 
 481 
 
 482 
 483 
 
 484 
 485 
 
 2313 61 
 2328 24 
 2332 89 
 2342 56 
 236225 
 
 111281611 
 
 111 980 168 
 
 112 678587 
 
 113 379 904 
 
 114 084 125 
 
 .002079002 
 .002074689 
 .002070393 
 .002066116 
 .002061856 
 
 436 
 437 
 438 
 439 
 4)0 
 
 19 00 96 
 19 09 69 
 19 18 44 
 19 27 21 
 19 36 00 
 
 82 881856 
 83453 453 
 81027 672 
 84 604 519 
 85184 000 
 
 .002293578 
 
 .002288330 
 .002283105 
 .002277904 
 .002272727 
 
 486 
 487 
 488 
 489 
 490 
 
 23 6196 
 23 7169 
 23 8144 
 
 23 91 21 
 
 24 0100 
 
 114 791 256 
 
 115 501 303 
 
 116 214 272 
 
 116 930169 
 
 117 649 000 
 
 .002057613 
 .002053388 
 .002049180 
 .002044990 
 .002040816 
 
 441 
 442 
 443 
 444 
 445 
 
 19 44 81 
 19 53 61 
 19 62 49 
 19 71 36 
 19 80 25 
 
 85 766 121 
 
 86 350 888 
 86 938 307 
 87528 384 
 88121125 
 
 .002267574 
 .002262443 
 .002257336 
 .002252252 
 .002247191 
 
 491 
 492 
 493 
 494 
 495 
 
 211081 
 24 20 64 
 24 30 49 
 24 40 36 
 215025 
 
 118870771 
 
 119 095 488 
 
 119 823 157 
 
 120 553 784 
 121287375 
 
 .002036660 
 .0020*2520 
 .002028398 
 .002024291 
 ,002020202 
 
 446 
 447 
 448 
 449 
 
 450 
 
 19 8916 
 
 19 98 09 
 
 20 07 01 
 20 16 01 
 20 23 00 
 
 88716 536 
 89 314 623 
 
 89 915 392 
 
 90 518849 
 91125 000 
 
 .00224215Z 
 .0;)2237136 
 .002232143 
 ,0022271m 
 
 .002222222 
 
 496 
 497 
 
 498 
 499 
 500 
 
 24 60 16 
 24 70 09 
 24 80 04 
 
 24 90 01 
 
 25 00 00 
 
 122 023936 
 122763 473 
 
 123 505 992 
 
 124 251 499 
 
 125 000 000 
 
 .002016129 
 
 .002012072 
 .002008032 
 .002004008 
 .002000000 
 
USEffUI, TABLES. 
 
 TEIttPEKATUKES, CENTIGRADE AND 
 FAHRENHEIT. 
 
 c. 
 
 F. 
 
 c. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 -40 
 
 -40. 
 
 26 
 
 78.8 
 
 92 
 
 197.6 
 
 158 
 
 316.4 
 
 224 
 
 485.2 
 
 2&0 
 
 554 
 
 950 
 
 1742 
 
 -39 
 
 -38.2 
 
 27 
 
 80.6 
 
 93 
 
 199.4 
 
 159 
 
 818. 2 
 
 225 
 
 437. 
 
 .300 
 
 572 
 
 960 
 
 1760 
 
 -38 
 
 -36.4 
 
 28 
 
 82.4 
 
 94 
 
 201.2 
 
 160 
 
 320. 
 
 226 
 
 438.8 
 
 310 
 
 590 
 
 970 
 
 1778 
 
 -37 
 
 —34 6 
 
 29 
 
 84.2 
 
 95 
 
 203. 
 
 161 
 
 821.8 
 
 227 
 
 440.6 
 
 320 
 
 608 
 
 980 
 
 1796 
 
 -36 
 
 —32.8 
 
 30 
 
 86. 
 
 96 
 
 204.8 
 
 162 
 
 323.6 
 
 228 
 
 442.4 
 
 W 
 
 626 
 
 990 
 
 1814 
 
 -35 
 
 -31. 
 
 31 
 
 87.8 
 
 97 
 
 206. a 
 
 163 
 
 825.4 
 
 229 
 
 444.2 
 
 H r ~ 
 
 644 
 
 1000 
 
 1832 
 
 -34 
 
 —29.2 
 
 32 
 
 89.6 
 
 98 
 
 208.4 
 
 164 
 
 327.2 
 
 230 
 
 446. 
 
 f-.",0 
 
 662 
 
 1010 
 
 1850 
 
 -33 
 
 —27.4 
 
 33 
 
 91.4 
 
 99 
 
 210.2 
 
 165 
 
 329. 
 
 231 
 
 447.8 
 
 ,-r 
 
 680 
 
 1020 
 
 1868 
 
 -32 
 
 -25.6 
 
 34 
 
 93.2 
 
 100 
 
 212. 
 
 166 
 
 380.8 
 
 232 
 
 449.6 
 
 370 
 
 698 
 
 1030 
 
 1886 
 
 -31 
 
 -23.8 
 
 35 
 
 95. 
 
 101 
 
 213.8 
 
 167 
 
 332.6 
 
 233 
 
 451.4 
 
 .380 
 
 716 
 
 1040 
 
 1904 
 
 -30 
 
 -22. 
 
 36 
 
 96.8 
 
 102 
 
 215.6 
 
 168 
 
 334.4 
 
 234 
 
 453.2 
 
 ■:A 
 
 734 
 
 1050 
 
 1922 
 
 -29 
 
 -20.2 
 
 37 
 
 98.6 
 
 103 
 
 217.4 
 
 169 
 
 336.2 
 
 235 
 
 455. 
 
 400 
 
 752 
 
 1060 
 
 1940 
 
 -28 
 
 -18.4 
 
 33 
 
 100.4 
 
 104 
 
 219.2 
 
 170 
 
 338. 
 
 236 
 
 456.8 
 
 4!0 
 
 770 
 
 1070 
 
 1958 
 
 -27 
 
 -16.6 
 
 39 
 
 102.2 
 
 105 
 
 221. 
 
 171 
 
 339.8 
 
 237 
 
 458.6 
 
 420 
 
 788 
 
 1080 
 
 1976 
 
 -26 
 
 -14.8 
 
 40 
 
 104. 
 
 106 
 
 222.8 
 
 172 
 
 341.6 
 
 238 
 
 460.4 
 
 430 
 
 806 
 
 1090 
 
 1994 
 
 -25 
 
 -13. 
 
 41 
 
 105.8 
 
 107 
 
 224. Q 
 
 173 
 
 343.4 
 
 239 
 
 462.2 
 
 440 
 
 824 
 
 1100 
 
 2012 
 
 -24 
 
 -11.2 
 
 42 
 
 107.6 
 
 108 
 
 226.4 
 
 174 
 
 345.2 
 
 240 
 
 464. 
 
 450 
 
 842 
 
 1110 
 
 2030 
 
 -28 
 
 - 9.4 
 
 43 
 
 109.4 
 
 109 
 
 228.2 
 
 175 
 
 347. 
 
 241 
 
 465.8 
 
 460 
 
 860 
 
 1120 
 
 2048 
 
 -22 
 
 -7.6 
 
 44 
 
 111.2 
 
 110 
 
 230. 
 
 176 
 
 348.8 
 
 242 
 
 487.6 
 
 470 
 
 878 
 
 1130 
 
 2066 
 
 -21 
 
 — 5.8 
 
 45 
 
 118. 
 
 111 
 
 231.8 
 
 177 
 
 350.6 
 
 243 
 
 469.4 
 
 480 
 
 896 
 
 1140 
 
 2084 
 
 -20 
 
 - 4. 
 
 -,, 
 
 114.8 
 
 112 
 
 233 6 
 
 178 
 
 352.4 
 
 244 
 
 471.2 
 
 ;.:-■•:< 
 
 914 
 
 1150 
 
 2102 
 
 -19 
 
 - 2.2 
 
 4? 
 
 116.6 
 
 113 
 
 235.4 
 
 179 
 
 354.2 
 
 245 
 
 478. 
 
 500 
 
 932 
 
 1160 
 
 2120 
 
 -18 
 
 - 0.4 
 
 48 
 
 118.4 
 
 114 
 
 237.2 
 
 180 
 
 856. 
 
 246 
 
 474.8 
 
 510 
 
 950 
 
 il70 
 
 2138 
 
 -17 
 
 + 1.4 
 
 49 
 
 120.2 
 
 115 
 
 239. 
 
 181 
 
 357.8 
 
 247 
 
 476.6 
 
 55.0 
 
 968 
 
 1180 
 
 2156 
 
 -18 
 
 3.2 
 
 50 
 
 122. 
 
 116 
 
 240.8 
 
 182 
 
 359.6 
 
 248 
 
 478.4 
 
 ooC 
 
 986 
 
 1190 
 
 2174 
 
 -15 
 
 5. 
 
 51 
 
 123.8 
 
 117 
 
 242.6 
 
 183 
 
 361.4 
 
 249 
 
 480.2 
 
 "■:■-;: 
 
 1004 
 
 1200 
 
 2192 
 
 -14 
 
 6.8 
 
 5S 
 
 125.6 
 
 118 
 
 244.4 
 
 184 
 
 363.2 
 
 250 
 
 482. 
 
 : V. 
 
 1022 
 
 1210 
 
 2210 
 
 -13 
 
 8.6 
 
 53 
 
 127.4 
 
 119 
 
 246.2 
 
 185 
 
 365. 
 
 251 
 
 483.8 
 
 560 
 
 1040 
 
 1220 
 
 2228 
 
 -12 
 
 10.4 
 
 54 
 
 129.2 
 
 120 
 
 248. 
 
 186 
 
 366.8 
 
 252 
 
 485.6 
 
 c/( 
 
 1058 
 
 1230 
 
 2246 
 
 -11 
 
 12.2 
 
 55 
 
 131. 
 
 121 
 
 249.8 
 
 187 
 
 368.6 
 
 253 
 
 487.4 
 
 m. 
 
 1076 
 
 1240 
 
 2264 
 
 -10 
 
 14. 
 
 56 
 
 132.8 
 
 122 
 
 251.8 
 
 188 
 
 370.4 
 
 254 
 
 489.2 
 
 590 
 
 1094 
 
 1250 
 
 2282 
 
 - 9 
 
 15.8 
 
 57 
 
 134.6 
 
 123 
 
 253.4 
 
 189 
 
 372.2 
 
 255 
 
 49r. 
 
 600 
 
 1112 
 
 1260 
 
 2300 
 
 - 8 
 
 17.6 
 
 58 
 
 136.4 
 
 124 
 
 255.2 
 
 190 
 
 374. 
 
 256 
 
 492.8 
 
 '/,i 
 
 1130 
 
 1270 
 
 2318 
 
 - 7 
 
 19.4 
 
 59 
 
 138.2 
 
 126 
 
 257. 
 
 191 
 
 375.8 
 
 257 
 
 494.6 
 
 620 
 
 1148 
 
 1280 
 
 2336 
 
 - 6 
 
 21.2 
 
 60 
 
 140. 
 
 126 
 
 258.8 
 
 192 
 
 377.6 
 
 258 
 
 496.4 
 
 ..: 
 
 1166 
 
 1290 
 
 2354 
 
 - 5 
 
 23. 
 
 61 
 
 141.8 
 
 127 
 
 260.6 
 
 193 
 
 379.4 
 
 259 
 
 498,2 
 
 - 
 
 1184 
 
 1300 
 
 2372 
 
 - 4 
 
 24.8 
 
 62 
 
 143.6 
 
 128 
 
 262.4 
 
 194 
 
 381.2 
 
 260 
 
 500. 
 
 650 
 
 1202 
 
 1310 
 
 2390 
 
 - 3 
 
 26.6 
 
 63 
 
 145.4 
 
 129 
 
 264.2 
 
 195 
 
 383. 
 
 261 
 
 501.8 
 
 660 
 
 1220 
 
 1320 
 
 2408 
 
 - 2 
 
 28.4 
 
 64 
 
 147.2 
 
 130 
 
 266. 
 
 196 
 
 384.8 
 
 262 
 
 303.6 
 
 670 
 
 123# 
 
 1330 
 
 2426 
 
 - 1 
 
 80.2 
 
 65 
 
 149. 
 
 131 
 
 267.8 
 
 197 
 
 386.6 
 
 263 
 
 505.4 
 
 1680 
 
 1256 
 
 1340 
 
 2444 
 
 
 
 32. 
 
 66 
 
 150.8 
 
 132 
 
 269.6 
 
 198 
 
 388.4 
 
 264 
 
 507.2 
 
 6v30 
 
 1274 
 
 135C 
 
 2462 
 
 f 1 
 
 33.8 
 
 67 
 
 152.6 
 
 133 
 
 271.4 
 
 199 
 
 890.2 
 
 265 
 
 509. 
 
 \ 
 
 1292 
 
 1360 
 
 2480 
 
 2 
 
 35.6 
 
 68 
 
 154.4 
 
 134 
 
 273.2 
 
 200 
 
 392. 
 
 266 
 
 510.8 
 
 710 
 
 1810 
 
 1870 
 
 2498 
 
 8 
 
 37.4 
 
 69 
 
 156.2 
 
 135 
 
 275. 
 
 201 
 
 393.8 
 
 267 
 
 512.6 
 
 72011828 
 
 138C 
 
 2516 
 
 4 
 
 39.2 
 
 70 
 
 158. 
 
 136 
 
 276.8 
 
 202 
 
 395.6 
 
 268 
 
 514.4 
 
 780 1346 
 
 1390 
 
 2534 
 
 5 
 
 41. 
 
 71 
 
 159.8 
 
 137 
 
 278.6 
 
 203 
 
 397.4 
 
 269 
 
 616.2 
 
 74011364 
 
 1400 
 
 2552 
 
 6 
 
 42.8 
 
 72 
 
 161.6 
 
 138 
 
 280.4 
 
 204 
 
 399.2 
 
 270 
 
 518. 
 
 750 
 
 1382 
 
 1410 
 
 2570 
 
 7 
 
 44.6 
 
 n 
 
 163.4 
 
 139 
 
 282.2 
 
 205 
 
 401. 
 
 271 
 
 519.8 
 
 76C 
 
 1400 
 
 1420 
 
 2588 
 
 8 
 
 46.4 
 
 74 
 
 165.2 
 
 140 
 
 284. 
 
 206 
 
 402.8 
 
 272 
 
 521.6 
 
 770 
 
 1418 
 
 1430 
 
 2606 
 
 9 
 
 48.2 
 
 75 
 
 167. 
 
 141 
 
 285.8 
 
 207 
 
 404.6 
 
 273 
 
 274 
 
 523.4 
 
 78C 
 
 1436 
 
 1440 
 
 2624 
 
 10 
 
 50. 
 
 76 
 
 168.8 
 
 142 
 
 287.6 
 
 208 
 
 406.4 
 
 525.2 
 
 7&0 
 
 1454 
 
 1450 
 
 2642 
 
 11 
 
 5T.8 
 
 77 
 
 170.6 
 
 143 
 
 289.4 
 
 209 
 
 408.2 
 
 225 
 
 527. 
 
 800 
 
 1472 
 
 1460 
 
 2660 
 
 12 
 
 53.6 
 
 78 
 
 172.4 
 
 144 
 
 291.2 
 
 210 
 
 410. 
 
 276 
 
 528.8 
 
 810 
 
 1490 
 
 1470 
 
 2673 
 
 13 
 
 55.4 
 
 79 
 
 174.2 
 
 145 
 
 293. 
 
 211 
 
 411.8 
 
 277 
 
 530.6 
 
 820 
 
 1508 
 
 1480 
 
 269(r 
 
 14 
 
 57.2 
 
 80 
 
 176. 
 
 146 
 
 294.8 
 
 212 
 
 413.6 
 
 278 
 
 532.4 
 
 830 
 
 1526 
 
 1490 
 
 2714 
 
 £ 
 
 59. 
 
 81 
 
 177.8 
 
 147 
 
 296.6 
 
 213 
 
 415.4 
 
 279 
 
 534.2 
 
 610 
 
 1544 
 
 1500 
 
 2732 
 
 16 
 
 60.8 
 
 'A 
 
 179.6 
 
 148 
 
 298.4 
 
 214 
 
 417.2 
 
 280 
 
 536. 
 
 ,<-,- 
 
 1562 
 
 1510 
 
 2750 
 
 S 
 
 62.6 
 
 83 
 
 181.4 
 
 149 
 
 300.2 
 
 215. 
 
 419. 
 
 281 
 
 537.8 
 
 860 
 
 1580 
 
 1520 
 1530 
 
 2768 
 
 64.4 
 
 84 
 
 183.2 
 
 150 
 
 302. 
 
 216 
 
 420.8 
 
 282 
 
 539.6 
 
 870 
 
 1598 
 
 2786 
 
 19 
 
 66.2 
 
 85 
 
 185.- 
 
 151 
 
 303.8 
 
 217 
 
 422,6 
 
 283 
 
 541.4 
 
 880 
 
 1616 
 
 1540 
 
 2804 
 
 20 
 
 68. 
 
 86 
 
 186.8 
 
 152 
 
 305.6 
 
 218 
 
 424.4 
 
 284 
 
 543.2 
 
 890 
 
 1634 
 
 1550 
 
 2822 
 
 J21 
 
 69.8 
 
 87 
 
 188.6 
 
 153 
 
 307.4 
 
 219 
 
 426.2 
 
 285 
 
 545. 
 
 900 
 
 1652 
 
 1600 
 
 2912 
 
 22 
 
 71.6 
 
 88 
 
 190.4 
 
 154 
 
 309.2 
 
 220 
 
 428. 
 
 286 
 
 546.8 
 
 910 
 
 1670 
 
 1650 
 
 3002 
 
 23 
 
 73.4 
 
 89 
 
 192.2 
 
 155 
 
 311. 
 
 221 
 
 429.8 
 
 287 
 
 548.6 
 
 920 
 
 1688 
 
 1700 
 
 3092 
 
 24 
 
 75.2 
 
 90 
 
 194. 
 
 156 
 
 312.8 
 
 222 
 
 431.6 
 
 288 
 
 550.4 
 
 930 
 
 1706 
 
 1750 
 
 3182 
 
 25 
 
 77. 
 
 91 
 
 195.8 
 
 157 
 
 314.6 
 
 223 
 
 433.4 
 
 289 
 
 552.2 
 
 940 
 
 1724 
 
 1800 
 
 8272 
 
USEFUL TABLES. 
 
 
 1 
 
 E3 
 
 IPER 
 
 ATI 
 
 LIRE 
 
 S, FAHRENHEIT AND 
 
 
 
 
 CENTIGRAUE. 
 
 F. 
 
 C. 
 
 F. 
 26 
 
 C. 
 
 F 
 
 92 
 
 C. 
 
 33.3 
 
 F 
 158 
 
 C. 
 
 70. 
 
 F. 
 224 
 
 c. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 -40 
 
 -40. 
 
 -3.3 
 
 106.7 
 
 290 
 
 143.3 
 
 360 
 
 182.2 
 
 —39 
 
 -39.4 
 
 27 
 
 - 2.8 
 
 93 
 
 33.9 
 
 159 
 
 70.6 
 
 225 
 
 107.2 
 
 291 
 
 143.9 
 
 370 
 
 187.8 
 
 -38 
 
 -38.9 
 
 28 
 
 — 2 2 
 
 94 
 
 34.4 
 
 100 
 
 71.1 
 
 226 
 
 107.8 
 
 202 
 
 144.4 
 
 380 
 
 193.3 
 
 -37 
 
 -38.3 
 
 29 
 
 — 1.7 
 
 95 
 
 35. 
 
 161 
 
 71.7 
 
 227 
 
 108.3 
 
 im 
 
 145. 
 
 890 
 
 198.9 
 
 -36 
 
 -37.8 
 
 30 
 
 - 1.1 
 
 96 
 
 35.6 
 
 162 
 
 72.2 
 
 228 
 
 108.9 
 
 294 
 
 145.6 
 
 400 
 
 204.4 
 
 -35 
 
 -37.2 
 
 31 
 
 - 0.6 
 
 97 
 
 36.1 
 
 163 
 
 72.8 
 
 229 
 
 109.4 
 
 295 
 
 146.1 
 
 410 
 
 210. 
 
 -34 
 
 -36.7 
 
 32 
 
 0. 
 
 98 
 
 36.7 
 
 164 
 
 73.3 
 
 230 
 
 110. 
 
 220 
 
 146.7 
 
 420 
 
 215.6 
 
 -33 
 
 -36.1 
 
 33 
 
 -f 0.6 
 
 99 
 
 37.2 
 
 165 
 
 73.9 
 
 23! 
 
 110.6 
 
 297 
 
 147.2 
 
 480 
 
 221.1 
 
 -32 
 
 —35.6 
 
 34 
 
 1.1 
 
 100 
 
 37.8 
 
 166 
 
 74.4 
 
 232 
 
 111.1 
 
 228 
 
 147.8 
 
 410 
 
 226.7 
 
 -31 
 
 -35, 
 
 35 
 
 1.7 
 
 101 
 
 .38.3 
 
 167 
 
 75 
 
 
 111.7 
 
 299 
 
 148.3 
 
 4.50 
 
 232 2 
 
 -30 
 
 —34.4 
 
 36 
 
 2.2 
 
 102 
 
 38.9 
 
 168 
 
 75.6 
 
 234 
 
 112.2 
 
 300 
 
 148.9 
 
 460 
 
 237.8 
 
 —29 
 
 -33.9 
 
 87 
 
 2.8 
 
 103 
 
 "39.4 
 
 169 
 
 76.1 
 
 
 112.8 
 
 301 
 
 149 4 
 
 470 
 
 243.3 
 
 —28 
 
 -33.3 
 
 38 
 
 3.3 
 
 104 
 
 40. 
 
 170 
 
 76.7 
 
 236 
 
 113.3 
 
 302 
 
 150. 
 
 480 
 
 248 9 
 
 -27 
 
 -32.8 
 
 39 
 
 3.9 
 
 105 
 
 40.6 
 
 171 
 
 77.2 
 
 237 
 
 113.9 
 
 825' 
 
 150.6 
 
 490 
 
 254.4 
 
 —26 
 
 -32.2 
 
 40 
 
 4.4 
 
 106 
 
 41.1 
 
 572 
 
 77 8 
 
 2-8 
 
 114.4 
 
 301 
 
 151.1 
 
 500 
 
 260. 
 
 —25 
 
 -31.7 
 
 41 
 
 5. 
 
 107 
 
 41.7 
 
 173 
 
 78.3 
 
 239 
 
 115. 
 
 305 
 
 151.7 
 
 510 
 
 265.6 
 
 —24 
 
 -31.1 
 
 42 
 
 5.6 
 
 108 
 
 42.2 
 
 174 
 
 78.9 
 
 24(. 
 
 115.6 
 
 220 
 
 152.2 
 
 520 
 
 271.1 
 
 -23 
 
 -30.6 
 
 43 
 
 6.1 
 
 109 
 
 42.8 
 
 175 
 
 79.4 
 
 211 
 
 116.1 
 
 So; 
 
 152.8 
 
 5.30 
 
 276.7 
 
 -22 
 
 —30. 
 
 44 
 
 6.7 
 
 110 
 
 43.3 
 
 176 
 
 80. 
 
 242 
 
 116.7 
 
 -,,8 
 
 153.3 
 
 540 
 
 282.2 
 
 -21 
 
 —29.4 
 
 45 
 
 7.2 
 
 111 
 
 43.9 
 
 177 
 
 80.6 
 
 243 
 
 117.2 
 
 309 
 
 153.9 
 
 550 
 
 287.8 
 
 -20 
 
 -28.9 
 
 46. 
 
 7.8 
 
 112 
 
 44 4 
 
 178 
 
 81.1 
 
 244 
 
 117.8 
 
 310 
 
 154.4 
 
 560 
 
 293.3 
 
 -19 
 
 -28.3 
 
 47 
 
 8.3 
 
 113 
 
 45. 
 
 179 
 
 81.7 
 
 245 
 
 118.3 
 
 311 
 
 155. 
 
 570 
 
 298.9 
 
 -18 
 
 -27.8 
 
 48 
 
 8.9 
 
 114 
 
 45.6 
 
 ISO 
 
 82.2 
 
 246 
 
 118.9 
 
 312 
 
 155.6 
 
 580 
 
 304.4 
 
 -17 
 
 —27.2 
 
 49 
 
 9.4 
 
 115 
 
 46.1 
 
 181 
 
 82.8 
 
 247 
 
 119.4 
 
 313 
 
 156.1 
 
 590 
 
 310. 
 
 -16 
 
 —26.7 
 
 50 
 
 10. 
 
 116 
 
 46.7 
 
 182 
 
 83.3 
 
 2J8 
 
 120. 
 
 314 
 
 156.7 
 
 600 
 
 315.6 
 
 -15 
 
 -26.1 
 
 51 
 
 10.6 
 
 117 
 
 47.2 
 
 183 
 
 83.9 
 
 249 
 
 120.6 
 
 315 
 
 157.2 
 
 61.0 
 
 321.1 
 
 -14 
 
 -25.6 
 
 52 
 
 11.1 
 
 118 
 
 47.8 
 
 lti4 
 
 84.4 
 
 s,<, 
 
 121.1 
 
 316 
 
 157.8 
 
 620 
 
 326.7 
 
 —13 
 
 -25. 
 
 53 
 
 11.7 
 
 119 
 
 48.3 
 
 185 
 
 85. 
 
 251 
 
 121.7 
 
 317 
 
 158.3 
 
 ©so 
 
 332.2 
 
 -12 
 
 —24.4 
 
 54 
 
 12.2 
 
 120 
 
 48.9 
 
 186 
 
 85.6 
 
 2 re 
 
 122.2 
 
 ole 
 
 158.9 
 
 640 
 
 337.8 
 
 —11 
 
 -23.9 
 
 55 
 
 12.8 
 
 121 
 
 49.4 
 
 187 
 
 86.1 
 
 253 
 
 122.8 
 
 319 
 
 159.4 
 
 650 
 
 343.3 
 
 —10 
 
 -23.3 
 
 58 
 
 13.3 
 
 122 
 
 50. 
 
 is> 
 
 86.7 
 
 254 
 
 123.3 
 
 J 
 
 160. 
 
 660 
 
 348.9 
 
 - 9 
 
 -22.8 
 
 57 
 
 13.9 
 
 123 
 
 50.6 
 
 189 
 
 87.2 
 
 255 
 
 123.9 
 
 821 
 
 160.6 
 
 670 
 
 354.4 
 
 - 8 
 
 —22.2 
 
 58 
 
 14.4 
 
 124 
 
 51.1 
 
 190 
 
 87.8 
 
 251, 
 
 124.4 
 
 322 
 
 161.1 
 
 
 360. 
 
 — 7 
 
 -21.7 
 
 59 
 
 15. 
 
 125 
 
 51.7 
 
 191 
 
 88.3 
 
 257 
 
 125. 
 
 323 
 
 161.7 
 
 690 
 
 365.6 
 
 — 6 
 
 -21.1 
 
 60 
 
 15.6 
 
 126 
 
 52.2 
 
 192 
 
 88.9 
 
 25'- 
 
 125.6 
 
 324 
 
 162.2 
 
 700 
 
 371.1 
 
 — 5 
 
 -20.6 
 
 61 
 
 16.1 
 
 127 
 
 52.8 
 
 19? 
 
 89.4 
 
 259 
 
 126.1 
 
 ■•- 
 
 162.8 
 
 710 
 
 376.7 
 
 - 4' 
 
 -20. 
 
 62 
 
 16.7 
 
 128 
 
 53.3 
 
 194 
 
 90. 
 
 261 
 
 126.7 
 
 -. 
 
 163.3 
 
 720 
 
 382.2 
 
 - 3 
 
 —10.4 
 
 C3 
 
 17.2 
 
 129 
 
 53.9 
 
 195 
 
 90.6 
 
 261 
 
 127.2 
 
 ■ - 
 
 163.9 
 
 730 387.8 
 
 - 2 
 
 -18.9 
 
 64 
 
 17.8 
 
 130 
 
 54.4 
 
 196 
 
 91.1 
 
 262 
 
 127.8 
 
 .- :■ 
 
 164.4 
 
 740 
 
 393.3 
 
 - 1 
 
 —18 3 
 
 65 
 
 18.3 
 
 131 
 
 55. 
 
 197 
 
 91.7 
 
 263 
 
 128.3 
 
 829 
 
 165. 
 
 750 
 
 398.9 
 
 
 
 -17.8 
 
 66 
 
 18.9 
 
 132 
 
 55.6 
 
 \9r 
 
 92.2 
 
 264 
 
 128.9 
 
 330 
 
 165.6 
 
 760 
 
 404.4 
 
 + 1 
 
 —17.2 
 
 67 
 
 19.4 
 
 133 
 
 56.1 
 
 199 
 
 92.8 
 
 265 
 
 129.4 
 
 331 
 
 166.1 
 
 770 
 
 410. 
 
 2 
 
 -16.7 
 
 68 
 
 20. 
 
 134 
 
 56.7 
 
 20!" 
 
 93.3 
 
 266 
 
 130. 
 
 - - 
 
 166.7 
 
 780 
 
 415.6 
 
 3 
 
 -16.1 
 
 63 
 
 20.6 
 
 135 
 
 57.2 
 
 201 
 
 93.9 
 
 207 
 
 130.6 
 
 ;>: 
 
 167.2 
 
 790 
 
 421.1 
 
 4 
 
 —15.6 
 
 70 
 
 21.1 
 
 136 
 
 57 8 
 
 202 
 
 94. 4 
 
 .' 
 
 131.1 
 
 334 
 
 167.8 
 
 SOO 
 
 426.7 
 
 5 
 
 -15. 
 
 71 
 
 21.7 
 
 137 
 
 58.3 
 
 203 
 
 95. 
 
 269 
 
 131.7 
 
 335 
 
 168.3 
 
 810 
 
 432.2 
 
 6 
 
 —14.4 
 
 72 
 
 22.2 
 
 138 
 
 58.9 
 
 204 
 
 95.6 
 
 270 
 
 132.2 
 
 336 
 
 168.9 
 
 820 
 
 437.8 
 
 7 
 
 -13.9 
 
 73 
 
 22.8 
 
 139 
 
 59.4 
 
 205 
 
 96.1 
 
 271 
 
 132.8 
 
 337 
 
 169.4 
 
 830 
 
 443.3 
 
 8 
 
 —13.3 
 
 74 
 
 23.3 
 
 140 
 
 60. 
 
 206 
 
 96.7 
 
 272 
 
 133.3 
 
 338 
 
 170. 
 
 840 
 
 448.9 
 
 9 
 
 —12.8 
 
 75 
 
 23.9 
 
 141 
 
 60.6 
 
 207 
 
 97.2 
 
 273 
 
 133.9 
 
 222; 
 
 170.6 
 
 8.50 
 
 454.4 
 
 10 
 
 -12.2 
 
 76 
 
 24.4 
 
 142 
 
 61.1 
 
 208 
 
 97.8 
 
 274 
 
 134.4 
 
 340 
 
 171.1 
 
 860 
 
 460. 
 
 11 
 
 -11.7 
 
 77 
 
 25. 
 
 143 
 
 61.7 
 
 209 
 
 98.3 
 
 
 135. 
 
 341 
 
 171.7 
 
 870 
 
 465.6 
 
 12 
 
 —11.1 
 
 78 
 
 25.6 
 
 144 
 
 62.2 
 
 210 
 
 98.9 
 
 270 
 
 135.6 
 
 342 
 
 172.2 
 
 880 
 
 471.1 
 
 13 
 
 -10.6 
 
 79 
 
 26.1 
 
 145 
 
 62.8 
 
 211 
 
 99 4 
 
 
 136.1 
 
 : -, 
 
 172.8 
 
 890 
 
 476.7 
 
 14 
 
 -10. 
 
 80 
 
 26.7 
 
 146 
 
 63.3 
 
 212 
 
 100. 
 
 
 136.7 
 
 344 
 
 173.3 
 
 900 
 
 482.2 
 
 15 
 
 — 9.4 
 
 81 
 
 27.2 
 
 147 
 
 63.9 
 
 213 
 
 100.0 
 
 279 
 
 137.2 
 
 345 
 
 173.9 
 
 910 
 
 487.8 
 
 16 
 
 — 8.9 
 
 82 
 
 27.8 
 
 148 
 
 64.4 
 
 214 
 
 101.1 
 
 
 137.8 
 
 346 
 
 174.4 
 
 920 
 
 493.3 
 
 17 
 
 — 8.3 
 
 83 
 
 28.3 
 
 149 
 
 65. 
 
 215 
 
 101.7 
 
 
 138.3 
 
 347 
 
 175. 
 
 930 
 
 498.9 
 
 18 
 
 — 7.8 
 
 84 
 
 28.9 
 
 150 
 
 65.6 
 
 216 
 
 102.2 
 
 
 138.9 
 
 348 
 
 175.6 
 
 940 
 
 504.4 
 
 19 
 
 — 7.2 
 
 85 
 
 29.4 
 
 151 
 
 66.1 
 
 217 
 
 102.8 
 
 222 
 
 139.4 
 
 349 
 
 176.1 
 
 950 
 
 510; 
 
 20 
 
 — 6.7 
 
 86 
 
 30. 
 
 152 
 
 66.7 
 
 
 103.3 
 
 284 
 
 140. 
 
 350 
 
 176.7 
 
 
 515.6 
 
 21 
 
 — 6.1 
 
 87 
 
 30.6 
 
 153 
 
 67.2 
 
 219 
 
 103.9 
 
 285 
 
 140.6 
 
 351 
 
 177.2 
 
 970 
 
 521.1 
 
 22 
 
 - 5.6 
 
 88 
 
 31.1 
 
 154 
 
 67.8 
 
 
 104.4 
 
 286 
 
 141.1 
 
 
 177.8 
 
 980 
 
 526.7 
 
 23 
 
 — 5. 
 
 89 
 
 31.7 
 
 155 
 
 68.3 
 
 221 
 
 105. 
 
 
 141.7 
 
 353 
 
 178.3 
 
 990 
 
 532.2 
 
 24 
 
 - 4.4 
 
 90 
 
 32.2 
 
 156 
 
 68.9 
 
 
 105.6 
 
 
 142.2 
 
 354 
 
 178.9 
 
 1000 
 
 537.8 
 
 25 
 
 t- 3.9 
 
 91 
 
 32.8 
 
 157 
 
 69.4 
 
 
 106.1 
 
 
 142.8 
 
 355 
 
 179.4 
 
 1010 543.3 
 
USEFUL TABLES. 
 
 DECIMALS OF A. FOOT FOR EACH & OF 
 AN INCH. 
 
 Inch. 
 
 o" 
 
 1" 
 
 2" 
 
 3" 
 
 4" 
 
 5" 
 
 
 
 
 
 .0833 
 
 .1667 
 
 2500 
 
 3333 
 
 4167 
 
 i 
 
 .0013 
 0026 
 .0039 
 .0052 
 
 .0848 
 .0859 
 .0872 
 .0885 
 
 .1680 
 .1693 
 .1708 
 • 1719 
 
 .2513 
 .2526 
 .2539 
 .2552 
 
 .3346 
 .3359 
 .3372 
 .3385 
 
 .4180 
 .4193 
 .4206 
 .4219 
 
 'A 
 
 i 
 
 i 
 
 0085 
 .0078 
 .0091 
 .0104, 
 
 .0898 
 .0911 
 .0924 
 .0937 
 
 .1732 
 .1745 
 .1758 
 .1771 
 
 .2565 
 .2578 
 .2591 
 .2604 
 
 .3398 
 .3411 
 .3424 
 .3437 
 
 .4232 
 .4245 
 .4258 
 .4271 
 
 A 
 A 
 
 8 
 
 .0117 
 .0130 
 .0143 
 .0156 
 
 .0951 
 .0984 
 .0977 
 .0990 
 
 .1784 
 .1797 
 1810 
 .1823 
 
 .2617 
 .2630 
 .2643 
 .2656 
 
 3451 
 .3464 
 .3477 
 .3490 
 
 .4284 
 .4297 
 .4310 
 .4323 
 
 
 .0169 
 .0182 
 0195 
 .0208 
 
 .1003 
 .1016 
 .1029 
 .1042 
 
 .1836 
 .1849 
 .1862 
 .1875 
 
 .2669 
 .2682 
 .2695 
 .2708 
 
 .3503 
 .3516 
 .3529 
 .3542 
 
 .4336 
 .4349 
 .4362 
 .4375 
 
 if 
 
 .0221 
 .0234 
 .0247 
 .0260 
 
 .1055 
 .1038 
 .1081 
 .1094 
 
 .1888 
 .1901 
 .1914 
 .1927 
 
 .2721 
 .2734 
 ,2747 
 .2760 
 
 .3555 
 .3568 
 .3581 
 .3594 
 
 .4388 
 .4401 
 .4414 
 .4427 
 
 If 
 
 1 
 
 .0273 
 .0286 
 .0299 
 0312 
 
 .1107 
 .1120 
 .1133 
 .1146 
 
 .1940 
 .1953 
 .1966 
 .1979 
 
 .2773 
 .2786 
 .2799 
 .2812 
 
 .3607 
 .3620 
 .3633 
 .3646 
 
 .4440 
 .4453 
 .4466 
 .4479 
 
 11 
 1 
 
 .0326 
 .0339 
 0352 
 .0365 
 
 .1159 
 .1172 
 .1185 
 .1198 
 
 .1992 
 .2005 
 2018 
 .2031 
 
 .2826 
 .2839 
 .2852 
 .2865 
 
 .3659 
 3672 
 3685 
 .3698 
 
 .4492 
 .4505 
 .4518 
 .4531 
 
 * 
 
 .0378 
 0391 
 .0404 
 .0417 
 
 .1211 
 .1224 
 .1237 
 .1250 
 
 .2044 
 •2057 
 .2070 
 .2083 
 
 .2878 
 .2891 
 .2904 
 .2917 
 
 .3711 
 .3724 
 .3737 
 .3750 
 
 .4544 
 .4557 
 .4570 
 .4583 
 
USEFUL TABIDS. 
 
 203 
 
 DECIMALS OP A FOOT FOR EACH ^ OF 
 AN INCH 
 
 Inch. 
 
 *6" 
 
 7" 
 
 8' 
 
 P-" 
 
 10" 
 
 U" 
 
 
 
 5000 
 
 5833 
 
 .6667 
 
 7500 
 
 .8333 
 
 9167 
 
 <h 
 
 6013 
 
 5846 
 
 .6680 
 
 .7513 
 
 .8346 
 
 .9180 
 
 A 
 
 .5026 
 
 5859 
 
 6693 
 
 .7526 
 
 .8359 
 
 .9193 
 
 A 
 
 .5039 
 
 5872 
 
 .6706 
 
 .7539 
 
 8372 
 
 .9206 
 
 A 
 
 .5052 
 
 .6885 
 
 .6719 
 
 .7552 
 
 .8385 
 
 .9219 
 
 A 
 
 .5065 
 
 .5898 
 
 .6732 
 
 .7565 
 
 .8398 
 
 .9232 
 
 & 
 
 .5078 
 
 5911 
 
 .6745 
 
 .7578 
 
 .8411 
 
 .9245 
 
 A 
 
 .5091 
 
 .5924 
 
 .6758 
 
 7591 
 
 .8424 
 
 .9258 
 
 i 
 
 5104 
 
 5937 
 
 .6771 
 
 .7604 
 
 .8437 
 
 ,9271 
 
 A 
 
 .5117 
 
 .6951 
 
 .6784 
 
 .7617 
 
 .8451 
 
 .9284 
 
 A 
 
 .6130 
 
 .5964 
 
 .6797 
 
 .7630 
 
 .8464 
 
 .9297 
 
 H 
 
 •5143 
 
 .5977 
 
 .6810 
 
 .7643 
 
 .8477 
 
 .9310 
 
 A 
 
 .5156 
 
 .5990 
 
 .6823 
 
 .7656 
 
 .8490 
 
 .9323 
 
 H 
 
 .5169 
 
 .6003 
 
 .6838 
 
 7669 
 
 .8503 
 
 .9336 
 
 A 
 
 5182 
 
 .6016 
 
 .6849 
 
 .7682 
 
 .8516 
 
 .9349 
 
 if 
 
 5195 
 
 .6029 
 
 .6862 
 
 .7695 
 
 .8529 
 
 .9362 
 
 1 
 
 .5208 
 
 .6042 
 
 .6875 
 
 .7708 
 
 .8542 
 
 .9375 
 
 tf 
 
 .5221 
 
 .6055 
 
 .6888 
 
 .7721 
 
 .8555 
 
 .9388 
 
 A 
 
 .5234 
 
 6068 
 
 .8901 
 
 .7734 
 
 .8568 
 
 .9401 
 
 If 
 
 .5247 
 
 .6081 
 
 .6914 
 
 .7747 
 
 .8581 
 
 .9414 
 
 A 
 
 .5260 
 
 .6094 
 
 .6927 
 
 .7760 
 
 .8594 
 
 .9427 
 
 ft 
 
 .5273 
 
 .6107 
 
 .6940 
 
 .7773 
 
 .8607 
 
 .9440 
 
 H 
 
 .5286 
 
 .6120 
 
 .6953 
 
 .7786 
 
 .8620 
 
 .9453 
 
 ** 
 
 .5299 
 
 .6133 
 
 .6966 
 
 .7799 
 
 .8633 
 
 .9466 
 
 t 
 
 .5312 
 
 .6146 
 
 .6979 
 
 .7812 
 
 .8646 
 
 .9479 
 
 ft 
 
 .5326 
 
 .6159 
 
 .6992 
 
 .7826 
 
 .8669 
 
 .9492 
 
 tt 
 
 .5339 
 
 .6172 
 
 .7005 
 
 .7839 
 
 .8672 
 
 .9505 
 
 ¥ 
 
 .5352 
 
 .6185 
 
 .7018 
 
 .7852 
 
 .8685 
 
 .9518 
 
 A 
 
 .5365 
 
 .6198 
 
 .7031 
 
 .7865 
 
 .8698 
 
 9531 
 
 H 
 
 .5378 
 
 .6211 
 
 .7044 
 
 .7878 
 
 .8711 
 
 .9544 
 
 « 
 
 .5391 
 
 .6224 
 
 .7057 
 
 .7891 
 
 .8724 
 
 .9557 
 
 ¥ 
 
 .5404 
 
 .6237 
 
 .7070 
 
 .7904 
 
 .8737 
 
 .9570 
 
 i 
 
 .5417 
 
 6250 
 
 .7083 
 
 .7917 
 
 .8750 
 
 .9583 
 
204 
 
 USEFUL TABLES. 
 
 DECIMALS OF A FOOT FOR EACH & OF 
 AN INCH. 
 
 Inch. 
 
 
 
 1" 
 
 2" 
 
 3" 
 
 4" 
 
 5" 
 
 « 
 
 s 
 
 .0430 
 .0443 
 .0456 
 .0409 
 
 .1263 
 .1276 
 .1289 
 .1302 
 
 .2096 
 .2109 
 .2122 
 .2135 
 
 .2930 
 .2943 
 .2956 
 .2969 
 
 .3763 
 .3776 
 .3789 
 .3802 
 
 ,4596 
 .4609 
 .4622 
 .4635 
 
 If 
 
 .0482 
 .0495 
 .0508 
 .0521 
 
 .1315 
 .1328 
 .1341 
 .1354 
 
 .2148 
 .2101 
 .2174 
 .2188 
 
 .2982 
 .2995 
 .3008 
 ,3021 
 
 .3815 
 .3828 
 .3841 
 .3854 
 
 .4648 
 .4661 
 .4674 
 .4688 
 
 ft 
 
 H 
 
 II 
 
 .0534 
 .0547 
 .0500 
 .0573 
 
 .1367 
 .1380 
 .1393 
 .1406 
 
 .2201 
 .2214 
 .2227 
 .2240 
 
 .3034 
 .3047 
 .3060 
 .3073 
 
 .3867 
 .3880 
 .3893 
 .3903 
 
 .4701 
 .4714 
 .4727 
 .4740 
 
 If 
 
 I 
 
 .0586 
 .0599 
 .0012 
 .0625 
 
 .1419 
 .1432 
 .1445 
 .1458 
 
 .2253 
 .226*? 
 .2279 
 .2292 
 
 .3088 
 .3099 
 .3112 
 .3125 
 
 .3919 
 .3932 
 .3945 
 .3958 
 
 .4753 
 .4766 
 .4779 
 .4792 
 
 ft 
 If 
 
 .0838 
 .0051 
 .0004 
 .0677 
 
 .1471 
 .1484 
 .1497 
 .1510 
 
 .2305 
 .2318 
 .2331 
 .2344 
 
 .3138 
 .3151 
 .3164 
 .8177 
 
 .3971 
 .3984 
 .3997 
 .4010 
 
 .4805 
 .4818 
 .4831 
 .4844 
 
 ft 
 
 1 
 
 .0690 
 .0703 
 .0716 
 .0729 
 
 .1523 
 .1536 
 .1549 
 .1502 
 
 .2357 
 .2370 
 .2383 
 2396 
 
 .3190 
 .3203 
 .3216 
 .3229 
 
 .4023 
 .4036 
 .4049 
 •4062 
 
 .4857 
 .4870 
 .4883 
 •4896 
 
 ft 
 
 If 
 
 If 
 it 
 
 .0742 
 .0755 
 .0768 
 .0781 
 
 .1576 
 .1589 
 .1602 
 .1615 
 
 .2409 
 .2422 
 .2435 
 .2448 
 
 .3242 
 .8255 
 .3268 
 .3281 
 
 .4070 
 .4089 
 .4102 
 .4115 
 
 .4909 
 .4922 
 .4935 
 .4948 
 
 ft 
 ft 
 
 f 
 
 .0794 
 .0807 
 .0820 
 
 .1628 
 1641 
 .1054 
 
 .2461 
 .2474 
 .2487 
 
 .3294 
 .3307 
 .3320 
 
 .4128 
 .4141 
 .4154 
 
 .4961 
 .4974 
 .4987 
 
USEFUL TABLES. 
 
 205 
 
 DECIMALS OF A FOOT FOR EACH & OF 
 AN INCH. 
 
 Inoh. 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 11" 
 
 If 
 H 
 fl 
 A 
 
 .5430 
 5443 
 .5456 
 .5469 
 
 .6263 
 .6276 
 .6289 
 .6302 
 
 .7096 
 .7109 
 .7122 
 .7135 
 
 .7930 
 .7943 
 .7956 
 .7969 
 
 .8763 
 .8776 
 .8789 
 .8802 
 
 .9596 
 .9609 
 .9622 
 .9635 
 
 
 5482 
 5495 
 5508 
 .5521 
 
 .6315 
 .6328 
 .6341 
 .6354 
 
 .7148 
 .7161 
 •7174 
 .7188 
 
 .7982 
 .7995 
 8008 
 .8021 
 
 .8815 
 .8828 
 .8841 
 .8854 
 
 9648 
 .9661 
 .9674 
 .9688 
 
 It 
 
 .5534 
 
 .5547 
 5560 
 5573 
 
 6367 
 .6380 
 .6393 
 .6408 
 
 7201 
 .7214 
 .7227 
 .7240 
 
 .8034 
 .8047 
 .8060 
 8073 
 
 .8867 
 .8880 
 8893 
 .8906 
 
 .9701 
 .9714 
 .9727 
 .9740 
 
 II 
 
 23 
 32 
 
 1 
 
 .5586 
 5599 
 .5612 
 .5625 
 
 6419 
 6432 
 .6445 
 .6458 
 
 .7253 
 7266 
 
 .7279 
 .7292 
 
 .8086 
 .8099 
 8112 
 8125 
 
 .8919 
 .8932 
 8945 
 8958 
 
 .9753 
 9766 
 9779 
 9792 
 
 25 
 32 
 51 
 61 
 
 11 
 
 5638 
 5651 
 5664 
 5677 
 
 6471 
 .6484 
 .6497 
 6510 
 
 .7305 
 .7318 
 .7331 
 .7344 
 
 .8138 
 .8151 
 8164 
 .8177 
 
 8971 
 .8984 
 .8997 
 .9010 
 
 .9805 
 .9818 
 9831 
 .9844 
 
 If 
 
 H 
 
 f 
 
 .5690 
 .5703 
 5716 
 .5729 
 
 .6523 
 .6536 
 .6549 
 .6562 
 
 .7357 
 .7370 
 .7383 
 .7396 
 
 .8190 
 .8203 
 .8216 
 .8229 
 
 9023 
 .9036 
 9049 
 .9062 
 
 9857 
 .9870 
 9883 
 9896 
 
 5.7. 
 
 6? 
 29 
 32 
 
 M 
 
 15 
 
 .5742 
 .5755 
 .5768 
 .5781 
 
 .6576 
 .6589 
 .6602 
 .6615 
 
 .7409 
 .7422 
 .7435 
 .7448 
 
 .8242 
 .8255 
 .8268 
 .8281 
 
 .9076 
 .9089 
 .9102 
 9115 
 
 .9909 
 .9922 
 .9935 
 •9948 
 
 n 
 
 31 
 32 
 
 tt 
 
 1 
 
 5794 
 5807 
 .5820 
 
 .6628 
 .6641 
 G654 
 
 .7461 
 .7474 
 .7487 
 
 .8294 
 .8307 
 .8320 
 
 .9128 
 .9141 
 .9154 
 
 .9961 
 
 .9974 
 
 .9987 
 
 1.0000 
 
206 
 
 USEFUI, TABLES. 
 
 DECIMALS OP AN INCH FOR EACH ^fth. 
 
 ■g^ds. 
 
 ^ths. 
 
 Decimal. 
 
 Fraction 
 
 •g^ds. 
 
 B^ths. 
 
 Decimal. 
 
 Fraction 
 
 
 1 
 
 .015625 
 
 
 
 33 
 
 .515625 
 
 
 1 
 
 2 
 
 .03125 
 
 
 17 
 
 34 
 
 .53125 
 
 
 
 3 
 
 .046875 
 
 
 
 35 
 
 .546875 
 
 
 2 
 
 4 
 
 .0625 
 
 1-16 
 
 18 
 
 36 
 
 .5625 
 
 9-16 
 
 
 5 
 
 .078125 
 
 
 
 37 
 
 .578125 
 
 
 3 
 
 6 
 
 .09375 
 
 
 19 
 
 38 
 
 .59375 
 
 
 
 7 
 
 .109375 
 
 
 
 39 
 
 .609375 
 
 
 4 
 
 8 
 
 .125 
 
 1-8 
 
 20 
 
 40 
 
 .625 
 
 5-8 
 
 
 9 
 
 .140625 
 
 
 
 41 
 
 .640625 
 
 
 5 
 
 10 
 
 .15625 
 
 
 21 
 
 42 
 
 .65625 
 
 
 
 11 
 
 .171875 
 
 
 
 43 
 
 .671875 
 
 
 6 
 
 12 
 
 .1875 
 
 3-16 
 
 22 
 
 44 
 
 .6875 
 
 11-16 
 
 
 13 
 
 .203125 
 
 
 
 45 
 
 .703125 
 
 
 7 
 
 14 
 
 .21875 
 
 
 23 
 
 46 
 
 .71875 
 
 
 
 15 
 
 .234375 
 
 
 
 47 
 
 .734375 
 
 
 8 
 
 16 
 
 .25 
 
 1-4 
 
 24 
 
 48 
 
 .75 
 
 3-4 
 
 
 17 
 
 .265626 
 
 
 
 49 
 
 .765625 
 
 
 9 
 
 18 
 
 .28125 
 
 
 25 
 
 50 
 
 .78125 
 
 
 
 19 
 
 .296875 
 
 
 
 51 
 
 .796875 
 
 
 10 
 
 20 
 
 .3125 
 
 5-16 
 
 26 
 
 52 
 
 .8125 
 
 13-16 
 
 
 21 
 
 .328125 
 
 
 
 53 
 
 .828125 
 
 
 11 
 
 22 
 
 .34375 
 
 
 27 
 
 54 
 
 .84375 
 
 
 
 23 
 
 .359375 
 
 
 
 55 
 
 .859375 
 
 
 12 
 
 24 
 
 .375 
 
 3-8 
 
 28 
 
 56 
 
 .875 
 
 7-8 
 
 
 25 
 
 .390625 
 
 
 
 57 
 
 .890625 
 
 
 13 
 
 26 
 
 .40625 
 
 
 29 
 
 58 
 
 .90625 
 
 
 
 27 
 
 .421875 
 
 
 
 59 
 
 .921875 
 
 
 14 
 
 28 
 
 .4375 
 
 7-16 
 
 30 
 
 60 
 
 .9375 
 
 15-16 
 
 
 29 
 
 .453125 
 
 
 
 61 
 
 .953125 
 
 
 15 
 
 30 
 
 .46875 
 
 
 31 
 
 62 
 
 .96875 
 
 
 
 31 
 
 .484375 
 
 
 
 63 
 
 .984375 
 
 
 16 
 
 32 
 
 .5 
 
 1-2 
 
 32 
 
 64 
 
 1. 
 
 1 
 
USEFUL TABLES. 
 
 207 
 
 TABLES FOR CALCULATING THE HORSE POWER 
 OF WATER. 
 
 
 MINERS' INCH TABLE. 
 
 
 CUBIC FEET TABLE. 
 
 The following table gives 
 
 the Horse- 
 
 The following table gives the Horse- 
 
 Power of one miner's inch of water un- 
 
 Powe 
 
 r of one cubic foot of water pe» 
 
 der heads from one up to e 
 
 even huu- 
 
 minute under heads from one up to 
 
 dred feet. This in 
 
 :h equals 
 
 i>2 cubic 
 
 eleven hundred feet. 
 
 
 feet per minute. 
 
 
 
 
 
 
 
 Heads 
 in Feet. 
 
 Horse Power 
 
 in Feet. 
 
 Horse Power. 
 
 Heads 
 in Feet. 
 
 Horsepower. 
 
 in Feet. 
 
 Horse Power. 
 
 1 
 
 .0024147 
 
 320 
 
 .772704 
 
 1 
 
 .0016098 
 
 320 
 
 .515136 
 
 20 
 
 .0482294 
 
 330 
 
 .796851 
 
 20 
 
 .032196 
 
 330 
 
 .531234 
 
 30 
 
 .072441 
 
 340 
 
 .820998 
 
 30 
 
 .048294 
 
 340 
 
 .547332 
 
 40 
 
 .090588 
 
 350 
 
 .845145 
 
 40 
 
 .064392 
 
 350 
 
 .563430 
 
 50 
 
 .120735 
 
 360 
 
 .869292 
 
 50 
 
 .080490 
 
 360 
 
 .579528 
 
 
 .144S82 
 
 370 
 
 .898439 
 
 60 
 
 .096588 
 
 370 
 
 .595626 
 
 70 
 
 .169029 
 
 380 
 
 .917586 
 
 70 
 
 .112686 
 
 380 
 
 .611724 
 
 SO 
 
 .193176 
 
 390 
 
 .941733 
 
 80 
 
 .128784 
 
 390 
 
 .627822 
 
 90 
 
 .217323 
 
 400 
 
 .965S80 
 
 90 
 
 .144892 
 
 400 
 
 .643920 
 
 100 
 
 .241470 
 
 410 
 
 .990027 
 
 100 
 
 .160980 
 
 410 
 
 .660018 
 
 110 
 
 .265617 
 
 420 
 
 1.014174 
 
 110 
 
 .177078 
 
 420 
 
 .676116 
 
 120 
 
 .289764 
 
 430 
 
 1.038321 
 
 120 
 
 .193173 
 
 430 
 
 .692214 
 
 130 
 
 .313911 
 
 440 
 
 1.062468 
 
 130 
 
 .209274 
 
 440 
 
 .708312 
 
 140 
 
 .338058 
 
 450 
 
 1.0S6615 
 
 140 
 
 .225372 
 
 450 
 
 .724410 
 
 150 
 
 .362205 
 
 460 
 
 1.110762 
 
 150 
 
 .241470 
 
 460 
 
 .740503 
 
 160 
 
 .386352 
 
 470 
 
 1.134909 
 
 160 
 
 .257568 
 
 470 
 
 .756606 
 
 170 
 
 .410499 
 
 480 
 
 1.159056 
 
 170 
 
 .273666 
 
 480 
 
 .772704 
 
 180 
 
 .434646 
 
 490 
 
 1.183206 
 
 180 
 
 .289764 
 
 490 
 
 .788802 
 
 190 
 
 .458793 
 
 500 
 
 1.207350 
 
 190 
 
 .305862 
 
 500 
 
 .804900 
 
 200 
 
 .482940 
 
 520 
 
 1.255644 
 
 200 
 
 .321960 
 
 520 
 
 .837096 
 
 210 
 
 .507087 
 
 540 
 
 1.303938 
 
 210 
 
 .338058 
 
 540 
 
 .869292 
 
 220 
 
 .531234 
 
 560 
 
 1.352232 
 
 220 
 
 .354156 
 
 560 
 
 .90148? 
 
 230 
 
 .555381 
 
 580 
 
 1.400526 
 
 230 
 
 .370254 
 
 580 
 
 .933684 
 
 240 
 
 .579528 
 
 600 
 
 1.44«820 
 
 240 
 
 .386352 
 
 600 
 
 .965880 
 
 250 
 
 .603675 
 
 650 
 
 1.569555 
 
 250 
 
 .402450 
 
 650 
 
 1.046370 
 
 260 
 
 .627822 
 
 700 
 
 1.690290 
 
 260 
 
 .418548 
 
 700 
 
 1.126860 
 
 270 
 
 .651969 
 
 750 
 
 1.811025 
 
 270 
 
 .434646 
 
 750 
 
 1.207350 
 
 280 
 
 .676116 
 
 800 
 
 1.931760 
 
 280 
 
 .450744 
 
 800 
 
 1.287840 
 
 290 
 
 .700263 
 
 900 
 
 2.173230 
 
 290 
 
 .466842 
 
 900 
 
 1.448820 
 
 300 
 
 .724410 
 
 1000 
 
 2.414700 
 
 SCO 
 
 .482940 
 
 1000 
 
 1.609800 
 
 310 
 
 .748557 
 
 1100 
 
 2.656170 
 
 310 
 
 .499038 
 
 1100 
 
 1.770780 
 
 WHEN THE EXACT HEAD IS FOUND IN ABOVE TABLE. 
 
 Example. — Have 100 foot head and 50 inches of water. How many Horse- 
 Power? 
 
 By reference to above table the Horse Power of 1 inch under 100 ft. head 
 is .241470. This amount multiplied by the number of inches. 50, will give 12.07 
 Horse Power. 
 
 WHEN EXACT HEAD IS NOT FOUND IN TABLE. 
 
 Take the Horse Power of 1 inch under 1 ft. head and multiply by the num- 
 ber of inches, and then by number of feet head. The product will be the required 
 Horse Power. 
 
 The above formula will answer for the cubic feet table, by substituting the 
 the equivalents therein for those of miner's inches. 
 
 Note. — The above tables are based upon an efficiency of 85%. 
 
208 
 
 USKFUI. TABLES. 
 
 LOSS OF HEAD IN PIPE BY FRICTION. 
 
 The following tables show the loss of head by friction in each 100 feet in length of different 
 diameters of pipe when discharging the following quantities of water per minute: 
 
 INSIDE DIAMETER OF PIPE IN INCHES. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Vein 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cublo 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Lose of 
 
 Cubic 
 
 
 
 feet 
 
 
 feet 
 
 head 
 
 
 
 
 
 feet 
 
 
 feet 
 
 per 
 
 In 
 
 ppx 
 
 in 
 
 
 in 
 
 
 in 
 
 
 in 
 
 per 
 
 in 
 
 
 
 feet. 
 
 
 feet. 
 
 mln. 
 
 feet 
 
 min. 
 
 feet. 
 
 min. 
 
 feet. 
 
 
 feet. 
 
 min. 
 
 2.0 
 
 2.87 
 
 .65 
 
 1.185 
 
 2.62 
 
 .791 
 
 5.89 
 
 .593 
 
 10.4 
 
 .474 
 
 16.3 
 
 .395 
 
 23.5 
 
 2.2 
 
 2.80 
 
 .73 
 
 1.404 
 
 2.88 
 
 .936 
 
 0.48 
 
 .702 
 
 11.5 
 
 .561 
 
 18. 
 
 .408 
 
 25.9 
 
 2.4 
 
 3.27 
 
 .79 
 
 1.639 
 
 3.14 
 
 1.093 
 
 7.07 
 
 .819 
 
 12.5 
 
 .050 
 
 19.6 
 
 .547 
 
 28.2 
 
 2.0 
 
 3.78 
 
 .86 
 
 1.891 
 
 3.40 
 
 1.26 
 
 7.05 
 
 .945 
 
 13.6 
 
 .757 
 
 21.3 
 
 .631 
 
 30.6 
 
 28 
 
 4.32 
 
 .92 
 
 2.16 
 
 3.66 
 
 1.44 
 
 8.24 
 
 1.08t 
 
 14.6 
 
 .864 
 
 22.9 
 
 .720 
 
 32.9 
 
 8.0 
 
 4.89 
 
 .99 
 
 2.44 
 
 3.92 
 
 1.62 
 
 8.83 
 
 1.22 
 
 15.7 
 
 .978 
 
 24.6 
 
 .815 
 
 35.3 
 
 S.2 
 
 5.47 
 
 1.06 
 
 2.73 
 
 4.18 
 
 1.82 
 
 9.42 
 
 1,37 
 
 16.7 
 
 1.098 
 
 26.2 
 
 .915 
 
 37.7 
 
 S.4 
 
 6.09 
 
 1.12 
 
 3.05 
 
 4.45 
 
 2.04, 
 
 10.00 
 
 1.52 
 
 17.8 
 
 1.22 
 
 27.8 
 
 1.021 
 
 40. 
 
 3.6 
 
 6.76 
 
 1.19 
 
 3.38 
 
 4.71 
 
 2.26 
 
 10.60 
 
 1.69 
 
 18.8 
 
 1.35 
 
 29.4 
 
 1.131 
 
 42.4 
 
 3.8 
 
 7.48 
 
 1.20 
 
 3.74 
 
 4.97. . 
 
 2.49. 
 
 11.20 
 
 1.87 
 
 19.9 
 
 1.49 
 
 31. 
 
 1.25 
 
 44.7 
 
 4.0 
 
 8.20 
 
 1.32 
 
 4.10 
 
 5.23 
 
 2.73 
 
 11.80 
 
 2.05 
 
 20.9 
 
 1.64 
 
 32.7 
 
 lv37 
 
 47.1 
 
 4.2 
 
 8.97 
 
 1.39 
 
 4.49 
 
 5.49 
 
 2.98 
 
 12.30 
 
 2.24 
 
 22.0 
 
 1.79 
 
 34.3 
 
 1.49 
 
 49.5 
 
 4.4 
 
 9.77 
 
 1.45 
 
 4.89 
 
 5.76 
 
 3.25 
 
 12.90 
 
 2.43 
 
 23.0 
 
 1.95 
 
 36.0 
 
 1.02 
 
 51.8 
 
 4.0 
 
 10.00 
 
 1.52 
 
 5.30 
 
 6.02 
 
 3.53 
 
 ■13.50 
 
 2.64 
 
 24.0 
 
 2.11 
 
 37.6 
 
 1.76 
 
 54.1 
 
 4.8 
 
 11.46 
 
 1.58 
 
 5.72 
 
 6.28 
 
 3:81 
 
 14.10 
 
 2.85- 
 
 25.1 
 
 2.27 
 
 39.2 
 
 1:90 
 
 56.5 
 
 6.0 
 
 12.33 
 
 1.65 
 
 6.17 
 
 6.54 
 
 4.11 
 
 14.70 
 
 3.08 
 
 26.2 
 
 2.46 
 
 40.9 
 
 2.05 
 
 58.9 
 
 6.2 
 
 13.24 
 
 1.72 
 
 0.02 
 
 6.80 
 
 4.41 
 
 15.30 
 
 3*31 
 
 27.2 
 
 2.65 
 
 42.5 
 
 2.21 
 
 61.2 
 
 6.4 
 
 14.20 
 
 1.78 
 
 7.10 
 
 7.00 
 
 4.73 
 
 15.90 
 
 3.55 
 
 28.2 
 
 2.84 
 
 44.2 
 
 2.37 
 
 63.6 
 
 6.0 
 
 16.16 
 
 1.85 
 
 7.58 
 
 7.32 
 
 5.06 
 
 10.50 
 
 3.79 
 
 29.3 
 
 3.03 
 
 45.8 
 
 2.53 
 
 65.9 
 
 6.8 
 
 10.17 
 
 1.91 
 
 8.09 
 
 7.58 
 
 5.40 
 
 17.10 
 
 4.04 
 
 30.3 
 
 3.24 
 
 47.4 
 
 2.70 
 
 68.3 
 
 6.0 
 
 17.23 
 
 
 8.01 
 
 7.85 
 
 5.74 
 
 17.70 
 
 4.31 
 
 31.4 
 
 3.45 
 
 49.1 
 
 2.87 
 
 70.7 
 
 7.0 
 
 22.89 
 
 2k 
 
 11.46 
 
 9.16 
 
 7.62 
 
 20.6 
 
 5.72 
 
 30.6 
 
 4.57 
 
 57.2 
 
 3.81 
 
 82.4 
 
 INSIDE DIAMETER OF PIPE IN INCHES. 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 Velo 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubio 
 
 Loss of 
 
 Cubic 
 
 In ft. 
 
 
 feet 
 
 
 feet 
 
 head 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 in 
 
 per 
 
 
 per 
 
 
 per 
 
 
 per 
 
 
 per 
 
 
 
 sec. 
 
 feet. 
 
 
 feet. 
 
 min. 
 
 feet. 
 
 min. 
 
 feet. 
 
 min. 
 
 feet. 
 
 
 feet. 
 
 mm. 
 
 2.0 
 
 .338 
 
 32.0 
 
 .296 
 
 41.9 
 
 .264 
 
 53. 
 
 .237 
 
 05.4 
 
 .210 
 
 79.2 
 
 .198 
 
 94.2 
 
 2.2 
 
 .401 
 
 35.3 
 
 .351 
 
 46.1 
 
 .312 
 
 58.3 
 
 .281 
 
 72. 
 
 .255 
 
 87.1 
 
 .234 
 
 103. 
 
 2.4 
 
 .408 
 
 38.5 
 
 .410 
 
 60.2 
 
 .365 
 
 63.6 
 
 .327 
 
 78,5 
 
 .297 
 
 95.0 
 
 .273 
 
 113. 
 
 2.6 
 
 .540 
 
 41.7 
 
 .473 
 
 54.4 
 
 .420 
 
 68.9 
 
 .378 
 
 85.1 
 
 .344 
 
 103*. 
 
 .315 
 
 122. 
 
 2.8 
 
 .617 
 
 449 
 
 .540 
 
 58.6 
 
 .480 
 
 74.2 
 79.5 
 
 .432 
 
 91.0 
 
 .392 
 
 111. 
 
 .360 
 
 132. 
 
 3.0 
 
 .098 
 
 43.1 
 
 .611 
 
 62.8 
 
 .544 
 
 .488 
 
 98.2 
 
 .444 
 
 119. 
 
 .407 
 
 141. 
 
 3.2 
 
 .785 
 
 61.3 
 
 .686 
 
 67'. 
 
 .609 
 
 84.8 
 
 .549 
 
 105. 
 
 .499 
 
 127. 
 
 .457 
 
 151. 
 
 3.4 
 
 .876 
 
 54.5 
 
 .765 
 
 71.2 
 
 .680 
 
 90.1 
 
 .612 
 
 111. 
 
 .557 
 
 134. 
 
 .510 
 
 160. 
 
 3.0 
 
 .969 
 
 57.7 
 
 .848 
 
 75.4 
 
 .755 
 
 95.4 
 
 .679 
 
 118. 
 
 .017 
 
 142. 
 
 .566 
 
 169. 
 
 8.8 
 
 lfi70 
 
 60.9 
 
 .936 
 
 79.0 
 
 .831 
 
 101. 
 
 .749 
 
 124. 
 
 .080 
 
 150. 
 
 .624 
 
 179. 
 
 4.0 
 
 1.175 
 
 C4.1 
 
 1.027 
 
 83.7 
 
 :913 
 
 106. 
 
 .822 
 
 131. 
 
 .747 
 
 158. 
 
 .685 
 
 188. 
 
 4.2 
 
 1.28 
 
 07.3 
 
 1,122 
 
 87.9 
 
 .998 
 
 111. 
 
 .897 
 
 137. 
 
 .810 
 
 166. 
 
 .749 
 
 198. 
 
 4.4 
 
 1.39 
 
 70.5 
 
 1.22 
 
 92,1 
 
 1.086 
 
 116. 
 
 .977 
 
 144. 
 
 .888 
 
 174. 
 
 .815 
 
 207. 
 
 4.0 
 
 1.51 
 
 73.7 
 
 1.32 
 
 96.3 
 
 1.177 
 
 122. 
 
 1.059 
 
 150. 
 
 .903 
 
 182, 
 
 .883 
 
 217. 
 
 4.8 
 
 a.63 
 
 70.9 
 
 1.43 
 
 100.0 
 
 1.27 
 
 127. 
 
 1.145 
 
 167. 
 
 1.040 
 
 190. 
 
 .954 
 
 226 
 
 6.0 
 
 1.76 
 
 80.2 
 
 1.54 
 
 105. 
 
 1.37 
 
 132. 
 
 1.23 
 
 163. 
 
 1.122 
 
 198. 
 
 1.028 
 
 235. 
 
 6.2 
 
 1.89 
 
 83.3 
 
 1.65 
 
 109. 
 
 1.47 
 
 138. 
 
 1.32 
 
 170. 
 
 1.20 
 
 206. 
 
 1.104 
 
 245 
 
 6.4 
 
 2.03 
 
 80.0 
 
 1.77 
 
 113. 
 
 1.57 
 
 143. 
 
 1.41 
 
 177. 
 
 1.28 
 
 214. 
 
 1.183 
 
 254. 
 
 6.0 
 
 2.17 
 
 89.8 
 
 1.89 
 
 117. 
 
 1.08 
 
 148. 
 
 1.51 
 
 183. 
 
 1.37 
 
 222. 
 
 1.26 
 
 264. 
 
 5.8 
 
 2.31 
 
 
 2.01 
 
 121. 
 
 1.80 
 
 154. 
 
 1.61 
 
 190. 
 
 1.46 
 
 229. 
 
 134 
 
 273. 
 
 6.0 
 
 2.4S 
 
 96^2 
 
 2.15 
 
 125. 
 
 1.92 
 
 159. 
 
 1.71 
 
 196. 
 
 1.56 
 
 237. 
 
 1.43 
 
 283. 
 
 7.0 
 
 3.20 
 
 112.0 
 
 2.S5 
 
 140. 
 
 2.52 
 
 185. 
 
 2.28 
 
 229. 
 
 2.07 
 
 277. 
 
 1.91 
 
 330. 
 
USEFUL TABLES. 
 
 209 
 
 LOSS OF HEAD IN PIPE BY FRICTION. 
 
 The following tables show the loss of head by friction in each 100 feet in length of different 
 diameters of pipe when discharging the following quantities of water per inipute: 
 
 INSIDE DIAMETKR OF PIPE IN INCHES. 
 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 In ft. 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 reet 
 
 
 feet 
 
 
 In 
 
 
 
 
 In 
 
 
 
 
 
 
 
 
 
 feet. 
 
 
 feet. 
 
 
 feet. 
 
 
 feet. 
 
 mln. 
 
 feet. 
 
 
 
 mm. 
 
 2.0 
 
 .183 
 
 110. 
 
 .169 
 
 128. 
 
 .158 
 
 147. 
 
 .147 
 
 167. 
 
 .132 
 
 212. 
 
 .119 
 
 262. 
 
 2.2 
 
 .216 
 
 J21. 
 
 .200 
 
 141. 
 
 .187 
 
 162. 
 
 .175 
 
 184. 
 
 .156 
 
 233. 
 
 .140 
 
 
 2.4 
 
 .252 
 
 133. 
 
 .234 
 
 154. 
 
 .218 
 
 176. 
 
 .205 
 
 201. 
 
 .182 
 
 254. 
 
 .164 
 
 314. 
 
 2.6 
 
 .290 
 
 144. 
 
 .270 
 
 167. 
 
 .252 
 
 191. 
 
 .236 
 
 218. 
 
 .210 
 
 275. 
 
 .189 
 
 340. 
 
 2.8 
 
 .332 
 
 156. 
 
 .308 
 
 179. 
 
 .288 
 
 206. 
 
 ,270 
 
 234. 
 
 .240 
 
 297. 
 
 .216 
 
 366. 
 
 8.0 
 
 .375 
 
 166. 
 
 .349 
 
 192. 
 
 .325 
 
 221. 
 
 .306 
 
 251. 
 
 .271 
 
 318. 
 
 .245 
 
 393. 
 
 3.2 
 
 .422 
 
 177. 
 
 .392 
 
 205. 
 
 .366 
 
 235. 
 
 .343 
 
 
 .305 
 
 339. 
 
 .275 
 
 419. 
 
 3.4 
 
 .471 
 
 188. 
 
 438 
 
 218. 
 
 .408 
 
 250. 
 
 .383 
 
 284. 
 
 .339 
 
 360. 
 
 .306 
 
 445. 
 
 J.6 
 
 .522 
 
 199. 
 
 .485 
 
 231. 
 
 .452 
 
 265. 
 
 .425 
 
 301. 
 
 .377 
 
 382. 
 
 .339 
 
 471. 
 
 3.8 
 
 .576 
 
 210. 
 
 .535 
 
 243. 
 
 .499 
 
 280. 
 
 .468 
 
 318. 
 
 .416 
 
 403, 
 
 .374 
 
 497. 
 
 4.0 
 
 .632 
 
 221. 
 
 .587 
 
 256. 
 
 .543 
 
 294. 
 
 .513 
 
 335. 
 
 .456 
 
 424. 
 
 .410 
 
 523. 
 
 4.2 
 
 .691 
 
 232. 
 
 .641 
 
 
 .598 
 
 309. 
 
 .561 
 
 352. 
 
 .499 
 
 445. 
 
 .449 
 
 550. 
 
 4.4 
 
 .751 
 
 243. 
 
 .698 
 
 282. 
 
 .651 
 
 324. 
 
 .611 
 
 368. 
 
 .542 
 
 466. 
 
 .488 
 
 576. 
 
 4.6 
 
 .815 
 
 254. 
 
 .757 
 
 295. 
 
 .707 
 
 339. 
 
 .662 
 
 385. 
 
 .588 
 
 488. 
 
 .529 
 
 602. 
 
 4.8 
 
 .881 
 
 265. 
 
 .818 
 
 308. 
 
 .763. 
 
 353. 
 
 .715 
 
 402. 
 
 .636 
 
 509. 
 
 .572 
 
 628. 
 
 6.0 
 
 .949 
 
 276. 
 
 .881 
 
 321. 
 
 .822 
 
 363. 
 
 .770 
 
 419. 
 
 .685 
 
 530. 
 
 .617 
 
 654. 
 
 5.2 
 
 1.020 
 
 287. 
 
 .947 
 
 833. 
 
 .883 
 
 
 .828 
 
 435. 
 
 .736 
 
 551. 
 
 .662 
 
 680. 
 
 5.4 
 
 1.092 
 
 298. 
 
 1.014 
 
 346. 
 
 .947 
 
 397. 
 
 .888 
 
 452. 
 
 .788 
 
 572. 
 
 .710 
 
 707. 
 
 5.6 
 
 1.167 
 
 309. 
 
 1.083 
 
 359. 
 
 1.011 
 
 412. 
 
 .949 
 
 169. 
 
 .843 
 
 594. 
 
 .758 
 
 733. 
 
 5.8 
 
 1.245 
 
 821. 
 
 1.155 
 
 372. 
 
 1078 
 
 427. 
 
 1.011 
 
 486. 
 
 .899 
 
 615. 
 
 .809 
 
 759.- 
 
 fi.0 
 
 1.325 
 
 332. 
 
 1.229 
 
 385. 
 
 1.148 
 
 442. 
 
 1.076 
 
 502. 
 
 .957 
 
 636. 
 
 .861 
 
 785. 
 
 7.0 
 
 1.75 
 
 387. 
 
 1.63 
 
 449. 
 
 1.52 
 
 515. 
 
 1.43 
 
 586. 
 
 1.27 
 
 742. 
 
 1.143 
 
 916. 
 
 INSIDE DIAMETER OF PIPE IN INCHES. 
 
 
 22 
 
 21 
 
 26 
 
 28 
 
 30 
 
 36 
 
 Vein. 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 Loss of 
 
 Cubic 
 
 I.OSSOf 
 
 cubic 
 
 
 heud 
 
 feet 
 
 
 feet 
 
 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 PIT 
 
 
 
 In 
 
 
 in 
 
 
 in 
 
 
 in 
 
 
 
 
 sec. 
 
 feet. 
 
 
 feet. 
 
 mm. 
 
 feet. 
 
 
 feet. 
 
 
 feet. 
 
 mln. 
 
 
 
 2.0 
 
 .108 
 
 316 
 
 .098 
 
 377. 
 
 .091 
 
 44? 
 
 .084 
 
 513. 
 
 .079 
 
 5S9. 
 
 .0(56 
 
 848. 
 
 22 
 
 .127 
 
 348 
 
 .116 
 
 414. 
 
 .108 
 
 486 
 
 .099 
 
 564. 
 
 .093" 
 
 648. 
 
 
 
 2.4 
 
 .149 
 
 380 
 
 .136 
 
 452. 
 
 .126 
 
 531 
 
 .116 
 
 616. 
 
 .109 
 
 707. 
 
 .091 
 
 1018. 
 
 2.6 
 
 .171 
 
 412 
 
 .157 
 
 490. 
 
 .145 
 
 575 
 
 .134 
 
 667. 
 
 .126 
 
 766. 
 
 .104 
 
 1100. 
 
 2.8 
 
 .195 
 
 443 
 
 .180 
 
 528. 
 
 .165 
 
 619 
 
 .153 
 
 718. 
 
 .144 
 
 824. 
 
 .119 
 
 1183. 
 
 3.0 
 
 .222 
 
 475 
 
 .204 
 
 565. 
 
 .188 
 
 663 
 
 .174 
 
 770. 
 
 .163 
 
 883. 
 
 .135 
 
 1273. 
 
 3.2 
 
 .249 
 
 507 
 
 .229 
 
 603. 
 
 .211 
 
 70S 
 
 .195 
 
 821. 
 
 .182 
 
 942. 
 
 .152 
 
 1357. 
 
 3.4 
 
 .273 
 
 538 
 
 . .255 
 
 641. 
 
 .235 
 
 75? 
 
 .218 
 
 872. 
 
 .204 
 
 1C01. 
 
 .169 
 
 1442. 
 
 3.6 
 
 .308 
 
 570 
 
 .283 
 
 
 .261 
 
 796 
 
 .242 
 
 923. 
 
 .226 
 
 1060. 
 
 .188 
 
 1527. 
 
 3.8 
 
 .340 
 
 601 
 
 .312 
 
 716. 
 
 .288 
 
 840 
 
 .267 
 
 974. 
 
 .249 
 
 1119. 
 
 .207 
 
 1612. 
 
 4.0 
 
 .373 
 
 633 
 
 .342 
 
 754. 
 
 .315 
 
 885 
 
 .293 
 
 1026. 
 
 .273 
 
 1178. 
 
 .228 
 
 1697. 
 
 4.2 
 
 .408 
 
 665 
 
 .374 
 
 791. 
 
 .345 
 
 9V!9 
 
 .320 
 
 1077. 
 
 .299 
 
 1237. 
 
 .249 
 
 1782. 
 
 4.4 
 
 .444 
 
 697 
 
 .407 
 
 829. 
 
 .375 
 
 973 
 
 
 1129. 
 
 .325 
 
 1296. 
 
 .271 
 
 1866. 
 
 4.6 
 
 .482 
 
 728 
 
 .441 
 
 867. 
 
 .407 
 
 1017 
 
 .378 
 
 1180. 
 
 .353 
 
 1355. 
 
 .294 
 
 1951 
 
 4.8 
 
 .521 
 
 760 
 792 
 
 .476 
 
 905. 
 
 .440 
 
 106? 
 
 .409 
 
 1231. 
 
 Ml 
 
 1414. 
 
 .318 
 
 2036. 
 
 5.0 
 
 .561 
 
 .513 
 
 942. 
 
 .474 
 
 llOfl 
 
 .440 
 
 1283. 
 
 .411 
 
 1472. 
 
 .312 
 
 212L 
 
 5.2 
 
 .602 
 
 823 
 
 .552 
 
 980. 
 
 .510 
 
 1150 
 
 .473 
 
 1334. 
 
 .441 
 
 1531. 
 
 .368 
 
 2206.. 
 
 5.4 
 
 .645 
 
 855 
 
 .591 
 
 1018: 
 
 .546 
 
 1194 
 
 .507 
 
 1885. 
 
 .473 
 
 1590. 
 
 .394 
 
 2291. 
 
 5.6 
 
 .690 
 
 887 
 
 .632 
 
 1055. 
 
 .683 
 
 1?39 
 
 .542 
 
 1437. 
 
 .506 
 
 1649. 
 
 .421 
 
 2376. 
 
 5.8 
 
 .735 
 
 yi8 
 
 .674 
 
 1093. 
 
 .622 
 
 19183 
 
 .578 
 
 1488. 
 
 .540 
 
 1708. 
 
 .450 
 
 2460. 
 
 6.0 
 
 .782 
 
 950 
 
 .717 
 
 1131. 
 
 .662 
 
 1327 
 
 .615 
 
 1539. 
 
 .574 
 
 1767. 
 
 .479 
 
 2545. 
 
 7.0 
 
 1.040 
 
 J 109 
 
 .953 
 
 1319. 
 
 .879 
 
 1548 
 
 .817 
 
 1796. 
 
 .762 
 
 2061. 
 
 .636 
 
 2858. 
 
USKFUIv TABLES. 
 
 TABLE OF SHEET IRON HYDRAULIC PIPE. 
 
 i 
 
 © . 
 
 3- 
 
 la, 
 
 if 
 
 f hi 
 
 ~£ 
 
 
 
 
 
 
 
 
 S-= 
 
 £* 
 
 -* . 
 
 sfS'gp. 
 
 r* 
 
 s.g 
 
 ^2 
 
 ££ 
 
 So-3 
 
 §f££ 
 
 £is 
 
 3 
 
 7 
 
 18 
 
 400 
 
 9 
 
 2 
 
 4 
 
 12 
 
 18 
 
 350 
 
 16 
 
 2* 
 
 4 
 
 12 
 
 16 
 
 525 
 
 16 
 
 3 
 
 5 
 
 20 
 
 18 
 
 325 
 
 25 
 
 3* 
 
 o 
 
 20 
 
 16 
 
 500 
 
 25 
 
 4} 
 
 o 
 
 20 
 
 14 
 
 675 
 
 25 
 
 5 
 
 a 
 
 28 
 
 18 
 
 296 
 
 36 
 
 4| 
 
 6 
 
 28 
 
 16 
 
 487 
 
 36 
 
 6* 
 
 6 
 
 28 
 
 14 
 
 743 
 
 36 
 
 7} 
 
 
 38 
 
 18 
 
 254 
 
 50 
 
 5} 
 
 7 
 
 38 
 
 16 
 
 419 
 
 50 
 
 6* 
 
 7 
 
 38 
 
 14 
 
 640 
 
 50 
 
 8} 
 
 8 
 
 50 
 
 16 
 
 367 
 
 63 
 
 7* 
 
 8 
 
 50 
 
 14 
 
 560 
 
 63 
 
 9h 
 
 8 
 
 50 
 
 12 
 
 854 
 
 63 
 
 13 
 
 y 
 
 63 
 
 16 
 
 327 
 
 80 
 
 8* 
 
 !) 
 
 63 
 
 14 
 
 499 
 
 80 
 
 10£ 
 
 9 
 
 63 
 
 12 
 
 761 
 
 80 
 
 14* 
 
 10 
 
 78 
 
 16 
 
 295 
 
 100 
 
 9* 
 
 so 
 
 78 
 
 14 
 
 450 
 
 100 
 
 in 
 
 10 
 
 78 
 
 12 
 
 687 
 
 100 
 
 15f 
 
 10 
 
 78 
 
 11 
 
 754 
 
 100 
 
 17* 
 
 10 
 
 78 
 
 10 
 
 900 
 
 100 
 
 19} 
 
 11 
 
 95 
 
 16 
 
 269 
 
 120 
 
 n 
 
 11 
 
 95 
 
 14 
 
 412 
 
 120 
 
 13 
 
 11 
 
 95 
 
 12 
 
 626 
 
 120 
 
 17* 
 
 11 
 
 95 
 
 11 
 
 687 
 
 120 
 
 18jf 
 
 11 
 
 95 
 
 10 
 
 820 
 
 120 
 
 ' 21 
 
 12 
 
 113 
 
 16 
 
 246 
 
 142 
 
 in 
 
 12 
 
 113 
 
 14 
 
 377 
 
 142 
 
 14 
 
 12 
 
 113 
 
 12 
 
 574 
 
 142 
 
 18} 
 
 12 
 
 113 
 
 11 
 
 630 
 
 142 
 
 19| 
 
 12 
 
 113 
 
 10 
 16 
 
 753 
 
 142 
 
 22| 
 
 13 
 
 132 
 
 228 
 
 170 
 
 12 
 
 13 
 
 132 
 
 14 
 
 348 
 
 170 
 
 15 
 
 13 
 
 132 
 
 12 
 
 530 
 
 170 
 
 20 
 
 13 
 
 132 
 
 11 
 
 583 
 
 170 
 
 22 
 
 13 
 
 132 
 
 10 
 
 696 
 
 170 
 
 24} 
 
 14 
 
 153 
 
 16 
 
 211 
 
 200 
 
 13 
 
 14 
 
 153 
 
 14 
 
 324 
 
 200 
 
 16 
 
 14 
 
 153 
 
 12 
 
 494 
 
 200 
 
 214 
 
 14 
 
 153 
 
 11 
 
 543 
 
 200 
 
 23* 
 
 14 
 
 153 
 
 10 
 
 648 
 
 200 
 
 *6 
 
 15 
 
 176 
 
 16 
 
 197 
 
 225 
 
 13f 
 
 15 
 
 176 
 
 14 
 
 302 
 
 225 
 
 17 
 
 15 
 
 176 
 
 12 
 
 460 
 
 225 
 
 23 
 
 15 
 
 176 
 
 11 
 
 507 
 
 225 
 
 24* 
 
 15 
 
 176 
 
 10 
 
 606 
 
 225 
 
 28 
 
 16 
 
 201 
 
 16 
 
 185 
 
 255 
 
 14* 
 
 16 
 
 201 
 
 14 
 
 283 
 
 255 
 
 17* 
 
 46 
 
 201 
 
 12 
 
 432 
 
 255 
 
 24* 
 
 16 
 
 201 
 
 11 
 
 474 
 
 255 
 
 26* 
 
 i£ 
 
 I 201 
 
 10 
 
 567 
 
 255. 
 
 29J 
 
 || 
 £.5 
 
 & 
 
 p. 
 
 If 
 
 is 
 
 P 
 
 ill 
 
 K5.TS 
 
 •°.seS 
 
 
 18 
 
 254 
 
 16 
 
 165 
 
 320 
 
 16* 
 
 18 
 
 254 
 
 14 
 
 252 
 
 320 
 
 20* 
 
 18 
 
 254. 
 
 12 
 
 385 
 
 320 
 
 2;* 
 
 18 
 
 254 
 
 11 
 
 424 
 
 320 
 
 30 
 
 ,18 
 
 254 
 
 10 
 
 505 
 
 320 
 
 34 
 
 20 
 
 314 
 
 16 
 
 148 
 
 400 
 
 18 
 
 20 
 
 314 
 
 14 
 
 227 
 
 400 
 
 22} 
 
 20 
 
 314 
 
 12 
 
 346 
 
 400 
 
 30 
 
 20 
 
 314 
 
 11 
 
 380 
 
 400 
 
 324 
 
 20 
 
 314 
 
 10 
 "16 
 
 456 
 135" 
 
 400 
 4«0 
 
 36} 
 
 n 
 
 380 
 
 20 
 
 22 
 
 380 
 
 14 
 
 206 
 
 480 
 
 m 
 
 22 
 
 380 
 
 12 
 
 316 
 
 480 
 
 32$ 
 
 22 
 
 380 
 
 H 
 
 347 
 
 480 
 
 35$ 
 
 22 
 
 380 
 
 10 
 
 415 
 
 480 
 
 40 
 
 24 
 
 452 
 
 14 
 
 188 
 
 570 
 
 27* 
 
 24 
 
 452 
 
 12 
 
 290 
 
 570 
 
 35* 
 
 24 
 
 452 
 
 11 
 
 318 
 
 570 
 
 39 
 
 24 
 
 452 
 
 10 
 
 379 
 
 570 
 
 43* 
 
 24 
 
 452 
 
 8 
 
 466 
 
 570 
 
 53 
 
 26 
 
 530 
 
 14 
 
 175 
 
 670 
 
 29* 
 
 26 
 
 530 
 
 12 
 
 267 
 
 670 
 
 38* 
 
 26 
 
 530 
 
 11 
 
 294 
 
 670 
 
 42 
 
 26 
 
 530 
 
 10 
 
 352 
 
 670 
 
 47 
 
 26 
 
 530 
 
 8 
 
 432 
 
 670 
 
 57* 
 
 28 
 
 615 
 
 14 
 
 102 
 
 775 
 
 31* 
 
 28 
 
 615 
 
 12 
 
 247 
 
 775 
 
 41* 
 
 28 
 
 615 
 
 11 
 
 273 
 
 775 
 
 45 
 
 28 
 
 615 
 
 10 
 
 327 
 
 775 
 
 50* 
 
 28 
 
 615 
 
 8 
 
 400 
 
 775 
 
 61* 
 
 30 
 
 706 
 
 12 
 
 231 
 
 890 
 
 44 
 
 30 
 
 706 
 
 11 
 
 254 
 
 890 
 
 48 
 
 30 
 
 706 
 
 10 
 
 304 
 
 890 
 
 54 
 
 30 
 
 706 
 
 8 
 
 375 
 
 890 
 
 65 
 
 30 
 
 706 
 
 7 
 
 425 
 141 
 
 890 
 
 74 
 
 83 
 
 1017 
 
 11 
 
 1300 
 
 58 
 
 m 
 
 1017 
 
 10 
 
 155 
 
 1300 
 
 67 
 
 36 
 
 1017 
 
 8 
 
 192 
 
 1300 
 
 78 
 
 36 
 
 1017 
 
 7 
 
 210 
 
 1300 
 
 88 
 
 40 
 
 1256 
 
 10 
 
 141 
 
 1600 
 
 71 
 
 40 
 
 1256 
 
 8 
 
 174 
 
 1600 
 
 86 
 
 40 
 
 1256 
 
 7 
 
 189 
 
 1600 
 
 97 
 
 40 
 
 1256 
 
 6 
 
 213 
 
 1600 
 
 108 
 
 40 
 
 1256 
 
 4 
 
 250 
 
 1600 
 
 126 
 
 4 s ? 
 
 1385 
 
 10 
 
 135 
 
 1760 
 
 74* 
 
 4->, 
 
 1385 
 
 8 
 
 165 
 
 1760 
 
 91 
 
 A?, 
 
 1385 
 
 7 
 
 180 
 
 1760 
 
 102 
 
 4", 
 
 1385 
 
 6 
 
 210 
 
 1760 
 
 114 
 
 42 
 
 1385 
 
 4 
 
 240 
 
 1760 
 
 133 
 
 49, 
 
 1385 
 
 y 
 
 270 
 
 1760 
 
 137 
 
 4'* 
 
 1385 
 
 3 
 
 300 
 
 1760 
 
 145 
 
 42 
 
 1385 
 
 tV 
 
 321 
 
 1760 
 
 177 
 
 42 
 
 1385 
 
 ■ : fi 
 
 363 
 
 . 1760 
 
 216 
 
USEFUL TABLES. 
 
 ?*i 
 
 rt 
 
 K3 
 
 c< 
 
 o 
 
 *> 
 
 W 
 
 N 
 
 Cr 
 
 N 
 
 CO 
 
 
 00 
 
 . 
 
 vS 
 
 \ 
 
 
 2 i 
 
 fO 
 
 * 
 
 <o 
 
 so 
 
 K 
 
 CO 
 
 CO 
 
 =0 
 
 CQ 
 
 SO 
 
 «i 
 
 f\ 
 
 - 
 
 «1 
 
 
 > i 
 
 <r.. 
 
 <o 
 
 S8 
 
 K. 
 
 CT 
 
 - 
 
 m 
 
 <o 
 
 N 
 
 rt 
 
 N. 
 
 
 \£> 
 
 <r 
 
 W 
 
 
 
 Q 
 
 o 
 
 o 
 
 o 
 
 
 
 
 
 
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 «) 
 
 rO 
 
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 <« 
 
 
 
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 o 
 
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 o 
 
 
 
 o 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 }i 
 
 N 
 
 CO 
 
 cr 
 
 
 
 H 
 
 ■3* 
 
 
 CO 
 
 
 
 fc 
 
 <j 
 
 <o 
 
 
 
 
 
 
 
 i«r 
 
 -T 
 
 T 
 
 ^r 
 
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 s 
 
 <0 
 
 so 
 
 so 
 
 N 
 
 N 
 
 93 
 
 cr 
 
 
 
 Q) 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 w 
 
 '- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 - 
 
 f> 
 
 w 
 
 o 
 
 NO 
 
 o 
 
 rO 
 
 * 
 
 ■3- 
 
 d 
 
 CO 
 
 * 
 
 CO 
 
 _ 
 
 
 cO 
 
 > E 
 
 
 
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 >-n 
 
 
 
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 CO 
 
 o 
 
 H 
 
 •T 
 
 ^0 
 
 N. 
 
 cr 
 
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 rl 
 
 >N^ 
 
 
 
 .pi 
 
 S3 
 
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 <a 
 
 o 
 
 - 
 
 rt 
 
 rO 
 
 <o 
 
 X) 
 
 rv, 
 
 <o 
 
 <3- 
 
 o 
 
 d 
 
 fO 
 
 ^ 
 
 
 CO 
 
 CH 
 
 CO 
 
 cr 
 
 cr 
 
 •<r 
 
 cr 
 
 cr 
 
 cr 
 
 <T 
 
 o-> 
 
 c- 
 
 o 
 
 o 
 
 <i 
 
 o 
 
 
 
 wt""- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 - 
 
 ~ 
 
 O 
 
 z^i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "^3 
 
 > 
 
 ;»c!l 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i ■ •* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J >« s 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 o 
 
 
 
 o 
 
 o 
 
 
 
 o 
 
 
 
 O 
 
 CV 
 
 iyj 
 
 
 -5 * 
 
 
 
 
 rt 
 
 •0 
 
 
 CO 
 
 »0 
 
 cr 
 
 o 
 
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 (a 
 
 so 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 
 
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 o 
 
 5 
 
 r: J ! J" 
 
 
 £% 
 
 «■ 
 
 vS 
 
 m 
 
 to 
 
 fO 
 
 N 
 
 CO 
 
 <n 
 
 CO 
 
 cr- 
 
 K. 
 
 « 
 
 <o 
 
 <o 
 
 H 
 
 5*, 
 
 N 
 
 <o 
 
 «o 
 
 
 
 K 
 
 <*> 
 
 cr- 
 
 <o 
 
 
 
 *o 
 
 <i 
 
 <o 
 
 T 
 
 fO 
 
 K 
 
 
 •Ji 
 
 S9 
 
 T 
 
 so 
 
 s3 
 
 CO 
 
 ss 
 
 so 
 
 IN 
 
 
 
 so 
 K 
 
 
 
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 CO 
 
 CO 
 
 CO 
 
 CO 
 
 
 r £ * % ■* 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■^ «> £ > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iT^j cc s <» 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 IS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 j 
 
 
 
 
 
 „ 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 Q 
 
 
 
 
 ^ 
 
 > 
 
 
 V 
 
 N 
 
 00 
 
 rj- 
 
 
 
 — 
 
 N 
 
 eo 
 
 ^T 
 
 k) 
 
 VJ> 
 
 K 
 
 «D 
 
 cr 
 
 
 
 - 
 
 1 "1 ! ! ! - 
 
 
 
 - 
 
 — 
 
 si 
 
 Pi 
 
 N 
 
 Csf 
 
 rt 
 
 M 
 
 cv 
 
 rj 
 
 w 
 
 n 
 
 r0 
 
 (0 
 
 *.« 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 Jr'*" r p z 
 
 
 
 
 
 
 
 
 
 
 
 ^ili££^ 
 
 « 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2^ 
 
 H 
 
 so 
 
 to 
 
 "0 
 
 K 
 
 sO 
 
 <r 
 
 fc 
 
 d 
 
 N 
 
 _ 
 
 N 
 
 t 
 
 fO 
 
 *\ 
 
 1 1 
 
 i's 
 
 m 
 
 (O 
 
 T 
 
 
 
 rt 
 
 H 
 
 
 
 \0 
 
 
 <r 
 
 T^ 
 
 CO 
 
 cr 
 
 cr 
 
 eo 
 
 
 £ j. 
 
 - 
 
 so 
 
 
 
 T 
 
 r\ 
 
 o 
 
 fO 
 
 <o 
 
 CO 
 
 o 
 
 rt 
 
 <r 
 
 vO 
 
 <o 
 
 o 
 
 U) C±T 
 
 ■I s * 
 
 ol 
 
 d 
 
 flO 
 
 m 
 
 /o 
 
 ^r 
 
 ^r 
 
 ^ 
 
 'T 
 
 <o 
 
 h 
 
 lo 
 
 b 
 
 <<5 
 
 so 
 
 
 vn" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 o 
 
 O 
 
 o 
 
 
 Q 
 
 
 
 
 
 
 o 
 
 o 
 
 
 
 
 o 
 
 o 
 
 
 
 * u 
 
 f< 
 
 m 
 
 <t 
 
 fc 
 
 SO 
 
 K 
 
 00 
 
 <r 
 
 
 
 - 
 
 rt 
 
 <f) 
 
 <r 
 
 <n 
 
 ^ 
 
 I 
 
 r -5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
USEFUL TABIDS. 
 
 The following is a very useful table and should be employed 
 in Compressed Air distribution. The efficiency of many plants 
 would be increased if the piping followed these proportions: 
 
 Equation of Pipes.— It is frequently desired to know what number 
 of pipes of a given size are equal in carrying capacity to one pipe of a larger 
 size. At the same velocity of flow the volume delivered by two pipes of 
 different sizes is proportional to the squares of their diameters; thus, one 
 4-inch pipe will deliver the same volume as four 2-iuch pipes. With the same 
 head, however, the velocity is less in the smaller pipe, and the volume de- 
 livered varies about as the square root of the fifth power (i.e., as the fc.5 
 power). The following table has been calculated on this basis. The figures 
 opposite the intersection of any two sizes is the number of the smaller-sized 
 pipes required to equal one of the larger. Thus, one 4-inch pipe is equal to 
 5.7 2-inch pipes. 
 
 c3 a 
 
 5'" 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 2 
 
 5.7 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 15.6 
 
 2.8 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 32 
 
 5.7 
 
 2.1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 55.9 
 
 9.9 
 
 3.6 
 
 17 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 88.2 
 
 15.6 
 
 5 7 
 
 2.8 
 
 1.6 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 130 
 
 22.9 
 
 8 3 
 
 4.1 
 
 2.3 
 
 1.5 
 
 1 
 
 
 
 
 
 
 
 
 
 
 8 
 
 181 
 
 32 
 
 11.1 
 
 5.7 
 
 3.2 
 
 2.1 
 
 1.4 
 
 1 
 
 
 
 
 
 
 
 
 
 9 
 
 243 
 
 43. 
 
 15.6 
 
 76 
 
 4.3 
 
 2 8 
 
 1.9 
 
 1.3 
 
 1 
 
 
 
 
 
 
 
 
 10 
 
 316 
 
 55.9 
 
 20.3 
 
 9.9 
 
 5.7 
 
 3.6 
 
 2.4 
 
 1.7 
 
 1 3 
 
 1 
 
 
 
 
 
 
 
 11 
 
 401 
 
 70.9 
 
 25.7 
 
 12.5 
 
 7.2 
 
 4.6 
 
 3.1 
 
 2.2 
 
 1.7 
 
 1.3 
 
 
 
 
 
 
 
 12 
 
 499 
 
 88.2 
 
 32 
 
 15.6 
 
 8.9 
 
 5.7 
 
 3 8 
 
 2.8 
 
 2.1 
 
 1.6 
 
 1 
 
 
 
 
 
 
 13 
 
 609 
 
 108 
 
 39.1 
 
 19 
 
 10.9 
 
 7.1 
 
 4.7 
 
 3.4 
 
 2.5 
 
 1.9 
 
 1.2 
 
 
 
 
 
 
 14 
 
 733 
 
 130 
 
 47 
 
 22.9 
 
 13.1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3.0 
 
 2 3 
 
 1.5 
 
 1 
 
 
 
 
 
 15 
 
 787 
 
 154 
 
 .55.9 
 
 27.2 
 
 15.6 
 
 9.9 
 
 6.7 
 
 4.8 
 
 3 6 
 
 2 8 
 
 1.7 
 
 1.2 
 
 
 
 
 
 16 
 
 
 181 
 
 65.7 
 
 32 
 
 18.3 
 
 11.7 
 
 7.9 
 
 5.7 
 
 4.2 
 
 3.2 
 
 2.1 
 
 1.4 
 
 1 
 
 
 
 
 17 
 
 
 213 
 
 76.4 
 
 37.2 
 
 21.3 
 
 13.5 
 
 9.2 
 
 6.6 
 
 4.9 
 
 3.8 
 
 2.4 
 
 1.6 
 
 1.2 
 
 
 
 
 18 
 
 
 243 
 
 88.2 
 
 43 
 
 24.6 
 
 15.6 
 
 10 6 
 
 7.6 
 
 5.7 
 
 4.3 
 
 2.8 
 
 1.9 
 
 1.3 
 
 1 
 
 
 
 19 
 
 
 278 
 
 101 
 
 49.1 
 
 28.1 
 
 17.8 
 
 12.1 
 
 8.7 
 
 6.5 
 
 5 
 
 3.2 
 
 2.1 
 
 1.5 
 
 1.1 
 
 
 
 20 
 
 
 MIC 
 
 115 
 
 559 
 
 32 
 
 20.3 
 
 13 8 
 
 9.9 
 
 7.4 
 
 5.7 
 
 3.6 
 
 2.4 
 
 1.7 
 
 1.3 
 
 1 
 
 
 22 
 
 
 401 
 
 N6 
 
 70 9 
 
 40.6 
 
 25.7 
 
 17.5 
 
 12.5 
 
 9.3 
 
 7.2 
 
 4.6 
 
 3.1 
 
 2.2 
 
 1.7 
 
 1.3 
 
 
 24 
 
 
 109 
 
 181 
 
 88 2 
 
 50.5 
 
 32 
 
 21 8 
 
 15.6 
 
 11.6 
 
 8.9 
 
 5.7 
 
 3 8 
 
 2.8 
 
 2.1 
 
 1.6 
 
 1 
 
 26 
 
 
 609 
 
 221 
 
 108 
 
 61.7 
 
 39.1 
 
 26.6 
 
 19. 
 
 14.2 
 
 10.9 
 
 7.1 
 
 4.7 
 
 3 4 
 
 2.5 
 
 1.9 
 
 1.2 
 
 28 
 
 
 733 
 
 266 
 
 130 
 
 74.2 
 
 47 
 
 32 
 
 22.9 
 
 17 1 
 
 13.1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3 
 
 2.3 
 
 1.5 
 
 30 
 
 
 7S7 
 
 316 
 
 154 
 
 S8.2 
 
 55.9 
 
 38 
 
 27.2 
 
 
 15.6 
 
 9.9 
 
 6.7 
 
 4.8 
 
 3.6 
 
 2.8 
 
 1.7 
 
 36 
 
 
 
 199 
 
 243 
 
 130 
 
 88.2 
 
 60 
 
 43 f32 
 
 24.6 
 
 15.6 
 
 10.6 
 
 7.6 
 
 5.7 
 
 4.3 
 
 2.8 
 
 42 
 
 
 
 733 
 
 357 
 
 205 
 
 130 
 
 88.2 
 
 63.2|47 
 
 
 1.9 
 
 15 6 
 
 11.2 
 
 8.3 
 
 6.4 
 
 4.1 
 
 48 
 
 
 
 
 409 
 
 286 
 
 181 
 
 123 
 
 88.2162.7 
 
 50.5 
 
 32 
 
 25.8 
 
 15.6 
 
 11.6 
 
 8.9 
 
 5.7 
 
 54 
 
 
 
 
 670 
 
 383 
 
 243 
 
 105 
 
 118 ]88.2 67.8 
 
 43 
 
 29.2 
 
 20.9 
 
 15.6 
 
 12 
 
 7.6 
 
 60 
 
 
 
 
 787 
 
 409 
 
 316 
 
 215 
 
 154 
 
 115 
 
 88.2 
 
 55.9 
 
 38 
 
 27.2 
 
 20.3 
 
 15.6 
 
 9.9 
 
USEFUL TABIDS 
 
 213 
 
 Used in the calculation of problems in Isothermal Compres- 
 sion and .Expansion of Compressed Air. 
 
 
 
 HYPERBOLIC 
 
 LOGARITHMS. 
 
 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 1.01 
 
 .0099 
 
 1.45 
 
 .3716 
 
 1.89 
 
 .6366 
 
 2.33 
 
 .8458 
 
 2.77 
 
 1.0188 
 
 1.02 
 
 .0198 
 
 1.46 
 
 .3784 
 
 1.90 
 
 .6419 
 
 2.34 
 
 .8502 
 
 2.78 
 
 1.0225 
 
 1.03 
 
 .0296 
 
 1.47 
 
 .3853 
 
 1.91 
 
 .6471 
 
 2.35 
 
 .8544 
 
 2.79 
 
 1.0260 
 
 1.04 
 
 .0392 
 
 1.48 
 
 .3920 
 
 1.92 
 
 .6523 
 
 2.36 
 
 .8587 
 
 2.80 
 
 1.0296 
 
 1.05 
 
 .0488 
 
 1.49 
 
 .3988 
 
 1.93 
 
 .6575 
 
 2.37 
 
 .8629 
 
 2.81 
 
 1.0332 
 
 1.06 
 
 .0583 
 
 1.50 
 
 .4055 
 
 1.94 
 
 .6627 
 
 2.38 
 
 .8671 
 
 2.82 
 
 1.0367 
 
 1.07 
 
 .0677 
 
 1.51 
 
 .4121 
 
 1.95 
 
 .6678 
 
 2.39 
 
 .8713 
 
 2.83 
 
 1.0403 
 
 1.08 
 
 .0770 
 
 1.52 
 
 .4187 
 
 1.96 
 
 .6729 
 
 2.40 
 
 .8755 
 
 2.84 
 
 1.0438 
 
 1.09 
 
 .0862 
 
 1.53 
 
 .4253 
 
 1.97 
 
 .6780 
 
 2.41 
 
 .8796 
 
 2.85 
 
 1.0473 
 
 1.10 
 
 .0953 
 
 1.54 
 
 .4318 
 
 1.98 
 
 .6831 
 
 2.42 
 
 .8838 
 
 2.86 
 
 1.0508 
 
 1.11 
 
 .1044 
 
 1.55 
 
 .4383 
 
 1.99 
 
 .6881 
 
 2.43 
 
 .8879 
 
 2.87 
 
 1.0543 
 
 1.12 
 
 .1133 
 
 1.56 
 
 .4447 
 
 2.00 
 
 .6931 
 
 2.44 
 
 .8920 
 
 2.88 
 
 1.0578 
 
 1.13 
 
 .1222 
 
 1.57 
 
 .4511 
 
 2.01 
 
 .6981 
 
 2.45 
 
 .8961 
 
 2.89 
 
 1.0613 
 
 1.14 
 
 .1310 
 
 1.58 
 
 .4574 
 
 2.02 
 
 .7031 
 
 2.46 
 
 .9002 
 
 2.90 
 
 1.0647 
 
 1.15 
 
 .1398 
 
 1.59 
 
 .4637 
 
 2.03 
 
 .7080 
 
 2.47 
 
 .9042 
 
 2.91 
 
 1.0682 
 
 1.16 
 
 .1484 
 
 1.60 
 
 .4700 
 
 2.04 
 
 .7129 
 
 2.48 
 
 .9083 
 
 2.92 
 
 1.0716 
 
 1.17 
 
 .1570 
 
 1.61 
 
 .4762 
 
 2.05 
 
 .7178 
 
 2.49 
 
 .9123 
 
 2.93 
 
 1.0750 
 
 1.18 
 
 .1655 
 
 1.62 
 
 .4824 
 
 2.06 
 
 .7227 
 
 2.50 
 
 .9163 
 
 2.94 
 
 1.0784 
 
 1.19 
 
 .1740 
 
 1.63 
 
 ,4886 
 
 2.07 
 
 .7275 
 
 2.51 
 
 .9203 
 
 2.95 
 
 1.0813 
 
 1.20 
 
 .1823 
 
 1.64 
 
 .4947 
 
 2.08 
 
 .7324 
 
 2.52 
 
 .9243 
 
 2.96 
 
 1.0852 
 
 1.21 
 
 .1906 
 
 1.65 
 
 .5008 
 
 2.09 
 
 .7372 
 
 2.53 
 
 .9282 
 
 2.97 
 
 1.0886 
 
 1.22 
 
 .1988 
 
 1.66 
 
 .5068 
 
 2.10 
 
 .7419 
 
 2.54 
 
 .9322 
 
 2.98 
 
 1.0919 
 
 1.23 
 
 .2070 
 
 1.67 
 
 .5128 
 
 2.11 
 
 .7467 
 
 2.55 
 
 .9361 
 
 2.99 
 
 1.0953 
 
 1.24 
 
 .2151 
 
 1.68 
 
 .5188 
 
 2.12 
 
 .7514 
 
 2.56 
 
 .9400 
 
 3.00 
 
 1.0986 
 
 1.25 
 
 .2231 
 
 1.69 
 
 .5247 
 
 2.13 
 
 .7561 
 
 2.57 
 
 .9439 
 
 3.01 
 
 1.1019 
 
 1.26 
 
 .2311 
 
 1.70 
 
 .5306 
 
 2.14 
 
 .7608 
 
 2.58 
 
 .9478 
 
 3.02 
 
 1.1053 
 
 1.27 
 
 .2390 
 
 1.71 
 
 ,5365 
 
 2.15 
 
 .7655 
 
 2.59 
 
 .9517 
 
 3.03 
 
 1.1086 
 
 1.28 
 
 .2469 
 
 1.72 
 
 .5423 
 
 2.13 
 
 .7701 
 
 2.60 
 
 .9555 
 
 3.04 
 
 1.1119 
 
 1.29 
 
 .2546 
 
 1.73 
 
 .5481 
 
 2.17 
 
 .7747 
 
 2.61 
 
 .9594 
 
 3.05 
 
 1.1151 
 
 1.30 
 
 .2624 
 
 1.74 
 
 .5539 
 
 2.18 
 
 .7793 
 
 2.62 
 
 .9632 
 
 3.06 
 
 1.1184 
 
 1.31 
 
 .2700 
 
 1.75 
 
 .5596 
 
 2.19 
 
 .7839 
 
 2.63 
 
 .9670 
 
 3.07 
 
 1.1217 
 
 1.32 
 
 .2776 
 
 1.76 
 
 .5653 
 
 2.20 
 
 .7885 
 
 2.64 
 
 .9708 
 
 3.08 
 
 1.1249 
 
 1.33 
 
 .2852 
 
 1.77 
 
 .5710 
 
 2.2! 
 
 .7930 
 
 2.65 
 
 .9746 
 
 3.09 
 
 1.1282 
 
 1.34 
 
 .2927 
 
 1.78 
 
 .5766 
 
 2.22 
 
 .7975 
 
 2.66 
 
 .9783 
 
 3.10 
 
 1.1314 
 
 1.35 
 
 .3001 
 
 1.79 
 
 .5822 
 
 2.28 
 
 .8020 
 
 2.67 
 
 .9821 
 
 3.11 
 
 1.1346 
 
 1.36 
 
 .3075 
 
 1.80 
 
 .5878 
 
 2.24 
 
 .8065 
 
 2.68 
 
 .9858 
 
 3.12 
 
 1.1378 
 
 1.37 
 
 .3148 
 
 1.81 
 
 .5933 
 
 2.25 
 
 .8109 
 
 2.69 
 
 .9895 
 
 3.13 
 
 1.1410 
 
 1 tt 
 
 .3221 
 
 1.82 
 
 .5988 
 
 2.26 
 
 .8154 
 
 2.70 
 
 .9933 
 
 3.14 
 
 1.1442 
 
 1.33 
 
 .3293 
 
 1.83 
 
 .6043 
 
 2.27 
 
 .8198 
 
 2.71 
 
 .9969 
 
 3.15 
 
 1.1474 
 
 :ao 
 
 .3365 
 
 1.84 
 
 .6098 
 
 2.28 
 
 .8242 
 
 2.72 
 
 1.0006 
 
 3 16 
 
 1.1506 
 
 1.41 
 
 .um 
 
 1.85 
 
 .6152 
 
 2.29 
 
 ,8286 
 
 2.73 
 
 1.0043 
 
 3.17 
 
 1.1537 
 
 1.42 
 
 .3507 
 
 1.86 
 
 .<>206 
 
 2.30 
 
 .8329 
 
 2.74 
 
 1.0080 
 
 3.18 
 
 1.1569 
 
 1.43 
 
 .3577 
 
 1.87 
 
 .6259 
 
 2.31 
 
 .8372 
 
 2.75 
 
 1.0116 
 
 3.19 
 
 1.1600 
 
 1.44 
 
 .3646 
 
 1.88 
 
 .6313 
 
 2.32 
 
 • 8416 
 
 2.76 
 
 1.0152 
 
 3.20 
 
 1.1632 
 
214 
 
 USEFUL TABLES. 
 HYPERBOLTC LOGARITHMS. 
 
 No.. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 3.21 
 
 1.1663 
 
 3.87 
 
 1.3533 
 
 4.53 
 
 1.5107 
 
 5.19 
 
 1.6467 
 
 5.85 
 
 1.7664 
 
 3.22 
 
 1.1694 
 
 3.88 
 
 1.3558 
 
 4.54 
 
 1.5129 
 
 5.20 
 
 1.6487 
 
 5.86 
 
 1.7681 
 
 3.23 
 
 1.1725 
 
 3.89 
 
 1.3584 
 
 4.55 
 
 1.5151 
 
 5.21 
 
 1.6506 
 
 5.87 
 
 1.7699 
 
 3.24 
 
 1.1756"" 
 
 3.90 
 
 1.3610 
 
 4.56 
 
 1.5173 
 
 5.22 
 
 1.6525 
 
 5.88 
 
 1.7716 
 
 3.25 
 
 1.1787 
 
 3.91 
 
 1.3635 
 
 4.57 
 
 1.5195 
 
 5.23 
 
 1.6514 
 
 5.89 
 
 1.7733 
 
 3.26 
 
 1.1817 
 
 3.92 
 
 1.3661 
 
 4.58 
 
 1.5217 
 
 5.24 
 
 1.6563 
 
 5.90 
 
 1.7750 
 
 3.27 
 
 1.1848 
 
 3.93 
 
 1.3686 
 
 4.59 
 
 1.5239 
 
 5.25 
 
 1.6582 
 
 5.91 
 
 •1.7766 
 
 3.28 
 
 1.1878 
 
 3.94 
 
 1.3712 
 
 4.60 
 
 1.5261 
 
 5.26 
 
 1.6601 
 
 5.92 
 
 1.7783 
 
 3.29 
 
 1.1909 
 
 3.95 
 
 1.3737 
 
 4.6i 
 
 1.5282 
 
 5.27 
 
 1.6620 
 
 5.93 
 
 1.780C 
 
 3.30 
 
 1.1939 
 
 3.96 
 
 1.3762 
 
 4.62 
 
 1.5304 
 
 5.28' 
 
 1.6639 
 
 5.94 
 
 1.7817 
 
 3.31 
 
 1 1969 
 
 3.97 
 
 1.3788 
 
 4.63 
 
 1.5326 
 
 5.29 
 
 1.6658 
 
 5.95 
 
 j .7834 
 
 3.32 
 
 1.1999 
 
 3.98 
 
 1.3813 
 
 4.64 
 
 1.5347 
 
 5.30 
 
 1.6677 
 
 5.96 
 
 1.7851 
 
 3.33 
 
 1.2030 
 
 3.99 
 
 1.3838 
 
 4.65 
 
 1.5369 
 
 5.31 
 
 1.6696 
 
 5.97 
 
 1.7867 
 
 3.34 
 
 1.2060 
 
 4.00 
 
 1.3863 
 
 4.66 
 
 1.5390 
 
 5.32 
 
 1.6715 
 
 5.98 
 
 1.7884 
 
 3.35 
 
 1.2090 
 
 4.01 
 
 1.3888 
 
 4.67 
 
 1.5412 
 
 5.33 
 
 1.6734 
 
 5.99 
 
 1.7901 
 
 3.36 
 
 1.2119 
 
 4.02 
 
 1.3913 
 
 4.68 
 
 1.5433 
 
 5.34 
 
 1.6752 
 
 6.00 
 
 1.7918 
 
 8.37 
 
 1.2149 
 
 4.03 
 
 1.3938 
 
 4.69 
 
 1.5454 
 
 5.35 
 
 1.6771 
 
 6.01 
 
 1.7934 
 
 3.38 
 
 1.2179 
 
 4.01 
 
 1.3962 
 
 4.70 
 
 1.5476 
 
 5.36 
 
 1.6790 
 
 6.02 
 
 1.7951 
 
 3.39 
 
 1.2208 
 
 4.05 
 
 1.3987 
 
 4.71 
 
 1.5497 
 
 5.37 
 
 1.6808 
 
 6.03 
 
 1.7967 
 
 3.40 
 
 1.2238 
 
 4.06 
 
 1.4012 
 
 4.72 
 
 1.5518 
 
 5.38 
 
 1.6827 
 
 6.04 
 
 1.7984 
 
 3.41 
 
 1.2267 
 
 4.07 
 
 1.4036 
 
 4.73 
 
 1.5539 
 
 5.39 
 
 1.6845 
 
 6.05 
 
 1.8001 
 
 3.42 
 
 1.2296 
 
 4.08 
 
 1.4061 
 
 4.74 
 
 1.5560 
 
 5.40 
 
 1.6864 
 
 6.06 
 
 1.8017 
 
 3.43 
 
 1.2326 
 
 4.09 
 
 1.4085 
 
 4.75 
 
 1.5581 
 
 5.41 
 
 1.6882 
 
 6.07 
 
 1.8034 
 
 3.44 
 
 1 .2355 
 
 4.10 
 
 1.4110 
 
 4.76 
 
 1.5602 
 
 5.42 
 
 1.6901 
 
 6.08 
 
 1.8050 
 
 3.45 
 
 1.2384 
 
 4.11 
 
 1.4134 
 
 4.77 
 
 1.5623 
 
 5.43 
 
 1.6919 
 
 6.09 
 
 1.8066 
 
 3.46 
 
 1.2413 
 
 4.12 
 
 1.4159 
 
 4.78 
 
 1.5644 
 
 5.44 
 
 1.6938 
 
 6.10 
 
 1.8083 
 
 3.47 
 
 1.2442 
 
 4.13 
 
 1.4183 
 
 4.79 
 
 1.5665 
 
 5.45 
 
 1.6956 
 
 6.11 
 
 1.8099 
 
 3.48 
 
 1.2470 
 
 4.14 
 
 1.4207 
 
 4.80 
 
 1.5686 
 
 5.46 
 
 1.6974 
 
 6.12 
 
 1.8116 
 
 3.49 
 
 1.2499 
 
 4.15 
 
 1.4231 
 
 4.81 
 
 1.5707 
 
 5.47 
 
 1.6993 
 
 6.13 
 
 1.8132 
 
 3.50 
 
 1.2528 
 
 4.16 
 
 1.4255 
 
 4.82 
 
 1.5728 
 
 5.48 
 
 1.7011 
 
 6.14 
 
 1.8148 
 
 3.51 
 
 1.2556 
 
 4.17 
 
 1.4279 
 
 4.83 
 
 1.5748 
 
 5.49 
 
 1.7029 
 
 6.15 
 
 1.8165 
 
 3.52 
 
 1.2585 
 
 4.18 
 
 1.4303 
 
 4.84 
 
 1 .5769 
 
 5.50 
 
 1.7047 
 
 6.16 
 
 1.8181 
 
 3.53 
 
 1.2613 
 
 4.19 
 
 1.4327 
 
 4.85 
 
 1.5790 
 
 5.51 
 
 1.7066 
 
 6.17 
 
 1.8197 
 
 3.54 
 
 1.2641 
 
 4.20 
 
 1.4351 
 
 4.86 
 
 1.5810 
 
 5.52 
 
 1.7084 
 
 6.18 
 
 1.8213 
 
 3.55 
 
 1.8669 
 
 4.21 
 
 1.4375 
 
 4.87 
 
 1.5831 
 
 5.53 
 
 1.7102 
 
 6.19 
 
 1.8229 
 
 3.56 
 
 1.2698 
 
 4.22 
 
 1.4398 
 
 4.88 
 
 1.5851 
 
 5.54 
 
 1.7120 
 
 6.20 
 
 1.8245 
 
 3.57 
 
 1.2726 
 
 4.23 
 
 1 .4422 
 
 4.89 
 
 1.5872 
 
 5.55 
 
 1.7138 
 
 6.21 
 
 1.8262 
 
 3.58 
 
 1.2754 
 
 4.24 
 
 1.4446 
 
 4.90 
 
 1.5892 
 
 5.56 
 
 1.7156 
 
 6.22 
 
 J. 8278 
 
 3.59 
 
 1.2782 
 
 4.25 
 
 1.4469 
 
 4.91 
 
 1.5913 
 
 5.57 
 
 1.7174 
 
 6.23 
 
 1.8294 
 
 3.60 
 
 1.2809 
 
 4.26 
 
 1.4493 
 
 4.92 
 
 1.5933 
 
 5.58 
 
 1.7192 
 
 6.24 
 
 1.8310 
 
 3.61 
 
 1.2837 
 
 4.27 
 
 1.4516 
 
 4.93 
 
 1.5953 
 
 5.59 
 
 1.7210 
 
 6.25 
 
 1.8326 
 
 3.62 
 
 1.2865 
 
 4.28 
 
 1.4540 
 
 4.94 
 
 1.5974 
 
 5.60 
 
 1.7228 
 
 6.26 
 
 1.8342 
 
 3.63 
 
 1.2892 
 
 4.29 
 
 1.4563 
 
 4.95 
 
 1.5994 
 
 5.61 
 
 1.7246 
 
 6.27 
 
 1.8358 
 
 3.64 
 
 1.2920 
 
 4.30 
 
 1.4586 
 
 4.96 
 
 1.6014 
 
 5.62 
 
 1.7263 
 
 6.28 
 
 1.8374 
 
 3.65 
 
 1.2947 
 
 4.31 
 
 1.4609 
 
 4.97 
 
 1.6034 
 
 5.63 
 
 1.7281 
 
 6.29 
 
 1.8390 
 
 3.66 
 
 1.2975 
 
 4.32 
 
 1.4633 
 
 4.98 
 
 1.6054 
 
 5.64 
 
 1.7299 
 
 6.30 
 
 1.8405 
 
 3.67 
 
 1.3002 
 
 4.33 
 
 1 .4656 
 
 4.99 
 
 1.6074 
 
 5.65 
 
 1.7317 
 
 6.31 
 
 1.8421 
 
 3.68 
 
 1.3029 
 
 4.34 
 
 1.4679 
 
 5.00 
 
 1.6094 
 
 5.66 
 
 1.7334 
 
 6.32 
 
 1.8437 
 
 3.69 
 
 1.3056 
 
 4.35 
 
 1.4702 
 
 5.01 
 
 1.6114 
 
 5.67 
 
 1.7352 
 
 6.33 
 
 1.8453 
 
 3.70 
 
 1.3083 
 
 4.36 
 
 1.4725 
 
 5.02 
 
 1.6134 
 
 5.68 
 
 1.7370 
 
 6.34 
 
 1.8469 
 
 3.71 
 
 1.3110 
 
 4.37 
 
 1.4748 
 
 5.03 
 
 1.6154 
 
 5.69 
 
 1.7387 
 
 6.35 
 
 1.8485 
 
 3.72 
 
 1.3137 
 
 4.38 
 
 1.4770 
 
 5.04 
 
 1.6174 
 
 5.70 
 
 1.7405 
 
 6.36 
 
 1.8500 
 
 3.73 
 
 1.3164 
 
 4.39 
 
 1.4793 
 
 5.05 
 
 1.6194 
 
 5.71 
 
 1.7422 
 
 6.37 
 
 1.8516 
 
 3.74 
 
 1.3191 
 
 4.40 
 
 1.4816 
 
 5.06 
 
 1.6214 
 
 5.72 
 
 1 .7440 
 
 6.38 
 
 1.8532 
 
 3.75 
 
 1.3218 
 
 4.41 
 
 1.4839 
 
 5.07 
 
 1.6233 
 
 5.73 
 
 1.7457 
 
 6.39 
 
 1.8517 
 
 3.76 
 
 1.3244 
 
 4.42 
 
 1.4861 
 
 5.08 
 
 1.6253 
 
 5.74 
 
 1.7475 
 
 6.40 
 
 1.8563 
 
 3.77 
 
 1.3271 
 
 4.43 
 
 1.4884 
 
 5.09 
 
 1.6273 
 
 5.75 
 
 1.7492 
 
 6.41 
 
 1.8579 
 
 3.78 
 
 1.3297 
 
 4.44 
 
 1.4907 
 
 5.10 
 
 1.6292 
 
 5.76 
 
 1.7509 
 
 6.42 
 
 1.8594 
 
 3.79 
 
 1.3324 
 
 4.45 
 
 1.4929. 
 
 5.11 
 
 1.6312 
 
 5.77 
 
 1.7527 
 
 6.43 
 
 1.8610 
 
 3.80 
 
 1.3350 
 
 4.46 
 
 1.4951 
 
 5.12 
 
 1.6332 
 
 5.78 
 
 1.7544 
 
 6.44 
 
 1.8625 
 
 3.81 
 
 1.3376 
 
 4.47 
 
 1.4974 
 
 5.13 
 
 1.6351 
 
 5.79 
 
 1.7561 
 
 6.45 
 
 1.8641 
 
 3.82 
 
 1.3403 
 
 4.48 
 
 1.4996 
 
 5.14 
 
 1.6371 
 
 5.80 
 
 1.7579 
 
 6.46 
 
 1.8056 
 
 3.83 
 
 1.3429 
 
 4.49 
 
 1.5019 
 
 5.15 
 
 1 .6390 
 
 5,81 
 
 -1.7596 
 
 6.47 
 
 1.8672 
 
 3.84 
 
 1.3455 
 
 4.50 
 
 1.5041 
 
 5.16 
 
 1.6409 
 
 5.82 
 
 1.7613 
 
 6.48 
 
 1.8687 
 
 3.85 
 
 1.3481 
 
 4.51 
 
 1.5063 
 
 5.17 
 
 1.6429 
 
 5.83 
 
 1 .76% 
 
 6.49 
 
 1.8703 
 
 3.86 
 
 1.3507 
 
 4.52 
 
 1.5085 
 
 5.18 
 
 1.6448 
 
 5.84 
 
 1.7647 1 
 
 6.50 
 
 1.8718 
 
USEFUL TABLES. 
 
 215 
 
 Volume, wensity, and Pressure of Air at Various 
 
 Temperatures. (D.K.Clark.) 
 
 
 Volume at Atinos. 
 
 
 Pressure at Constant 
 
 
 Pressure. 
 
 Density, lbs. 
 
 Volume. 
 
 
 
 per Cubic Foot at 
 Atmos. Pressure. 
 
 
 
 Fahr. 
 
 
 
 
 
 
 Cubic Feet 
 
 Compara- 
 
 
 Lbs. per 
 
 Compara- 
 tive Pres. 
 
 
 in 1 lb. 
 
 tive Vol. 
 
 
 ' Sq. In. 
 
 
 
 11.583 
 
 .881 
 
 .086331 
 
 12.96 
 
 .881 
 
 32 
 
 12.387 
 
 .943 
 
 .080728 
 
 13.86 
 
 .943 
 
 40 
 
 12.586 
 
 .958 
 
 .079439 
 
 14.08 
 
 .958 
 
 50 
 
 12.840 
 
 .977 
 
 .077884 
 
 14.36 
 
 .977 
 
 62 
 
 13.141 
 
 1.000 
 
 .076097 
 
 14.70 
 
 1.000 
 
 70 
 
 13.342 
 
 1.015 
 
 .074950 
 
 14.92 
 
 1.015 
 
 80 
 
 13.593 
 
 1.Q34 
 1.054 
 
 .073565 
 
 15.21 
 
 1.034 
 
 90 
 
 13.845 
 
 .072230 
 
 15.49 
 
 1.054 
 
 100 
 
 14.096 
 
 1.073 
 
 .070942 
 
 15.77 
 
 1.073 
 
 no 
 
 14.344 
 
 1.092 
 
 .069721 
 
 16.05 
 
 1.092 
 
 120 
 
 14.592 
 
 1.111 
 
 .06^500 
 
 16.33 
 
 1.111 
 
 130 
 
 14.846 
 
 1.130 
 
 .067361 
 
 16.61 
 
 1.130 
 
 140 
 
 15.100 
 
 1.149 
 
 .066221 
 
 16.89 
 
 1.149 
 
 150 
 
 15.351 
 
 1.168 
 
 .065155 
 
 17.19 
 
 1.168 
 
 160 
 
 15.603 
 
 1.187 
 
 .064088 
 
 17.50 
 
 1.187 
 
 170 
 
 15.854 
 
 1.206 
 
 .063089 
 
 17.76 
 
 1.206 
 
 180 
 
 16.106 
 
 1.226 
 
 .062090 
 
 18.02 
 
 1.226 
 
 200 
 
 16.606 
 
 1.264 
 
 .060210 
 
 18.58 
 
 1.264 
 
 210 
 
 16.860 
 
 1.283 
 
 .059313 
 
 18.86 
 
 1.283 
 
 212 
 
 16.910 
 
 1.287 
 
 .059135 
 
 18.92 
 
 1.287 
 
2l6 
 
 USEFUL TABLES, 
 
 Volumes, mean Pressures per Stroke, Temperatures, etc.. 
 in the Operation of Air-compression from 1 Atmosphere 
 
 and 60° Fahr, (F. Richards, Am. Mack., March 30, 1893.) 
 
 
 
 
 
 
 
 
 
 t- _• i t. 
 
 
 
 6 
 
 3 
 
 | 
 
 9- 
 i 
 
 CO 
 
 w 
 O 
 
 s 
 
 |1 
 
 < 
 
 * O 
 
 to ft 
 
 a, jj c 
 
 m 
 
 o 
 
 3 
 
 <i 
 •si 
 
 o 
 
 ft 
 
 3 
 
 6 
 
 3 
 
 3 
 
 9 
 ft 
 i 
 
 3 
 
 CO 
 
 u 
 
 ft 
 O 
 
 a 
 
 - a, 
 1% 
 
 So 
 
 < 
 
 ■si 
 
 V 
 
 0/ . 
 
 0> 
 
 p a 
 
 3 — "O 
 
 £ i>'o 
 
 «5-^ 
 
 c 
 
 3 
 
 O O 
 o 
 
 ft 
 
 § 
 
 «5 
 
 
 ©^ 
 
 o 
 
 JJCQ 
 
 0)73 
 
 
 cd 
 
 
 0*> 
 
 o 
 
 Vrn 
 
 0)02 
 
 35 
 
 < 
 
 > * 
 
 5> 
 
 § 
 
 H 
 
 o 
 
 < 
 
 > a 
 
 > 
 
 £T 
 
 s 
 
 1 
 
 S 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 
 1 
 
 1 
 
 1 
 
 
 
 
 
 60° 
 
 80 
 
 6. 442. 1552 
 
 .267 
 
 27.38 
 
 36.64 
 
 "432 
 
 1 
 
 J. 068 
 
 .9363 
 
 .95 
 
 .96 
 
 .975 
 
 71 
 
 85' 6.182 
 
 .1474 
 
 2566 
 
 28.16 
 
 37.94 
 
 447 
 
 2 
 
 1.136 
 
 .8803 
 
 .91 
 
 1.87 
 
 .1.91 
 
 80.4 
 
 90! 7.122 
 
 .1404 
 
 .248 
 
 28.89 
 
 39.18 
 
 459 
 
 3 
 
 1.204 
 
 .8305 
 
 .876 
 
 2.72 
 
 2 8 
 
 88.9 
 
 95 ! 7.462 
 
 .134 
 
 .24 
 
 29.57 
 
 40.4 
 
 472 
 
 4 
 
 1.272 
 
 .7861 
 
 .84 
 
 3.53 
 
 H 67 
 
 98 
 
 100 1 7.802' 1281 
 
 .232 
 
 30.21 
 
 41.6 
 
 485 
 
 5 
 
 1.34 
 
 .7462 
 
 .81 
 
 4.3 
 
 4 5 
 
 106 
 
 1051 8.1421 1228 
 
 2254 
 
 30.81 
 
 42.78 
 
 496 
 
 10 
 
 1 68 
 
 .5952 
 
 .69 
 
 7.62 
 
 8.27 
 
 145 
 
 110 8 483 .1178 
 
 .2189 
 
 31.39 
 
 43.91 
 
 507 
 
 15 
 
 2.02 
 
 .495 
 
 .606 
 
 10.33 
 
 11.51 
 
 178 
 
 1151 8 823' .1133 
 
 .2129 
 
 31.98 
 
 44.98 
 
 518 
 
 SO 
 
 2.36 
 
 .4237 
 
 .543 
 
 12.62 
 
 14.4 
 
 207 
 
 120, 9.163' 1091 
 
 .2073 
 
 32.54 
 
 46.04 
 
 529 
 
 25 
 
 2.7 
 
 .3703 
 
 .494 
 
 14.59 
 
 17.01 
 
 234 
 
 125 9. 503.. 1052 
 
 .2020 
 
 33.07 
 
 47.06 
 
 540 
 
 30 
 
 3!oi 
 
 3289 
 
 .4538 
 
 16.34 
 
 19.4 
 
 252 
 
 130 9.843 .1015 
 
 .1969 
 
 33.57 
 
 48.1 
 
 550 
 
 35 
 
 3.3S1 
 
 .2957 
 
 .42 
 
 17.92 
 
 21.6 
 
 281 
 
 135 10.183' 0981 
 
 .1922 
 
 34.05 
 
 49.1 
 
 560 
 
 40 
 
 3.721 
 
 .2687 
 
 393 
 
 19.32 
 
 23 66 
 
 302 
 
 140 10.5?3'.095 
 
 .1878 
 
 34.57 
 
 50.02 
 
 570 
 
 45 
 
 1.061 
 
 .2462 
 
 .37 
 
 20.57 
 
 *5.59 
 
 321 
 
 145 10.864 .0921 
 
 .1837 
 
 35.09 
 
 51. 
 
 580 
 
 MJ 
 
 4.401 
 
 .2272 
 
 .35 
 
 21.69 
 
 27.39 
 
 339 
 
 150 11.204 .0892 
 
 .1796 
 
 35.48 
 
 51.89 
 
 589 
 
 r>r> 
 
 4.741 
 
 .2109 
 
 331 
 
 22.76 
 
 29.11 
 
 357 
 
 160 11.88 
 
 .0841 
 
 .1722 
 
 36.29 
 
 53.65 
 
 607 
 
 fiO 
 
 5.081 
 
 .1968 
 
 .3144 
 
 23 . 78 
 
 30 75 
 
 375 
 
 170 12.56 
 
 0796 
 
 .1657 
 
 37.2 
 
 55.39 
 
 624 
 
 65 
 
 0.423 
 
 .1844 
 
 .301 
 
 24.75 
 
 32 32 
 
 389 
 
 180 13 24 
 
 0755 
 
 .1595 
 
 37.96 
 
 57.01 
 
 640 
 
 70 
 
 5.762 
 
 .1735 
 
 288 
 
 25 67 
 
 33.83 
 
 405 
 
 190 13.92 
 
 .0718 
 
 .154 
 
 38.68 
 
 58.57 
 
 657 
 
 ?S 
 
 6.102 
 
 .1639 
 
 .276 
 
 26.55 
 
 35.2? 
 
 420 
 
 200 14.6 
 
 .0685 
 
 .149 
 
 39.42 
 
 60.14 
 
 672 
 
USEFUL TABLES. 
 
 Mean and Terminal Pressures of Compressed AJr used 
 Expansively for Gauge-pressares from 60 to 100 lbs. 
 
 (Frank Richards, Am. Mack, April 13, 5893.) 
 
 Initial 
 Pres- 
 
 60. 
 
 70. 
 
 80. 
 
 90. 
 
 100 
 
 sure. 
 
 
 
 
 
 
 ojb 
 
 SU§ 
 
 .Si 5 
 
 B . 2 
 
 Bc.3 
 
 « 1 
 * u S 
 
 * s 
 
 3 ". *■ 
 
 *3 a) 
 
 0) 
 
 *3 © 
 
 .5.- % 
 
 O 3 
 
 £<% 
 
 £<% 
 
 
 %<% 
 
 £^£ 
 
 l<l 
 
 4T-5 " 
 
 WJ 
 
 m 
 
 &o 
 
 a 
 
 b* a 
 
 ft 
 
 £ fe 
 
 a 
 
 £ S. 
 
 39 04 
 
 £ p, 
 J4.91 
 
 ft 
 
 £ ft 
 
 .25 
 
 23.6 
 
 10 65 
 
 28.74 
 
 12.07 
 
 33.89 
 
 13.49 
 
 44.19 
 
 1.33 
 
 .30 
 
 28.9 
 
 13.77 
 
 34.75 
 
 6 
 
 40 61 
 
 2.44 
 
 46 46 
 
 4.27 
 
 53.32 
 
 6 11 
 
 l A 
 
 32.13 
 
 ,96 
 
 38.41 
 
 3.09 
 
 44.69 
 
 5 22 
 
 50.98 
 
 7 35 
 
 57 26 
 
 9 48 
 
 .35 
 
 33.66 
 
 2.33 
 
 40. T5 
 
 4.38 
 
 46.64 
 
 6.66 
 
 53.13 
 
 8 95 
 
 59 62 
 
 11.23 
 
 & 
 
 35.85 
 
 3.85 
 
 42 63 
 
 6.36 
 
 49.41 
 
 7.88 
 
 56 2 
 
 11.39 
 
 62 98 
 
 13.559 
 
 37.93 
 
 5.64 
 
 44.99 
 
 8.39 
 
 52.05 
 
 11.14 
 
 59.11 
 
 13.88 
 
 66 16 
 
 16.64 
 
 ,45 
 
 41.75 
 
 10.71 
 
 49.31 
 
 12.61 
 
 56.9 
 
 15.86 
 
 64 45 
 
 19.11 
 
 72.02 
 
 22.36 
 
 .50 
 
 45.14 
 
 13.26 
 
 53.16 
 
 17 
 
 61.18 
 
 20 81 
 
 69.19 
 
 24 56 
 
 77.21 
 
 2S.33 
 
 ,60 
 
 50.75 
 
 21.53 
 
 59.51 
 
 26.4 
 
 68.28 
 
 31 27 
 
 77.05 
 
 36.14 
 
 85.82 
 
 41 01 
 
 % 
 
 51.92 
 
 23.69 
 
 60.84 
 
 28.85 
 
 69.76 
 
 34.01 
 
 78.69 
 
 39.16 
 
 87.61 
 
 44.32 
 
 ft 
 
 53.67 
 
 27.94 
 
 62 83 
 
 33.03 
 
 71.99 
 
 38.68 
 
 81 14 
 
 44 33 
 
 90.32 
 
 49 97 
 
 54.93 
 
 30.39 
 
 64 25 
 
 36 44 
 
 73.57 
 
 42.49 
 
 82 9 
 
 48.54 
 
 92.22 
 
 54.59 
 
 .75 
 
 56.52 
 
 35.01 
 
 66.05 
 
 41.68 
 
 75.59 
 
 48.35 
 
 85.12 
 
 55.02 
 
 94.66 
 
 61 69 
 
 .80 
 
 57.79 
 
 30.78 
 
 67.5 
 
 47.08 
 
 77.2 
 
 54.38 
 
 86.91 
 
 61.69 
 
 96.61 
 
 68.99 
 
 % 
 
 59.15 
 
 47.14 
 
 69.03 
 
 55.43 
 
 78.92 
 
 63.81 
 
 88.81 
 
 72. 
 
 9S.7 
 
 80 28 
 
 .90 
 
 59.46 
 
 49.65 
 
 69.38 
 
 58.27 
 
 79 31 
 
 66 89 
 
 89.24 
 
 75.52 
 
 99.17 
 
 87 82 
 
 The pressures in the table are all gauge-pressures except those in italics 
 which are absolute pressures (above a vacuum). 
 
218 
 
 USEFUL TABIDS. 
 
 R 
 
 K 
 
 PV, 
 
 p, 
 
 R 
 
 t 
 
 PV» 
 
 p, 
 
 2 
 
 . o5 
 
 /99s 
 
 5 
 
 • ^ 
 
 .5218 
 
 1 8 
 
 .055 
 
 . 5.I 6 I 
 
 4.4 4 
 
 . z zs 
 
 . 5^08 
 
 I 6 
 
 . 06* 
 
 . 2ZS8 
 
 4. 
 
 . z 5 
 
 . 5^65 
 
 1 5 
 
 . 6 66 
 
 . IhjZ 
 
 3. 6 3 
 
 . 2,7 S 
 
 . 6*3o5 
 
 1 4 
 
 . 07/ 
 
 . 25^ 
 
 3.3 3 
 
 . 3 
 
 . 6"6i 5 
 
 13.33 
 
 . 0/5 
 
 . Z6cj 
 
 3 
 
 .333 
 
 .6-^3 
 
 1 3 
 
 • 07/ 
 
 . ^74^ 
 
 2.86 
 
 . 3 S 
 
 . 7.7. 
 
 1 X 
 
 . o83 
 
 . 2(|.0^ 
 
 Z6 6 
 
 . 3 7 S 
 
 ,/44 
 
 1 1 
 
 .091 
 
 . 3o8cj 
 
 Z- So 
 
 •4 
 
 .^6et4 
 
 1 
 
 . 1 
 
 . 33e>3 
 
 Z.ZZ 
 
 . 4 5" 
 
 . 8095 
 
 q 
 
 .III 
 
 . 3 55^ 
 
 2. 
 
 ♦ 5 
 
 . 8465 
 
 8 
 
 . ins 
 
 . sa^ 
 
 1. SZ 
 
 , 5 s 
 
 . 8/86 
 
 7 
 
 .143 
 
 . 4AI 
 
 A. 6 6 
 
 . 6 
 
 . 9066 
 
 6.6 6 
 
 • / 5" 
 
 .434/ 
 
 1.6 
 
 . 6a5 
 
 • 9 ' 8 7 
 
 6 
 
 . !66 
 
 . 4653 
 
 1.5-4 
 
 . 6 5* 
 
 .QJLCJ2 
 
 S. 7 i 
 
 • i 7 5- 
 
 .^807 
 
 1.4 8 
 
 , 6 j S 
 
 . C}4 o5 
 
 J T^U 
 
 •€. of Mean Absolute Pressures 
 
 l/anows Decrees of IsotkeTmaL Expansion — » 
 
 
 _f.r 
 
 P, i«, rtv«, 
 
 P», IS tf» 
 
 R_ ,s 4 
 
 C 3 W» 
 
 ± inel.< 
 
 B, 
 
 — In this Table 
 
 Absolute. Pressure. o»V whick. Sticuw. ev\T"er.S M\e. C 
 e. corveipondma Mian Absolut*. Pressure. , 
 e. Hate of E*p* wJ »' OM -, '"•"•• Hve. /Ratto «f Hit VoWd v 
 
 o\e.T , I'weW.'n^ CUo.ra.wc, U U\i Volunn* of Lw«- SVt»w, 
 ftttS Hit point- of Cu.r.off, ifc.fU Ratio of Hie. h>Ul Vol 
 v ft. rUt Voho.1 Volume of Cvli'i*cUv <xr U»«. End of H10. S 
 
 yli'wder, 
 
 
 
 
USEFUL TABLES. 
 
 219 
 
 Nowi 1 v\o.l 
 
 lv»cK»6 — 
 
 Actw.ev.1 
 
 N»Wll'M«l 
 Wciabl- 
 
 — Utf 
 
 Number »f Tkrea^j 
 of Scrtw 
 
 a. 
 
 * * 
 
 «a. 2 z 
 
 14 
 
 *•! 
 
 2.- J 
 
 Z- 8 z. 
 
 1 4 
 
 *'k 
 
 *•* 
 
 3- 1 3 
 
 1 4 
 
 *•! 
 
 3 
 
 3- ^ 5" 
 
 1 4 
 
 3. 
 
 3.J; 
 
 4-16 
 
 I 4 
 
 *•* 
 
 A- 4 
 
 4 4$ 
 
 1 4 
 
 3-5 
 
 3-1 
 
 4/8 
 
 J 4 
 
 »•* 
 
 4 
 
 5. 5*6 
 
 I 4 
 
 4 
 
 4-4 
 
 6. 
 
 1 4 
 
 4-k 
 
 4£ 
 
 <£. 3 6 
 
 I 4 
 
 4-s 
 
 4-.* 
 
 /.7 3 
 
 1 4 
 
 4-J 
 
 5" 
 
 7io 
 
 1 H 
 
 (5" 
 
 54 
 
 g.2 
 
 \H 
 
 *fc 
 
 5.± 
 
 *■ 62, 
 
 1 4 
 
 *J 
 
 6 
 
 I . 4 6 
 
 1 4 
 
 ** 
 
 *f 
 
 M- 5-8 
 
 1 M 
 
 *f 
 
 7 
 
 12.34 
 
 1 4 
 
 74 
 
 7% 
 
 J 3. s-s 
 
 i M 
 
 M 
 
 8 
 
 1 5- A 1 
 
 u4 
 
 8.* 
 
 |.f 
 
 / 6 . e^ 
 
 II.. £ 
 
 ••f 
 
 °l 
 
 17.^0 
 
 M-i 
 
 vf 
 
 1 
 
 A 1 • «J 
 
 ' '£ 
 
 1 6. ? 
 
 • 
 
 I 1 
 
 2 67^ 
 
 Mi 
 
 M'f 
 
 1 2. 
 
 3 35" 
 
 M-i 
 
 14 £ 
 
 • 3 
 
 33.7 8 
 
 l|£ 
 
 « ^ i 
 
 J 4 
 
 42o2, 
 
 « ' i 
 
 .4 i 
 
 » 5" 
 
 A 7 6 6 
 
 1 »•£ 
 
 Ui 
 
 1 6 
 
 St*/ 
 
 »' k 
 
 fc LiSf «f Well CqJl'wa. 
 
 - 
 
USEFUL TABLES. 
 
 . Bwtt -Welded 
 
 Nom.'wat 
 
 Actual 
 
 . — lv\fct\t6 . _ 
 
 
 — Lbs — 
 
 N«*wb«y «(TlvY««<l» 
 of ScYtVV 
 
 8 
 
 . 4 
 
 .066 
 
 . 2.4 
 
 *7 
 
 4 
 
 . $•*■ 
 
 • 8 8 
 
 • 4a. 
 
 1 8 
 
 3 
 8 
 
 • V 
 
 ••1' 
 
 . 5-6 
 
 1 e 
 
 J 
 
 • 84 
 
 • I a\ 
 
 . 8* 
 
 1 * 
 
 3 
 2f 
 
 J. ©S - 
 
 • l l 3 
 
 lix 
 
 1 * 
 
 1 
 
 I. 31 
 
 > 1 3 4 
 
 1C7 
 
 ' • i 
 
 1 I 
 
 1-66 
 
 . I 4 
 
 i.ji 
 
 " £ 
 
 — - Lap- Wcl4ed — — - 
 
 NtMl'-MAl 
 
 twSi'da. 
 
 ActwoJ ' 
 
 O i A vucfa f 
 
 TVcKnets 
 
 N»iwi*m*I 
 
 [>»t Fo.h 
 — L>4 
 
 |»«.t IhcK 
 of Screw 
 
 »i 
 
 l.<? 
 
 .14 5 
 
 2.6 8 
 
 1 l.£ 
 
 Z 
 
 2.3/ 
 
 . / 5-4 
 
 3. 6» 
 
 I ȣ 
 
 2. 1 
 
 2 8? 
 
 • iel 
 
 S. 7 * 
 
 $ 
 
 3 
 
 d. r 
 
 .117 
 
 7.3-4 
 
 8 
 
 5 i 
 
 4 
 
 •2*6 
 
 <} 
 
 8 
 
 4 
 
 4-5* 
 
 .43/ 
 
 1 0.66 
 
 8 
 
 A i 
 
 s- 
 
 . m; 
 
 ia.34 
 
 3 
 
 S 
 
 S.& 
 
 .i5-q 
 
 '1450 
 
 8 
 
 6 
 
 6.62. 
 
 . a. 6 
 
 \S.76 
 
 8 
 
 7 
 
 ? 6*. 
 
 • 3« 1 
 
 i.3 2.7 
 
 8 
 
 8 
 
 8.62. 
 
 .jai 
 
 as / a 
 
 a 
 
 9 
 
 cj. «8 
 
 • *44 
 
 3 3. 7 * 
 
 a 
 
 / 
 
 I 075" 
 
 • $66 
 
 4o 
 
 8 
 
 i 1 
 
 1 1. 75- 
 
 • 375* 
 
 45 
 
 8 
 
 > i 
 
 12.7* 
 
 .3^5 
 
 4Q 
 
 8 
 
 i 3 
 
 14 
 
 • 37^ 
 
 54 
 
 8 
 
 1 H 
 
 IS 
 
 • 37* 
 
 S8 
 
 » 
 
 1$ 
 
 16 
 
 .3 7 5- 
 
 6X 
 
 8 
 
 — List of Sffcawv, A»r «\h«i Ware/ P.>*S . 
 
 - 
 
INDEX. 
 
 PAGE 
 
 A ir Compressors— General Remarks 81 
 
 Air Engines 38 
 
 Air Engines, Exhaust Temperatures and Reheating 50 
 
 Air Receivers 182 
 
 Available Work at Complete Expansion, Curve of. 30 
 
 Available Work at Full Expansion, Table of. 31 
 
 Blacksmith Tools 186 
 
 Capacity of Compressors 84 
 
 Calculation of H. P. of Water, Table of 207 
 
 Circumferences and Areas of Circles 191 
 
 Column Mountings 180 
 
 Compressed Air, General Principles 3 
 
 COMPRESSORS— 
 
 Combined Duplex Steam Actuated and Shaft-driven Com- 
 pressors, Class G 105 
 
 Compound Corliss Actuated Compressors, Class J 110 
 
 Direct Acting Steam Actuated Duplex Compressors, Light 
 
 Duty, Class L 119 
 
 Duplex Steam Actuated Compressors, Class A 86 
 
 Duplex Shaft-driven Compressors, Class D 95 
 
 Duplex Tandem Sectional Shaft-driven Compressors, Class E. 99 
 
 Light Duty Compressor or Vacuum Pump, Class K 117 
 
 Single Steam Compressors, Class B 91 
 
 Single Steam Actuated Compressors, Self-contained Type, 
 
 Class C 93 
 
 Single Shaft-driven Compressors, Class F 102 
 
 Single Corliss Actuated Compressors, Class 1 113 
 
 Steam Actuated Vertical Compressors, Class H 108 
 
 Steam Actuated Single Air Compressors, Class M 121 
 
 Consumption of Air 40 
 
 Consumption of Air, Single Cylinder Automatic Engines 41 
 
 Consumption of Air, Compound Automatic Engines 42 
 
 Consumption of Air, Single Cylinder Corliss Engines 43 
 
 Consumption of Air, Compound Corliss Engines 44 
 
 Consumption of Air, Corliss Compound Pneumatic Motors, Table 
 
 of 51 
 
 Consumption of Air for pumps 61 
 
 Consumption of Air, Rock Drills 85 
 
 Decimals of a Foot per Each Sixty-fourth of an Inch 202 
 
 Decimals of an Inch for Each Sixty-fourth 206 
 
 Difference of Level in Use of Compressed Air 35 
 
 Difference of Level in Use of Compressed Air, Table of 37 
 
 Equation of Pipes 212 
 
 Expansion of Air 45 
 
INDEX. 
 
 PAGE 
 
 Fifth Roots and Fifth Powers 194 
 
 General Hints 178 
 
 Hyperbolic logarithms 213 
 
 Indicated Horse Power to Compress Air 56 
 
 Indicated Horse Power to Compress Air, Curve for 57 
 
 Loss of Pressure in Pipes ". 21 
 
 Loss of Pressure through Bends 33 
 
 Loss of Pressure through Bends, Table of 34 
 
 Loss of Head in Pipes! by Friction 208 
 
 Lubricators and Lubricants 187 
 
 Mean and Terminal Pressures of Compressed Air 217 
 
 Mean Absolute Pressures Tor Various Degrees of Isothermal 
 
 Expansion, Table of 218 
 
 Mean Effective Pressures, Curve of 58 
 
 Pneumatic Governors 127 
 
 Pneumatic Hoist 52 
 
 Pneumatic Locomotive 70 
 
 Pneumatic Plant at Grass Valley 134 
 
 Pneumatic Torpedo Plant at Presidio, S. F 140 
 
 Power Transmission by Compressed Air 71 
 
 Pressure in Vertical Pipes 59 
 
 Quantity of Air Compressed per Indicated Horse Power 53 
 
 Quantity of Air Compressed per Indicated Horse Power, Curve 
 
 for 54 
 
 Reheater 48 
 
 Refrigeration by Compressed Air 63 
 
 Rix Patent Hose Couplings 186 
 
 ROCK DRILLS— 
 
 Rock Drills 158 
 
 Rock Drills, Rix, Table of 170 
 
 Roak Drills, Giant, Table of 171 
 
 Rock Drills, Plug and Feather 176 
 
 Sheet Iron Hydraulic Pipe, Table of 210 
 
 Squares, Cubes, and Reciprocals 195 
 
 Tripod Mountings 165 
 
 Temperatures, Centigrade, and Fahrenheit 200 
 
 Volume, Density, and Pressure of Air at Various Temperatures. 215 
 
 Volumes, Mean Pressure per Stroke, Temperatures 216 
 
 Well Casing, List of 219 
 
 Wrought Iron Pipe, List of 220 
 


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