.m ^K^U fyxntll Winxvmxi^ | pilrt^tg THE GIFT OF ^V PuodO^J^T. - ^..ZIXZI^ 10 :id.i.s.. 6561 olin,anx 3 1924 032 226 676 The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924032226676 EXPEEIMENTAL EESEAHeHES ON THE SPECIFIC GMVITY AND THE DI#LACEMENT OF SOME SALINE SOUJTIONS J. Y. J^cmNAN; to,;- ^^ COMMiirbBTril BB L'OBME DB ST CffAJtMB T)E MOKACO, CHEMIST AOT) PibsiOlSI OF THJS. J*'ea«LliU;NQBk''. BXPBDITIOH, . ,:,.■•,' VICB-PKESlDSSIJTFDTr OOMIT* DE jpMWf BOTmifiqjlMBK* DB ' L*IN8tl]?tri 004AlfOBK:^4|^> ^;(iqNliAMON AlBBKl? I??J, PBWOT DB MONAOb); ■?;■, of'iifit^y^ Sotddy of MdMftjCi\ Vol. Xlpi:.^J^g/>fli%^: FROM J. Y. BUCHANAN, F.R.S., 26 NORFOLK STREET, LONDON, W. INDEX SLIP. Trans. R.S.E., Vol. XLIX. Pakt I. Buchanan, J. Y. — Experimental Researches on the Specific Gravity and the Displacement of some Saline Solutions, Trans. Roy. Soc. Edin., vol. xlix., 1912, pp. 1-225. Experimental Researches on the Specific Gravity and the Displacement of some Saline Solutions. J. Y. Buchanan. Trans. Roy. Soc. Edin., vol. xlix., 1912, pp. 1-225. Displacement of some Saline Solutions, Experimental Researches on the Specific Gravity and the. J. Y. Buchanan. Trans. Roy. Soe. Edin., vol. xlix., 1912, pp. 1-225. Saline Solutions, Experimental Researches on the Specific Gravity and the Displacement of some. J. Y. Buchanan. Trans. Roy. Soc. Edin., vol. xlix., 1912, pp. 1-225. .s. DNACO, xpEnrTioN, UT 0015AN0GRAPHIQUE a) Vol. XLIX., Part I., 1912] ilD EXPERIMENTAL RESEARCHES ON THE SPECIFIC GRAVITY AND THE DISPLACEMENT OF SOME SALINE SOLUTIONS J. Y. BUCHANAN, M.A., F.R.S. COMMANDBUR BE l'oHDRE DB ST CHARLES DB MONACO, CHEMIST AND PHYSICIST OF THE " OHALLBNGER " EXPEDITION, VICE-PRESIDENT DU OOMITlS DE PBRFEOTIONNEMENT DE l'iNSTITUT OC^ANOOBAPUIQUE (FONDATION albert I™, PRINCE DB MONACO) [Reprinted from the Transactions of the Royal Society of Edinburgh, Vol. XLIX., Part I., 1912] PRINTED BY NEILL & CO., LIMITED BELLEVUE, EDINBUBGH 1912 2> Experimental Researches on the Specific Gravity and the Displacement of some Saline Solutions. By J. Y. Buchanan, F.E.S. TABLE OF CONTENTS. SECTION I. Introduction. PAK. PAGE 1. The Principles of Archimedes. They embody the fundamental principles of the hydro- 17 meter. Archimedes considered the immersion of a body in only one fluid, but the principles hold good when it is immersed in more than one fluid. 2. Hydrometer suitable for Demonstrations on the Lecture Table. It was constructed originally 1 7 in the year 1871 for use in tutorial classes in the University of Edinburgh, and especially to exhibit the determination of the specific gravity of solids lighter as well as heavier than water. A remarkable feature of the instrument is that no determination of weight is required either in its construction or its use. The only measurements made are those of length. 3. Usefulness of the Hydrometer in the Study of Mineral Waters. It suggested itself while 19 working as student and assistant of Fresenius (1863-1867), and later as Chemist and Physicist of the Challenger Expedition, during which it was used in investigating some mineral waters in the Philippine Islands. 4. The Hydrometer in the " Challenger " Expedition. Early preparations for work in the 20 expedition which lasted three and a half years. Indirect methods rejected. Adoption of the hydrometrio method for determining the specific gravity of the water of the ocean. 5. In designing the hydrometer, units in the fourth place of decimals were to be exact, and 20 the exactness to be pushed as far as possible into the fifth place. Multiple sets of hydrometers rejected. One suitable hydrometer was designed, and its weight could be altered by the addition of accessory weights. 6. The series of accessory weights prepared enabled the determination of the densities of all 21 sea-waters, up to and including that of the Eed Sea, to be made with the same glass hydrometer. But in the design of the series only single observations were contem- plated. Duplicate observations were occasionally obtained. The volume of the hydrometer was determined by floating it in distilled water at different temperatures. TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 1 MR J. Y. BUCHANAN ON THE PAK. PAGE Full specification is given of the hydrometer and the accessory weights which were used in all the determinations made during the voyage of the Challenger. 7. Importance of constancy of temperature in the practice of the hydrometrin method. This 23 was secured in the Challenger by her construction, and by the climate of the seas in which she cruised. The laboratory door was always looked while specific gravity observa- tions were being made. Table VIII. gives the instances of duplicate observations on identical samples of water with the same hydrometer differently weighted made in situ during the voyage. In voyages later than that of the Challenger hydrometric observa- tions were usually made in triplicate, and, later still, in series of nine. 8. Quotation from the Report of the Sixth International Geographical Congress held in 25 London in 1895, dealing with misunderstandings regarding the principle of the instru- ment and the qualifications required for the successful practice of the hydrometric method. SECTION II. The Peinciplb and Constbtjction of the Closed Hyrdbombter. 9. Experiments assumed to be made in vacuo at the sea-level in lat. 45°. True weight of the 26 hydrometer determined and its approximate volume determined by immersion in distilled water. Determination of weight of hydrometer in air and allowance for buoyancy of hydrometer when being weighed, and of exposed stem when floating in the liquid. 10. Developments of the above for multiple observations. 27 11. Preparation of Accessory WeighU. These weights are made of wire, the heavier of brass 29 and the lighter of aluminium. The pressure which they exert on the hydrometer, when in use, is due to their weight in air. 12. Exposed Stem. The effect of buoyancy of the exposed stem is, in practice, almost 30 inappreciable. 13. Final Determination of the Weight of the Hydrovieter. This is effected at different dates 31 and under different meteorological conditions, from which the true weight in vacuo is obtained. A table gives the exact weights in vacuo of hydrometers Nos. 17, 21 and 3. 14. Experiments for the determination of the displacement of the hydrometer in distilled water, 33 and description of Tables, A, in which these results are recorded. 15. Correction for the Departure of the Mean Reading from 50 mm. 35 16. Correction for Temperature. 35 17. Tables Aj to Aj give details of the determination of the displacement in distilled water of 36 hydrometer No. 17 at 15°, 19-5°, 23° and 26° C. ; and of hydrometer No. 21 at 19-5° C. Table B gives the observed weights of hydrometers Nos. 17, 21 and 3 when floating at the 50-mm. mark in distilled water at various temperatures. SECTION III. Determination of the Specipio Gravity of a Saline Solution. 18. Details of three series of observations made with hydrometer No. 17 in a solution of 1/8 CsCl 44 in 1000 grams of water at 19'5° C. are given in Table C, which is arranged in the same manner as Tables A. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 3 PAR. PAQB 19. Influence of the Meniscus. The weight which causes the immersion of the hydrometer is 46 its own weight plus that of the liquid meniscus which it carries on the stem above the line of flotation. This holds good when the hydrometer is floating in the solution and in distilled water alike. Each meniscus exerts the pressure of its own weight and con- tributes to the displacing weight of the instrument when it floats in the distilled water and the solution respectively. Data regarding the surface-tension of distilled water and of saline solutions have been taken from Tables 124 to 129 of the Smithsonian Collec- tion of Physical Tables, 5th edition, 1910. In a table, in this paragraph, the effect of introducing the weight of the meniscus in the hydrometric determination of the specific gravity of some solutions has been calculated, with the result that, for a solution of NaCl having a specific gravity of r036 when the weights of both meniscuses are disregarded, the apparent specific gravity is increased by I '3 in the fifth place of decimals when effect is given to the weight of both meniscuses. As the density of average oceanic water is not greater than 1'027, the influence of the meniscus on its density would be represented, at the most, by 1 in the fifth place. Therefore my practice, adopted at the beginning, of disregarding the influence of meniscus on the density of sea-water, as determined by my hydrometric method, is justified. 20. Serial Determination of the Specific Gravity of a Saline Solution. The table gives the 48 specific gravity of 1/32 EbCl in 1000 grams of water at 19'5° C. In it the specific gravity is deduced from each individual observation of four series of nine observations each, making in all thirty-six independent determinations, and they agree well with each other. The solutions of twenty-seven salts form the subject of the tables in Section V. They are KCl, EbCl, CsCl, KBr, EbBr, CsBr, KI, Rbl, Csl, which form the ennead* having the general formula MR; KCIO3, EbClOg, CsClOj, KBrOg, RbBrOg, CsBrOj, KIO3, RblOj, CsIOg, which form the ennead having the general formula MRO3 ; and NaCl, KNO3, RbNOg, CsNOg, LiNOj, NaNOg, Sr(N03)2, Ba(N0g)2 and Pb(N03)2. The concentrations of these solutions vary from 1/2 to 1/1024 gram-molecule of salt per 1000 grams of water. In the cases of strong solutions the concentrations were from 1 gram-molecule per 1000 grams of water upwards. 21. Statistics relating to the Range of Variation of Temperature during a Series of Observations. 51 The table gives statistics of the variations of the temperature of the liquid while a total of 1316 series, of nine observations each, was made with hydrometers Nos. 17 and 21, namely, 837 with No. 17 and 479 with No. 21. There M'as no sensible variation of temperature in 68 per cent, of those made with No. 17, and in 55-2 per cent, of those made with No. 21. Considering the series made with both hydrometers for which the variation of temperature was not greater than 0'05° C, the percentages are almost identical, namely, 89-5 for No. 17 and 89-2 for No. 21. The maximum departure of the mean temperature from the standard (T), during any single series of observations, was 0'12° C. ; the mean departure was 0'0075° C. The maximum range of temperature while a series of nine observations was being made was 0'30° C. ; the mean range of temperature for the 1316 series, of nine observations each, was 0'018° C. SECTION IV. The Control of the Temperature of the Laboratory. 22-25. The temperature chosen is dictated by the facility of its maintenance. Four such tempera- 52 tures are used, namely, 15°, 19'5°, 23° and 26° G. The great majority of observations has been made at 19'5° C, which is a suitable temperature for an inhabited room. The * From the Greek hv^is, which signifies a body of nine. PAK. PAGE MR J. Y. BUCHANAN ON THE maintenance of a constant temperature in the laboratory requires careful study, details of which, with examples, are given. The room used as laboratory should be of moderate dimensions, because it is to be occupied only by the experimenter, who must have absolute control over it. It should be illuminated by the light of the northern sky, and the direct rays of the suu must be absolutely excluded. When these primary con- ditions are given, the experimenter must do the rest. SECTION V. Tables. 26. A. General Tables Nos. 1 to 37, giving the facts of observation. 27. B. Tables Nos. 38 to 61, giving particulars relating to the exactness of the determinations 73 of the specific gravity given in Tables A, in cases in which two hydrometers were used. 28. C. Tables Nos. 62 to 71, giving a summary of the specific gravity of the solutions of 80 different salts at different temperatures. 29. D. Tables Nos. 72 to 81, giving a summary of the increment of displacement, v, caused 84 by the dissolution of m gram-molecules of salt in 1000 grams of water at different temperatures. 30. E. Tables Nos. 82 to 91, giving the values of v/m, that is, the mean increment of dis- 89 placement calculated for the dissolution of 1 gram-molecule of salt in 1000 grams of water at different temperatures. 31. A. Tables Nos. 92 to 103, giving the facts of observation for strong solutions. 94 32. Tables Nos. 104 to 124, of the Classes C, D and E, for strong solutions. 61 98 SECTION VI. General Description of the Tables. 33. Explanation of symbols in tables of Class A. With the exception of the determination 100 of temperature, the result of every series of observations depends only on determina- tions of weight, and is independent of the work of others. The necessity for study and practice before the experimenter can be confident of his power to control the tem- perature of the solution and of the laboratory is insisted on. Failure to appreciate this has interfered with the general use of the hydrometric method. 34. The measure of the displacement of a body having the temperature T is the weight of dis- 101 tilled water having the temperature T which the body displaces when totally immersed in the water. Under this definition the unit of displacement is the space occupied by 1 gram of water at T. The symbol for the unit of displacement is G^ or G, , in which G represents 1 gram, and T or ;f the common temperature of the body and of the water displaced by it. When the unit of weight is the kilogram, the unit of displacement is expressed by the symbol K^ or K,. The effect of concentration on the displacement produced by dissolving a given amount of salt in water or in solution is pointed out. Dilution of solutions for which m is >l/8 produces contraction; when m is less than 1/16 expansion occurs in many cases. This could not have been ascertained except by the hydrometric method. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 5 PAK. PAGE 35. Discussion of tables of Class B, dealing with the exactness of the results. 103 36-37. Discussion of tables of Class C, dealing with the specific gravities of the solutions. Dis- 104 cussion of tables of Class D, dealing with increments of displacement, and the effect on the solutions of salts of the double ennead (MR, MROg) for which ot= 1/16 is shown in a table and a diagram. The tables of Class E exhibit the comparative volumetric effect produced by dissolving different quantities of different salts in 1000 grams of water. Each entry in these tables is derived from the corresponding entry, v, in the corre- sponding table of Class D by increasing it in the proportion m : 1, whence we obtain the value of v/m. 38. Contains a table giving the specific gravities and the increments of displacement for solu- 105 tions of all the salts of the double ennead (MR, MROg) for which 7»=1/16. The values of the increments of displacement are also exhibited graphically in a diagram. SECTION VII. The Displacement of the Solutions. 39. The changes of displacement produced in a constant quantity of water by the dissolution 107 of successive quantities of a salt in it are compared with those which would take place under one of two hypotheses. 40. First Hypothesis. — It is assumed that, when a quantity of salt, insufficient for saturation, 108 is dissolved in a quantity of water, it takes possession of the quantity of water which it requires in order to produce a saturated solution, and saturates it, after which the saturated solution disseminates itself through the remaining water, forming a .simple mixture with it. If this law is followed by the solutions of a particular salt, then equal increments of salt dissolved in a constant quantity of water produce equal increments in the displacement of the solutions. This is expressed by the equation -— - = Const. an 4L Second Hypothesis. — It is assumed that, when a quantity of salt, insufficient to produce 108 saturation, is dissolved in a quantity of water, it exercises no selection, but salinifies every particle of the water alike, producing a homogeneous solution of uniform concen- tration ; and that, when a second quantity of salt, equal to the first, is dissolved in this solution, it intensifies its salinity uniformly and produces an increased displacement, which bears the same proportion to that of the first solution as the displacement of the first solution bore to that of the original quantity of water; further, that when a third equal quantity of salt is added to the solution of the second quantity, it intensifies its salinity uniformly and produces an increased displacement, which bears the same relation to that of the second solution as the displacement of the second solution bore to that of the first, and as that of the first bore to that of the original water ; and so on. Con- formity with this law is expressed by the equation ^M^ = Const. an 42. A table for a hypothetical case is given, which affords the means of comparing the effect 110 produced by diluting or concentrating a given solution with that which would be pro- duced if it took place in terms of the first or second of these hypotheses. 43. When the tables in this memoir are studied, it is found that in the solutions of the majority 111 of the salts the values of dA/dm and v/m reach a minimum for the values of m in the MR J. Y. BUCHANAN ON THE PAGE vicinity of 1/32, and that they increase whether the concentration is increased or diminished. In the ennead ME, the solutions of the caesium salts and the iodides approach most nearly to conformity with the law of the first hypothesis. The solutions of chlorides and salts of lighter molecular weight conform more nearly to the geometric law of the second hypothesis. 44. When the solutions of a salt follow strictly the law of the second hypothesis, the general HI expression for the displacement of a solution containing mME in 1 kilogram of water is A„ = Ai"', where A^ expresses the displacement of the solution when m= 1. When the solution does not follow this law exactly, the displacement for any particular value of m is expressed by A„ = A/. Then the degree in which the solution conforms to the law is indicated by the difference x-m when m is greater than 1. For solutions where m is less than 1, and is expressed by vulgar fractions, the expression x-m is replaced by l/m- l/x. 45. The displacements of most of the solutions are treated in this sense in Tables I. to VII. 112 Tables VIII. to X. give for a number of solutions the values of log A„/log A^ = x; or, ° 2 the exponent of the displacement A„ when the exponent of A_is taken as unity. If the solutions conform to the geometric law of the second hypothesis, the value of x is 2. SECTION VIII. Comments on the Chakqes in the Values of dA -v foe Different Values of m in the Case of Solutions op Individual Salts of the Type ME and MEG,. 46. The increment of displacement (v) due to the dissolution of m gram-molecules of a salt in 1000 116 grams of water may be looked on as being the result of two operations, namely : (a) the dissolution of m/2 gram-molecules of the salt in 1000 grams of water, which produces the first increment of displacement ; and (6) the further dissolution of m/2 of salt in the solution so formed, which produces the second increment of displacement. Tliese incre- ments of displacement are rarely alike ; the second portion of salt dissolved generally produces a greater increment of displacement than the first, and this has been very generally held to be the law. One of the principal motives for making this research was to find out, by the use of the more refined hydrometric method, if there is any point in the dilution of a saline solution at which further dilution is accompanied by expansion in place of contraction. The general result of the work is to show that in the solutions having the concentrations here used, where m is less than 1/16, cases of expansion on dilution are not uncommon. A table gives the values of m for which the value of dA - 1! is positive and becomes negative for the next lower value of m. That is, the value oi dA -V changes sign at some concentration lower than that indicated by m and higher than that indicated by m/2. 47. The method of treating the displacements of the solutions of the salts of the enneads 117 ME and MEO3 is described in the case of solutions of KCl. 48. The influence of possible error in the determinations of specific gravity on the values of 118 dA-v is discussed. 49. A table furnishes evidence of the agreement in the results obtained by different experi- 119 menters at different dates and using different instruments. 50. A specimen table indicates the stages in the calculations used in the discussion of the 121 values of v and dA in the case of solutions of KCl of different concentrations. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 7 PAK. PAGE 51-52. Tables I. to XVIII. illustrate the method of arriving at the volumetric effect produced 123 by changing the concentration of solutions of each of the salts of the two enneads. 53. Summary table giving the volumetric effect produced on changing the concentration of 129 certain solutions of these salts. 54. Eemarks on the tables referring to solutions of the salts MR. 129 55. Remarks on the tables referring to solutions of the salts MRO3. 131 SECTION IX. Notes on the Values of v fob the Enneads MR and MRO3. 50. Tables I. and II. give details regarding the change of displacement in solutions of salts of 132 the ennead ME when changes are effected in the metal or the metalloid of the salt. 57. Tables III. and IV. give corresponding values for solutions of salts of the ennead MRO3. 134 Table V. gives corresponding differences between the value of v in solutions of salts of the ennead MRO3 when EO3 is replaced by R. 58. Remarks on the tables relative to solutions of the ennead MR. 135 59. Remarks on the tables relative to solutions of the ennead MRO3. 137 60. Consideration of the effect produced on their solutions by the addition of the three oxygen 139 atoms to the salts of the halides to form the corresponding salts of the oxyhalides. 61. A general comparison and summary of the variation in the values of the mean increment of 139 displacement for dilute solutions of salts of the two enneads MR and MRO3. Diagram illustrating the variation of v/m with m for values of in= 1/32 to 1/512. 62. The eighteen salts of the double ennead (MR, MROg) can be divided into three hexads, 142 the members of each hexad containing a common metallic element K, Rb or Cs, and into three other hexads having a common metalloidal element CI, Br or 1. The relation between the values of v/m and to for the three hexads having the nucleus 01, Br or I for solutions 1/32 gram-molecule of salt and under are represented graphically in the diagram in §61. 63. Consideration of the order in which the salts of each hexad follow each other when 142 arranged in ascending order of v/m without paying attention to their numerical values. Graphic representation of each hexad of salts by a hexagon, the centre of which is occupied by the common element, metal or metalloid, as nucleus. The angles of the hexagon are supposed to be occupied by the residues of the salt after the abstraction of the common element, arranged in ascending order of magnitude of v/7n,, the lowest value occupying the lowest angle on the paper, and the other values occupying the other angles seriatim in ascending order of magnitude and going round from left to right. Inside each hexagon we have the common element M or R, and above it the value of m for the particular concentration. For concentrations higher than m = 1/64 the arrange- ment of residues is the same as that given for m = 1/64 in the six hexagons corresponding to the common elements CI, Br, I, K, Rb, Cs. The hexagon corresponding to the nucleus R and concentration m is represented by the symbol m [R], as, for example, 1/64 [CI]. The residues of the hexad after the abstraction of the common element CI are K, Rb, Cs, KO,, RbOg, CSO3, and these residues, in conformity with the values of v/m which correspond to them, follow each other in this order round the corners of the hexagon considered. 64-66. Twelve hexagons of type to[R] and twelve of type ?)i[M] are given in the text, and the 144 different ordinal sequences of the residues for different hexads as exhibited in the hexagons are fully discussed. MR J. Y. BUCHANAN ON THE SECTION X. Experimental Observations on the Displacement op Solutions of Sodium Chloride. PAR PAGE 67. Although sodium chloride is not a member of the enneads which form the principal material 148 of this research, its importance in nature justifies its inclusion in it. General table of results of experiments made on solutions of sodium chloride varying in concentration from 1 gram-molecule to 1/512 gram-molecule per 1000 grams of water. 68. Preparation of solutions forming arithmetic series. '•*" 69. Tables giving results of solutions for which m forms a geometric series of the usual type. 150 70. Discussion of specific gravity. 71. Discussion of displacement. '■"^ 72. Experiments on solutions forming arithmetic series. ^"1 73. Series of experiments on solutions having the common difference din = l/128. ISl 74. Discussion of differences of displacement. Table confirming the reality of the remarkable 151 changes of displacement in high dilutions. 75. Table giving further confirmation of this. 152 76. Table giving series of experiments on solutions having the common difference of concentra- 153 tion dm= 1/64. 77. Discussion of displacement and differences of displacement. 153 78. Diagram giving graphic representation of remarkable changes in the values of v/m at high 154 dilution. SECTION XI. The Prinoiple and Construction of the Open Hydrometer. 79. The hydrometer is left open so that its weight may be increased or reduced by additions 155 to, or removals from, its ballast or internal load. The extent to which additions can be made to the weight supported by the stem of the instrument is limited by its stability. The Challenger hydrometer, which was closed, could be used in a saturated solution of sodium chloride carrying an accessory weight of 32 grams. In a solution of greater density, the external weight required produced a "list." 80. The open hydrometer may be of the same size as the closed instrument, and is made after 155 the ordinary pattern, but the millimetre scale is etched on the stem, the paper scale being impossible when the internal load is to be varied. When concentrated solutions of salts which are both very soluble and very expensive are used, it is convenient to use a hydrometer of less bulk than that of the closed instrument. 81-84. The weight of the instrument is not constant, because the internal ballast is altered from 157 time to time, and the weight of the air in the hydrometer varies with the meteorological conditions. The first step in the preparation of the hydrometer for use is to weigh the glass instrument empty as it comes from the glass-blower. It is then weighed with the ballast (lead shot) in it. Knowing the density of the glass and that of the lead, we obtain the volumes of the glass and the lead respectively. When the instrument is SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. PAK. immersed in distilled water and accessory weights are added until it floats almost totally immersed in the water, the sum of the accessory weights, the weight of the glass, and that of the lead give the weight of the water displaced, and from this the external volume, or the displacement, of the instrument is obtained. The volume of the air inside the hydrometer is then given by the difference between the external volume of the instrument and the sum of the volumes of the glass and lead. Full details of the experimental work required in order to obtain the exact weight of the hydrometer under particular conditions are given. SECTION XII. NuMEBiCAL Details illustrating the Use op the Open HydhombtbR. 85. Details are furnished relating to the experimental determination of the weight of the 165 liquid displaced by the instrument designated Hydrometer A. 86. Scheme for logging the observations made with the hydrometer in the experimental 167 liquid at the selected standard temperature, T. A table gives numerical examples using (a) distilled water, and (&) a 7 gram-molecule solution of rubidium chloride. 87. Correction for the buoyancy of the non-immersed portion of the stem. As in the case of 169 the closed hydrometer, this is practically inappreciable. 88. The degree of accuracy attainable by the use of the open hydrometer is illustrated by the 169 results of five series of observations, each series consisting of eleven independent observations, made in a solution of calcium chloride containing 6'3 gram-molecules of CaClg in 1000 grams of water. Of the five series, three were made with hydrometer A and two with hydrometer B. The values of the mean specific gravities, S, furnished by each series and its probable error ( + r^), expressed in units of the sixth decimal place, are collected in a table. 89. Precautions to be taken in order to secure trustworthy results. My practice in the 171 Challenger was, when I began hydrometric observations, to lock the door, and I still adhere to this practice. Attention is called to the effect of the low specific heat of concentrated solutions, such as 6 3 CaClg, in increasing the thermal nimbleness of the solution. 90. Table of specific gravities calculated from single observations made with hydrometers A 172 and B when floating in a solution of calcium chloride containing 6'3 gram-molecules of CaClj in 1000 grams of water. This table includes the individual observations the means of which were given in S 88. SECTION XIII. On the Specific Gravity and Displacement op Solutions op Salts op the Ennbad MR which HAVE nearly THB SAME MoLECULAR WbIGHT AND MAY BE LOOKED ON A3 " ISOMBRIC." 91. These salts are RbCl, KBr, K ^^. 172 92. A table gives the results of specific gravity determinations made upon the solutions of 173 these salts at 19'5' C. 93. The solubility of each of the above salts was determined. 174 TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 2 10 MR J. Y. BUCHANAN ON THE PAR. PAGE 94. The specific gravities of the solutions were adjusted to the value which they would have if 174 their gram-molecules had the uniform weight 121, which is the actual molecular weight of tlie heaviest of the three, namely, rubidium chloride. This adjustment of the molecular weights does not materially affect the relations of the solutions as regards their specific gravities. The displacements of these solutions are compared. 95. The differences of displacement are discussed. 1 ' " 96. The displacement of solutions of the artificial isomer (k — -!l_j is considered in reference 176 to the displacement of solutions of the constituent salts. 97. Comparison of displacement of solutions of the artificial isomer as obtained by experiment 177 and as calculated. SECTION XIV. The Specipio Gravity and the DispijAcbment of Solutions op the Chlorides of Beryllium, Magnesium and Calcium. 98. Preparations of weak solutions — m = 1/2 to 1/1024 — of each of the three salts, and of strong 178 solutions of MgClg and CaClj for m = l up to supersaturation. The solutinns saturated with MgClg and CaClj at 19'5° C. contain 5'918 and 6'613 gram-molecules respectively in 1000 grams of water. A supersaturated solution of magnesium chloride contained 5 982 MgClj in 1000 grams of water. This solution was formed with moderate absorp- tion of heat and crystallised very readily. The supersaturated solution of calcium chloride contained 7"225 CaClj per 1000 grams of water. This solution was formed with great absorption of heat, and offered considerable resistance to crystallisation. It was found that when the quantities of the crystallised salt MgCl26H20 and water used were such as to produce a solution containing about 2 MgClj per 1000 grams of water, there was an appreciable liberation of heat. When further salt was dissolved this gave place to absorption of heat, and, at saturation, the temperature of the solution was lower than the initial temperature of the water used. 99. Table giving the results of specific gravity determinations made upon solutions of 179 the chlorides of beryllium, magnesium and calcium of different concentrations at 19-5° C. 100. While the bases BeO, MgO and GaO give an alkaline reaction with litmus paper, the 180 chlorides of magnesium and calcium are neutral, while that of beryllium is acid. The beryllium chloride solution was made from the sulphate by double decomposition with barium chloride. The more dilute solutions were prepared by diluting the more con- centrated ones. The specific gravities of the strong solutions were made with open hydrometers A and B, and those of the weak solutions with closed hydrometers Nos. 3 and 17. Comparison of (S - 1) with m. A table is given from which it is apparent that the values of (S - 1) produced by dissolving 1/2 MR in 1000 grams of water are exactly proportional to the molecular weights of the salts in the case of MgClj and CaCL, and that tliis proportionality is maintained for values of m=l/16 and 1/128. In the ca«e of beryllium chloride the proportionality fails. The specific gravities of the solutinns of beryllium chloride for which m= 1/512 and m = 1/1024 fall below unity, from which it follows that the displacement of these two solutions must be greater than the sum of the displacements of the salt and water which they respectively contain. The values of dS for solutions of CaClj which are near saturation are disijussed. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 11 PAR. PAGE 101. Discussion of the values of d^/dm and v/m especially for solutions for which m is less 182 than 1. 102. The values of dA-y &v& discussed. The principal feature of the table illustrating them 183 is the pronounced expansion which accompanies the dilution of solutions of beryllium chloride for which m is less than 1/16. 103. The relations between the exponents of the solutions x and m are discussed, and a table 184 of the values of log A„/log A„, for solutions of each of the three salts is given. SECTION XV. On a Rkmarkable Statb of Unrest in a Supersaturated Solution of Calcium Chloride before Crystallising. 104. The supersaturated solution was 7 '225 CaCljH- 1000 grams of water. It was expected that 185 this solution would crystallise easily and furnish a truly saturated solution. As it showed no inclination to crystallise although every opportunity was offered it to do so, it was adopted as an example of a supersaturated solution peculiarly adapted to closer study. Table I. contains the constants of the open hydrometers A and B, as loaded for the experiments of this section, [a) when floating in distilled water, and (6) when float- ing in the supersaturated solution of calcium chloride. 105. The experiments showing the state of unrest were made 11th May 1910, in the Davy- 186 Faraday Laboratory. A series of observations had been made with each hydrometer, and further observations were proceeding when it was noticed that discrepancies between successive readings and corresponding ones in the earlier experiments made with the same added weights were occurring, and that these were far greater than any which could be attributed to error of observation. They persisted while four series of obser- vations were made, two sets with each hydrometer, and were so great that in the fifth series of observations it was necessary to reduce the initial added weight in order that the complete series of observations might be made. The temperature of the solution was perfectly constant at 19'5°C. during each series. 106. After removal of the hydrometer from the experimental solution on completion of the fifth 187 series of observations, the solution was stirred as usual with the standard thermometer, and its temperature was found to be 19'50°, that of the air being 19'30°. It was not until after these observations had been made that a cloudiness indicating the commence- ment of crystallisation appeared in the solution. It increased rapidly, and the tem- perature rose smartly to 23'16° C, and remained constantly at that temperature from 1.10 p.m. to 2.35 p.m., a period of 85 minutes, when tiie temperature began to fall. The supersaturated solution (7-225 CaClg-l-lOOO grams of water) contained 44'48 per cent. CaClg. When the temperature of the mixture of crystals and solution had fallen somewhat, the cylinder was placed in water having the temperature 19'3°, and was cooled to 19'5°. The mother-liquor was then found to have the specific gravity 1-423500, and to contain 42-33 per cent, of CaClj. 107. The crystals along with the mother-liquor were then heated in the cylinder to a tempera- 187 ture of 30° C. by placing the cylinder in a water-balh of about that temperature, and keeping it there until the crystals were redissolved. The system was then allowed to cool in the air, the temperature of which remained constant at 19-3°, and the tempera- ture of the cooling liquid was taken at intervals of 30 seconds. The series of observa- tions extended over 41 minutes, during which the temperature fell from 23-82° to 12 MR J. Y. BUCHANAN ON THE PAK. I-AGE 21-99°, and the solution remained liquid to the end. The cooling had proceeded for 13 minutes before the temperature fell to 23-16°, and the loss of heat was taking place quite regularly. The following are the temperatures observed at each ^ minute for 2 minutes before and 2 minutes after the temperature of 23-16° was passed : — Time in minutes : -2-0 -1-5 -TO -0-5 0-0 +0-5 10 1-5 20 Temperature: 23-23° 23-21° 23-19° 23-17° 23-16° 23-14° 23-12° 23-09° 23-07° During the 4 minutes the temperature fell 0-16°, whence 0-04° per minute represents the mean rate of fall of temperature when the system has the temperature 23-16° and is cooling in air of constant temperature 19-30° C. 108. Calculation of Heat liberated during Crystallisation. When crystallisation was started, 188 the temperature of the system rose in less than a minute from 19-5° to 23-16°. During this phase the temperature of the cylinder with its contents was raised 3-66°. The heat liberated in this act was found to be 2217 gram-degrees (gr.° C). During the second phase the rate of liberation of heat was equal to its rate of dis.sipation, which was represented by a fall of temperature of 0-04° per minute. This was maintained for 85 minutes, which requires a liberation of 2059 gr.° C. of heat; so that the total heat liberated in the act of crystallisation was 4276 gr.° C. 109. Verification of the constitution of the crystals as CaCl26H20. According to Thomsen, the 188 heat of solution of CdCl^QRfi is —4340 gr.°C. ; therefore on thermal evidence alone 215-5 grams or 0-984 CaCi.26H30 has separated out. On the basis of analytical estima- tions made on the supersaturated solution and the mother-liquor, 210-3 grams or 0-96 CaCl26H20 must have separated out. The agreement of these two computed values is excellent. 110. Description of Tables 11a. and IIb. In Table IIa. are given the individual observations 189 of specific gravity forming together the five series, of eleven observations each, on the supersaturated solution 7-225 CaClj when it was exhibiting the state of unrest which preceded crystallisation. In Table IIb. are given the individual observations forming five series of eleven observations each, on the non-saturated solution 6-3 CaClj. Table lie. contains the individual observations forming three series of eleven observa- tions each, on the supersaturated solution 7-196 CaClg. It crystallised suddenly after the third series. Table III. forms a time-table of the observations on the supersaturated solution 7-225 CaClg. 111. Discussion of conditions of temperature maintained while the operations recorded in 193 Tables IIa. and IIb. were being made. 112. Further discussion of Tables IIa. and IIb. Considering the five mean specific gravities of 194 7-225 CaClg, it is found that the maximum amplitude of variation is 689 units in the sixth decimal place, while the five mean specific gravities of 6-3 CaClj exhibit a maximum amplitude of only 26 such units. When the observations of individual series are considered, the maximum amplitude of variation in the fifth series for 7-225 CaClj is 833 in the sixth decimal place. These large and rapid variations of specific gravity in the supersaturated solution furnish the evidence of the state of unrest existing in it. 113. The displacement of the solution is subject to variations corresponding to those of the 195 specific gravity. They afford evidence of spasmodic acts of expansion and contraction, not accompanied by any change of temperature of the solution or of the external pressure to which it is subjected. They exhibit a veritable species of labour going on SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 13 PAH. PAGE in the solution in its efforts to become a mother-liquor. In this it is finally successful, but not before it has succeeded in forcing the door which confined its store of heat. The birth of the crystal was synchronous with and dependent on the liberation of heat. 114. It is shown that the change of displacement which occurred in the transition of the solution 196 7-225 CaClj from a condition of supersaturation to that of a mixture of saturated solu- tion and crystals at the common temperature 19'5° C. is a shrinkage amounting to 2-2 per cent, of the original volume of the supersaturated solution. 115. Comparison of the behaviour of supersaturated solutions of MgCl2 and CaClj with respect 196 to readiness in starting, and heat exchange accompanying, crystallisation. The variations of the density of the liquid before the first element of crystal appears revealed only by the skilled use of the hydrometer. The diagram illustrates the changes of displacement corresponding to the changes of density in the 7-225 CaClg and the 7-196 CaClj super- saturated solutions, compared with the -accidental changes observed in the stable solu- tion 6-3 CaClj. In the case of the 7-225 CaClj solution the state of unrest persisted during the 140 minutes that the experiments lasted, and it seems to be not improbable that a supersaturated solution is never at rest even in a closed vessel. 116. Analogy between the crystallisation of a supersaturated saline solution and the formation 197 of ice when a non-saturated solution or when pure water is cooled below its freezing point. When the mass of water is small and the capacity for heat of the vessel which contains it is large, the temperature of the system may be reduced so far that when freezing begins the whole of the water may be frozen without the temperature of the system rising to 0° C. Experimental illustration of this. Possibility of detecting oscillations of density in water before freezing begins, by determining its specific gravity hydrometrically with the necessary precautions in a room having a constant temperature between — 4° and - 5° C. 117. Calculation of the increment of pressure required to counteract the stretching of the 200 7-225 CaClj solution before the beginning of crystallisation. It is found to be 38 atmospheres. 118. Resemblance between the state of unrest preceding the crystallisation of a supersaturated 200 solution and that preceding the liquefaction of a gas under a pressure not inferior to its critical pressure, when its temperature is reduced slightly below its critical temperature. 119. It is only in the conditions of Andeews' experiment on COg that we can witness a substance 201 persisting in the gaseous state under a pressure greater than its critical pressure, and having a temperature lower than its critical temperature, because it is only when the gas and the envelope which contains it have been maintained at a temperature higher than the critical temperature of the gas, that the inner walls of the envelope have a chance of being perfectly dry, that is, free from every trace of the liquid substance. We do not know the temperature at which a dry gas can liquefy on the dry walls of its envelope, but so soon as the first, even the minutest, trace of the liquid substance appears, the temperature of liquefaction is defined, because the gas is then condensing on itself as a liquid. U MR J. Y. BUCHANAN ON THE SECTION xvr. The Determination of the Specific Gravity of the Cetstals op a Soluble Salt bt Displacement IN its own Mothee-Liquob, and the Volumetric Eblations between the Crystals and the Mother-Liquor which are established by the Experiment. pak. page 120. This work was undertaken owing to the arrival of the great anticyclone or heat-wave of 202 the summer of 1904, which made observations of specific gravity at 19-5° impossible. The liquid in which every soluble salt is quite iiLsoluble is its own mother-liquor at the temperature at which the one parted from the other. It was in this liquid that the specific gravity of the crystals of the salts of the two enneads MK and MRO3 was determined. It is obvious that this method is applicable only to salts which have a mother-liquor, such as KCl, RbBr, CaC'l26H20, BaCl22H20. It is inapplicable to salts such as CaCl^, BaCl2, and the like, which have no legitimate mother-liquor. The anti- cyclone prevailed throughout the greater part of July and August 1904, during which time the determinations of the specific gravity of the crystals and the mother-liquors of the salts of the ennead MR were determined. 121. Precautions to be observed in making the experiment. 203 122. Determinations of the solubility of the salts RbBr, Rbl, CsCl, CsBr and Csl were made, 203 as there were uo published data regarding them. The preliminary experiments are here described. 123. Contains Table I. in which the experimental data and details are given in full in the case 204 of one salt, namely, CsCl. All the weights as given represent the weight in vacuo. Further necessary details of the experimental method are here given. 124. Precautions to be observed when bringing the crystals together with the mother-liquor in 206 the pyknometer. The experimenter must realise that their common temperature when mixed is to be exactly that of crystallisation or equilibrium, and he must take such measures as his experience dictates to arrive at this end. 125. Contains Table II., which gives for each salt the temperature, T, of equilibrium between 207 crystals and mother-liquor, and in condensed form the experimental data of the determina- tion of S, the specific gravity at T of the mother-liquor, that of water at the same temperature being unity ; of m, the concentration of the mother-liquor in gram-mole- cules of salt per 1000 grams of water; and of Dj, 1)^ ,T)^, the three observed values, as well as D, the finally accepted value of the specific gravity of the salt, all at T, and referred to that of water at the same temperature as unity. 126. General discussion of the results. 209 127. Contains Table III., giving numerical relations between the crystallised salts of the ennead 209 MR and their mother-liquors. 128. Discussion relative to the mother-liquor. 211 129. Consideration of saturated solutions as products of substitution. 212 130. Comparison of the displacement of the salt in crystal and the increment of displacement 213 of 1000 grams of water which is produced by its dissolution. It is shown that the crystallisation of the potassium and rubidium salts of the ennead must be hindered by increase of pressure, while that of the csesium salts must be helped by the same agency. SPECIFIC GRAYITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 15 PAR. PAGE 13 L Account of similar experimental researches for the crystals and mother-liquors of the salts 214 of tlie ennead MROg. The investigation was made on a plan exactly similar to that used in the case of the salts of the ennead MR. Table IV. corresponds to Table II. of the ennead MR, and gives in a condensed form the data bearing upon the observed values of the specific gravity of the salts. 132. Table V. gives the results of observations made with the crystals and mother-liquors of 214 the salts of the ennead MRO3. It is arranged on the same plan as Table III. for the salts of the ennead MR, and consists of a number of sub-tables, the nature of each of which is specified in its title. 133. Contains a table giving the specific gravities, D, of the salts of the ennead MRO3, and 215 their differences. The observations recorded in Tables IV. and V. are further discussed. 134. The molecular displacement, MRO3/D, of the crystal expressed in grams and molecules of 218 water is considered. 135. The molecular concentration of the mother-liquor is discussed. The value of m does not 218 in any case exceed 1/2. The values of the concentrations are derived from the specific gravity of the mother-liquor. 136. The values of — ^-^--^are discussed. As they are all positive, crystallisation is in 218 D m every case accompanied by expansion. 137. In a table are given the differences between the molecular displacements in crystal of 218 the corresponding salts of the two eimeads, MRO3 and ]\IR, and these are commented on. 138. Concluding remarks. 219 Appendix A. — Densities of the solutions at T. Appendix B. — Table giving the number of series as well as the number of single observations made with the various Hydrometers, from which the results recorded in this Memoir were obtained. Index, 226 SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 17 Section I. — Introduction. § 1. The Principles of Archimedes* — It is well known that the mechanics of floating bodies, and the laws which govern their equilibrium, were established and enunciated by Archimedes, the Sicilian, in the third century before our era. The following pro- positions, demonstrated in the first book of his treatise on this subject, embody the fundamental principles of the hydrometer : — (a) The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth. {h) Of solids, those which, size for size, are of equal weight with a fluid will, if let down into the fluid, be immersed so that they do not project above the surface, but do not sink lower. (c) A solid lighter than a fluid will, if immersed in it, not be completely submerged, but part of it will project above the surface. (d) A solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. (e) If a solid lighter than a fluid be forcibly immersed in it, the solid will be driven upwards by a force equal to the diff"erence between its weight and the weight of the fluid displaced. {f) A solid heavier than a fluid will, if placed in it, descend to the bottom of the fluid, and the solid will, when weighed in the fluid, be lighter than its true weight by the weight of the fluid displaced. Archimedes considered only one solid and one fluid, and his laws regulate exactly what takes place in such a system when the solid is totally immersed in the fluid ; or, if only partially immersed in it, when the non-immersed portion of the solid is immersed in no other fluid — in other words, when the experiment is being made in a vacuum, or in a medium the density of which is insensible. When, however, the experiment is being made in air, it is not necessary to postulate that its density is insensible; Archimedes' laws still hold good, only the solid falls to be considered as divided into two, one of which is completely immersed in the one fluid (the liquid), and the other is completely immersed in the other fluid (the air). If the solid was immersed in three fluids, as, for instance, water, oil, and air, and floated at rest when part of it was immersed in each of these fluids, it would fall to be divided into three portions, each of which is totally immersed in one of the three fluids, Archimedes' laws would still be applicable, and the final total eff"ect would be the sum of the partial effects. S 2. Hydrometer suitable for Demonstrations on the Lecture Table. — I constructed an instrument of this kind for use in lectures which I gave as assistant in the * The Worlcs of Archimedes, edited in Modern Notation, by T. L. Heath, Sc.D., Cambridge University Press, 1897, pp. 253-268. TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 3 MR J. Y. BUCHANAN ON THE M m -4 - 5 University Laboratory in Edinburgh, under Professor Crum Beown, in the years 1869 to 1872. A description of it was published in the Berichte der Deutschen Chemische Gesellschaft (1871), iv. 338. Fig. 1 is a sketch of it. The stem of this instrument was made of glass tube having an external diameter of about 1 centimetre, and a truly circular section of uniform diameter. A slip of paper is attached inside the stem. It is graduated on any convenient scale of equal lengths, and the divisions are numbered upwards and downwards from the zero point in the middle. The numerals from upwards have the positive sign, and those running from the downwards have the negative sign. The hydrometer is ballasted with mercury or shot, so that, in its completed state, it sinks in the liquid used, at the atmo- spheric temperature, exactly to the zero division in the middle of the stem. The lower extremity of the instrument takes the form shown in the figure, terminating in a hook K. The upper extremity of the stem is closed with a cork, to which a suitable disc of cardboard, M, is attached by sealing-wax. The hydrometer was originally constructed in order to illus- trate the determination of the specific gravity of solid bodies. The liquid in which it is to be immersed may be distilled water, but other liquids, for instance sea-water, may also be used. It is contained in a suitable cylinder, and should have the temperature of the room in which the experiment is being made. When it is proposed to exhibit the determination of the specific gravity of any particular solid body, the hydrometer is immersed in the liquid, in which it sinks until the zero division on the scale is exactly in the plane of the surface of the liquid. A suitable fragment or piece of the solid body is then placed on the platform M, and the extent to which the immersion of the stem in the water is increased is noted. The solid body is then removed from the platform M and attached to the hook K, and the hydrometer is again im- mersed in the water. When equilibrium of flotation has been established, the immersion of the stem is again read on the scale. Let the former of these two numbers be expressed by a and the latter by b. a and b are lengths of a cylinder of uniform diameter and of circular section ; therefore the volumes of these cylinders are proportional to their lengths ; and, as the same liquid is displaced in each case, the weights of the liquids so displaced are also proportional to FlQ. 1. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 19 the lengths a and b. It follows, therefore, that the expression {a-b) represents the weight of a volume of the liquid equal to that of the solid body, and that the specific gravity of the solid body, referred to that of the liquid as unity, is D = ^. a- When a solid body is placed on the platform M, the hydrometer always sinks deeper in the liquid ; therefore a is always positive. When a solid body consists of a substance which is denser than the liquid, then, when it is attached to the hook K and is immersed with the instrument in the liquid, it causes the hydrometer to sink deeper in it, and b is also positive in this case. When the substance of the solid body is less dense than the liquid, a is positive as before ; but when the body is attached to the hook, and is immersed with the hydrometer in the liquid, it exerts a pressure upwards, which causes the hydrometer, to emerge and expose a part of the stem below the point 0. On this part of the scale the numerals have the negative sign, and the weight of the volume of liquid displaced by the solid body is, as before, (a — b); and its specific gravity is, also as before, D = -^-. a-b The identity of the expressions of the experimental data in determining the specific gravity of substances so dissimilar as, for instance, a stone and a cork never failed to arrest the attention of the students. It will be noticed that, by using this method, the specific ijravlty of a solid body is obtained without any determination of weight having been made, either in the production of the itistrument or in its use, and that the only measurements made are those of length. § 3. Usefulness of the Hydrometer in the Study of Mineral Waters. — But the hydrometer and its uses had always had a fascination for me. I began to pay particular attention to the subject in Wiesbaden, when working as a student with Fresenius, and afterwards (1866-67) as an assistant in his private analytical laboratory. During this period I became much interested in the mineral waters which abound in the (then) Duchy of Nassau and the neighbouring parts of the Ehineland, and especially in the Kochbrunnen of Wiesbaden, perhaps the most celebrated of them all. I had great curiosity to investigate the variations, if any, in its concentration at diff"erent times and seasons ; but, as a student, I had to follow the plan of instruction laid down, and, in the private laboratory of the final referee in Germany regarding all matters of dispute or arrangement which could be decided by chemical analysis, the important and responsible work entrusted to me made it impossible for me to occupy myself with anything else at the same time. During the voyage of the Challenger, I many times made up my mind, on my return to Europe, to visit Wiesbaden and use the hydrometer in carrying out "a systematic investigation in this sense ; but my intention has not been realised. 20 MR J. Y. BCrCHANAN ON THE § 4. The Hydrometer in the "Challenger" Ex'peditiun. — The dispatch of the Challenger Expedition was decided before the end of the year 1871, and Sir AVyville Thomson, who was then Professor of Natural History in the University of Edinburgh, was chosen for its leader. He did me a great honour and a very substantial service in selecting me for the post of chemist and physicist of the expedition quite a year before the date fixed for its departure. I cannot adequately express the gratitude which I feel for the confidence which he thus showed in me, and for the privilege which it gave me of taking an active part in this memorable expedition. The expedition lasted less than four years, yet these years are fuller of recollections than all the rest of my life. During the year which elapsed between my selection and my official appointment, I occupied myself almost exclusively in preparing for my work at sea, and I considered that the specific gravity of the water of the ocean, and its variations, would be one of the most important matters for continuous observation. Here I had in view the variations of specific gravity which occur in the open ocean and far from all influence of the land. These were only imperfectly known, but there was reason to conclude that they were confined within narrow limits. I chose the hydrometer, or " araeometer," as it is called abroad, because it appeared to me to be the only type of instrument which furnished directly the information demanded, namely, the specific gravity of the water, and that with the exactness required when the variations of specific gravity are so small. Even at that early date indirect methods of all kinds were recommended to me. In theory, any physical constant of a saline solution, the * expression of which includes a term depending on its specific gravity, can be used for this purpose. But indirect methods are, in the nature of things, affected tvith at least a double quantity of eiro)-s. There are the errors with ivhich the datum directly supplied by the vicarious method used is affected, ctnd there ai-e tlwse ivhich affect the operation of comfa'i'ison by which that datum, obtaius its densim,etric inte7^pretation. I had then, and I have still, an instinctive dislike of all indirect methods in science ; I therefore adhered to my own purpose, believing that, if nothing but manipulative difficulties stood in the way, they could be overcome by perseverance and a determina- tion not to accept defeat too readily ; and, as is so often the case, the difficulties apprehended turned out to be in no way formidable. § 5. In designing the hydrometer I decided that, in the values of the specific gravity obtained with it, units in the fourth place of decimals must be exact, and that the exactness should be pushed as far as possible into the fifth place. As a knowledge of the physical constants of the instrument is of the first importance, I rejected the plan of having a series of hydrometers, each to be used in the waters the specific gravity of which corresponded to the limits of its scale. I decided to have one hydrometer, made of glass, in which the dimensions of the stem and of the body should be in such pro- SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 21 portion as to ensure the degree of accuracy above indicated, and provision for extending its range of usefulness to sea-waters of all specific gravities should be made by suitable alterations of its weight. Considerations of stability suggested attaching the accessory weights necessary for this purpose to the lower extremity of the hydrometer. But this would involve their being immersed in the liquid the specific gravity of which was to be determined, and was therefore inadmissible. The only alternative was to attach them to the upper extremity of the stem. A length of 10 centimetres of the stem was graduated into millimetres, and the external diameter of the stem was such that its graduated portion displaced rather less than I gram of distilled water. The body of the instrument was constructed so as to have a volume of approximately 160 cubic centimetres. The hydrometer was ballasted with mercury, so as to float in distilled water of ordinary temperature with the whole of the graduated part of the stem exposed. The system of accessory weights designed for increasing the range of the hydrometer included, as first weight, a small brass table which fitted on to the top of the stem. Its weight was designed so that, if the hydrometer alone floated at the lowest division of the scale in a particular water, and the table was then affixed to the top of the stem, the hydrometer would sink until it floated at a division near the top of the scale in the same water. Of the further weights, the first of the series was a mass of brass of about the same weight as the table. When the hydrometer carrying the table on the stem floated at the lowest division of the scale in a particular water, then, by placing the further weight on the table, the hydrometer sank until it floated at a division near the top of the scale. The weight of the next weight of the series was made approximately double that of the table, so that when the hydrometer, loaded with the table and the previous weight, floated at the lowest division on the scale in a particular water, and the previous weight was replaced on the table by the present one, the hydrometer floated in the same water at a division near the top of the scale ; and so on. § 6. The series of weights was carried so far that waters of all densities from that of distilled water to that of water more dense than that of the Red Sea could be determined with the same hydrometer. The accessory weights form roughly an arithmetical series, the common difference of which is equal to the flrst term, namely, that of the little table to be placed on the top of the stem and to carry the other weights, when required. As produced, the weights fulfilled all the conditions demanded of them, and all that it was necessary to know was the exact weight of each, and this was determined. From the design of the system of accessory weights, it will be seen that provision was made for single observations of specific gravity. Duplicate observations were possible only in cases where the salinity and temperature of the water combined to produce such a specific gravity that it could be observed with one of the sets of weights near the lowest division of the scale. In that case its specific gravity could be obtained also with the next higher weight at a division near the top of the scale, because the 22 MR J. Y. BUCHANAJST ON THE diflPerence between the successive weights was rather less than that required to immerse the divided portion of the stem. On rare occasions multiple observations were made on a single water, using ordinary decigram weights, but this was found to be very inconvenient. Nevertheless, the advantage of multiple observations was clearly perceived, and provision for their being made was included in the specification of all later instruments. Also, the system of numbering the centimetres on the stem was altered. In the Challenger instrument the number 10 marks the lowest division on the stem, and marks the highest. In all later instruments the lowest division is 0, and the centimetres are numbered 1, 2, 3, ... 10 upwards. In every determination of the specific gravity of a sample of water, the weight of the volume of it which was displaced by the hydrometer floating in it at an observed division on the scale was represented by the sum of the weights of the hydrometer, the table, and the accessory weight used. The volume of the water so displaced by the hydrometer was arrived at as the result of an extensive series of observations made with it in distilled water at difi'erent temperatures. The relation between the weight and the volume of a mass of distilled water at all ordinary temperatures, as determined by KoPP, was accepted as correct, and was used in reducing the observations made with the hydrometer in distilled water so as to arrive at the volume of its body, that is, the whole of the hydrometer below the lowest division on the stem at all ordinary temperatures. Its rate of thermal dilatability was taken to be constant within the limits of temperature considered, and its probable value was obtained by taking the mean of all those observed. The final result was stated by giving the volume of the body of the instrument up to the lowest division on the stem at 0° C. as V, and the rate of its dilatability, dNjdt, as e. Thus the full specification of the hydrometer, that is, the glass instrument alone, is furnished by four data. For the hydrometer used in the Challenger they are : — Weight in vacuo of the hydrometer . Volume of body of hydrometer up to lowest division on stem at 0° C. Rate of expansion of body per ° C. . Total volume of divided stem (100 mm.) The specification of the set of accessory weights which were used with this hydrometer is as follows : — w ] 60-2128 gra V 160-277 c.c. e 0-00455 c.c. V 0-8650 c.c. No. . . . 0. I. II. III. IV. V. VI. Weight ill grams . 0-8360 0-8560 1-6010 2-4225 3-2145 4-0710 4-8245 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 23 Weight No. is the small brass table which can be affixed to the top of the stem, and on it any further weight that might be required was placed. The distinctive number of the hydrometer which was used for all the determinations made in the Challenger was 0. In the tabulated results the combination used is indicated in the column headed "Number of Hydrometer." Thus, OOV means that Hydro- meter No. 0, table No. 0, and weight No. V. were used. The combinations almost exclusively used were OOlV and OOV, which weighed 164'2633 and 165'n98 grams respectively. In this memoir we make no use of the volume of the hydrometer, because in all the experiments the temperature is a constant, and we obtain directly the dis- ■placement, that is, the weight of distilled water displaced by the same volume of saline solution, both being at the same temperature, from which we obtain directly the specific gravity of the solution at that temperature, referred to that of distilled water at the same temperature as unity. This result is arrived at from the two observations alone, and is independent of the work of others. As it was certain that during the voyage of the Challenger the specific gravity of the sea-water would have to be observed at many different temperatures, it was convenient, after having determined the displacement of the hydrometer in distilled water at different temperatures, to express the result in terms of the volume of the displacing hydrometer in standard cubic centimetres, but the difference from the later practice is only in the form of expression. § 7. In order to obtain all the precision of which the hydrometric method is capable, the temperature of the water must remain perfectly constant while the hydrometer is floating in it, and the temperature of the hydrometer must be the same as that of the water before it is immersed in it. In ordinary work on shore and in our latitudes this is the condition which it is most difficult to realise. In the Challenger it provided itself. Nearly three out of the three and a half years that the voyage lasted were spent between latitudes 40° N. and 40° S. Here the temperature of the air is relatively high, but its diurnal variation is very slight. Moreover, the Challenger was a wooden ship, and the laboratory was lighted and ventilated by a large main-deck gun-port, the result of which was that, especially in the tropics, the temperature of the air was almost constant, day and night. The temperature of the surface water was usually slightly higher than that of the air, but only by a fraction of a degree, so that its specific gravity could be determined immediately after collection. Samples of water brought up from the bottom and the inferior depths arrived on board having a temperature much lower than that of the air, and it was impossible, even if it had been convenient, to proceed at once to the determinations of their specific gravity. A case containing eight large stoppered bottles was kept in the laboratory for the purpose of receiving these samples as they arrived, and they were kept in the laboratory until the next day, and their specific gravities were then determined one after the other. The 24 MR J. Y. BUCHANAN ON THE twenty-four hours' sojourn in the laboratory equalised their temperature and brought it to agree sensibly with that of the air of the laboratory and that of the hydrometer, which was always kept in the laboratory. By working according to this system, the specific gravities of the waters obtained from, different depths at the same station were determined at the same time and at the same temperature, and their relative specific gravities at a common temperature were thus given directly by experiment. This is an important advantage, and it is often overlooked. A subjective precaution, but one of great importance for assuring accuracy of observation, was adopted at the beginning of the voyage and was never departed from. Before beginning to make hydrometric observations on the samples of water, or to carry out any other operation, such as the boiling out of the gases or the deter- mination of the carbonic acid, / lodged fhe dooj- of the laboratory, and it was not unlocked nutil the operation, iraa Jiiiished. Consequently none of my colleagues, or anyone else in the ship, ever witnessed the determination of the specific gravity of the water, or any other of the operations carried on in the laboratory, at any time from the beginning to the end of the voyage. I found that exactness of observation was promoted by freedom from disturbance. Table VIII.* (Jiviru/ Duplicate Observations of the same Sample of Water with the same Hydrometer differently weighted. No. of Sample. Density observed wilh Difference. OOIV -OOV. No. of Siimplc. Density observed with Difference. OOIV -OOV. OOIV. OOV. OOIV. OOV. 120 127 135 139 181 1-02412 1-02414 1-02406 1-02407 1-02428 1-02411 1-02409 1-02413 1-02414 1-02427 + 1 + 5 -7 -7 + 1 274 826 829 830 831 1-02416 1-02411 1-02411 1-02400 1-02421 1-02412 1-02411 1-02408 1-02405 1-02418 + 4 + 3 -5 + 3 After the Challenger Expedition I used in all my deep-sea work hydrometers with sets of weights designed for making multiple observations in each water. The principal stepping-stone between the Challeiujer hydrometer and that used in the investigations of this memoir was one in which the observations were made in triplicate, the difi"erence between successive added weights being 0'25 or 0'3 gram. One reading was made near the middle of the stem, and the other two were made near the middle of the lower and the upper halves of the stem respectively. A very complete and important set of observations on this scheme was made in 1885, on a voyage from Southampton to Buenos Ayres, and then from Valparaiso following the west coast of South America to Panama, and thence along the west coast * "Report on the Specifir Gravity of Ocean WatiT," I'hijsirx ami Ghemistry, vol. i., Part IL, Table VIII. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 25 of North America to San Francisco. This pattern of hydrometer was also used a good deal in cable ships. In all work at sea three observations, or perhaps four, are quite sufficient. When four observations are made, their arithmetical mean has theoretically two-thirds of the value of the arithmetical mean of a series of nine. § 8. As much misunderstanding seemed to exist not only regarding the qualifications required for the successful practice of the hydrometric method, but also, to some extent, of the principles on which the legitimacy of the method depends, I took occasion at the meeting of the Sixth International Geographical Congress, held in London in 1895, at which I read a paper entitled " A Retrospect of Oceanography during the last Twenty Years," to deal with some of these misapprehensions. The following passage may be quoted here with advantage : — " Many writers, in passing judgment on the hydrometer as an instrument for the determination of the density of liquids, have only in their minds the hydrometer whose indications are determined by comparison with another or standard instrument ; or by immersion in solutions the densities of which have been otherwise ascertained. These instruments have no greater value than that of more or less carefully constructed copies of a standard, the method and the principle of the construction of which is not always given. Rightly, therefore, they prefer the density as determined by weighing a vessel filled with the liquid and comparing it with the weight of distilled water of the same temperature filling the same vessel. The hydrometer which I constructed for the Challenger Expedition, and used during the whole of it, is not a hydrometer in the above sense : it does not give comparative results ; it gives absolute ones. By its means, the weights of equal volumes of the solution and of the distilled water of the same temperature are determined directly. It is neither more nor less than a pykno- meter, where the volume of liquid excluded up to a certain mark is weighed, instead of that included up to a similar mark. In the pyknometer, the internal surface per unit of length of the stem can be made smaller than the external surface per unit of length of stem of the hydrometer. On the other hand, the volume of the hydrometer can safely be made many times larger than that of the pyknometer, the dimensions of which must always be kept small on account of the difficulty of ascertaining the true tempera- ture of its contents, which must be guessed, because it cannot be measured directly. The temperature of another mass of liquid is measured, and the two are assumed to be identical. With the hydrometer, the liquid being in large quantity and outside of the instrument, its temperature can be immediately ascertained with every required accuracy. " Again, for every determination with the ordinary pyknometer, the weight of the liquid contained in it has to be determined by a separate operation of weighing. With the hydrometer, the weight of the liquid displaced, being always equal to its own, is determined once for all by repeated series of weighings, where every refinement is used to secure the true weight of the instrument. This weight can be increased at will by placing suitable small weights on the upper extremity of the stem. Their weight is TRANS. ROY. SOO. EDIN., VOL. XLIX., PART I. (NO. 1). 4 26 MR J. Y. BUCHANAN ON THE also most carefully determined once for all, so that at any moment the total weight of the displacing instrument is accurately known." * Section II. — The Principle and Construction of the Closed Hydrometer. § 9. It will be convenient to follow in detail the preparation of the hydrometer for use. The instrument being closed, its true weight is constant. Let it be assumed that our experiments are actually made in vacuo, A-l at the sea-level in lat. 45°. In these conditions the standard gram exerts a vertical pressure of 1 gram (true). We weigh the hydrometer and find its weight to be W grams. We now float it in distilled water contained in a suitable cylinder. In the construction of the hydrometer the internal load has been so adjusted that, when immersed in distilled water of the standard temperature T, which is to remain unaltered during the whole of the experiments, the surface of the water shall cut the stem in some line C, near its junction with the body of the instrument. Then the weight of the water displaced by the hydrometer is exactly W grams. Let pressure be now applied to the top of the stem, A, until it is completely immersed. Let the measure of this pressure be w grams. Then the weight of water displaced by the instrument when totally immersed at temperature T is (W + w) grams. \ / We assume that the stem is a uniform cylinder of circular section and \«.,^ ^ terminated by a plane surface. If we apply pressure so as to immerse y^ ^s the stem to the line D, which is midway between A and C, the pressure -D -C w required will be — grams ; and, if the portion of stem so immersed, CD, Fig. 2. stands in any other ratio to the total length CA, the pressure required to produce the immersion will stand in the same ratio to w. Let the experiments be made in air of temperature T, and of pressure and humidity such that 1 cubic centimetre of it weighs 1 "2 milligram. When the experiment was made in the vacuum and the surface of the water cut the stem in C, the weight of the water so displaced was exactly equal to that of the hydrometer, namely, W grams. After air has been admitted, the surface of the water no longer cuts the stem exactly in C, but at a point a little lower. This diff'erence between the lines of flotation is due to the fact that, while experimenting in vacuo, the portion of the stem which is not immersed in the water is immersed in a medium the density of which is insensible, whereas, after the air has been admitted, it is immersed in a medium of which 1 cubic centimetre weighs 1 "2 milligram, and this exerts an upward pressure, in opposition to * RepoH of the Sixth Ivfernational Geographical Congress, held in London, 1895, p. 412. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 27 gravity, at the rate of 1 "2 milligram per cubic centimetre of stem so immersed in air. This upward pressure lifts the hydrometer until it displaces a weight of water less than it did in vacuo by the weight of air which the exposed stem displaces after air has been admitted. Therefore, in ordinary laboratory practice, when the hydrometer floats in the liquid at any line C on the stem, the true weight of the liquid so displaced is equal to the true weight in vacuo of the hydrometer less the weight of the air displaced by the exposed portion of the stem. If s be the weight of the air displaced by the exposed portion of the stem, and W, as before, be the weight in vacuo of the instrument, the effective vertical pressure exercised by the hydrometer when floating in equilibrium on the water is H = (W-s), and this is the measure of its displacement in distilled water of temperature T under existing atmospheric conditions. § 10. In instruments of the pattern, fig. 3, § 80, which I construct for use in dilute saline solutions I aim at a displacement of 180 grams distilled water. The stem is made from tubing selected with the greatest care so as to secure uniformity of calibre. Its total length is about 130 millimetres, and its external diameter is such that a length of 10 centimetres displaces something less than a cubic centimetre. This condition is satisfied if the glass-blower selects a suitable piece of tube having an external diameter of 3 to 3 '5 millimetres by the callipers. If the diameter of the tube is exactly 3"56825 millimetres and its section circular, 10 centimetres of it will displace at 4° C. 1 cubic centimetre. The graduated portion of the stem occupies a length of 10 centimetres, which is divided into millimetres numbered at every centimetre from below upwards : 0, 1, 2, ... 10. The zero is about 1 centimetre above the junction of the stem with the body, and the highest division, numbered 10, is found at a distance of about 2 centimetres below the top of the stem. The total length of the instrument should not exceed 33 centimetres. If the hydrometer floats in distilled water of temperature T so that the surface of the water cuts the stem at 5 millimetres above the zero of the scale (I express this shortly by saying, the hydrometer floats at 5), and the weight of air so displaced by the exposed stem is Sj, then the true weight of water so displaced is The other conditions remaining the same, let the distilled water in the cylinder be replaced by a saline solution at temperature T. Let the hydrometer be floated in it ; the surface of the liquid will cut the stem or the body of the instrument at a lower level than the 5th millimetre on the scale. In order to immerse the instrument exactly to the 5th millimetre, we have to place a certain weight on the top of the stem. Let its weight in vacuo be w^ grams. Then the weight of liquid displaced by the system is H'j == W - s, + W5 - dw^, where dw^ is the weight of the air displaced by the small added weight w^. 28 MR J. Y. BUCHANAN ON THE We have then two independent observations, namely, those of the weights of the distilled water and of the saline solution respectively, which occupy the same volume under identical conditions. The ratio of these two weights is the specific gravity of the heavier liquid referred to that of the lighter at the same temperature as unity. It is : — ^ H,- W-S5 Let us now repeat the double experiment, all the conditions remaining the same, except that, when the hydrometer has been immersed in the distilled water and floats at 5, a small weight ^i^ is added which immerses the hydrometer until it floats exactly at 15. Let Sib be the weight of air displaced by the exposed stem above the 15th division, and let dv^f, be the weight of air displaced by the small weight ^15. Then the weight in vacuo of the distilled water displaced by the hydrometer below line 15 is Let the hydrometer be now immersed in the heavier liquid, and let weights be placed on the top of the stem until it floats exactly at 15. As before, the weight of this liquid so displaced is and the specific gravity of the liquid must be Now Hj and H'j are the weights of equal volumes of distilled water and of a heavier liquid respectively, and H15 and H'15 are also weights of equal volumes of distilled water and of the same heavier liquid respectively : therefore in the two ratios ==-^ and ==.— we have two independent values of the specific gravity of the heavier liquid under identical conditions, namely, R = * and S — 16 O5 — — d,UU Oj5 — g— 5 15 As the specific gravity of each liquid has remained the same, these two independent determinations ought to give identical values for S : that is, S5 = S15. It is evident that we can increase at will the number of independent determinations of the specific gravity of the heavier liquid as referred to that of distilled water under constant conditions, and obtain from them a mean value of continually increasing exactness. It will be observed that the values of the specific gravity so obtained depend on our own observations alone. We have therefore the means of appraising their value exactly. Moreover, their value depends almost exclusively on determinations of weight : and this is the physical constant of a body which can be directly determined with perhaps greater precision than any other. SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 29 § 11. Preparation of Accessory Weights. — We have now to consider the prepara- tion or manufacture of the small weights to be placed on the top of the stem in order to produce small increments of the immersion of the hydrometer. They are made of wire. This is wound into spiral cones for the heavier and into lings for the lighter weights. The lighter weights are made of aluminium and the heavier ones of brass. Generally a set of weights consists of aluminium spirals weighing 0*2, 0"5, and TO gram, and rings of the same metal weighing 0'2 and O'l gram, also rings 0"05 and 0'02 gram. The brass weights are rings of 0"5 and 1*0 gram and spirals of 1, 3, 5, and 7 grams. At every operation I aim at making a series of nine independent obser^^a- tions of the displacement. In the first observation the lightest added weight is used and the reading (Ri) is near the zero of the scale. The succeeding observations are made while the added weight is increased by 01 gram between each observation of the series. The observations thus obtained are spread over the whole of the scale on the stem. The weights may be made so that their nominal weight is their true weight in vacuo, but, as they are always used in air, it is preferable to adjust them by balancing them against standard weights in air. The standard weights exert their nominal vertical pressure only in vacuo, at the sea-level in latitude 45° ; but we have assumed that we are in fact working at the sea-level in latitude 45°, therefore the nominal pressure of the standard weight is affected only by the density of the medium in which it is immersed. When we are actually working in a vacuum the density of the medium is insensible ; when we are working in air its density is ascertained by observation. Our standard weights, which have been verified at Kew, are made of brass (gilt) for weights of 1 gram and upwards, and of platinum for weights under 1 gram. The weights destined for use on the stem of the hydrometer are also made of brass for those of 1 gram and upwards, and for those of 1 gram and under they are made of aluminium. There are gram weights and half-gram weights of both brass and aluminium. We will consider (a) the preparation of a gram weight of brass as balanced against a standard gram of brass ; and (6) the preparation of a gram weight of aluminium as balanced against a standard gram of platinum. (a) As we are dealing with only one kind of material, it is sufficient to equilibrate our weight of brass wire against the brass standard gram in air of known density to obtain a weight which in vacuo exerts a vertical pressure equal to that of the standard gram, and it must exert the same vertical pressure as does the standard gram in air of the same density. Taking the specific gravity of brass wire at 8 "38, 1 gram of it displaces 0'119 cubic centimetre of air, which, at r2 milligram per cubic centimetre, weighs 0'1428 milligram. Therefore, when reckoning the effective pressure exerted by the brass weights placed on the top of the hydrometer in air of the density above specified, we make a deduction from their nominal weight in vacuo in the proportion of O'l 428 milligram per gram used. 30 MR J. Y. BUCHAJSTAN ON THE (b) Let us now consider the preparation of a weight of 1 gram in aluminium for the hydrometer, against a standard gram weight in platinum. We take the specific gravity of aluminium at 2'5 and that of platinum at 21. The volume of a gram of platinum is therefore l/21 cubic centimetre, and it displaces this volume of air, which weighs 0-057 milligram. Therefore the standard platinum gram weighs in air 0'999943 gram or 0'057 milligram less than in vacuo. If we are working actually in the vacuum and we equilibrate the platinum gram with a mass of aluminium, both masses exert the same vertical pressure. But when we admit the air the platinum gram loses only 0-057 milligram of apparent weight, whereas the aluminium gram loses — =0-48 milligram of weight, and its vertical pressure m air is only Z 'D 0-99952 gram. A more useful result is obtained by equilibrating the platinum and aluminium in air. Let the standard gram of platinum be placed on the one pan of the balance, and let a mass of aluminium which in vacuo weighs 1 standard gram be placed on the other pan. The two masses which, in vacuo, would exactly balance each other, now appear to have different weights. By immersion in the air the platinum gram has lost 0*057 milligram and the aluminium gram has lost 0-48 milligram. Let aluminium be added to the aluminium weight until the balance shows equilibrium. The amount so added weighs in air 0-423 milligram. The vertical pressures exerted in the air by the masses of platinum and aluminium respectively are then equal. But this pressure is still short of the standard pressure of 1 gram by 0-057 milligram. Let this weight of aluminium be added to the mass of aluminium already on the pan. When this addition has been made, the total mass of aluminium will exert in air, weighing 1 -2 milligram per cubic centimetre, a vertical pressure of 1 gram true. No account has been taken of the buoyancy of the last two additions to the mass of aluminium, because its effect is insensible on our balance. In practice the aluminium weights used in any experiment never exceed 1 gram by more than one or two tenths ; therefore, if they have been simply balanced against the corresponding platinum weights in air, the deduction for buoyancy is insensible ; and we have seen that, if the brass weights have been prepared against brass standards in air, the deduction for buoyancy is at the rate of 0-14 milli- gram per gram when 1 cubic centimetre of air weighs r2 milligram per cubic centimetre. § 12. Exposed Stem. — Let us consider the effect on the resulting value of the specific gravity of a liquid when the correction for the buoyancy of the exposed stem is applied or is neglected. The effect of buoyancy will evidently be the greater, the greater the length of the exposed stem. Let us take the case of the hydrometer suitably loaded, floating at mm., or the lowest division on the stem, both in the distilled water and in the solution. The volume of the exposed stem is 1-25 cubic SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 31 centimetres in both cases, and the air which it displaces, at r2 milligram per cubic centimetre, weighs 1*5 milligram. In order to avoid complication, we suppose that the necessary "added weights" have been added to the internal load of the closed hydrometer, and that the dis- placing weight of the hydrometer quoted for each immersion is its true weight in vacuo, and that nothing which can affect the immersion of the instrument in the liquid is immersed in air excepting the exposed portion of the stem itself This disengages the effect produced by the buoyancy of the stem from that of every other cause. Let the weight of the hydrometer so floating at mm. in distilled water be 180 '25 grams ; and let its weight when floating also at mm. in the solution be 185 '25 grams; then, neglecting the buoyancy of the stem, the specific gravity of the solution is 1 '027739. But the effect of buoyancy is to reduce the effective weight in both cases by 1"5 milligram, so that the specific gravity of the solution corrected for buoyancy of stem is ^; — =1 "027740. Therefore, when the whole of the stem is exposed, its 180-2485 ^ buoyancy affects the resulting specific gravity to the extent of only a unit in the sixth decimal place. § 13. Determination of the Weight of the Hydrometer. — For this purpose the hydrometer is placed on the right-hand pan of the balance in an upright position, and is brought to equilibrium with weights and rider on the left-hand pan. The hydrometer is then removed and equilibrium again established by means of standard weights. These are then replaced by the hydrometer and equilibrium re-established by shifting the rider of the counterpoise if it has been disturbed. The hydrometer is again removed and replaced by standard weights until equilibrium is established. In this way four independent weighings by replacement by standard weights are obtained. The temperature of the air is noted, also the temperature of the wet-bulb thermo- meter and the height of the barometer. Three such series of weighings are made on different days when the meteorological conditions are different. Each series is treated by itself. In order to obtaia the vacuum correction we require to know the weight of the air displaced by the hydrometer and by the weights respectively. The difference of these two weights, the net buoyancy, is the correction to be added to the apparent weight of the hydrometer. We take as an example of the method the determination of the weight in vacuo of hydrometer No. 17. \st Determination. 5th March 1894. Barometer = 740 '8 6 mm. Temperature, dry bulb = 6 IS", wet bulb = 5'V C. Whence the vapour tension is 6 "08 mm., and the weight of 1 litre of this air is 1-2288 gram. 32 MR. J. Y. BUCHANAN ON THE Four weighings of the hydrometer by replacement with standard weights were made in air. The weights found were : — 180'7141 grams. 180-7137 „ 180'7136 „ 180-7137 „ Mean = 180'7138 „ As the hydrometer floats without added weights in distilled water with only a part of the stem exposed, we take its weight in air, 1807138 grams, as expressing, to first approximation, its volume in cubic centimetres. The correction for net huoyancy, that is, the difference between the weight of air displaced by the hydrometer and that displaced by the weights, is (taking dry air at 6'15° C. and 741 mm.) 0'1961 gram, whence the first approximation to the weight in vacuo of the instrument is I807138 + 0-1961 = 180-9099 grams. It was found that by the addition of r698 gram to the weight of the hydrometer it floated totally immersed in distilled water at 6'15"C. ; that is, if the weight were diminished ever so little the top of the stem became exposed, and if it were increased ever so little the instrument began to sink to the bottom. Taking now the first approximation to the weight in vacuo, 180 '9099 grams, and adding r6980 gram, we have the sum 182'6079 grams. This is the first approximation to the weight in vacuo of the mass of distilled water which is displaced by the whole hydrometer at a temperature of 6'1.5°C. Taking the volume of 1 kilogram of water at 6'15° C. to be 1000'034 cubic centimetres, we find the volume of the hydrometer at 6'15° C. to be 182"6139c.c. ; and this is the volume of air which it displaces at 6'15° C. We have found that 1 litre of the air in the balance-room at the time weighed r2288 gram. Therefore the exact weight of the air displaced by the hydrometer when being weighed was 182'6139 x 0-0012288 = 0-22439 gram, and taking the weights as consisting of brass of the density 8-38, we find the weight of air displaced by them to be 0'02650 gram, whence the net buoyancy = 0' 19789 gram, and the true weight in vacuo of the hydrometer is 180'7138 + 0*1979 = 180-9117 grams. The weight in vacuo was determined on two other days, namely 24th April and 2nd June 1894; on each of these days four determinations were made of the weight in air, which on the first of these days weighed r2081 gram per litre, and on the second 1-2037 gram per litre. The weights in vacuo deduced from these observations were 180-9109 and 180-9113 grams respectively. The mean of the three determina- tions is 180-9113 grams, which is accepted as the final value of the weight in vacuo of hydrometer No. 17. The weights of the other hydrometers, Nos. 21 and 3, were determined in the same way ; the particulars are collected in the following table : — SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 33 Deter- mination No. Date. Mean Weight of Hydro- meter in Air. Grams. Number of Weigh- ings in Air. Barometer. Thermometer. Dry Bulb. Wet Bulb. Vapour Pressure. Milli- metres. Weight of 1 litre of this Air. Grams. Exact net Buoyancy. Grams. Exact Weight in vacuo of Hydrometer. Grams. Hydrometer No. 17. 5/3/1894 24/4/1894 2/6/1894 180-7138 180-7165 180-7175 4 4 4 740-86 740-46 747-01 615 1050 1390 5°10 8-90 11-50 6-03 7-70 8-89 1-2288 1-20S1 1-2037 0-1979 1944 0-1938 Mean = 180-9117 180-9109 1809113 180-9113 Hydrometer No. 21. 24/11/1893 5/12/1893 27/ 4/1894 187-5771 187-5764 187-5809 4 4 4 74905 7r)5-40 743-65 ■ 8-25 9-85 13-40 6-70 8-00 1105 6-56 7-07 8-65 1-2327 1-2361 1-2006 1 0-2060 2069 0-2006 Mean = 187-7831 187-7830 187-7815 187-7825 Hydrometer No. 3. 9/3/1894 10/5/1894 2/6/1894 178-1785 4 731-36 9°-45 7°70 6-98 1-1982 0-1904 178-1786 4 740-20 14-10 10-75 7-97 1-1924 0-1895 178-1776 4 746-89 13-95 11-50 8-87 1-2032 0-1912 Mean = 178-3689 178-3681 178-3688 178-3686 No. 17. No. 21. No. 3. Final weight in vacuo accepted for each hydrometer, 180911 3 grams. 187-7825 grams. 178-3686 grams. § 14. As the displacement in distilled water figures in all the determinations of density, we begin by making a number of series of observations of the displacement of the hydrometer in it at the standard temperature chosen. We take as an example the case of hydrometer No. 17 in distilled water of 15 "00° C. as it is given in Table A;^. Table A-^. — This table gives in detail the data from which is derived the total weight displaced by hydrometer No. 17 when floating at the 50-mm. mark in distilled water at 15'00°C. Each line in the table is distinguished by a letter — a, h, c, etc. In line a we have the number and particulars of the hydrometer used. In line h is given a reference to the laboratory note-book in which the original observations were entered, followed by the date of the experiment, line c. Lines d and i give TRANS. ROY. SCO. EDIN., VOL. XLIX., PART Li(NO. 1). 5 34 MR J. Y. BUCHANAN ON THE the times at which the hydrometer is immersed and removed, while the temperatures of the water at these times are given in lines e and /, with their mean, T, in line k ; the range of temperature over which the series of observations was carried out is shown in line /. Although it is intended that the temperature shall be uniform during an experiment, it sometimes happens that it varies, and this has to be provided for in the table. Line fa gives the headings w, the weights used to sink the hydrometer in the Hquid, and E, the reading on the scale of the instrument corresponding to these weights. Lines /^ to /g give, under w, the values of the weights, and under R, the corresponding scale readings, obtained during the series of observations. The value of the mean added weight, w, is given in line g, while the mean reading, R, is shown in line h. The departure of the mean reading from 50 mm., 50 — R, is entered in line m; it is given in the headings as dr. In line n we have the weight which is equivalent to df\ expressed as du\ (see § 15). The weight required to immerse the hydrometer to the 50-mm. mark, iv + dw„ irrespective of temperature corrections, is shown in line o, being that weight which would cause the instrument to float with the scale division at 50 mm. in the plane of the surface of the liquid, at the mean temperature, T. The difference of the mean temperature, T, from the standard temperature, T, is given in the line p, and is expressed as T — T = dt; the weight corresponding to the difference di is entered in line q ; it is expressed as dwt (see § 16). The total corrected added weight required to immerse the hydrometer to the 50-mm. mark at the standard temperature, T, is w + div^ + dw^, and is given in line 7\ The total weight of liquid displaced by the hydrometer when floating in the liquid at the 50-mm. mark at the standard temperature, T, is entered in line s, and is equal to the weight of the instrument in racuo plus w + dto^-\-du't. Having explained the meaning of the lines, we will proceed to inspect the results of the observations in Table A^. After preliminary trial, the first weight added to the hydrometer at the commence- ment of a series of observations is chosen so that the mean of the nine series of immersions or scale readings produced by successive added weights, each increasing by O'l gram, shall approximate closely to 50 mm. It is evident that the initial, or first, added weight might be different for each series of observations. In the ten series of observations detailed in Table Aj, however, the first added weight in each case was 0'525 gram, and therefore the nine added weights are given only once, under iv in lines /^ to /g of the first column. Each of the ten succeeding columns contains a complete series of observations of the immersions produced by the nine added weio-hts, and tlie steps in the calculation of the total weight of the hydrometer when floating at the 50-mm. mark at the standard temperature. SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 35 § 15. Correction for Departure of the Mean Reading from 50 m/m. — If the mean reading, R, be exactly 50 mm., then the weight which must be added to the hydrometer to immerse it to the 50-mm. mark is the mean added weight, w. If, however, the mean reading, R, be less or greater than 50, the mean added weight must be increased or diminished by the weight, dw^, which would increase or diminish the immersion by the difference df between the observed mean reading, R, and 50. The calculation of this correction, dw^, is best explained by taking the series of observations, XVII. 73, Table A^, as an example. In this case the mean reading, R, is 5072, and cZf = 50-5072= -072 (line m). The immersion in the whole series of observations is increased by 8 9 "2 mm. of the stem by an addition of O'SOO gram. Hence an increase of 1 mm. in the stem immersion is caused by the addition of = '00897 gram, and a difference of ^ 89-2 ^ 072 mm. in the immersion must be produced by the weight 0'00897 x - 072 = - 0'0064 gram, which is the required correction, dw^ (line n). As the mean reading, R, is in this case greater than 50, the weight required to immerse the hydrometer to 50 mm. must be less than the mean added weight, w, by the amount of the correction, dw^, and is, therefore, 0'925 — 0'0064 = 0*9186 gram (line o). If the mean reading, R, were less than 50 mm., the correction, dw„ would be calculated in the same manner, but would require to be added to the mean added weight. § 16. Correction for Temperature. — The weight required to be added to the hydro- meter to cause it to float at the 50-mm. mark in distilled water of the mean observed temperature of 15'01° C, as found above, is 0'9]86 gram. A correction [dwt, line q) must now be applied to reduce the displacement observed at the mean temperature, T, to the standard temperature, T, which is in this case 15 '00° C. Before this can be done we must determine the value of dw^ for 0"01° C. at 15"00° C. This is found as follows. A series of observations is made with the hydrometer in distilled water at various temperatures, the results of which are expressed in a curve, having displacements as abscissae and temperatures as ordinates. Suppose we wish to find the temperature correction at, say, 23'00° C, we proceed as follows. Draw horizontal lines through T = 23'5° and T = 22-5° C, cutting the curve at a and h respectively. From a drop a perpendicular on cb, meeting it at c. Then the length ac represents 1° C, while ch is the difference in the total displacement for this 1° difference in the temperature. Knowing the value of the abscissa OX in grams per unit length, say grams per millimetre, we measure accurately the length ch and multiply it by this constant. This gives us the value of dWt for 1° difference of temperature at 23° C. The value of dw^, per 0"01° C. is simply the former figure divided by 100. This process is repeated at each of the temperatures at which observations are being made. The value of dw^ in grams per 0"01° C. at 15'00° C. has been taken as 0*00026. 36 MR J. Y. BUCHANAN ON THE The temperature at the commencement of the observations in our example was ]5'00°, and at the end 15 "02°, the mean being 15 •01°. The departure of the mean temperature from 15*00° is, T — T = c?i = IS'Ol — 15"00 = 0"01° (line_p). Therefore the amount by which the added weight must be increased for the difference dt is (iwt = 0'00026 x 1 =0'00026 gram (line q). The mean tempera- ture observed during the time the observations were being made was higher than the standard, so that in this case we must add the correction for temperature to the added weight required to immerse the stem to 50 mm. at 15 "00° C. .m. 1-2.25 p.m. 3.10 p.m. 4.2 p.m. 12.15 p.m. 12.33 p.m. 12.60 p.m. 1.15 p.m. 3.2 p.m. 3.20 p.m. 3.45 p.m. 19-50° 19-56° 19-53° 19-53° 19-50° 19-50° 19 51° 19-66° 19-50° 19-65° 19-53° 19-50° 19-54° 19-515° 19-515° 19-50° 19-50° 19-50° 19-53° 19-60° 19-525° 19-52° 0-00 0-02° 0-03° 0-03° 0-00 0-00 0-01° 0-06° 0-00 0-05° 0-02° -0-12 -0-19 -0-31 -0-27 -0-01 -0-06 0-06 -0-26 0-06 -0-32 -0-16 -0-0010 -0-0017 -0-0027 -0-0024 0-0000 -0 0004 0-0005 -0-0023 0-0004 -0-0U28 -0-0014 0-7990 0-7983 0-7973 0-7976 0-8000 0-7996 0-8006 0-7977 0-8004 0-797-2 0-7986 0-04° 0-016° 0-015° 0-03° 0-025° 0-02° 0-0010 0004 0-0004 0-0008 0-0008 0-0005 0-7990 0-7993 0-7977 0-7979 0-8000 0-7996 0-'8()05 0-7985 O-8O04 0-7979 0-7991 181-7103 181-7106 181-7090 181-7092 181-7113 181-7109 181-7118 181-7098 181-7117 181-7092 181-7104 4 40 MR J. Y. BUCHANAN ON THE Table Hydrometer No. 17. Details of Determination of the Total Weight of the Hydrometer Piirticulars of hydrometer, Reference to laboratory note-book, Date of experiment, . Time at start, . Teinper.iture at start, Added weight, w, and reading, First added weight or reading, Second ,, ,, Third Fourth Filth Sixth Seven til ,, ,, Eighth Ninth ,, ,, Mean added weight, w, Mean reading, 5, Time at finish, . Final temperature, _. Mean temperature, T, Range of temperature. Difference of mean reading from 50 mm. {50 -R = df), Weight ei|Uivalent to displacement, df { = dw,' Weight reijiiired to immerse Ijydrometer to fiO-mm. mark at mean tempera- ture. T, (U' + dWr), Diiference of mean temperature, T, from standard temperature {T-T=dl), Correction for dlH'erenue rfi (=dw(), Weight reqnired to immerse hydrometer to 50-mm. mark at standard tem- perature, T, (=w + dwr + dwi), Total weight displaced by hydrometer when floating at 50-mm. mark at standard temperature, T, a b c d e fo w f\ 0-25 fo 0-35 U 0-45 f\ 0-55 u 0-B5 h 75 fl 0-85 fn 0-95 A 105 <7 0-65 h I 3 k I m lb P 9 r s XXVIII. 59 1905 June 6 10.52 a.m. 23-05° R 2 2 13-5 24-8 35-8 47 58-0 690 800 90-8 46-79 11.15 a.m. 22-85° 22-95° 0-20° 3-21 0-0290 0-6790 -0-05° -0-0015 0-6775 181-5888 Hydrometer No. 17. XXVIII, 61 1905 June 6 11.42 a.m. 23 00° R 1-8 12-2 23-8 35 46-2 57-2 68-5 79-5 905 46-08 12.00 p.m. 22-90° 22-95° 0-10° 3-92 0-0354 0-6854 -0-05° -0-0015 6839 181-5952 XXVIII. 1905 June 6 12.25 p.m. 23-03° R 2-2 12-5 24-5 35-8 46-8 57-2 68-8 79-2 91-2 46-47 12.40 p.m. 23-0-2° 23 025° 0-01° 3-53 0-0319 6819 025° 00007 0-6826 181-5938 Table Hydrometer No. 17. Details of Determination of the Total Weight of the Hydrometer Particulars of hydrometer, . . . . Reference to laboratory note-book. Date of experiment, Time at start, ... . . Temperature at start, . . . . Added weight, w, and reading, R, . . . First added weight or reading, . .... Second ,, ,, . ... Third „ ,, ... Fourth ,, ,, • • • . Fifth „ ,, . . Sixth ,, ,, Seventh ,, ,, ... Eighth ,, ,, . . Ninth 1. _" • ■ Mean added weight, >r, Mean reading, R, . Time at finish. Final temperature, _ . ... Mean temperature, T, Range of temperature, . . . . ,_ . Difference of mean reading from 50 mm. (50 - R = dr), Weight equivalent to displacement rff (=c?M!r), . . _ Weight lequired to immerse hydrometer to 50-mm. mark at mean temperature, T, {w + dwr). Difference of mean temperature, T, from standard temperature (T-T = rff), Correction for difference d<( = (^«)(), Weight leqnired to immerse hydrometer to .'iO-mm. marlc at standard temperature, T, ( =w + dWT + dwt), Total weight displaced by hydrometer when floating at 50-mm. mark at standard temperature, T, d e h A h U /4 h h h A fA "S-S Is H 3 ? i > s o S- / /^ 1 ^^ Radiator. ^^ For a typical working day the 6th December 1911 has been selected. On arriving at the laboratory about 10.0 a.m. the room temperature was IT'e'C, although the radiator was working at full pressure. The meteorological conditions, such as pressure and relative humidity, were noted and recorded for the purpose of reducing weights "to vacuo" where solutions were to be prepared. The temperature of the air by this time was about 18 "5° C, and the day was cold. A bunsen was lit in the fume chest, which is at the back of the experimenter when 56 MR J. Y. BUCHANAN ON THE seated at the table making observations. The door of the fume chest being closed, the heat from the bunsen is very evenly distributed into the room. The two hydrometers which were used in the experiments were taken from their cases, were each immersed in a small cylinder containing distilled water at about 1 9 '6^ C, and left in to attain a temperature about 19'50° C, a temperature at which the specific gravity observations were to be made. The solution used on this occasion was a yq gram-molecule solution of the potassium chloride and iodide mixed in equimolecular proportions, the molecular weight assigned being the mean between the molecular weight of potassium chloride and that of potassium iodide. The weight of salt represented by y-g gram-molecule was dissolved in 1000 grams of water and was prepared overnight. The bottle of solution had been standing near the radiator for some time to attain a temperature near to 19 '50° C. The solution was now poured into the cylinder used for the experiments, and the quantity was such that when the largest hydrometer was immersed to its fullest extent the surface of the solution was fully an inch below the rim of the cylinder, a precaution which obviates difficulties in reading likely to be occasioned by irregularities in the glass occurring near the top. The cylinder containing the solution was then placed on the table at a convenient altitude for making observations (the foot of the cylinder resting on a thickness of sixteen folds of soft German filter paper to form a non-conducting surface), and the temperature, as observed with a standard thermometer divided into yoths inch, each division being of such a size as to enable one to read y^ths of a degree in temperature with comparative ease, was 1870° C, the air temperature by this time being 19-0° C. An expeditious and effective method for rapidly raising the temperature of the cylinder and contents, by stroking the side of the cylinder with the palms of the hands, was adopted, and by this means the temperature was quickly raised to 19"50°C. exactly. The time was then 10.50 a.m., and the room temperature lO'l C, so the bunsen was lowered somewhat, and the radiator turned to half way. On removing the hydrometers from their respective cylinders and drying them, the temperature of the water in which they had l)een immersed was 19-35° C. in both cases, so that the hydrometers were presumably at that temperature. The temperature of the solution was still at 19-50° C, and the air temperature 19-20° C, so that the conditions were suitable for commencing observations. After removing the thermometer from the solution and immersing it in one of the cylinders of distilled water, the hydrometer No. 17 was taken from its case and gently lowered into the solution, and an initial added weight placed on the top of the stem of the hydrometer, the time of commencement of the experiment being noted. Nine successive readings, as the results of addition of nine weights, eight of them SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 57 having the value of 0"1 gram each, were taken, and after the ninth observation the thermometer was taken out of the distilled water and dried; the hydrometer was removed from the experimental solution and put into the cylinder containing the distilled water, and the temperature of the experimental solution observed by immersing the thermometer and gently stirring the solution. The hydrometer was then dried and replaced in its case. To complete the experimental data, the air temperature and time of completion of the experiment were noted. The following is the record of the experiment : — Cl + I Y^ gram-molecule solution K — ; — . A Hydrometer 17. A.ir temperature . . = 19'20° C. Initial solution temperature = 19'50° C. Time . . . . =11.3 a.m. Added Weight. r32 grams. Heading. 5 "2 millimetres. 1-42 „ 16-3 'S 1-52 , 27-5 J? 1-62 , 38-4 )9 1-72 , 49-4 33 1-82 , 59-2 3» 1-92 , 70-1 3) 2-02 , 82-1 J5 2-12. , 930 35 Mean added weight , = 172 gram. Mean reading . . = 49 '02 millimetres Air temperature . = 19-30° C. Final solution temperature = 19-50° C. Time . = 11.16 a.m. It will be seen that the air temperature rose 0-1" C. during the experiment, which occupied 1 3 minutes, and the solution temperature remained constant ; so the bunsen in the fume chest was lowered to a further extent, and then preparations for the next experiment, conducted in precisely the same manner with hydrometer No. 3, were made. As this section deals only with temperature conditions, the following table has been drawn up to show the temperature conditions which prevailed during the experiments which were made on the ^ and -^ gram-molecule solution of the potassium salt of the mixed halides (chloride and iodide), these being the two solutions experimented upon during the day : — TRANS. ROY. SCO. EDIN., VOL. XLIX., PART I. (NO. 1). 8 58 MR J. Y. BUCHANAN ON THE Quantity of Salt Hydro- meter used. Number of Experi- ment. in 1000 grams of Water, expressed in gram-molecules. m. Initial Air Tempera- ture. Initial Solution Tempera- ture. Time of Commence- ment of Experiment. Final Air Tempera- ture. Final Solution Tempera- ture. Time of Com- pletion of Experiment. Duration of Experi- ment in Minutes. °0. °C. °C. °C. No. 17 1 1 19-20 19-50 11.3 a.m. 19-30 19-50 11.16 a.m. 13 >, 3 2 19-30 19-50 11.20 „ 19-30 19-50 11.34 „ 14 ,, 17 3 )) 19-30 19-50 11.40 „ 19-30 19-50 11.54 „ 14 „ 3 4 )) 19-30 19-50 11.59 „ 19-30 19-50 12.12 p.m. 13 „ 17 5 }} 19-30 19-50 12.17 p.m. 19-30 19-50 12.31 „ 14 „ 3 6 )» 19-30 19-50 12.36 „ 19-30 19-50 12.50 „ 14 No. 17 7 1 ^"2 19-30 19-50 1.45 p.m. 19-30 19-50 1.57 p.m. 12 „ 3 8 19-30 19-50 2.5 „ 19-30 1950 2.17 „ 12 „ 17 9 19-30 19-50 2.22 „ 19-30 19-50 2.34 „ 12 „ 3 10 19-35 19-50 2.45 „ 19-35 19-50 2.59 „ 14 „ 17 11 19-30 19-50 3.4 „ 19-35 19-50 3.16 „ 12 „ 3 12 19-30 19-50 3.22 „ 19-30 19-50 3.35 „ 13 „ 17 13 19-30 19-50 3.42 „ 19-30 19-50 3.56 „ 14 It will be seen that the initial and final solution temperatures were constant to within 0"01° C. throughout the series of experiments. There were slight variations in the air temperature of the room, the widest range being from 19'20°C. to 19"35° C. The rise was occasioned by turning on the radiator full for a few minutes and opening the door for fresh air, but no change occurred in solution temperature, so that latitude can be given in the range of air temperatures ; but from experience it is not advisable to go below 19-2° C. unless direct radiation can be supplied to the solution, as shown in the earlier part of this section, the source of which can be effectively controlled. In the conditions which obtain in this laboratory, it is possible to conduct a series of experiments extending over the day and to maintain the temperature of each solution constant for at least fourteen minutes if the temperature of the air is kept 0"3° lower than that of the solution. § 25. While the conditions which have been described are all essential for complete success in hydrometric work from the point of view of constant temperature, it may, and does occasionally, happen that, even after adopting all the precautions mentioned above, a series of observations will be taken, and then the solution temperature will be found to have changed, and with this change there has been a deviation in the value of specific gravity, certainly in the most extreme case amounting to only a few units in the 5th decimal place ; but the deviation coupled with the temperature change has, in the most recent work, justified its elimination from the remaining series of observa- tions which are perfect, in that the results of the other series agree inter se and no change in solution temperature has occurred. An example of such an occurrence happened on 4th April 1911, when a series of hydrometric observations was made upon a solution containing -^ gram-molecule NaOl in 1000 grams water. It was the first series of the day, and although the initial and final air temperatures for this experiment were both 19-30° C, the solution temperature SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 59 changed from 19-50° C. at the commencement of the experiment to 19-41° C. when the observations were completed. The value of the specific gravit}^ as calculated from this experiment was 1-004542. This value was not included in the accepted results, and the second series of experiments with the same hydrometer, where no change of tempera- ture occurred in the solution during the experiment, gave a specific gravity value of 1"004570, while the mean of the whole series was rO04579. This variation in the solution temperature could only be due to the temperature of the hydrometer itself being considerably lower than that of the solution, and this factor operates in the twofold manner of lowering the solution temperature, and by virtue of the fact that there is a contraction in the volume of the hydrometer at a lower tempera- ture, the added weight to sink it to a given scale division is less than at the higher temperature, so that the specific gravity value is lower than that obtained when the hydrometer is at the standard temperature. This is indubitably the explanation of the change in the solution temperature during the experiment quoted above, and may not improbably account for the observation that the first reading of the day is sometimes not comparable with the later results obtained in observations made on the same solution. It is not possible to directly ascertain the temperature of the hydrometer, and since it is necessary that it should be acclimatised to the experimental temperature, the precaution of immersing the hydrometers in distilled water at the experimental tem,perature for some time before commencing hydrometric observation is important. It ensures that the hydrometer shall be at the experimental temperature and that its volume shall be normal for the given temperature. The water value of one of the hydrometers is 1 1 gram-degrees centigrade. It is possible to calculate the temperature of the hydrometer which would reduce the solution temperature from 19-50° C. to 19-41° C. in the instance mentioned above, assuming no loss of heat due to radiation (this loss is negligible in any case under the conditions of experiment). The weight of the water in solution is about 600 grams (specific heat= 1). Hence, applying the principle of the determination of specific heat by the method of mixtures, the temperature of the hydrometer to produce this must be 14-59° C. The effect of immersing the hydrometer at that temperature was to make the earlier readings lower than they would have been if the hydrometer were at normal temperature ; but the hydrometer is expanding, because it is in a warmer medium, so that the later readings in the same series of observations would approach the values that would have been obtained if the hydrometer had been at normal temperature. It is not difficult to show that the hydrometer was at this temperature (14-59° C.) at the beginning of the experiment, since we have its coefiicient of expansion, namely, 0-003 c.c. per degree difference of temperature. If we assume a mean hydrometer temperature of 17-00° C. — which is the mean between the initial and final hydrometer temperatures — then the volume of solution 60 MR J. Y. BUCHANAN ON THE not displaced on account of the shrinkage in bulk of the hydrometer due to lower temperature = 0"003 x 2'5 = 0'0075 c.c, and its weight is 0'00753 gram (specific gravity of solution being r004542). Hence, in correcting this value of specific gravity, the weight of solution displaced by the hydrometer is 182-53030 grams + 0'00753 gram= 182'53783 grams. The weight of distilled water displaced = 18170496 grams. The specific gravity is therefore 1 '004583, which closely agrees with the mean specific gravity of 1 '004579. The difi'erence of scale reading occasioned by this difi"erence due to temperature, and which is equivalent to an added weight of 0'00753 gram, is 0"82 mm., and is quite an appreciable quantity when it affects all the readings in a series to this extent. The importance, therefore, of the precaution for commencing the series of experi- ments with the hydrometers at the standard temperature by the simple device of immersing them in water at, or a little above, the standard temperature for^some time, and drying them before commencing the experiments, is at once apparent. In the following section the experimental work is embodied in a number of tables. Full explanation is given for each class of tables. Supplemental work which was done during the preparation of this memoir is described and discussed in later sections. [Tables. SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 61 Section V.— TABLES. § 26. A. General Tables, giving the Facts of Observation ; namely, W, the weight, in grams, of the solution which contains m gram-molecules of the salt dissolved in 1000 grams of water ; S, the specific gravity of this solution at the temperature, T, referred to that of distilled water at the same temperature as unity. From these data. A, the displacement of the solution, is obtained by the equation A = W/S, and it is expressed in grams of water having the temperature T. The symbol adopted for this unit is Gt. The numbers printed in italics refer to specific gravities observed at the temperature printed in italics. TRIAD OF CHLORIDES. Table No. 1. POTASSIUM CHLOEIDE. KCl = 74-6. T= 19-5° and 23-0° C. Weight of Solution. Specific Displacement. Dififerenoes of Differences of Lon^arithms of Grams. Gravity. Gi. Displacements. Displacements. TO. W. S. W/S = A. («A. d log A. 1/2 1037-3000 1-022977 1014001 (3-0060385)* 1/4 1018-6500 1-011670 1006-899 7-102 00030522 1/8 1009-3250 1-005889 1003-416 3-483 0-0015052 1/16 1004-6625 1-002973 1001-684 1-732 0-0007500 1/32 1002-3312 1-001489 1000-841 0-843 0-0003658 1/64 1001-1656 1-000741 1000-423 0-418 0-0001811 1/128 1000-5828 1-000365 1000-217 0-206 0-0000895 1/256 1000-2914 1-000193 1000-098 0-119 0-0000517 1/512 1000-1457 1-000082 1000-064 0-034 0-0000149 1/16 1004-6625 1-00292 J^ 1001-7 SS Table No. 2. RUBIDIUM CHLORIDE. RbCl= 121-0. T= 19-5° and ^^-O" C. 1/2 1060-5000 1-043144 1016-637 (3-0071662) 1/4 1030-2500 1-021868 1008-202 8-435 0-0036185 1/8 1015-1250 1-011023 1004-057 4-145 0-0017892 1/16 1007-5625 1-005531 1002-020 2037 0-0008819 1/32 1003-7812 1-002772 1001-006 1-014 0-0004397 1/64 1001-8906 1-00)400 1000 489 0-517 0-0002241 1/128 1000-9453 1-000707 1000-238 0-251 0-0001090 1/256 1000-4726 1-000350 1000-122 0-116 0-0000502 1/512 1000-2363 1-000163 1000-073 0-049 0-0000215 1/16 1007-5625 1-005485 1002066 Table No. 3. G^rSIUM CHLORIDE. CsCl=16! 3-5. T= 19-5° and f,?-0°C. 1/2 1084-2500 1-062572 1020-401 (3-0087709) 1/4 1042-1250 1-031739 1010-066 10-335 0-0044198 1/8 1021-0625 1-015994 1004-989 5-077 0-0021887 1/16 1010-5312 1-008036 1002-475 2-514 00010875 1/32 1005-2656 1-004035 1001-225 1-250 0-0005417 1/64 1002-6328 1-002027 1000-604 0-621 0-0002694 1/128 1001-3164 1-0010-25 1000-291 0-313 0-0001362 1/256 1000-6582 1-000514 1000-144 0-147 0-0000636 1/512 1000-3291 1-000249 1000079 0-065 0-0000280 1/16 1010-5312 1-007954 1002-557 * The entry in brackets in the column d log A gives log A for the solution of highest concentration in the series. With it and the foUomng values of d log A in the same column the values of log A for each solution in the series can be calculated. 62 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TRIAD OF BROMIDES. Table No. 4. POTASSIUM BROMIDE. KBr= 119-1. T=19-5 ° and mO° C. Weight of Solution. Specific Dis|ilaoement. Differences of Differences of Logarithms of Grams. Gravity. GT. Displacements. Displacements. m. W. S. W/S = A. rfA. d log A. 1/2 1059-.'5500 1-041278 1017 547 (3-0075546) 1/4 1029-7750 1-0-20903 1008 690 8-857 0-0037967 1/8 1014-8875 1-010528 1004 314 4-376 0-0018882 1/16 1007-4437 1-005279 1002 153 2-161 0-0009346 1/32 1003-7218 1-002638 1001 081 1-072 0-0004648 1/64 1001-S609 1-001306 1000 554 0-527 0-0002287 1/1 2.S 1000-9304 1-000652 1000 278 276 0-0001195 1/256 1000-4652 1-000325 1000 139 0139 00000602 1/512 1000-2326 1 000158 1000074 0-065 0-0000283 1116 1007-US7 1-005S06 1002-126 Table No. 5. RUBIDIUM BROMIDE. RbBr= 165-5. T = 19-5° C. 1/2 1082-7500 1-061247 1020-262 (3-0087116) 1/4 1041-3750 1-031081 1009-983 10-279 0-0043972 1/8 1020 6875 1-015669 1004-941 5-042 0-0021737 1/16 1010-3437 1-007868 1002-450 2-485 0-0010751 1/32 1005-1718 1-003945 1001-222 1-234 0-0005350 1/64 1002-5859 1001957 1000-627 0-595 0-0002578 1/128 1001-2929 1 -000984 1000-308 0-319 00(101385 1/256 1000-6464 1-000457 1000-189 0-119 0-0000518 1/512 1000 3232 1000233 1000-090 0-099 0-0000430 1/1024 1000-1616 1-000079 1000-082 0-008 0-0000033 Tablb No. 6. CESIUM BROMIDE. CsBr = 2 1 3 -0. T=19-5°C. 1/2 1106-5000 1-080935 1023-650 (3-0101517) 1/4 1053-2500 1-041011 1011-756 11-894 0-0050756 1/8 1026-6250 1-020702 1005-802 5-954 0-0025632 1/16 1013-3125 1-010409 1002-873 2-929 0-0012666 1/32 1006-6562 1-005182 1001-466 1-407 0-0006097 1/64 1003-3281 1-002631 1000-695 0-771 0-0003346 1/128 1001-6640 1-001270 1000-393 0-302 0-0001309 1/256 1000-8320 1-000607 1000-224 0-169 0-0000732 1/512 1000-4160 1-000308 1000-108 0-116 0-0000507 1/1024 1000-2080 1-000145 1000 063 0-045 0-0000195 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 63 A. GrBNBRAL Tables, giving the Facts of Observation in the columns under m, W, and S. TKIAD QF IODIDES. Table No. 7. POTASSIUM IODIDE. KI = T=19-5° G. 166-1. Weight of Solution. Qrams. Specific Gravity. Displacement. Gt. Differences of Displace riients. Differences of LogarithmB of Displacements. m. 1 3/4 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 W. 1166-1000 1124-5750 1083-0500 1041-5250 1020-7625 1010-3812 1005-1906 1002-5953 1001-2976 1000-6488 1000-3244 1000-1622 S. 1-114617 1-087124 1-058929 1-029906 1-015104 1-007588 1-003790 1-001899 1-000950 1-000480 1-000235 1-000122 W/S = A. 1046-189 1034-449 1022-778 1011-281 1005-574 1002-772 1001-395 1000-695 1000-347 1000168 1000-089 1000-040 dA. 11-740 11-671 11-497 5-707 2-802 1-377 0-700 0-348 0-179 079 0-049 d log A. (3-0196102) 0-0049008 00049276 0-0049095 0-0024579 0-0012119 0-0005967 0-0003038 00001509 0-0000775 0-0000345 0-0000212 Table No. 8. RUBIDIUM IODIDE. Rbl = 212-5. T=19-5'' C. 1/2 1/4 1/S 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1106-2500 1053-1250 1026-5625 1013-2812 1006-6406 1003-3203 1001-6601 1000-8300 1000-4150 1000-2075 1-078421 1-039778 1-020010 1-010046 1-005030 1-002505 1-001237 1-000612 1-000272 1-000146 1025-805 1012-836 1006-424 1003-203 1001-602 1000-813 1000-422 1000-218 1000-143 1000-061 12-969 6-412 3-221 1-601 0-789 0-391 0-204 0075 0-082 (3-0110649) 0-0055256 0-0027583 0-0013921 0-0006934 0-00U3423 0-0001695 0-0000888 0000325 0-0000353 Table No. 9. CESIUM IODIDE. Csl = 260-0. T=19-5°C. 1/2 1/4 1/8 1/18 1/32 1/64 1/128 1/256 1/512 1/1024 1130-0000 1065-0000 1032-5000 1016-2500 10081250 1004-0625 1002-0312 1001-0156 1000-5078 1000-2539 1-097427 1-049480 1-024973 1012529 1-006299 1-003120 1-001546 1-000738 1-000272 1-000100 1029-681 1014-788 1007-343 1003-675 1001-814 1000-939 1000-484 1000-277 1000-235 1000-153 14-893 7-4-15 3-668 1-861 0-875 0-455 0-207 0-042 0-082 (3-0127028) 0-0063273 0-0031978 0-0015845 0-0008057 0-0003795 0-0001975 0-0000898 0-0000181 0-0000355 64 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TRIAD OF IODIDES. Table No. 10. POTASSIUM IODIDE. KI = 166-1. T = 23-0° C. Weight of Solution. Specific Displacement. Differences of Differences of Logarithms of Displacements. Grama. Gravity. Gt. Displacements. m. W. S. W/S = A. dA. d log A. 1/2 1083-0500 1-058639 1023-058 - (3-0099005) 1/4 1041-5250 1-029717 1011-467 11-591 0-0049486 1/8 1020-76-25 1-014990 1005-687 5-780 0-0024888 1/16 1010-3812 1-007544 1002-816 2-871 0-0012416 1/32 1005-1906 1-003761 1001-424 1-392 0-0006034 1/64 1002-5953 1-001919 1000-675 0-749 0-0003249 1/128 1001-2976 1-000950 1000-347 0-328 0-0001420 1/256 1000-6488 1-000497 1000-152 0-195 0-0000849 Table No. 11. RUBIDIUM IODIDE. Rbl = 212 5. T = 23-0°C. 1/8 1026-5625 1-020075 1006-360 (3-0027534) 1/16 1013-2812 1-010092 1003-157 3-203 0-0013943 1/32 1006-6406 1-005043 1001-589 1-568 0-0006793 1/64 1003-3203 1-002555 1000-763 0-826 0-0003582 1/128 1001-6601 1-001277 1000-382 0-381 0-0001653 1/256 1000-8300 1-000653 1000-176 0-206 0-0000893 Table No. 12. CiESIUM IODIDE. Csl= 260-0 . T = 23-0° and 26-0° C. 1/8 1032-5000 1-025081 1007-237 (3-0031318) 1/16 1016-2500 1-012637 1003-608 3-629 0-0015675 1/32 1008-1250 1-006341 1001-772 1-836 0-0007950 1/64 1004-0625 1-003163 1000-896 0-876 0-0003799 1/128 lOO-J-0312 1-001596 1000-434 0-462 0-0002005 1/256 1001-0156 1-000814 1000-201 0-233 0-0001010 1116 1016-2600 1-012623 1003-682 SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 65 A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TRIAD OF NITRATES. Table No. 13. NITRATE. T=19-5°C. POTASSIUM NITRATE. KN03= 101-1. Weight of Solution. Specific Displacement. Differences of Differences of Logarithms of Displacements. Grams. Gravity. Gt. Displacements. m. W. S. W/S = A. rfA. d log A. 1/2 1050-5500 1-030564 1019-410 (3-0083492) 1/4 1025-2750 1-015533 1009-593 9-817 0-0042028 1/8 1012-6375 1-007873 1004-727 4-866 0-0020983 1/16 1006-3187 1-003968 1002-342 2-385 00010319 1/32 1003-1593 1-002013 1001-144 1-198 00005194 1/64 1001-5796 1-001004 1000-575 0-569 0-0002463 1/128 1000-7898 1-000509 1000-281 0-294 0-0001283 Table No. 14. RUBIDIUM NITRATE. RbN03 = 147-5. T=19-5°G. 1/2 1073-7500 1-050634 1022002 (3-0094517) 1/4 1036-8750 1-025698 1010-897 11105 0-0047448 1/8 1018-4375 1-012973 1005-394 5-503 0-0023704 1/16 1009-2188 1-006597 1002-604 2-790 0-0012068 1/32 1004-6094 1-003355 1001-250 1-354 0-0005870 1/64 1002-3047 1-001750 1000-553 0-697 0-0003024 1/128 1001-1523 1-000920 1000-232 0-321 0-0001393 1/256 1000-5762 1-000458 1000-118 0-114 0-0000495 Table No. 15. CESIUM NITRATE. CsN03 = 19£ •0. T = 19-5° C. 1/4 1048-7500 1-035619 1012-679 (3-0054720) 1/8 1024-3750 1017961 1006-301 6-378 00027440 1/16 1012-1875 1-009041 1003-118 3-183 0-0013757 1/32 1006-0937 1-004585 1001-501 1-617 0-0007006 1/64 1003-0468 1-002247 1000-798 0-703 0-0003049 1/128 1001-5234 1-001146 1000-376 0-422 0-0001830 1/256 1000-7617 1-000604 1000-157 0-219 0-0000952 TRANS. ROY. SOC. EDIN., VOL, XLIX. PART I. (NO. 1). 66 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TEIAD OF CHLORATES Table No. 16. POTASSIUM CHLORATE, T = 19-5° and 23-0° C. KC103= 122-6. Weight of Solution. Grams. Specific Gravity. Displacement. Gt. Differences of Displacements. Differences of Logarithms of Displacements. TO. W. S. W/S = A. '?A. d log A. 1/4 1030-6500 1-019081 1011-352 (30049025) 1/8 1015-3250 1-009638 1005-632 5-720 0-0024631 1/16 1007-6625 1-004863 1002-785 2-847 0-0012311 1/32 1003-8312 1-002490 1001-337 1-448 0-0006276 1/64 1001-9156 1-001253 1000-661 0-676 0-0002933 1/128 1000-9578 1-000633 1000-324 0-337 0-0001463 1/256 1000-4789 1-000320 1000-158 0-166 0-0000719 1/512 1000-2394 1-000182 1000-057 0-101 0-0000440 1/16 1007-6626 1-004769 1002-889 Table No. 17. ! I lUBIDIUM CHLORATE. RbCl03 = 169-0. ! T = 19-5° and !i3-(T C. 1/4 1042-2500 1-029153 1012-726 (3-0054919) 1/8 1021-1250 1-014679 1006-353 6-373 0-0027417 1/16 1010-5625 1-007356 1003-183 3-170 0-0013700 1/32 1005-2813 1-003691 1001-584 1-599 0-0006926 1/64 1002-6406 1-001863 1000-775 0-809 0-0003406 1/128 1001-3203 1-000919 1000-400 0-375 0-0001626 1/256 1000-6602 1-000459 1000-200 0-200 0-0000867 1/512 1000-3301 1-000218 1000-111 0-089 0-0000386 1/16 1010-6625 1-007 SSI lOOS-204 Tablb No. is. CESIUM CHLORATE. CsC103 = 2 16-5. T=19-5° and 2S-0° Q. 1/4 1054-1250 1-039043 1014-515 (3-0062587) 0-0031285 1/8 1027-0625 1-019686 1007-233 7-282 1/16 1013-5312 1-009825 1003-669 3-564 0-0016394 1/32 1006-7656 1-004953 1001-804 1-865 0-0008066 1/64 1003-3828 1-002409 1000-971 0-833 0-0003624 1/128 1001-6914 1-001216 1000-476 0-495 0-0002149 1/256 1000-8457 1-000552 1000-292 0-184 0-0000795 l/r)12 1000-4228 1-000210 1000-212 0-080 0-0000348 1/16 101S-5S12 1-009886 lOOS-609 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 67 A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TRIAD OF BROMATES. Table No. 19. POTASSIUM BEOMATE. KBr03= 167-1. T=19-5° and ZS-O" C. Weight of Solution. Grams. Specific Gravity. Displacement. Gt. Differences of Displacements. Differences of Logarithms of Displacements. ■m. 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 ijie W. 1041-7750 1020-8875 1010-4438 1005-2219 1002-6109 1001-3055 1000-6527 1000-3264 1010-4438 S. 1-030144 1-015227 1-007662 1-003846 1-001921 1-000958 1-000476 1-000237 1-007668 W/S = A. 1011-290 1005-576 1002-761 1001-370 1000-688 1000-347 1000-176 1000-089 1002-86^. dA. 5-714 2-816 1-391 0-682 0-341 0-171 0-087 d log A. (3-0048760) 0-0024613 0-0012173 0-0006026 0-0002959 0-0001482 0-0000740 0-0000379 Table No. 20. RUBIDIUM BROMATE. RbBr03 = 213-5. T = 19-5° and ^S-f^^C. 1/16 1/32 1/64 1/128 1/256 1/512 i/ie 1013-3438 1006-6719 1003-3359 1001-6680 1000-8340 1000-4170 lOlS-SJiBS 1-010255 1-005123 1-002566 1-001260 1-000642 1-000320 1-01016% 1003-057 1001-541 1000-767 1000-407 1000-191 1000-096 100S-U9 1-516 0-774 0-360 0-216 0-095 (3-0013258) 0-0006571 0-0003356 0-0001563 00000935 0-0000411 Table No. 21. CESIUM BROMATE. CsBr03 = 261-0. T= 19-5° and ^5-0° G. 1/16 1/32 1/64 1/128 1/256 1/512 ijie 1016-3125 1008-1562 1004-0781 1002-0390 1001-0195 1000-5097 1016-3126 1-012756 1-006377 1-003211 1001617 1-000784 1000375 1-012769 1003-511 1001-767 1000-864 1000-421 1000-235 1000-134 1003-508 1-744 0-903 0-443 0-186 0-101 (3-0015225) 0-0007554 0-0003918 0-0001920 00000810 00000437 68 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. TEIAD OF lODATES. Tablh No. 22. POTASSIUM lODATE. KI03 = 214-1. T=19-5° and 2S-0° C. Weight of Solution. Grams. Specific Gravity. Displacement. Gt. Differences of Displacements. Differences of Logarithms of Displacements. m. 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/16 W. 1053-5250 1026-7625 1013-3812 1006-6906 1003-3453 1001-6726 1000-8363 1000-4181 lois-ssn S. 1-044302 1-022327 1-011169 1-005589 1-002760 1-001403 1-000709 1-000361 1-011U7 W/S = A. 1008-832 1004-339 1002-189 1001-096 1000-584 1000-269 1000-127 1000-057 1002-210 rfA. 4-493 2-150 1-093 0-512 0-315 0-142 0-070 d log A. (3-0038187) 0-0019383 0-0009307 0-0004739 0-0002221 0-0001365 0-0000617 0-0000304 Table No. 23. RUBIDIUM lODATE. RbI03 = 260-5. T= 19-5° and ^5-0° C. 1/16 1/32 1/64 1/128 1/256 1/512 1/16 1016-2812 1008-1406 1004-0703 1002-0351 1001-0175 1000-5087 1016-2812 1-013677 1-006856 1-003405 1-001690 1-000827 1-000436 1-01S626 1002-576 1001-276 1000-661 1000-344 1000-190 1000-072 1002-618 1-300 0-615 0-317 0-154 0-118 (3-0011173) 0-0005636 00002669 0-0001377 0-0000669 0-0000510 ^l . ^, ,. AT.. CtA CESIUM lODATE. CsI03 = 308-0. T = 19-5° and ^3-0° C. 1/16 1019-2500 1-016299 1002-903 (3-0012590) 1/32 1009-6250 1-008142 1001-471 1-432 0-0006383 1/64 1004-8125 1-004023 1000-786 0-685 0-0002970 1/128 1002-4062 1-001948 1000-457 0-329 0-0001426 1/256 1001-2031 1-000930 1000-272 0-185 0-0000802 1/512 1000-6015 1-000449 1000-152 0-120 0-0000524 1/16 1019-2500 1-016226 1002-976 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 69 A. General Tables, giving the Facts of Observation in the columns under m, W, and S. Tablb No 25. POTASSIUM CHLOKIDE. KG1 = 74'6. T=15-0° C. Weight of '■' Solution. ! Grams. Specific Gravity. Displacement. Gt. Differences of Displacements. Differences of Logarithms of Displacements. in. W. S. W/S = A. dA. d log A. 1/2 1037'3000 1-023167 1013-813 (3-0059576) 1/4 1018-6500 1-011900 1006-671 7-142 0-0030702 1/8 1009-3250 1-005912 1003-393 3-278 0-0014163 1/16 1004-6625 1-002972 1001-685 1-708 0-0007399 1/32 1002-3312 1-001487 1000-842 0-843 0-0003653 1/64 1001-1656 1-000716 1000-449 0-393 0-0001708 1/128 1000-5828 1-000365 1000-218 0-231 0-0001003 Table No. 26. SODIUM CHLORIDE. NaCl = 58-5. T=15-0°C. 1/2 1029-2500 1 020564 1008-510 (3-0036805) 1/4 1014-6250 1-010433 1004-148 4-362 0-0018825 1/8 1007-3125 1-005258 1002-043 2-105 0-0009114 1/16 1003-6562 1-002650 1001-003 1-040 0-0004508 1/32 1001-8281 1-001322 1000-505 0-498 0-0002162 1/64 lOGO-9140 1-000655 1000-259 0-246 0-0001069 1/128 1000-4570 1-000322 1000-135 0-124 00000538 Table No. 27. RUBIDIUM BROMIDE. RbBr=l 65-5. T = 23-0° C. 1/8 1020-6875 1-015740 1004-870 (3-0021101) 1/16 1010-3437 1-007895 1002-429 2-441 0-0010563 1/32 1005-1718 1-003993 1001-174 1-255 0-0005441 1/64 1002-5859 1-001968 1000-616 0-558 0-0002420 1/128 1001-2929 1-000986 1000-306 0-310 0-0001343 Table No. 28. C^SIUxM BROMIDE. CsBr = 213 -0. T = 23-0° C. 1/8 1026-6-250 1-020672 1005-832 (3-0025257) 1/16 1013-3125 1-010386 1002-896 2-936 0-0012698 1/32 1006-6562 1-005246 1001-403 1-493 0-0006470 1/64 1003-3281 1-002634 1000-692 0-711 0-0003084 1/128 1001-6640 1-001332 1000-331 0-361 0-00U1563 70 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. Table No. 29. LITHIUM NITRATE. LiNO3 = 69 0. T=19-5° C. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 Weight 'of Solution. Grams. Specific GraTity. Displacement. (jt- w. 1034 1017 1008 1004 1002 1001 1000 •5000 ■2500 ■6250 ■3125 ■1562 ■0781 •5390 S. r019707 1-010033 1-005031 1-002548 1-001290 1-000654 1-000336 W/S = A. 1014-507 1007-145 1003-565 1001-759 1000-864 1000-423 1000-203 Differenoes of Displacements. 7-362 3-580 1-806 0-S95 0-441 0-220 Table No. 30. SODIUM NITRATE T = 15-0° and 19-6° C NaNO3 = 85-0. Differences of Logarithms of Displacements. d log A. (3-0062551) 0-0031631 0-0015418 0-0007865 0-0003882 0-0001914 0-0000957 1/16 1005-3125 1-003453 1001-852 (3-0008039) 1/32 1002-6562 1-001715 1000-939 0-913 0-0003962 1/64 1001-3281 1-000863 1000-464 0-475 0-0002061 1/128 1000-6640 1-000431 1000-232 0-232 0-0001005 11^ 1042-5000 1-027810 1014-292 (S-0061632) lU 1021-2500 1-01 412S 1007-027 7-265 0-00S1217 118 1010-6250 1-007119 1003-480 3-547 0015325 ijie 1005-S125 1-00S588 1001-718 1-762 0-00a76S5 HS2 1002-6562 1-ooisu.: 1000-862 0-866 0-0003752 HH 1001-S281 1-000900 1000-427 0-425 0-0001847 Table No. 31. POTASSIUM NITRATE. KNO3 = 101-l. T=15-0° C. 1/2 1050-5500 1/4 1025-2750 1/8 1012-6375 1/16 1006-3187 1/32 1003-1593 1/64 1001-5796 1/128 1000-7898 1-030874 1-015700 1-007974 1-003966 1-001974 1-000985 1-000490 1019-087 1009-427 1004-623 1002-343 1001-183 1000-594 1000-299 9-660 4-804 2-280 1-160 0-589 0-295 (3-0082113) 0-0041364 00020717 0-0009865 00005032 0-0002554 0-0001277 SPECIFIC GRAVITY AND DISPLACEMENT Of SOME SALINE SOLUTIONS. 71 A. General Tables, giving the Facts of Observation in the columns under m, W, and S. Table No. 32. RUBIDIUM NITRATE. RbN03 = 147-5. T = 23-0°C. Weight of Solution. Grains. Specific Gravity. Displacement. Gi. Dififerences of Displacements. Differences of Lngaiithms of Displacements. m. 1/4 1/8 1/16 1/32 1/64 1/128 1/256 W. 1036-8750 1018-4375 1009-2188 1004-6094 1002-3047 1001-1523 1000-5762 S. 1-025590 1-013065 1-006584 1-003354 1-001731 1-000955 1-000404 W/S = A. 1011-003 1005-303 1002-617 1001-251 1000-573 1000-197 1000-172 5-700 2-686 1-366 0-678 0-376 0-025 d log A. (3-0047526) 0-0024556 0-0011618 0-0005922 0-0002941 0-0001631 0-0000109 Table No. 33. CESIUM NITRATE. CsN03 = 195-0. T = 23-0''C. 1/8 1/16 1/32 1/64 1/128 1/256 1024-3750 1012-1875 1006-0937 1003-0468 1001-5234 1000-7617 1-017943 1-009035 1-004536 1-002288 1-001186 1-000580 1006-318 1003-124 1001-550 1000-757 1000-337 1000-181 3-1.94 1-574 0-793 0-420 0-156 (3-0027353) 0-0013804 0-0006818 0-0003445 0-0001822 0-0000673 Table No. 34. STRONTIUM NITRATE. Sr(N03)3 = 211-6. T=15-0°G. 1/32 1/64 1/128 1/256 1/512 1006-6125 1003-3062 1001-6531 1000-8265 1000-4132 1-005344 1-002673 1-001351 1-000666 1-000329 1001-261 1000-631 1000-302 1000-160 1000-084 0-630 0-329 0-142 0-076 (3-0005477) 0-0002734 0-0001430 0-0000615 0-0000331 72 MR J. Y. BUCHANAN ON THE A. General Tables, giving the Facts of Observation in the columns under m, W, and S. Table No. 35. BARIUM NITRATE. Ba(NO3)2 = 261'0. T = 150°C. Weight of Solution. Grams. Specific Gravity. Displacement. Gt. Differences of Displacements. Ditferenoes of Logarithms of Displacements. /;(. W. S. W/S = A. dA. d log A. 1/32 1008-1562 1-006719 1001-427 (3-0006197) 1/64 1004-0781 1-003377 1000-699 Q-11S, 0-0003164 1/128 1002-0390 1-001693 1000-345 0-354 0-0001535 1/256 1001-0195 1-000836 1000-183 0-152 0-0000700 1/512 1000-5097 1-000422 1000-088 0-095 0-0000416 1/1024 1000-2548 1-000218 1000-036 0-052 00000224 Table No. 36. ! BARIUM NITRATE. Ba(N03), = 261-0. T=19-5°C. 1/16 1016-3125 1-013302 1002-971 (3-0012884) 1/32 1008-1562 1-006697 1001-449 1-522 0-0006592 1/64 1004-0781 1-003367 1000-708 0-741 0-0003216 1/128 1002-0390 1-001710 1000-328 0-380 0-0001651 1/256 1001-0195 1-000856 1000-163 0-165 0-0000716 1/512 1000-5097 1-000433 1000-076 0-087 0-0000376 1/1024 1000-2548 1-000205 1000-049 0-027 0-0000115 Table No. 37. LEAD NITRATE. Pb(N03)2 = 33] L-0. T=19-5°C. 1/16 1020-6875 1-017788 1002-849 (3-0012356) 0-0006347 1/32 1010-3437 1-008947 1001-384 1-465 1/64 1005-1718 1-004504 1000-664 0-720 0-0003124 1/128 1002-5859 1-002250 1000-335 0-329 0-0001429 1/256 1001-2929 1-001128 1000-165 0-170 0-0000739 1/512 1000-6464 1-000577 1000-069 0-096 0-0000413 1/1024 1000-3232 1-000300 1000-023 0-046 0-0000203 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 73 § 27. B. Tables giving particulars relating to the exactness of the determinations of the specific gravity given in Tables A, in cases where two hydrometers have been used. In these tables we have, under Sj^, the mean specific gravity derived from s^^ series of observations made with Hydrometer No. 21 ; under Sjj, the mean specific gravity derived from Sjy series of observations with Hydrometer No. 17; under Sg, the mean specific gravity derived from Sg series of observations with Hydro- meter No. 3 ; and under S the mean of the sum, s, of these series of observations. Under r^ we have the probable error of S calculated by the method of least squares ; and under d, the maximum departure of the mean of any individual series from §. Numbers under r„ and d represent units in the sixth decimal place. Table No. 38. POTASSIUM CHLOEIDE. KCl = 74-6. T = 19-5° a.nd 23-0° G. m. s.,. ... ' Si,. s„. §. .-. '•o- d. 1/2 1-022986 4 1-022969 4 1-022977 8 2-9 18 1/4 1-011674 4 1-011665 4 1-011670 8 3-0 20 1/8 1-005895 4 1-005883 1 4 1-005889 8 2-1 16 1/16 1-002980 3 1-002967 , 3 1002973 6 3-6 18 1/32 1-001494 3 1-001485 i 4 1-001489 7 2-2 14 1/64 1-000756 4 1-000730 4 1-000741 8 3-1 27 1/128 1-000368 3 1-000361 3 1-000365 6 1-5 10 1/256 1-000199 4 1-000188 4 1-000193 8 2-2 14 1/512 1-000088 4 1-000076 4 1-000082 8 2-2 14 1/16 1-00^92 J^ 3 OS 1 Table No. 39. EUB IDIUM CHLORIDE. RbCl= 121-0. T = ]9-5° and ^5-0° C. 1/2 1-043150 4 1-043138 4 1-043144 8 2-2 19 1/4 1-021875 4 1-021858 3 1-021868 7 2-7 13 1/8 1-011027 4 1-011019 4 1-011023 8 1-5 10 1/16 1-005.130 4 1-005.'531 4 1005531 8 2-5 15 1/32 1-002776 4 1-002767 3 1-002772 7 2-4 13 1/64 1-001398 4 1-001402 3 1-001400 7 2-5 13 1/128 1-000710 4 1-000705 4 1-000707 8 1-8 12 1/256 1-000349 3 1-000350 4 1-000350 7 1-6 12 1/512 1-000163 3 1-000163 3 1-000163 6 0-6 3 1/16 1-0054.85 S 1-8 5 Table No. 40. C^ SIUM CHLORIDE. C sCl= 168-5. T=19-5° and 23-0° C. 1/2 1-062581 3 1-062566 4 1-062572 7 3-1 19 1/4 1-031742 4 1-031734 3 1-031739 7 1-6 7 1/8 1-015996 4 1-015991 3 1-015994 7 1-5 12 1/16 1-008044 3 1-008030 4 1-008036 7 3-2 20 1/32 1-004040 4 1-004029 3 1-004035 7 1-6 7 1/64 1-002032 4 1-002021 4 1-002027 8 2-0 14 1/128 1-001026 4 1-001024 3 1-001025 7 1-8 15 1/256 1-000517 4 1-000511 4 1-000514 8 1-6 13 1/512 1-000253 4 1-000244 3 1-000249 7 1-7 12 1/16 1-007954 S 2-0 6 TRANS. ROY. SOC. EDIN., VOL. XLIX. PART I. (NO. 1). 10 74 MR J. Y. BUCHANAN ON THE B. Tables giving the Probable Error {vq) of the Mean Specific Gravity (S) ; and the greatest Departure {d) of the mean of any individual series from S ; both r^ and d being expressed in units of the sixth decimal place. Table No. 41. POTASSIUM BEOMIDE. KBr = 119-1. T=19-5° a.nd SS-O" C. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/16 1-041284 1-020915 1-010534 1-005288 1-002649 1-001313 1-000650 1-000336 1-000163 Ssl- 4 4 4 4 3 3 3 4 2 1-t s„ 041272 020890 010521 005271 002630 001301 000654 000314 000153 006306 S],. 4 4 4 4 4 4 4 4 2 ^ s. -041278 -020903 •010528 -005279 -002638 -001306 -000652 -000325 ■000158 s. n- 8 2-8 8 3-6 8 2-4 8 3-8 7 2-7 7 3-1 7 1-6 8 3-1 4 6-6 2-0 d. 17 24 18 26 13 23 11 20 28 Table No. 42.-* RUBIDIUM BROMIDE. RbBr = 165-5. T=19-5° C. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1-061235 1-031081 1-015674 1-007865 1-003941 1-001949 1-000980 1-000478 1-000227 1-000090 S3. 3 l-( 3 l-( 3 l-( 3 1( 3 l-( 3 1- 1- 2 1- 2 1- 3 1- -061259 -031080 •015665 ■007870 -003949 -001964 -000988 -000446 -000238 •000070 hi- 3 3 4 3 3 3 2 4 3 1- 4 -061247 •031081 -015669 -007868 -003945 -001957 -000984 -000457 -000233 -000079 6 6 7 6 6 6 4 6 5 7 Table No. 43. CESIUM BEOMIDE. CsBr= 213-0. T = 19-5°C. 1-080943 1-041024 1-020708 1-010407 1-005203 1-002638 1-001269 1-000595 1-000317 1 000135 4 3 3 3 3 3 2 3 3 3 -080923 -040997 -020695 -010411 -005160 -002622 -001271 -000619 -000296 -000155 4-8 1-3 6-0 1-0 2-7 3-1 3-5 5-1 2-3 3-9 d. 26 6 30 6 17 16 15 22 11 28 3 1-080935 7 3-5 3 1-041011 6 5-5 3 1-020702 6 2-9 3 1-010409 6 2-0 3 1-005182 6 6-8 2 1-002631 5 3-3 4 1-001270 6 3-9 3 1-000607 6 3-7 3 1-000308 6 5-9 3 1-000145 6 3-3 24 17 14 10 34 16 18 28 26 16 In Tables Nos. 42, 43, 45, and 46 Hydrometer No. 3 has been used in place of No. 21, SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 75 B. Tables giving the Probable Error (ro) of the Mean Specific Gravity (S) ; and the greatest Departure (d) of the mean of any individual series from S ; both Vq and d being expressed in units of the sixth decimal place. 1 3/4 1/2 1/4 18 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 Table No. 44. POTASSIUM IODIDE. KI= 166-1. T = 19-5° C. S=i. ■114619 •087124 •058929 •029912 •015104 •007593 •003794 •001906 •000951 •000481 •000237 •000132 ''21- 1 3 2 1 2 2 2 2 2 2 3 2 •114617 •087124 •058929 •029904 •015103 •007583 •003786 •001893 •000949 •000479 •000232 •000115 s,,. 2 !• 3 I- 3 I- 2 1- 3 I- 2 !■( 2 1- 2 r( 2 !•( 2 l-( 3 L( 3 !•( s. •114617 •087124 •058929 •029906 •015104 •007588 ■003790 •001899 •000950 ■000480 •000235 •000122 s. '•O' d. 3 3^0 8 6 2^8 17 5 2'2 10 3 1^3 6 5 5-3 22 4 2^7 12 4 2^2 9 4 2^8 10 4 2-6 10 4 3^2 13 6 2^0 13 5 3-5 14 Table No. 45. EUBIDIUM IODIDE. Ebl = 212^5. T=19^5° C. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 S3. S3, Si,. s„. S. 1. »-o- 1 •078425 5 1-078416 5 1-078421 10 2-6 1^039781 3 1-039774 3 1-039778 6 4-6 L020020 4 1-020009 4 1-020010 8 4-2 1^0 10058 3 1010033 3 1-010046 6 4-2 1-005038 3 1-005032 3 1-005030 6 5-1 1 •002503 2 1-002506 4 1^002505 6 4-1 L001231 3 1-001240 4 1 ■001237 7 4-6 L000602 3 1000621 3 1^000612 6 4-3 1-000272 3 1-000269 3 ^000272 6 2-5 L000149 3 1-000139 3 L000146 6 3-4 21 25 27 23 25 23 23 23 12 20 Table No. 46. CESIUM IODIDE. Gsl = 260-0. T=19-5°C. 12 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 -097435 -049485 •024973 •012527 -006272 •003109 •001549 •000733 •000281 -000114 3 3 3 3 2 3 3 2 3 2 ■097420 ■049477 -024973 -012532 -006307 -003130 -001543 -000742 -000263 -000093 3 3 4 3 3 3 3 3 3 4 -097427 -049480 -024973 -012529 -006299 ■003120 ■001546 •000738 •000272 •000100 6 2^6 6 4^0 7 2^1 6 2^2 5 8^0 6 3^7 6 L7 5 2-8 6 3^1 6 3^9 15 19 13 11 35 21 11 13 16 15 76 MR J. Y. BUCHANAN ON THE B. Tables giving the Probable Error (r^) of the Mean Specific Gravity (S) ; and the greatest Departure (d) of the naean of any individual series from S ; both r^ and d being expressed in units of the sixth decimal place. Table No. 47. POTASSIUM IODIDE. KI= 166-1. T = 23-0°C. m. S.i. 2 Sl7. hi- s. s. '•o- d. 1/2 1-058643 1-058636 3 1-058639 5 1-8 9 1/4 1-029724 3 1-029705 2 1-029717 5 3-4 14 1/8 1-014981 2 1-014999 2 1-014990 4 3-6 12 1/16 1-007543 3 1-007536 2 1-007544 5 4-2 1 18 1/32 1-003767 2 1-003754 2 1-003761 4 2-5 8 1/64 1-001919 2 1-001918 2 1-001919 4 2-9 12 1/128 1-000958 2 1 000945 4 1-000950 6 2-4 9 1/256 1-000498 2 1-000495 2 1-000497 4 3-4 14 Table No. 48. RUBIDIUM IODIDE. Rbl = 212-5. T = 23-0° C. 1/8 1-020084 4 1-0200.55 2 1-020075 6 4-3 20 1/16 1-010091 2 1-010092 3 1-010092 5 0-8 3 1/32 1-005046 2 l-00.')040 1 3 1-005043 5 1-7 8 1/64 1-002565 3 1-002545 3 1-002555 6 3-6 17 1/128 1-001275 3 1001279 ' 3 1-U01277 6 1-5 8 1/256 1-000670 3 1-000635 1 3 1-000653 6 4-5 24 Table No. 49. C ^SIUM IODIDE. Cs [=260-0. T = 23-0 and ^5-0° 0. 1/8 1-025089 2 1-025075 3 1-025081 5 4-1 15 1/16 1-012644 7 1-012628 6 1-012637 13 2-6 23 1/32 1-006332 3 1-006355 2 1-006341 5 4-2 14 1/64 1-003165 3 1-003160 2 1-003163 5 1-3 7 1/128 1-001600 2 1-001593 2 1-001596 4 1-3 4 1/256 1-000826 2 1-000804 3 1-000814 5 4-4 13 1/16 1 -012635 i 1-012606 S 1-012623 7 4-1 25 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 11 B. Tables giving the Probable Error (ro) of the Mean Specific Gravity (S) ; and the greatest Departure {d) of the mean of any individual series from 8 ; both r^ and d being expressed in units of the sixth decimal place. Table No. 50. POTASSIUM CHLORIDE. KCl = 74-6. T=15-0° C. m. K- %• 8,7- Sj,. S. s. n- d,. 1/2 1-023170 4 1-023164 4 1-023167 8 2-0 20 1/4 1-011899* 3* 1-011900 3 1-011900 6 1-1 5 1/8 1-005912 4 1-005912 3 1-005912 7 1-7 14 1/16 1-002977 4 1-002967 4 1-002972 8 1-6 14 1/32 1-001493 4 1-001480 4 1-001487 8 2-1 13 1/64 1-000723 4 1-000706 3 1-000716 7 3-0 21 1/128 1-000365 4 1-000365 4 1-000365 8 2-0 10 Tablb No. 51. SODIUM CHLORIDE. NaCl=58-5. T = 15-0°C. 1/2* 1-020576 4 1-020552 4 1-020564 8 3-9 25 1/4 1-010436 4 1-010429 3 1-010433 7 2-5 14 1/8 1-005265 3 1-005253 4 1-005258 7 2-4 19 1/16 1-002654 4 1-002645 4 1-00-2650 8 1-7 11 1/32 1-001331 4 1-001312 4 1-001322 8 2-6 17 1/64 1-000658 3 1-000652 4 1-0U0655 7 2-6 14 1/128 1-000324 4 1-000320 4 1-000322 8 0-7 6 Table No. 52. RUBIDIUM BROMIDE. RbBr = 165-5. T = 23-0° C. 1/8 1-015751 2 1-015729 2 1-015740 4 4-2 11 1/16 1-007902 2 1-007888 2 1-007895 4 2-7 8 1/32 1-004002 2 1-003983 2 1-003993 4 3-7 10 1/64 1-001977 2 1-001962 3 1-001968 5 2-9 8 1/128 1-000972 2 1-000999 2 1-000986 4 5-2 14 Table No. 53. , CESIUM BROMIDE. CsBr = 213-0. T = 23-0° C. 1/8 1-020681 2 1-020662 2 1-020672 4 3-9 14 1/16 1-010395 2 1-010376 2 1-010386 4 3-7 10 1/32 1-005238 2 1-005251 3 l-0052i6 5 3-8 16 1/64 1-002636 3 1-002630 2 1-002634 5 1-9 11 1/128 1-001328 2 1-001335 3 1 1-001332 5 1-6 8 These observations were made with Hydrometer No. 3. 78 MR J. Y. BUCHANAN ON THE B. Tables giving the Probable Error (vo) of the Mean Specific Gravity (S) ; and the greatest Departure (d) of the mean of any individual series from S ; both r^ and d being expressed in units of the sixth decimal place. Table No. 54. LITHIUM NITEATE. LiNO3 = 69 0. T=19-5°C. m. Ooj* 111- S,y. hi- §, s. J-o- d. 1/2 1-019726 2 1-019688 2 1-019707 4 7-4 20 1/4 1-010026 2 1-010039 2 1-010033 4 2-5 7 1/8 1-005025 2 1-005036 3 1-005031 5 1-9 7 1/16 1-002535 2 1-002561 2 1-002548 4 5-1 13 1/32 1-001285 2 1-001294 2 1-001290 4 1-8 5 1/64 1-000649 2 1-000658 2 1-000654 4 1-8 5 1/128 1-000339 3 1-000332 2 1000336 5 1-6 6 Table No. 55. SODIUM NITRATE. NaNO3 = 85-0. 1 = 15-0° and 19-6° G. 1/16 1-003455 4 1-003450 4 1-003453 8 2-1 17 1/32 1-00 17 -24 4 1001706 4 1-001715 8 2-7 20 1/64 1-000866 4 1-000859 3 1-000863 7 2-4 12 1/128 1-000437 4 1-000425 4 1-000431 8 2-1 19 1/2 1-027814 S 1-027806 4 1-027810 7 2-1 15 114 1-0141S0 4 1-014.115 4 1-01412S 8 3-1 19 118 1-007122 4 1-007117 4 1-007119 8 2-4 15 1/16 1-00S59S 4 1-00S68S 4 1-003588 8 1-9 16 1/S2 1-001805 4 1-001798 4- 1-001802 8 1-3 10 l/6i 1-000907 S 1-000893 s 1-000900 6 2-6 15 Table No. 56. POTASSIUM NITRATE. KNOg = 101-l. T=19-5°C. 1/2 1-030565 2 1-030562 2 1-030564 4 3-6 13 1/4 1015533 2 1-015533 2 1-015533 4 3-7 13 1/8 1-007880 3 1-007866 3 1-007873 6 2-5 17 1/16 1-003978 6 1-003958 6 1-003968 12 3-1 22 1/32 1-002015 2 1-002010 2 1-002013 4 4-7 15 1/64 1-001011 3 1-000996 3 1-001004 6 2-5 11 1/128 1-000513 3 1-000503 2 1-000509 5 3-9 20 Table No. 57. STRONTIUM NITRATE Sr(N03)2 = 211-6. T=15-0°C. 1/32 1-005349 3 1-005338 3 1-005344 6 2-4 15 1/64 1-002675 4 1-002672 4 1-002673 8 1-4 9 1/128 1-001351 4 1-001350 4 1-001351 8 1-5 8 ]/2.'56 1-000675 4 1-000657 4 1-000666 8 2-8 16 1/512 1-000336 4 1-000323 4 1-000329 8 2-0 12 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 79 B. Tables giving the Probable Error (r,,) of the Mean Specific Gravity (S) ; and the greatest Departure (d) of the mean of any individual series from S ; both Vq and d being expressed in units of the sixth decimal place. Table No. 58. BARIUM NITRATE. Ba(N0g)2 = 261-0. T=150''C. m. °21* %■ Si,. hi- S. s. '■o- d. 1/32 1-006718 6 1006719 6 1-006719 12 1-0 11 1/64 1-003381 4 1-003373 4 1-003377 8 1-8 10 1/128 1-001694 4 1-001692 4 1-001693 8 1-8 14 1/256 1-000844 4 1-000827 4 1-000836 8 3-1 17 1/512 1-000424 4 1-000419 4 1-000422 8 2-1 14 1/1024 1-000221 3 1-000217 4 1-000218 7 1-8 13 Table No. 59. BARIUM NITRATE. Ba(N03)2 = 261-0. T = 19-5°C. 1/16 1-013304 6 1-013303 7 1-013302 13 1-4 15 1/32 1-006698 4 1-006695 4 1-006697 8 2-1 17 1/64 1-003370 4 1-003364 3 1-003367 7 3-0 23 1/128 1-001717 4 1-001703 3 1-001710 7 2-3 15 1/256 1-000856 8 1-000856 8 1-000856 16 1-3 17 1/512 1-000430 3 1-000435 4 1-000433 7 2-2 19 1/1024 1-000214 7 1-000196 7 1-000205 14 2-4 23 Table No. 60. LEAD NITRATE. Pb(N03)2= 331-0. T=19-5°C. 1/16 1-017791 3 1-017784 3 1-017788 6 2-8 14 1/32 1-008948 3 1-008946 3 1008947 6 0-2 13 1/64 1-004508 4 1-004502 3 1-004504 7 2-5 14 1/128 1-002262 3 1-002238 3 1-002250 6 6-4 40 1/256 1-001134 3 1-001123 4 1-001128 7 1-8 11 1/512 1-000589 4 1-000564 4 1-000577 8 3-8 24 1/1024 1-000305 4 1-000293 3 1-000300 7 2-1 13 Table No. 61. POTASSIUM NITRATE. KNO3=101-l. T=15-0°C. 1/2 1-030857 2 1-030891 2 1-030874 4 11-6 49 1/4 1-015701* 3* 1-015698 2 1-015700 5 1-5 7 1/8 1-007971* 3* 1-007977 3 1-007974 6 1-7 12 1/16 1-003970 4 1-003962 4 1-003966 8 1 6 13 1/32 1-001980 4 1-001968 4 1-001974 8 1-9 15 1/64 1-000989 4 1-000982 4 1 -000985 8 1-6 12 1/128 1000494 4 1-000487 4 1-000490 8 1-6 10 * These observations were made with Hydrometer No. 3. 80 MR J. Y. BUCHANAN ON THE 28. C. Tables giving a Summary of the Specific Gravities of the Solutions of different' Salts at different Temperatures. CHLORIDES, BROMIDES, AND IODIDES. Table No. 62. CHLORIDES. MCI. M = Na. K. K. Kb. Cs, K. Kb. Cs. T = 15-0° C. 19-5°C. 23-0° C. m. Specific Gravity. Specific Gravitj Specific Gravitj 1/2 r020564 1-023167 1-022977 1-043144 1-062572 1/4 1-010433 1-011900 1-011670 1-021868 1-031739 1/8 1/16 1-005258 1-005912 1-005889 1-011023 1-015994 1-002650 1-002972 1-002973 1-005531 1-008036 1-002924 1-005485 1-007954 1/32 1-001322 1-001487 1-001489 1-002772 1-004035 1/64 1-000655 1-000716 1-000741 1-001400 1-00:^027 1/128 1-000322 1-000365 1-000365 1-000707 1-001025 1/256 1-000193 1-000350 1-000514 1/512 1-000082 1-000163 1-000249 Table No. 63. BROMIDES. MBr. M = K Rb. Cs. K. Rb, Cs. T= 19-5° C. 23-0° C. m. Speoific_Gravity. Specific Gravity. 1/2 1-041278 1-061247 1-080935 1/4 1-020903 1-031081 1-041011 1/8 1-010528 1-015669 1-020702 1-015740 1-020672 1/16 1-005279 1-007868 1-010409 1-005306 1-007895 1-010386 1/32 1-002638 1-003945 1-005182 1-003993 1-005246 1/64 1-001306 1-001957 1-002631 1-001968 1-002634 1/128 1-000652 1-000984 l-00r270 1-000986 1-001332 1/256 1-000325 1-000457 1-000607 1/512 1-000158 1-000233 1-000308 1/1024 1000079 1-000145 Table No. 64. IODIDES. MI. M = K. Rb. Cs. K. Kb. Cs. Cs. T = 19-5° 0. 23-0'' C. 26-0° C. m. Specific Gravity 3pecific Gravity Specific Gravity. 1/2 1-058929 1-078421 1-097427 1-058639 14 1-029906 1-039778 1-049480 1-029717 18 1-015104 1-020010 1-024973 1-014990 1-020075 1-025081 1/16 1-007588 1-010046 1-012529 1-007544 1-010092 1-012637 1-012623 1/32 1-003790 1-005030 1-006299 1-003761 1-005043 1-006341 1/64 1-001899 1-002505 1-003120 1-001919 1-002555 1-003163 1/128 1-000950 1-0U1237 1 1-001546 1-000950 1-001277 1-001596 1/256 1-000480 1-000612 1-000738 1-000497 1-000653 1-000814 1/512 1-000235 1-000272 1-000272 I 1/1024 1-000122 1-000146 1-000100 SPECIFIC GRAVITY AJSID DISPLACEMENT OF SOME SALINE SOLUTIONS. 81 C. Tables giving a Summary of the Specific Gravities of the Solutions of different Salts at different Temperatures. Table No. 65. NITRATES. M'NO, and M"(NO^)^. M' orM'^= . Na. K. Sr". Ba". Li. Na. Ba". Pb". Rb. Cs. T = 15-0° C. IQ-S-G. 23-0° C. m. Specifio Gravity. Specific Gravity. Specific Gravity. 1/2 1-030874 1-019707 1-027810 1/4 1-015700 1-010033 1-014123 1-025590 1/8 1-007974 1-005031 1-007119 1-013065 1-017943 1/16 1-003453 1-003966 1-002548 1-003588 1-013302 1-017788 1-006584 1-009035 1/32 1-001715 1-001974 1-005344 1-006719 1-001290 1-001802 1-006697 1-008947 1-003354 1-004536 1/64 1-000863 1-000985 1-002673 1-003377 1-000654 1-000900 1-003367 1-004504 1-001731 1-002288 1/128 1-000431 1-000490 1-001351 1-001693 1-000336 1-001710 1-002250 1-000955 1-001186 1/256 1-000666 1-000836 1-000856 1-001128 1-000404 1-000580 1/512 1-000329 1-000422 1-000433 1-000577 1/1024 1-000218 1-000205 1-000300 Table No. 66. TRIADS OF NITRATES, CHLORATES, BROMATES, AND lODATES. MRO3. R03= NO3. CIO,. BrOj. IO3. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. T= 19-5° C. 19-5° 0. and gS-0° 0. 19-5° C. a.ndSS-0'G. 1 19-5° 0. and ^5-0°C. m. Specific Gravity. Specifio Gravity. Specific Gravity. Specific Gravity, 1/2 1-030564 1-050634 1/4 1-015533 1-025698 1-035619 1-019081 1-029153 1-039043 1-030144 1-044302 1/8 1-007873 1-012973 1-017961 1-009638 1-014679 1-019686 1-015227 1-022327 1/16 1-003968 1-006597 1-009041 1-004863 1-007356 1-009825 1-007662 1-010255 1-012756 1-011169 1-013677 1016299 1/32 1-C02013 1-003355 1-004585 1-002490 1-003691 1-004953 1-003846 1-005123 1-006377 1-005589 1-006856 1-008142 1/64 1-001004 1-001750 1-002247 1-001253 1-001863 1-002409 1-001921 1-002566 1-003211 1-002760 1-003405 1-004023 1/128 1-000509 1-000920 1-001146 1-000633 1000919 1-001216 1-000958 1-001260 1-001617 1-001403 1-001690 1-001948 1/256 1-000458 1-000604 1-000320 1-000459 1-000552 1-000476 1-000642 1-000784 1-000709 1-000827 1-000930 1/512 1-000182 1-000218 1-000210 1-000237 1000320 1-000375 1-000361 1-000436 1-000449 1/16 1-004759 1-007S31 1-009886 1-007B68 1-010162 1-01S759 1-011147 1-013625 1016226 TRANS. ROY. SOC. EDIN., VOL. XLIX. PART I. (NO. 1). 11 82 MR J. Y. BUCHANAN ON THE C. Tablks giving a Summary of the Specific Gravities of the Solutions of diiferent Salts at different Temperatures. POTASSIUM, RUBIDIUM, AND CESIUM SALTS. Table No. 67. POTASSIUM SALTS. KR and KRO, Ror R03= CI. NO3. CI. Br. I. NO3. CIO3. BrO,. IO3. CI. 1 Br. ! I. 1 1 OIO3. BrOj. IO3. T- 15-0° C. 19-5° C. 23 -O" 0. m. Specific Gravity. ."Specific Gravity. Specific Gravity. 1/2 1-023167 1-030874 1-022977 1-0412781-058929 1-030564 1-058639 1/4 1-011900 1-015700 1-011670 l-020903il -029906 1-015533 1-019081 1-030144 1-044302 1-029717 1/8 1-005912 1-007974 1-005889 1-010528 1-015104 1-007873 1-009638 1-015227 1-022327 1-014990 1/16 1-002972 1-003966,1-002973 1-005279 1-007588 1-003968 1-004863 1-007662 1011169 1-002924 1-005306 1-007544 1-004759 1-007568 1-011147 1/32 1-001487 1-001974 1-0014891-002638 1-003790 1-002013 1-002490 1-003846 1-005589 1-003761 1/64 1-000716 1-000985 1-000741 1-001306 1-001899 1-001004'1-001253'1-001921 1-002760 11-001919 1/128 1-000365 1-000490 1-000365 1-000652 1-000950 1 -000509, 1 -000633' 1 -000958 1-001403 1-000950 1/256 1-000193 1-000325 1-000480 1-000320,1-000476 1-000709 1-000497 1/512 1-000082 l-000158jl-000235 1-0001821-000237 1-000361 1/1024 1-000122 Table No. 68. RUBIDIUM SALTS. RbR and RbROg Ror R03 = CI. Br. I. NO3. OIO3. BrOs. IO3. CI. Br. 1 I. NO3. CIO3. B1O3. IO3. T = 19-5° C. 23-0° C. m. Specific Gravity. Specific Gravity. 1/2 1-043144 1-061247 1-078421 1-050634 1/4 1-021868 1-031081 1-039778 1-025698 1-029153 1-025590 1/8 1-011023 1-015669 1-020010 1-012973 1014679 1-015740 1-020075 1-013065 1/16 1-005531 1-007868 1-010046 1-006597 1-007356 1-010255 1-013677 1-005485 1-007895 1-010092 1-006584 ] -007331 1-010162 1-013625 1/32 1-002772 1-003945 1-005030 1-003355 1-003691 1-005123 1-006856 1-003993 1-005043 1-003354 1/64 1-001400 1-001957 1-002505 1-001750 1-001863 1-002566 1-003405 1-001968 1-002555 1-001731 1/128 1-000707 1-000984 1-001237 1 -000920 1-000919 1-001260 1-001690 1-000986 1-001277 1-000955 1/256 1-000360 1-000457 1-000612 1-000458 1-000459 1-000642 1-000827 1-000653 1-000404 1/512 1-000163 1-000233 1-000272 1-000218 1-000320 1-000436 1/1024 1-000079 1-000146 Table No. 69. CESIUM SALTS. CsR and CsROg. Ror R03 = CI. Br. I. NO3. CIO3. BrOj. IO3. CI. Br. I. NO3. CIO3. BrOj. IO3. I. T = 19-5° C. 23-0° C. 26-0" C. m. Specific Gravity. Specific Gravity. Specific Gravity. 1/2 1-062572 1-0809351-097427 1 1/4 1-031739 1-041011 1 -049480 1-035619:1-039043 1/8 1-015994 1-0207021 -024973 1-017961 1-019686 1-020672 1-025081 1-017943 1/16 L -008036 1-0104091 -012529 1-009041 1-009825 1-012756 1-016299 1-007954 1-010386 1-012637 1-009035 100988 31-01275! n -016226 1-012623 1/32 1 -004035 1-005182 1 -006299 1-004585 1-004953 1-006377 1-008142 1-005246 1-006341 1-004536 1/64 1-002027 1-002631 1 -003120 1-002247 1-002409 1-003211 1-004023 1-002634 1-003163 1-002288 1/128 1-001025 1-0012701 -001546 1-001146 1-001216 1-001617 1-001948 1-001332 1-001596,1-001186 1/256 1-000514 1 -000607 1 -000738 1-000604 1-000552 1-000784 1-000930 1-000814 1-000580 1/512 1-000249 1-0003081 -000272 1-000210 1-000375 1-000449 1/1024 1-0001451 -000100 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 83 C. Tables giving a Summary of the Specific Gravities of the Solutions of different Salts at different Temperatures. Table No, 70. The Ennbad, MR: -CHLORIDES, BROMIDES, AND IODIDES OF POTASSIUM, RUBIDIUM, AND CAESIUM. M = K. Rb. Cs. M = K. Rb. Cs. 1 T = 19-5° 0. T = 19-5° 0. m. 1/2 R. CI Br I S 1-022977 1-041278 1-058929 peoifio Gravity 1-043144 1-061247 1-078421 1-062572 1-080935 1-097427 m. 1/64 R. CI Br I Specific Gravity. 1-000741 1-001400 1-002027 1-001306 1-001957 1-002631 1-001899 1-002505 1-003120 1/4 CI Br I 1-011670 1-020903 1-029906 1-021868 1-031081 1-039778 1-031739 1-041011 1-049480 1/128 CI Br I 1-000365 1-000652 1-000950 1-000707 1-000984 1-001237 1-001025 1-001270 1 001546 1/8 CI Br I 1-005889 1-010528 1-015104 1-011023 1-015669 1-020010 1-015994 1-020702 1-024973 1/256 CI Br I 1-000193 1-000325 1-000480 1-000350 1-000457 1-000612 1-000514 1-000607 1-000738 1/16 CI Br I 1-002973 1-005279 1-007588 1-005531 1-007868 1-010046 1-008036 1-010409 1-012529 1/512 CI Br I 1-000082 1-000158 1-000235 1-000163 1-000233 1-000272 1-000249 1-000308 1-000272 1/32 CI Br I 1-001489 1-002638 1-003790 1-002772 1-003945 1-005030 1-004035 1-005182 1-006299 1/1024 CI Br I 1-000122 1-000079 1-000146 1-000145 1-000100 Table No. 71. The Ennead, MRO3 :— CHLORATES, BROMATES, AND lODATES OF POTASSIUM, RUBIDIUM, AND CESIUM. M = K. Rb. Cs. K. Rb. Cs. T= 19-5° 0. 23-0° C. m. RO3. Specific Gravity. Specific Gravity. 1/4 CIO3 Br03 IO3 1-019081 1-030144 1-044302 1-029153 1-039043 1/8 ClOg BrO, 10/ 1-009638 1-015227 1-022327 1-014679 1-019686 1/16 CIO3 1-004863 1-007356 1-009825 1-004759 1-007331 1-0098B6 Br03 1-007662 1-010255 1-012756 1-007568 1-010162 1-012759 IO3 1-011169 1-013677 1-016299 1-011147 1-013625 1-016226 1/32 CIO3 1-002490 1-003691 1-004953 Br03 1-003846 1-005123 1-006377 10, 1-005589 1-006856 1-008142 1/64 CIO3 1-001253 1-001863 1-002409 BrOg 1-001921 1-002566 1-003211 IO3' 1-002760 1-003405 1-004023 1/128 CIO3 1-000633 1-000919 1-001216 BrOg 1-000958 1-001260 1-001617 10,- 1001403 1-001690 1-001948 1/256 CIO3 1-000320 1-000459 1-000552 BrOg 1-000476 1-000642 1-000784 10, 1-000709 1-000827 1-000930 1/512 CIO3 1-000182 1-000218 1-000210 BrOj, 1-000237 1-000320 1-000375 IO3 1-000361 1-000436 1-000449 84 MR J. Y. BUCHANAN ON THE 29. D. Tables giving a Summary of the Increments of Displacement, v, caused by the Dissolution of m grm.-mol. Salt in 1000 grams Water at different Temperatures. i; = A-1000. CHLORIDES, BROMIDES, AND IODIDES. Table No. 72. CHLOEIDES. MCI. M = Na. K. K. Rb. Cs. K. Rb. Cs. T = 15-0° C, 19-5° C. 23-0° (J. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 8-510 4-148 2-043 1-003 0-505 0-259 0-135 13-813 6-671 3-393 1-685 0-842 0-449 0-218 14-001 6-899 3-416 1-684 0-841 0-423 0-217 0-098 0-064 16-637 8-202 4-057 2-020 1-006 0-489 0-238 0-122 0-073 20-401 10-066 4-989 2-475 1-225 0-604 0-291 0-144 0-079 1-733 V. 2-066 V. 2-557 Table No. 73. BEOMIDES. MBr. M = K. Eb. Cs. K. Rb. Cs. T = 19-5° G. 23-0° 0. m. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 V. 17-547 8-690 4-314 2-153 1-081 0-554 0-278 0-139 0-074 20-262 9-983 4-941 2-456 1-222 0-627 0-308 0-189 0-090 0-082 23-650 11-756 5-802 2-873 1-466 0-695 0-393 0-224 0-108 0-063 V. 2-126 V. 4-870 2-429 1174 0-616 0-306 V. 5-832 2-896 1-403 0-692 0-331 Table No. 74. IODIDES. MI. M = K. Rb. Cs. K. Rb. Cs. Cs. T= 19-5° 0. 23-0°C. 26-0° C. m. V. ■I). V. V. V, ■(/. V. 1/2 22-778 25-805 29-681 23-05K 1/4 11-281 12-836 14-788 11-467 1/8 5-574 6-424 7-343 5-687 6-360 7-237 1/16 2-772 3-203 3-675 2-816 3-157 3-608 3-582 1/32 1-395 1-602 1-814 1-424 1-589 1-772 1/64 0-695 0813 0-939 0-675 0-763 0-896 1/128 0-347 0-422 0-484 0-347 0-382 0-434 1/256 0-168 0-218 0-277 0-152 0-176 0-201 1/512 0-089 0-143 0-235 1/1024 0-040 0-061 0-153 SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 85 D. Tables giving a Summary of the Increments of Displacement, v, caused by the Dissolution of in grm.-mol. Salt in 1000 grams Water at different Temperatures. 'y = A-1000. Table No. 75. NITEATES. M'NOg and M"(N03)2. M'or M" = Na. K. Sr"- Ba". Li. Na. Ba". Pb". Kb. Os. T= - 15-0° 0. 19-5° 0. 23-0° C. m. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 I/512.__ 1/1024 V. 1-852 0-939 0-464 0-232 19-087 9-427 4-623 2-343 1-183 0-594 0-299 V. 1-261 0-631 0-302 0-160 0-084 0. 1-427 0-699 0-345 0-183 0-088 0-036 14-507 7-145 3-565 1-759 0-864 0-423 0-203 14-292 7-027 3-480 1-718 0-852 0-427 V. 2-971 1-449 0-708 0-328 0163 0-076 0-049 2-849 1-384 0-664 0-335 0-165 0-069 0-023 V. 11-003 5-303 2-617 1-251 0-573 0-197 0-172 V. 6-318 3-124 1-550 0-757 0-337 0-181 Table No. 76. TRIADS OF NITRATES, CHLORATES, BROMATES, AND lODATES. MROg. m,= NO3. OIO3. BrOj. IO3. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. T= ,, 19-5° 0. 19-5° C. and ^5 O'C. 19-5° 0. and 25-0° C. 19-5° C. and 25-0° C. m. V. V. ■u. V. V. '0. V. V. V. V. V. V. 1/2 19-410 22-002 1/4 9-593 10-897 12-679 11-352 12-726 14-515 11-290 8-832 1/8 4-727 5-394 6-301 5-632 6-353 7-233 5-576 4-339 1/16 2-342 2-604 3-118 2-785 3-183 3-669 2-761 3-057 3-511 2-189 2-576 2-903 1/32 1-144 1-250 1-501 1-337 1-584 1-804 1-370 1-541 1-767 1-096 1-276 1-471 1/64 0-575 0-553 0-798 0-661 0-775 0-971 0-688 0-767 0-864 0-584 0-661 0-786 1/128 0-281 0-232 0-376 0-324 0-400 0-476 0-347 0-407 0-421 0-269 0-344 0-457 1/256 0-118 0-157 0-158 0-200 0-292 0-176 0-191 0-235 0-127 0-190 0-272 1/512 0-057 0-111 0-212 0-089 0-096 0-134 0-0.^7' 0-072 0-152 1/16 2-889 S-SOi 3-609 2-854 3149 3-S08 2-210 2-618 2-976 86 MR J. Y. BUCHANAN ON THE D. Tablks giving a Summary of the Increments of Displacement, v, caused by the Dissolution of m grm.-mol. Salt in 1000 grams Water at different Temperatures. u = A-lOOO. POTASSIUM, RUBIDIUM, AND CESIUM SALTS. Table No. 77. POTASSIUM SALTS. KK and KKO, Ror R03 = T = CI. NO3. CI. Br. I. NO3. GIO3. 1 BrOj. IO3. CI. Br. I. CIO3. BrOj. IO3. 15-0° C. 19-5° C. 23-0°C. m. V. V. V. V. V. V. ■u. V. V. V. V. V. V. V. V. 1/2 13-813 19-087 14-001 17-547 22-778 19-410 23-058 1/4 6-671 9-427 6-899 8-690 11-281 9-593 11-352 11-290 8-832 ' 11-467 1/8 3-393 4-623 3-416 4-314 5-574 4-727 5-632 5-576 4-339 I 5-687 1/16 1-685 2-343 1-684 2-153 2-772 2-342 2-785 2-761 2-189' 1-733 2126 2-816 2-889 2-854 2-210 1/32 0-842 1-183 0-841 1-081 1-395 1-144 1-337 1-370 1-096 1-424 1/64 0-449 0-594 0-423 0-554 0-695 0575 0-661 0-688 0-584 0-675 1/128 0-218 0-299 0-217 0-278 0-347 0-281 0-324 0-347 0-269 0-347 1/256 0-098 0-139 0-168 0-158 0-176 0-127 0-152 1/512 0-064 0-074 0-089 0-057 0-089 0-057 1/1024 0-040 Table No. 78. EUBIDIUM SALTS. KbR and EbEOj. Ror R03 = CI. Br. I. NO3. ClOj. Br03. IO3. CI. Br. I. NO3. CIO3. BrOj. IO3. T= 19-5° C. 23-0° C. m. V. V. V. v. V. V. v. ■V. V. V. V. V. V. V. 1/2 16-637 20-262 25-805 22-002 1/4 8-202 9-983 12-836 ,10-897 12-726 11-003 1/8 4-057 4-941 6-424 ' 5-394 6-353 4-870 6-360 5-303 1/16 2-020 2-456 3-203 2-604 3-183 3057 2-576 2-066 2-429 3-157 2-617 3-204 3-149 2-618 1/32 1-006 1-222 1-602 1-250 1-584 1-541 1-276 1-174 1-589 1-251 1/64 0-489 0-627 0-813 0-5.53 0-775 0-767 0-661 0-616 0-763 0-573 1/128 0-238 0-308 0-422 0-232 0400 0-407 0-344 0-306 0-382 0-197 1/256 0-122 0-189 0-218 1 0-118 0-200 0-191 0-190 0-176 0-172 1/512 0-073 0090 0-143 ; 0-111 0-096 0-072 1/1024 0-082 0-061 Table No. 79. CESIUM SALTS. CsR and CsEO, Ror R0.,= T = m. CI. Br. I. ' NO3. CIO3. BrOj. IO3. 01. Br. I. NO3. CIO3. BrOj. IO3. Csl. 19 -6° G. 23-0°C. 26-0° C. V. V. V. V. V. V, V. V. V. V. ; V. V. v. V. V. 1/2 20-401 23-650 29-681 1/4 10-066 11-756 14-788 12-679:14-515 1/8 4-989 5-802 7-343 6-301 i 7-233 5-832 7-237 6-318 1/16 2-475 2-873 3-675 3-118 3-669 3-511 2-903 2-557 2-896 3-608 3-124 3-609 3-508 2-976 3-582 1/32 1-225 1-466 1-814 1-501 1-804 1-767 1-471 1-403 1-772 1-550 1/64 0-604 0-695 0-939 0-798 0-971 0-864 0-786 0-692 0-896 ! 0-757 1/128 0-291 0-393 0-484 0-376 0-476 0-421 0-457 0-331 0-434 0-337 1/256 0-144 0-224 0-277 0-157 0-292 0-235 0-272 0-201 0-181 1/512 0-079 0-108 0-235 0-212 0-134 0-152 1/1024 0-063 0-153 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 87 D. Table giving a Summary of the Increments of Displacement, v, caused by the Dissolution of m grm.-mol. Salt in 1000 grams Water at different Temperatures. v= A -1000. Table No. 80. The Ennbad, MR :— CHLORIDES, BROMIDES, AND IODIDES OF POTASSIUM, RUBIDIUM, AND CESIUM. M = K. Kb. Cs. K. Kb. Cs. T = 19-5° C. 23-0° 0. m. 1/2 R. CI Br I 14-001 17-547 22-778 16-637 20-262 25-805 20-401 23-650 29-681 V. 23-058 0. V. 1/4 CI Br I 6-899 8-690 11-281 8-202 9-983 12-836 10-066 11-766 14-788 11-467 1/8 CI Br I 3-416 4-314 5-574 4-057 4-941 6-424 4-989 5-802 7-343 5-687 4-870 6-360 5-832 7-237 1/16 CI Br I 1-684 2-153 2-772 2-020 2-456 3-203 2-475 2-873 3-675 1-733 2-126 2-816 2-066 2-429 3-157 2-557 2-896 3-608 1/32 CI Br I 0-841 1-081 1-395 1-006 1-222 1-602 1-225 1-466 1-814 1-424 1-174 1-589 1-403 1-772 1/64 CI Br I 0-423 0-554 0-695 0-489 0-627 0-813 0-604 0-695 0-939 0-675 0-616 0-763 0-692 0-896 1/128 CI Br I 0-217 0-278 0-347 0-238 0-308 0-422 0-291 0-393 0-484 0-347 0-306 0-382 0-331 0-434 1/256 CI Br I 0-098 0-139 0-168 0-122 0-189 0-218 0-144 0-224 0-277 0-152 0-176 0201 1/512 CI Bi- I 0-064 0-074 0-089 0073 0-090 0-143 0-079 0-108 0-235 1/1024 CI Br I 0-040 0-082 0-061 0-063 0-153 88 MR J. Y. BUCHANAN ON THE D. Table giving a Summary of the Increments of Displacement, v, caused by the Dissolution of m grm.-mol. Salt in 1000 grams Water at different Temperatures. 1; = A- 1000. Table No. 81. The Ennbad, MRO3 :— CHLORATES, BROMATES, AND lODATES OF POTASSIUM, RUBIDIUM, AND CESIUM. M = K. Rb. Cs. K. Rb. Cs. T = 19-5° C. 23-0° C. m. 1/4 RO3. CIO3 BrOo 11-352 11-290 8-832 12-726 14-515 V. f. ■f. 1/8 CIO3 Br03 IO3 0-632 5-576 4-339 6-353 7-233 1/16 CIO3 BrO„ 103^ 2-785 2-761 2-189 3-183 3-057 2-576 3-669 3-511 2-903 2-889 2-854 2-210 3-204 3-149 2-618 3-609 3-508 2-976 1/32 CIO3 Br03 IO3 1-337 1-370 1-096 1-584 1-541 1-276 1-804 1-767 1-471 1/64 CIO3 BrOg IO3 0-661 0-688 0-584 0-775 0-767 0-661 0-971 0-864 0-786 1/128 CIO3 BrOg IO3 0-324 0-347 0-269 0-400 0-407 0-344 0-476 0-421 0-457 1/256 CIO3 BrOa IO3 0-158 0-176 0-127 0-200 0-191 0-190 0-292 0-235 0-272 1/512 CIO3 BrOg IO3 0-057 0-089 0-057 0-111 0-096 0-072 0-212 0-134 0-152 1 I SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 89 30. E. Tables giving the Values of v/m, that is, the Mean Increments of Dis- placement (Tables D), calculated for the Dissolution of 1 grm.-mol. Salt in 1000 grams Water at different Temperatures. CHLORIDES, BROMIDES, AND IODIDES. Table No. 82. CHLOEIDES. MCI. M = Na. K. E. Rb. Cs. E. Rb. Cs. T = 15-0 °C. 19-6° C. 23-0°C. m. ■u/m. vim. vim. vim. vim. vim. vim. vim. 1/2 17-02 27-63 28-00 33-27 40-80 1/4 16-59 26-68 27-59 32-80 40-26 1/8 16-34 27-14 27-26 32-45 39-91 1/16 16-05 26-96 26-95 32-32 39-60 27-72 33-06 40-91 1/32 16-17 26-97 26-92 32-20 39-22 1/64 16-69 28-75 27-12 31-34 38-70 1/128 17-31 27-92 27-86 30-54 37-24 1/256 25-21 31-46 36-94 1/512 32-77 37-47 40-85 Table No. 83. BROMIDES. MBr. M= K. Rb. Cs. K. Rb. Cs. T= 19-5° C. 23-0° C. m. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 vim. 35-09 34-76 34-51 34-45 34-79 35-45 1 35-64 i 35-76 38-14 vim. 40-52 39-93 39-52 39-30 39-10 4017 39 51 48-46 46-18 84-48 «/m. 47-30 47-02 46-42 45-97 46-93 44-49 50-38 57-54 55-29 64-51 vim. 34-01 vim. 38-96 38-87 37-67 39-44 39-27 vim. 46-66 46-33 44-89 44-28 42-47 Table No. 84. IODIDES. ML M = K. Rb. Cs. K. Rb. Cs. Cs. T= 19-S°C. 23-0°C. 26-0°C. m. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 vim. 45-55 45-12 44-59 44-25 44-65 44-58 44-45 43-18 45-61 41-16 vim. 51-71 51-34 51-39 51-24 51-28 52-04 54-09 55-80 73-21 62-97 vim. 59-36 59-15 58-74 58-80 58-06 60-12 6200 71-01 120-67 157-49 v/m. 46-11 45-86 45-50 45-06 45-57 43-20 44-50 39-91 vim. 50-88 50-51 50-86 48-87 48-97 45-23 vim. 57-89 57-73 56-72 57-39 55-62 51-68 vim. 57-32 TKANS. ROY. SOC. EDIN., VOL. XLIX. PART I. (NO. 1). 12 90 MR J. Y. BUCHANAN ON THE E. Tables giving the Values of vjin, that is, the Mean Increments of Displacement (Tables D), calculated for the Dissolution of 1 grm.-mol. Salt in 1000 grams Water at different Temperatures. Tablb No. 85. NITRATES. M'NOs or M"(N03)2. M'or M"= Na. K. Sr". Ba". Li. Na. Ba". Pb". Eb. C8. T= 15-0° C. 19-5° C. 23-0° C. m. 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 ■w/m. 29-64 30-05 29-71 29-79 v/ni. 38-17 37-71 36-98 37-49 37-85 38-02 38-38 v/m. 40-37 40-42 38-66 41-08 43-05 v/m. 45-69 44-74 44-16 47-07 45-05 37-37 v/m. 29-01 28-58 28-52 28-15 27-66 27-10 25-98 v/m. 28-58 28-11 27-84 27-48 27-28 27-34 v/m. 47-53 46-39 45-34 41-99 41-72 39-11 50-89 v/m. 45-58 44-31 42-53 41-59 42-29 35-78 23-55 vjm. 44-01 42-42 41-88 4004 36-69 25-26 43-94 v/m. 50-54 49-98 49-62 48-43 43-13 46-51 Tablb No. 86. TEIAD8 OF NITRATES, CHLORATES, BROMATES, AND lODATES. MRO3. R03 = NO3. CIO3. BrOj. IO3. M = K. Eb. Cs. K. Eb. Cs. K. Eb. Cs. K. Eb. Cs. T = 19-5° C. 19-5° C. and S3 0°C. 19-5= C. and S3-0° C. 19-5° C. andSS-0°G. m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. 1/2 38-82 44-00 1/4 38-37 43-59 50-71 45-40 50-90 58-06 45-16 35-33 1/8 37-81 43-15 50-41 45-06 50-82 57-86 44-61 34-71 1/16 37-48 41-67 49-89 44-57 50-93 58-71 44-17 48-91 56-69 35-02 41-22 46-45 1/32 36-62 40-05 48-04 42-80 50-69 57-73 43-86 49-31 56-56 35-16 40-85 47-07 1/64 36-80 35-41 51-09 42-34 49-61 62-17 44-07 49-10 55-32 37-37 42-33 50-32 1/128 35-96 29-73 48-21 41-53 51-26 60-95 44-42 52-09 54-00 36-77 44-07 58-76 1/256 30-25 40-29 40-55 51-37 74-98 45-20 49-04 59-21 32-56 48-69 69-83 1/512 29-63 57-24 108-90 45-67 49-56 68-86 29-23 37-17 77-82 1/16 46-23 61-27 67-76 45-67 60-37 66-13 36-41 41-90 47-6I SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 91 E. Tables giving the Values of i;/m, tliat is, the Mean Increments of Displacement (Tables D), calculated for the Dissolution of 1 grm.-mol. Salt in 1000 grams Water at different Temperatures. POTASSIUM, RUBIDIUM, AND CiESIUM SALTS. Tablb No. 87. POTASSIUM SALTS. KR and KRO,. Ror R03= 01. NOj. CI. Br. I. NO3. CIO3. BrO<,. IO3. 01. Br. I. CIO3. BrOj. IO3. T = 15-0° C. 19-5° C. 23-0° C. m. v/m. v/m. v/m. v/m. vim. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. 1/2 27-63 38-17 28-00 35-09 45-55 38-82 46-11 1/4 26-68 37-71 27-59 34-76 45-12 38-37 45-40 45-16 35-33 45-86 1/8 27-14 36-98 27-26 34-51 4459 37-81 45-06 44-61 34-71 45-50 1/16 26-96 37-49 26-95 34-45 44-25 37-48 44-57 44-17 35-02 27-72 34-01 45-06 46-23 45-67 35-41 1/32 26-97 37-85 26-92 34-79 44-65 36-62 42-80 43-86 35-16 45-57 1/64 28-75 38-02 27-12 35-45 44-58 36-80 42-34 44-07 37-37 43-20 1/128 27-92 38-38 27-86 35-6^ 44-45 35-96 41-53 44-42 36-77 44-50 1/256 25-21 35-76 43-18 40-55 45-20 32-56 39-91 1/512 32-77 38-14 45-61 29-63 45-67 29-23 1/1024 41-16 Table No. 88. RUBIDIUM SALTS. RbR and RbRO, Ror R03 = 01. Br. I. NO3. CIO3. Br03. IO3. 01. Br. I. NO3. CIO3. Bi-03. IO3. T= 19-5° 0. 23-0° 0. m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. 1/2 33-27 40-52 51-71 4400 1/4 32-80 39-93 51-34 43-59 50-90 44-01 1/8 32-45 39-52 51-39 43-15 50-82 38-96 50-88 42-42 1/16 32-32 39-30 51-24 41-67 50-93 48-91 41-22 33-06 38-87 50-51 41-88 51-27 50-37 41-90 1/32 32-20 39-10 51-28 40-05 50-69 49-31 40-85 37-67 50-86 40-04 1/64 31-34 40-17 5204 35-41 49-61 49-10 42-33 39-44 48-87 36-69 1/128 30-54 39-51 54-09 29-73 51-26 52-09 44-07 39-27 48-97 25-26 1/256 31-46 48-46 55-80 30-25 51-37 49-04 48-69 45-23 43-94 1/512 37-47 46-18 73-21 57-24 49-56 3717 1/1024 84-48 62-97 Table No. 89. CESIUM SALTS. CsR and CsROg. Ror R03= 01. Br. I. NO3. CIO3. BrOj. IO3. 01. Br. I. NO3. OIO3. BrOj. IO3. I. T= 19-5" 0. 23-0° 0. 26-0° 0. m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. v/m. 1/2 40-80 47-30 59-36 14 1/8 40-26 47-02 59-15 50-71 58-06 39-91 46-42 58-74 50-41 57-86 46-66 57-89 50-54 1/16 1/32 39-60 45-97 58-80 49-89 58-71 56-69 46-45 40-91 46-33 57-73 49-98 57-75 56-13 47-61 57-32 39-22 46-93 58-06 48-04 57-73 56-56 47-07 44-89 56-72 49-62 1/64 1/128 1/256 1/512 38-70 44-49 60-12 51-09 62-17 55-32 50-32 44-28 57-39 48-43 37-24 50-38 62-00 48-21 60-95 54-00 58-76 42-47 55-62 43-13 36-94 57-54 71-01 40-29 74-98 59-21 69-83 51-68 46-51 40-85 55-29 120-67 108-90 68-86 77-82 1/1024 64-51 157-49 92 MR J. Y. BUCHANAN ON THE E. Table giving the Values of v/m, that is, the Mean Increments of Displacement (Tables D), calculated for the Dissolution of I grm.-mol. Salt in 1000 grams Water at different Temperatures. Table No. 90. The Ennead, MR :— CHLORIDES, BROMIDES, AND IODIDES OF POTASSIUM, RUBIDIUM, AND CESIUM. M = K. Rb. Cs. K. Eb. Cs. T = 19 -5° C. 23-0° C. TO. 1/2 R. CI Br I vim. 28-00 35-09 45-55 vim. 33-27 40-52 51-71 vim. 40-80 47-30 59-36 vjm. 46-11 vim. vim. 1/4 CI Br I 27-59 34-76 45-12 32-80 39-93 51-34 40-26 47-02 59-15 45-86 1/8 CI Br I 27-26 34-51 44-59 32-45 39-52 51-39 39-91 46-42 58-74 45-50 38-96 50-88 46-66 57-89 1/16 CI Br I 26-95 34-45 44-25 32-32 39-30 51-24 39-60 45-97 58-80 27-72 34-01 45-06 33-06 38-87 50-51 40-91 46-33 57-73 1/32 CI Br I 26-92 34-79 44-65 32-20 39-10 51-28 39-22 46-93 58-06 45-57 37-67 50-86 44-89 56-72 1/64 CI Br I 27-12 35-45 44-58 31-34 40-17 52-04 38-70 44-49 60-12 43-20 39-44 48-87 44-28 57-39 1/128 01 Br I 27-86 35-64 44-45 30-54 39-51 54-09 37-24 50-38 62-00 44-50 39-27 48-97 42-47 55-62 1/256 CI Br I 25-21 35-76 43-18 31-46 48-46 55-80 36-94 57-54 71-01 39-91 45-23 51-68 1/512 CI Br I 32-77 38-14 45-61 37-47 46-18 73-21 40-85 55-29 120-67 1/1024 CI Br I 41-16 84-48 62-97 64-51 157-49 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 93 E. Table giving the Values of v/m, that is, the Mean Increments of Displacement (Tables D), calculated for the Dissolution of 1 grm.-mol. Salt in 1000 grams Water at different Temperatures. Table No. 91. The Ennead, MEO3 :— CHLORATES, BROMATES, AND lODATES OF POTASSIUM, RUBIDIUM, AND CiESIUM. M = K. Eb. Cs. K. Rb. Cs. T= 19 -S" C. 23-0° 0, TO. 1/4 RO3. CIO3 BrO, IO3 vim. 45-40 45-16 35-31 ■u/m. 50-90 v/m. 58 06 v/m. v/m. v/m. 1/8 GIO3 Br03 IO3 45-06 44-61 34-71 50-82 57-86 1/16 CIO3 BrO, 44-57 44-17 35-02 50-93 48-91 41-22 58-71 56-69 46-45 46-23 45-67 35-41 51-27 50-37 41-90 57-75 56-13 47-61 1/32 CIO3 Br03 IO3 42-80 43-86 35-16 50-69 49-31 40-85 57-73 56-56 47-07 1/64 CIO3 Br03 IO3 42-34 44-07 37-37 49-61 49-10 42-33 62-17 55-32 50-32 1/128 CIO3 BrOg IO3 41-53 44-42 36-77 51-26 52-09 44-07 6095 5400 58-76 1/256 CIO3 BrOo 40 55 45-20 32-56 51-37 49-04 48-69 74-98 59-21 69-83 1/512 CIO3 BrO, lOs 29-63 45-67 29-23 57-24 49-56 37-17 108-90 68-86 77-82 94 MR J. Y. BUCHANAN ON THE STRONG SOLUTIONS. 31. A. General Tables giving, in the columns under m, W, and S, the Facts of Observation relating to concentrated Solutions of the Salts of the Ennead (K, Rb, Cs, CI, Br, I), the Specific Gravity of which has been determined with the Specific Gravity Bottle or Pyknometer. TRIAD OF CHL0RIDJ:S. Table No. 92. POTASSIUM CHLORIDE. KCl = 74-6. T=19-5°C. m. 1 2 3 4 Weiglit of Solution. Grams. W. 1074-6 1149-2 1223-8 1298-4 Specific Gravity. S. 1-0449 1-0853 1-1222 1-1562 Displacement. Gt. W/S = A. 1028-42 1058-87 1090-52 1122-93 Differences of Displacements. dA. 30-45 31-65 32-41 Differences of Logarithms of Displacements. d log A. ■012672 -012791 -012719 (3-050352) Table No. 93. RUBIDIUM CHLORIDE. RbCI= 121-0 T=19-5'C. 1/2 1 2 3 4 5 6 7 7-5 1060-5 1121-0 1242-0 13630 1484-0 1605-0 1726-0 1847-0 1907-5 1-0426 1017-17 1-0832 1034-89 1-1592 1071-43 1-2283 1109-66 1-2936 1147-18 1-3541 1185-29 1-4084 1225-85 1-4586 1266-28 1-4833 1285-98 17-72 -007503 36-54 -015066 38-23 -015228 37-52 •014442 38-11 -014190 40-56 -014613 40-43 -014092 19-70 -006704 (3-109235) Table No. 94. CJESIUM CHLORIDE. CsCl= 168-5. T=19-5°C. 1/2 1 2 3 4 5 6 7 8 9 1084-25 1168-5 1337-0 1505-5 1674-0 1842-5 2011-0 2179-5 2348-0 2516-5 1-0616 1188 2270 3245 4113 4956 5670 6374 7025 7590 1021-37 1044-39 1089-61 1136-59 1186-06 1231-88 1283-31 1331-03 1378-81 1430-59 23-02 45-22 46-98 49-47 45-82 51-43 47-72 47-78 51-78 (3 009679 018408 018333 018502 016462 017763 015856 015316 016010 155515) SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 95 STRONG SOLUTIONS. A. General Tables giving the Facts of Observation in the columns under m, W, and S. TRIAD OF BROMIDES. Table No. 95. POTASSIUM BROMIDE. KBr = 119-1. T=19-5°C. Weight of Solution. Grams. Specific Gravity. Displacement. G,. Differeuoes of Displacements, Differences of Logarithms of Displacements. m. 1 2 3 4 5 W. 1119-1 1238-2 1357-3 1476-4 1595-5 S. 1-0808 1-1545 1-2220 1-2843 1-3425 W/S = A. 1035-44 1072-49 1110-71 1149-57 1188-16 dA. 37-05 38-22 38-87 38-59 d log A. -015273 -015207 -014932 -014336 (3-074873) Table No. 96. RUBIDIUM BROMIDE. RbBr=165-5. T = 19-5°C. 1/2 1 2 3 4 5 6 1082-75 1165-5 1331-0 1496-5 1662-0 1827-5 1993-0 1-0613 1-1193 1-2281 1-3272 1-4178 1-5009 1-5772 1020-21 1041-26 1083-71 1127-56 1172-23 1217-56 1263-57 21-05 42-45 43-85 44-67 45-33 46-11 -008869 -017353 -017226 -016873 -016477 •016108 (3-101599) Table No. 97. CESIUM BROMIDE. CsBr = 213-0. T = 21-4°C. 1 2 3 4 5 1213-0 1426-0 1639-0 1852-0 2065-0 1-1590 1-3041 1-4326 1-6548 1-6624 1046-54 1093-45 1144-02 1191-10 1242-16 46-91 50-57 47-08 51-06 •019046 •018696 •017495 -018232 (3-094181) 96 MR J. Y. BUCHANAN ON THE STRONG SOLUTIONS. A. General Tables giving the Facts of Observation in the columns under m, W", and S. TRIAD OF IODIDES. Table No. 98. POTASSIUM IODIDE. KI = 166-1. T=19-5° C. Weight of Solution. Specific Displacement. Differences of Differences of Logarithms of Displacements. Grams. Gravity. Gr- Displacements. m. W. S. W/S = A, dA. d log A. 1 2 3 4 5 6 7 8 1166-1 1332-2 1498-3 1664-4 1830-5 1996-6 2162-7 2328-8 1-1146 1-2177 1-3128 1-3982 1-4766 1-5483 1-6141 1-6749 1046-20 1094-03 1141-30 1190-39 1239-67 1289-54 1339-88 1390-54 47-83 47-27 49-09 49-28 49-87 50-34 50^53 -019412 -018371 •018288 -017618 •017129 •016630 •016077 (3^143143) Table No. 99. EUBIDIUM IODIDE. Ebl = 212 -5. T = 19-5°C. 1/2 1 1106-25 1212-5 1-0771 1-1498 1026-99 1054-45 27-46 •011459 2 3 4 5 6 7 1425-0 16375 18500 2062-5 2275-0 2487^5 1-2835 1-4026 1-5102 1-6081 1-6962 1-7705 1110-22 1167-45 1224-93 1282-52 1341-22 1404-94 55-77 57-23 57-48 57-59 58-70 63-72 •022383 •021829 •020873 •019952 •019435 -020157 (3-147657) Table No. 100. CESIUM IODIDE. Csl = 260-C . T=23-r C. 1 1260^0 1-1847 1063-55 2 1520^0 1-3463 1128 96 65^41 •025920 3 1780-0 1-4924 1192-70 63'74 -023852 (3-076531) S-S8B 1880-1 1-5426 1218-76 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 97 STEONa SOLUTIONS. A. General Tables giving the Facts of Observation in the columns under TO, W, and S. Table No. 101. RUBIDIUM NITRATE. RbN03= 147-5. T = 19-5°C. m. 1/2 1 2 3 Weight of Solution. Grams. W. 107375 1147-5 1295-0 1442-5 Specific Gravity. S. 1-0505 1-0982 1-1861 1-2655 Displacement. Gt- W/S = A. 1022-13 1044-89 1091-81 1139-87 Differences of Displacements. (2a. 22-76 46-92 48-06 Differences of Logarithms of Displacements. d log A. -009564 -019077 •018705 (3-056853) Table No. 102. LITHIUM NITRATE. LiNO3 = 69-0. T = 19-5° C. 1 2 3 4 5 6 7 8 9 10 1069-0 1138 1207-0 1276-0 1345-0 1414-0 1483-0 1552-0 1621-0 1690-0 0389 0747 1081 1392 1684 1959 2214 2457 2684 2906 1028-97 1058-90 1089-25 1120-08 1151-14 1182-37 1214-18 1245-88 1277-98 1309-47 29-93 30-35 30-83 30-89 31-23 31-81 31-70 32-10 31-49 (3 012451 012273 012122 011880 011623 011528 011194 011048 010568 117095) Table No. 103. SODIUM NITRATE. NaNO3 = 85-0. T = 19-5°G. 1085-0 1170-0 1255-0 1340-0 1425-0 1510-0 1595-0 1680-0 1765-0 0542 1030 1478 1887 2267 2613 2939 3253 3539 1029-18 1060-72 1093-36 1124-64 1161-63 1197-11 1232-63 1267-57 1303-56 31-54 ■013109 32-64 -013162 31-28 -012250 36-99 -014054 35-48 •013066 35-52 -012698 34-94 -012139 35-99 -012159 (3-115131) TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 13 98 MR J. Y. BUCHANAN ON THE STRONG SOLUTIONS. § 32. Tables of the Classes C, D, and E, giving Summaries of their Specific Gravities (S), their Increments of Displacement, v, and their Mean Increments of Dis- placement per gram-molecule Salt, v/m, respectively. R= CHLORIDES. M = K. Rb. Cs. T = 19-5° C. Table No. 104. C. Specific Gravity. m. S. S. S, 1/2 1-0426 1-0616 1 1-0449 1-0832 1-1188 2 1-0853 1-1592 1-2270 3 1-1222 1-2283 1-3245 4 1-1562 1-2936 1-4113 5 1-3541 1-4956 6 1-4084 1-5670 7 1-4586 1-6374 8 17025 9 1-7590 Table No. 107. D. Licremput of Disiilacei nent. m. ■i). V. V. 1/2 17-17 21 37 1 28-42 34-89 44-39 2 58-87 71-43 89-61 3 90-52 109-66 136-59 4 122-93 147 18 186-06 5 185-29 231-88 6 225-85 283-31 7 266-28 331-03 8 378-81 9 430-59 Table No. 110. E. 1 Wean luerement of Displac gram-molecule. enient per m. vjm. v/m. v/m. 1/2 34-34 42-74 1 28-42 34-89 44-39 2 29-43 35-72 44-80 3 3017 36-55 45-53 4 30-73 36-79 46-51 5 3706 46-37 6 37-64 47-21 7 38-04 47-29 8 47-35 9 47-84 BROMIDES. K. Rb. Cs. 19-5° 0. 21 -4° C. Table No. 105. C. Specific Gravity. S. S. 1-0613 S. 1-0808 1-1193 1-1590 1-1545 1-2281 1-3041 1-2220 1-3272 1-4326 1-2843 1-4178 1-5548 1-3425 1-5009 1-5772 1-6624 Table No. 108. D. Increment of Displacement. V. 20-21 V. 35-44 41-26 46-54 72-49 83-71 93-45 110-71 127-56 144-02 149-57 172-23 191-10 188-16 217-56 263-57 242-16 Table No. 111. E. ilean Increment of Displacement per gram-molecule. vjm. vjm. 40-42 v/m. 35-44 41-26 46-54 36-25 41-85 46-72 36-90 4:2-52 48-00 37-39 43-05 47-77 37-63 43-51 43-92 48-43 IODIDES. K. Rb. 19-5° C. Cs. 23-1° C. Table No. 106. C. Specific Gravity. S. S. 1-0771 •1146 1-1498 -2177 1-2835 -3128 1-4026 -3982 1-5102 -4766 1-6081 -5483 1-6962 -6141 1-7705 •6749 s. 1-1847 1-3463 1-4924 Table No. 109. D. Increment of DLsplacement. 46-20 94-03 141-30 190-39 239-67 289-54 339-88 390-54 26-99 54-45 110-22 167-45 224-93 282-52 341-22 404-94 63-55 128-96 192-70 Table No. 112. E. Mean Increment of Displacement per gram-molecule. v/m. 46-20 47-02 47-10 47-59 47-93 48-26 48-55 48-81 v/m. 53-98 54-45 55-11 55-81 56-23 56-50 56-87 57-84 SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 99 STRONG SOLUTIONS. Tables of the Classes C, D, and E, giving Summaries of their Specific Gravities (S), their Increments of Displacement, v, and their Mean Increments of Displace- ment per gram-molecule Salt, v/m, respectively. POTASSIUM SALTS. KR. RUBIDIUM SALTS. RbR. R= T= CI Br. I. 19-5° C. Table No. 113. C. Specific Gravity. m. S. S. s. 1 1-0449 1-0808 1-1146 2 1-0853 1-1545 1-2177 3 1-1222 1-2220 1-3128 4 1-1562 1-2843 1-3982 5 1-3425 1-4766 6 1-5483 7 1-6141 8 1-6749 Table No. 116. I ). Increment of Displac ement. m. V. V. V. 1 28-42 35-44 46-20 2 58-87 72-49 94-03 3 90-52 110-71 141-30 4 122-93 149-57 190-39 5 188-16 239-67 6 289-54 7 339-88 8 390-54 Table No. 119. E. VLea.li Increment of Dis; per gram-molecule ilacement 771. v/m. v/m. v/m. 1 28-42 35-44 46-20 2 29-43 36-25 47-02 3 30-17 36-90 47-10 4 30-73 37-39 47-59 5 37-63 47-93 6 48-26 7 48-55 8 48-81 - R= T = CI. Br. 19-5° C. Table No. 114. 0. Specific Gravity. m. 1/2 1 2 3 4 5 6 7 7-5 s. -0426 -0832 •1592 •2283 -2936 -3541 -4084 -4586 -4833 s. 1-0613 1-1193 1-2281 1-3272 1-4178 1-5009 1-5772 S. •0771 -1498 -2835 -4026 -5102 •6081 -6962 -7705 Table No. 117. D. Increment of Displacement. 1/2 1 2 3 4 5 6 7 7-5 17-17 34-89 71-43 109-66 147-18 185-29 225-85 266-28 285-98 20-21 41-26 83-71 127-56 172-23 217-56 263-57 26-99 54-45 110-22 167-45 224-93 282-52 341-22 404-94 Table No. 120. Mean Increment of Displacement per gram-molecule. m. v/m. vjm. 1/2 34-34 40-42 1 34-89 41-26 2 35-72 41-85 3 36-55 42-52 4 36-79 43-05 5 37-06 43-51 6 37-64 43-92 7 38-04 7-5 38-13 v/m. 53-98 54^45 55-11 55-81 56-23 56-50 56-87 57-84 CESIUM SALTS. GsR. R= 01. Br. 19-5° C. 21-4° C. 23-1*0. Table No. 115. 0. Sijecific Gravity. m. 1/2 1 2 3 4 5 6 7 S. -0616 -1188 •2270 ■3245 -4113 ■4956 -5670 ■6374 -7025 -7590 S. 1-1590 1-3041 1-4326 1-5548 1-6624 S. 1-1847 1-3463 1-4924 Table No. 118. D. Increment of Displacement. m. 1/2 1 2 3 4 5 6 7 21-37 44-39 89-61 136-59 186-06 231-88 283-31 331-03 378'81 430-59 46-54 93-45 144-02 191-10 242-16 63-55 128-96 192-70 Table No. 121. Mean Increment of Displacement per gram-molecule. m. 1/2 1 2 3 4 5 6 7 v/m. 42-74 44-39 44-80 45-53 46-51 46-37 47-21 47-29 47-35 47-84 v/m. 46-54 46-72 48-00 47-77 48-43 v/m. 63-55 64-48 64-23 100 MR J. Y. BUCHANAN ON THE STEONG SOLUTIONS. Tables of the Classes C, D, and B, giving Summaries of their Specific Gravities (S), their Increments of Displacement, v, and their Mean Increments of Displace- ment per gram-molecule Salt, v/m, respectively. R= NITRATES. M = Li. Na. Rb. T = 19-6° C. Table No. 122. C. Specific Gravity. m. s. s. S. 1/2 1-0505 1 1-0389 1-0542 1-0982 2 1-0747 1-1030 1-1861 3 1-1081 1-1478 1-2655 4 1-1392 1-1887 5 1-1684 1-2267 6 1-1959 1-2613 7 1-2214 1-2939 8 1-2457 1-3253 9 1-2684 1-3539 10 1-2906 NITRATES. Li. Na. Rb. 19-5° C. Table No. 123. D. Increment of Diapl aceraeDt. V. V. V. 22-13 28-97 29-lS 44-89 58-90 60-72 91-81 89-25 93-36 139-87 120-08 124-64 151-14 161-63 182-37 19711 214-18 232-63 245-88 267-57 277-98 303-56 309-47 NITRATES. Li. Na. Rb. 19-5° C. Table No. 124. E. Mean Increment of Displacement per gram-molecule. vim. v/m. v/m. 44-26 28-97 29-18 44-89 29-45 30-36 45-90 29-75 31-12 46-62 3002 31-16 30-23 32-33 30-39 32-85 30-59 33-23 30-73 33-45 30-89 33-73 30-95 Section VI. — General Description op Tables. § 33. In the tables giving the results of the experiments made with solutions of a particular salt, the weights given are those which would have been used if the weighings had actually been made in a vacuum ; and the standard temperature, T, at which all the operations have been made, is given at the top with the name of the salt, both being constants. Of the variables, we have under m the (quantity of the salt, expressed as the number, whole or fractional, of gram-molecules, which is dissolved in 1000 grams of water, under W the weight in grams of the solution so produced, and under S the specific gravity of the solution referred to that of distilled water as unity, both having the standard temperature T. With the exception of the determination of the temperature, the result of every series of operations depends only on determinations of weight, and they are independent of the work of others. Even the tyro has no difficulty in being assured of the true weight of the hydrometer when floating up to the same mark in the solution and in distilled water respectively. The difficulty which requires manipulative skill, laboratory experience, and perseverance to overcome, is to satisfy the condition that the temperatures of the solution and of the distilled water respectively, and that of the SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 101 hydrometer when immersed in them, are identical, and are really the temperature shown by the thermometer, and that this temperature is exactly that chosen as the standard for the series of experiments. It requires much study and practice in a suitable room before even an experienced chemist or physicist can feel confident that he can produce this combination of equalities when required. It is to the failure to perceive the necessity of this preliminary education that, though the method has been the property of science for forty years, it has been used practically by none except myself and those whom I have personally instructed. § 34. In the tables of Class A all the facts of observation are to be found. In all the solutions the quantity of water is the same, namely, 1000 grams ; the quantity of salt dissolved in this mass of water is specified for each solution of the same salt in the first column under m, in terms of the gram-molecule. In the second column, under W, we have the weight in grams of each solution ; it is given by the sum 1000 + m. ME = W ; where MR represents the molecular weight of the salt. The symbol used to express the weight of salt dissolved in 1000 grams of water is w, whence w = m.MR. In the third column, under S, we have the specific gravity of the solution. The experimental data on which it is founded are the weight, H', in grams, of the hydrometer when it floats at a given division of the stem in the solution, and its weight, H, when it floats at the same division in distilled water, both of these liquids having the same temperature, T. The quotient HyH is the specific gravity, S, of the solution, as entered in the third column of the tables. If we divide the weight of the solution, W, by its specific gravity, S, we obtain the displacement of the solution, which is entered in the fourth column under A. It is the expression of the proportion H : H' : : A : W, in which H and A are weights of distilled water, and H' and W are weights of the solution. It may be expressed in words as follows : — The displacement of the solution. A, bears to its weight, W, the same relation as the weight H of distilled water displaced by the hydrometer bears to H', that of the solution displaced by the same portion of the same hydrometer at the same temperature, T. Therefore, the unit of displacement used in the tables is the space occupied by 1 gram of distilled water having the temperature T. Generally, our measure of displacement of a body having the temperature T is the weight of distilled water having the same temperature which the body displaces when totally immersed in the water. The body in question may be solid, liquid, or gaseous. The unit of displacement is then the unit of weight, gram or kilogram, of water having the particular temperature, T, which is chosen tg suit the conditions of the experiment, and it must be the common temperature of the body and the water. Under this convention the unit of displacement is the space occupied by, say, 1 gram water at T, whatever value T may have. Thus, in our experiments the value of T is in some 15°, in some 19 "5°, and in others 23° ; but whichever temperature is used as that of the distilled water, it is also that of the salt or saline solution which is supposed to displace it when its specific gravity is being determined. The use of displacement instead of volume to specify the amount of space occupied by a body is advantageous 102 MR J. Y. BUCHANAN ON THE only when there is a common temperature and it can be accepted as constant. In cases where the temperature is subject to variation, the specification of displacement must be by volume, because a weight is not affected by change of temperature. It is convenient to have a symbol to place after a number in order to indicate that its unit is that of displacement as specified above. It is to be used in cases corresponding to those in which the symbol c.c. is used when we express volumes in cubic centimetres. A suitable symbol for the unit of displacement is Gx or Gt , in which G is the unit of weight and T or ^ is the common temperature of the body and of the water displaced by it. In this research the unit of weight used is the gram, so that our unit of displace- ment expresses the space occupied by 1 gram of water at the temperature T. When the unit of weight used is the kilogram the symbol becomes K^. In naval architecture the displacement of a ship is always expressed in t07is, that is, tons of water of ordinary atmospheric temperature. In this research the units of displacement used are expressed by the symbols G15., Gjg.j., and G^y. If the adopted value of T were 4° C, then the unit of displacement would be G4., and this is the gravimetric symbol for the standard cubic centimetre. In the fifth column we have the values of c^A, the differences of consecutive values of A. The entries in this column have a peculiar interest owing to the fact that the values of m which indicate the concentration of the solutions form an ascending geometrical series with the common ratio 2. The quantity of water, 1000 grams, is the same in all the solutions. If we consider any two consecutive values of A, for instance, A^^ and Aj/^, the increment of displacement produced by dissolving 1/8 MR in 1000 grams of water is A^^- 1000, and the increment produced by dissolving a further quantity of salt equal to 1/8 MR in the solution the displacement of which is A^^g, is cZA = A^,^ — A^^g. These increments of displacement have been produced by equal quantities of the salt, which has been dissolved in the first case in 1000 grams of distilled water, and in the second case in (1/8 MR + 1000) grams of the solution so produced. If the corre- sponding values of (A,^-1000) and (A^^ — A,„) be studied, they will be found to be almost always different. Considering only the first nine tables relating to the salts of the ennead MR, we see that the difference of these increments {\m — ^ir) — (A^— 1000) is positive for values of m = ]/l6 and higher. It changes sign for a value of m lying between 1/16 and 1/32 in the case of KBr, KI, and Rbl ; for m lying between 1/32 and 1/64 in the case of KCl, RbBr, and Csl ; for m lying between 1/64 and 1/128 in the case of CsBr ; for m lying between 1/128 and 1/256 in the case of RbCl; and for m lying between 1/256 and 1/512 in the case of CsCl. The main object with which this experimental research was begun was to ascertain if such a change of sign occurs at any concentration. It was only by using the hydro- metric method that the question could be answered. In the sixth column we have the values qI d log A, the consecutive differences of the log-displacement. The space in this column corresponding to the highest value of m is occupied in brackets by the SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 103 logarithm of the corresponding highest value of A. With this, and the corresponding values of d log A, the log-displacement of each solution can be at once obtained. In Class A there are thirty-seven tables ; of these, twenty -four relate to solutions of chlorides, bromides, iodides, and nitrates of the alkalies and alkaline earths, the specific gravities of which have been determined with two hydrometers. The values of S given for each value of m in each of these tables is the mean of two groups of series of nine observations each, each group being made with a diflFerent hydro- meter. The hydrometers chiefly used were Nos. 17 and 21, and for each value of m either three or four series of observations were made with each of these hydrometers. The mean of each series is the mean of nine independent values of the specific gravity, so that the final mean, 8, is the mean of 72 independent observations when four series have been made with each hydrometer, and the mean of 54 independent observations when three series have been made with each hydrometer. § 35. In the tables of Class B, we have the particulars of the series of observations made with hydrometers 21 and 17 respectively from which the final mean value of S in the table is obtained. In the tables of this class m has the same signification as in those of Class A ; Sai gives the mean specific gravity for the particular value of m derived from % series of observations made with hydrometer No. 21 ; Si? the mean specific gravity similarly obtained from S17 series made with hydrometer No. 17. The final mean derived from s ( = Szi -I- S17), the sum of these series, is found under 8. Under r^ we have the probable error of 8 calculated by the method of least squares, and under d, the maximum departure of the mean of any individual series from the mean specific gravity, 8. Numbers under r^ and d are expressed in units of the sixth decimal place. For each table of Class A referring to specific gravities derived from observations with two hydrometers a corresponding table of Class B has been prepared. In the twenty -four tables of Class B there are 189 entries under S, r^, and d respectively. Summing those under s, we find that the experimental material on which these tables are founded consists of 1227 series, whence the mean number of series of observations per solution is 6 "49. Each series consists of nine individual observations, and when each of them is compared with the corresponding observation made under the same conditions in distilled water, they give a mean per solution of 5 8 "4 independent observations of the ratio of the weight of a given bulk of the saline solution to the same bulk of distilled water, both liquids being at the same temperature. The 1227 series accounted for in the twenty-four tables correspond to 11,043 independent observations of the hydrometric displacement, from each of which the specific gravity of the solution in which the instrument floated is deducible. The sum of the values of r^ in the twenty-four tables is 548'7, which divided by 189 gives ±2"90, in the sixth decimal place, as the mean probable error of the mean specific gravity found for any one of the solutions. We have seen that this depends on a mean of 6 '49 series per solution; therefore, admitting that the probable error 104 MR J. Y. BUCHANAN ON THE varies inversely as the square root of the number of observations, the mean probable error of the mean specific gravity derived from any number of series s is as follows : — s = 1 2 3 4 5 6 7 8 9 + r„ = 7-39 5'22 4-27 3-69 3-30 302 2-79 2-61 2-46 Further, the probable error of the mean of one series being ±7 "39, and each series consisting of nine individual observations, the probable error of a single observation must be 3 x 7'39 = ±22'17 in the sixth place, or ±2-22 in the fifth place. § 36. Following the tables of Class B we have those of Class C, which give a sum- mary of the specific gravities of the solutions of different salts at diff"erent temperatures. The salts included in each table have a common acid or a common base. Thus the first table of the class contains only chlorides, the second only bromides, and so on. These tables furnish the means of comparing the effect of concentration and of the specific nature of the salt dissolved on the specific gravity of the solution. § 37. The specific gravity, S, of one of our solutions expresses the weight in kilograms of the quantity of the solution having the composition m.MR grams of salt plus 1000 grams of water, which exactly displaces 1 kilogram of distilled water having the temperature T. When we compare the specific gravities of the different solutions, we are considering equal volumes of those solutions ; but the proportion between the salt and the water present in this volume of solution is different for different solutions. Therefore the specific gravities of the solutions alone do not offer a simple theme for discussion. The values of W, on the other hand, contain always the constant quantity of water in which the different salts are dissolved in quantities proportional to their molecular weights. It follows, therefore, that the values of (W-1000)=»' are always exactly proportional to the molecular weights of the salts used. If the increments of specific gravity (S- 1) were also proportional to the molecular weight of the salt dissolved, the quotient W/S = A would be constant for all the solutions of the different salts having the same molecular concentration. This is not found to be the case. The increments of specific gravity do not follow the periodic law exactly, although in the nature of things they cannot depart very far from it. But we may consider the specific gravity of a solution from another point of view. Let us consider a kilogram of water having the temperature T ; it fills a certain space which we may call 1 litre (L-r). We propose to make the solution having the con- centration 1/2 KCl-t- 1000 grams of water by dissolving portions of the salt KCl in the water, but removing so much pure water from the litre-fiask as to keep the sum of the volumes of water and salt always equal to the litre. When we have in this way prepared our litre of (1/2 KCI-FIOOO grams water), it weighs 1022'98 grams, and is composed of 36-78 grams KCl and 986-20 grams of water. As we started with 1000 grams of water, we have had to remove 13-8 grams of it in order to make room for the 36-78 grams KCl which have been dissolved. Consequently, in the construction of SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 105 the solution we have replaced water by KCl in the proportion of 2 "6 6 5 grams KCl per gram of water. We have carried out the calculation for the volume of a litre of initial water and final solution. It is much simpler when we take the volume displaced by the weight W of the solution, or A = W/S. For the solution 1/2 KCl +1000 grams water A =1014-001 Gt- We then take 1014"001 grams of water, and we add KCl, removing at the same time pure water so as to preserve the constant displacement 1014*001 Gj. We may imagine that equal small portions of KCl added take possession of the amount of water required to form with it a solution of the concentration (1/2 KCl + 1000 grams water), and that the remainder of the water is uncontaminated. We proceed on this principle with the fractional dissolution of the salt and removal of water so as to keep the displacement constant. When we have removed 14 001 grams of water, we find that we have dissolved 3 7 "3 grams or 1/2 KCl in the 1000 grams of water remaining. But the operation so described is one of substitution. Consequently it is legiti- mate to regard solutions as products of substitution. In fact, the result of the operation is that we have replaced 14 "001 grams of water by 1/2 KCl, so that the substitution has taken place at the rate of 28 "002 grams or 1*555 gram-molecules of water per gram-molecule of KCl. If we turn to Table No. 82, the first table in Class E, we find the first entry in the fourth column is 28 "00 as the value of vjin, or the mean increment of displacement per gram-molecule of KCl in the solution (1/2 KC1+ 1000 grams of water) at 19 "5° C. The tables of Class D give a summary of the Increments of Displacement, v, caused by the dissolution of m grm.-mol. of salt in 1000 grams of water at different temperatures. Here v = A — 1000. The arrangement of the tables in this class is similar to that of Class C. The tables in Class E enable us to see at a glance the comparative volumetric eff"ect of dissolving different quantities of different salts in 1000 grams of water. Each entry in these tables is derived from the corresponding entry, v, in the corre- sponding table of Class D, by increasing it in the proportion m : 1, whence we obtain the values vjin. § 38. In the following table we have solutions of the eighteen salts of the double ennead (MR, MRO3) for which m = l/l6. It gives under w the weight of 1/16 gram-molecule of the salt dissolved in 1000 grams of water ; under S, the specific gravity of this solution at 19'5° C, referred to that of distilled water at the same temperature as unity ; and under v, the increment of displacement caused by dissolv- ing 1/16 gram-molecule of the salt in 1000 grams of water, expressed in grams of distilled water having the temperature 19 "5° C. The solutions are arranged in three groups, each group containing six solutions of salts having the same metallic base (K, Rb, or Cs). These six solutions fall into two groups of three, or triads, the first three being the salts having the general formula MR, TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 14 106 MK J. Y. BUCHANAN ON THE and the second triad those having the general formula MROg. Each triad is entered in the ascending order of the molecular weights of the salts which compose it, and each group of three triads forms the ennead MR or MRO3 respectively. Salt in Solution. Molecular Weight of Salt. Weight of 1/16 grm.-mol. Salt. w. Specific Gravity of Solution of 1/16 grm.-mol. Salt in 1000 grams Water. S. Increment of Displacement iroduoed by the Dis- so ution of w grams Salt in 1000 grams Water. V. KCl 74-6 4-6625 1-002973 1-684 KBr 119-1 7-4437 1-005279 2-153 KI 166-1 10-3812 1-007588 2-772 KClOj 122-6 7-6625 1-004863 2-785 KBrOg 167-1 10-4443 1-007662 2-761 KIO3 2U-1 13-3812 1-011169 2-189 RbCl 121-0 7-5625 1-005531 2-020 RbBr 165-5 10-3437 1-007868 2-456 Rbl 212-5 13-2812 1-010046 3-203 RbClOg 169-0 10-5593 1-007354 3-183 RbBrOj 213-5 13-3412 1-010253 3-057 RblOg 260-5 16-2812 1-013673 2-576 CsCl 168-5 10-5312 1-008036 2-475 CsBr 213-0 13-3125 1-010409 2-873 Csl 260-0 16-2500 1-012529 3-675 CsClOg 216-5 13-5312 1-009825 3-669 CsBrOg 261-0 16-3125 1-012756 3-511 CsIOg 308-0 19-2500 1-016299 2-903 If we consider the increments of displacement, v, produced by the dissolution of 1/16 gram-molecule of each of these salts in 1000 grams of water, we see that, for the salts of the same metal, the values increase from the chloride to the bromide, and from the bromide to the iodide ; and that for the chlorates the values of v are almost identical with those for the iodides ; they diminish from the chlorates to the bromates, and suffer a considerable fall from the bromates to the iodates. There is also a decided fall in the value of V from that of the iodate of potassium or rubidium to that of the chloride of rubidium or caesium respectively. The following diagram, illustrative of the above table, shows graphically, by the heights of the columns, the different increments of displacement produced by the dissolution in 1000 grams of water at 19-5° C. of 1/16 gram-molecule of each salt of the double ennead (MR, MRO3). The columns representing the increment of displacement produced by salts of the ennead MRO3 are shaded. It shows in a very striking manner the regular periodic variation of values of v from ennead to ennead. It is unfortunate that a complete series of solutions of higher concentration of all the salts of the double ennead cannot be obtained, on account of the sparing solubility of the oxyhalides, especially those of rubidium and caesium. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 107 m o IS m si o |2i 3-675 3-669 ^ 3-511 3-203 ^^ $^ 3183 :::i:;-^ ^^^ ^::S-^ ^^^5^^ 3-057 ^:::~; ^i:::^ ^ J fl 2-903 2-873 ^ ^ ^ ^ ^ 2-785 2-772 ^^^^i;^:: ■^^^^^^^ ^^^T^^::; ^~*^*$--^ ^^^^:;:::>*^ ^ 2-761 1 ^ ^ J 2-576 2-475 ^ ^ 2-456 ^ ^ ^ ^ ^ ^ ^ ^ 2-189 ^ ^ ^ ^ ^ ^ 2-153 ^ ^ ^ ^ ^ ^ ^ ^ ^ 2-020 r~t I— 1 5D i^ 1— 1 o ip ip o « ■P lO o o ■p o~~ p 05 io •il< r-H iO oq OS m o 00 M 6 io 00 t—f CO (M CD fM CO r-t CD T-l CD »— < CD CD o I— 1 r-H r-t oq 1— 1 r-< a2 a number of the salts give solutions which conform nearly to the arithmetic law of the first hypothesis. The salts which furnish solutions which conform most closely to this law are those which contain at least one of the elements Li, Cs, or I. In the ennead MR, after the caesium salts and the iodides come some of the rubidium salts and the bromides ; the remainder of the bromides and nearly all the chlorides conform more nearly to the geometric law of the second hypothesis, and some of them may be said to conform exactly to it. § 44. From the equation log A„^ = 0-0172002 x m it follows that A,„ = (i-0404)"'. Therefore, if the solutions of a salt follow strictly the law expressed by our second hypothesis, the general expression for the displacement of a solution containing m.MR in 1 kilogram of water, when the displacement for any particular value of m — for instance, for m = 1 — is Aj, is A^ = Aj"'. 112 MR J. Y. BUCHANAN ON THE When the solution does not follow this law quite exactly, let the displacement for any particular value of m be A^ = Ai ; then the degree in which the solution conforms to the law is indicated by the diiference x—m. In the table, the displacements given in column 6 are calculated on the basis of the second hypothesis. For them, therefore, the relation A^ = Aj™ holds good, and the value of m (column 1) for any solution expresses not only its molecular concentration, but also the exponent of its displacement, that of A^ being taken as unity. The values of the displacement of the solutions in column 4 of the table are arrived at on the basis of our first hypothesis ; consequently any value of A in this column is given by the equation A„, = l-QOO + 0'04to. But none of the solutions dealt with in this memoir follow this law at all concentrations, though some of them approximate to it at high concentrations. It is therefore of use, in order to augment the illustrative value of the table, to determine the exponents of the values of A in column 4 when referred to that of A = 1 -020 for m = 1/2 as 1/2. This has been done, and the results are entered in the following table : — m. X. x-m. m. X. l/m-]/,v. 10 8-495 - 1-505 1/2 1/2 0-00 9 7-76 -1-24 1/4 1/3-98 + 0-02 8 7-00 -1-00 1/8 1/7-943 + 0-057 7 6-23 -0-77 1/16 1/15-873 + 0-127 6 5-43 -0-57 1/32 1/31-706 + 0-294 5 4-60 -0-40 1/64 1/63-412 + 0-588 4 3-75 -0-25 1/128 1/127-52 + 0-480 3 2-86 -0-14 1/256 1/254-06 + 1-940 2 1-94 -0 06 1/512 1/508-90 + 3-100 1 0-99 -0-01 1/2 0-50 O'OO § 45. In the following tables the displacements of most of the solutions have been treated along these lines. In the first four tables we have for the solutions of the salts of the ennead MR the values of x and ai x-m for the strong solutions, and those of X and \jm~\lx for the dilute solutions. For solutions of other salts the tables give only the values of x -m or \\m - l/x, as they are sufficient. The numbers representing the values of x and m for the strong solutions are the numerators of vulgar fractions having unity for common denominator. The numbers representing the values of l/x and 1/m for the weak solutions are the denominators of vulgar fractions having unity for common numerator. The measure of the departure of the displacements of solutions of a particular salt from the geometric law of the second hypothesis is found for the strong solutions in the column headed (x - m). For the weak solutions the corresponding column is headed (ijm-l/x), so that the signs prefixed to the numbers in these columns mean the same thing in both tables :— the + sign means that x>m, the - sign that xn--L JC-Bn+l - -Wn-l) 'v'n+X-v'n = dA' 1>n-l + U.Vn+1 - 1)„-l) = V' dA' - v' 8-250 12-580 4-193 4-170 4-080 6-182 2-OdO 2-057 2-023 3-051 1-017 1-024 0-999 1-531 0-510 0-505 0-494 + 0-090 +0-034 +0-025 +0-011 +0-006 -0-066 +0-009 0768 0-256 0-250 0-244 0-367 0-122 0-089 0-155 0-165 0-082 0-082 0-073 SuB-TABLB v"„+\-v"„ = dA" v' + v_ ,1 dA"-v" 8-411 8-226 + 0-185 4-158 4-068 + 0-090 2-047 2-021 + 0-026 1-019 0-511 0-250 0-103 0-065 1-002 0-491 0-241 0-138 0-073 + 0-017 + 0-020 + 0-009 -0-035 -0-008 Table in. CESIUM CHLORIDE. CsCl= 168-5. T=19-5°C. Sub-table ». Vn+l-V„ = dA A-1000 = j) dA-v 10-335 10066 + 0-269 5-077 4-989 + 0-088 2-514 2-475 0-039 1-250 1-225 + 0-025 0-621 0-604 + 0-017 0-313 0-291 + 0-022 0-147 0-144 + 0-003 0-065 0-079 -0-014 Sub-table b. i{Vn+l - Vn-l) v'n+1 - -B'n = dA' lln-l + M^n+l - ""Jt-l) = '"' dA'-v' 10-126 15 5 5 5 ■412 137 121 005 7-591 2-530 2-525 2-480 3-764 1-255 1-252 1-228 1-871 0-624 0-626 0-620 0-116 +0-045 +0-024 +0-024 +0-008 +0-003 -0-011 0-934 0-311 0-305 0-297 0-460 0-153 0-150 0-147 0-216 0-072 0-068 0-079 Sub-table e. v"n+l-v"n = dA" 2 dA"-v" 10-305 10-096 + -209 5-099 4-997 + 0-102 2-520 2-477 + 0-044 1-251 0-6-23 0-309 0-149 0-070 1-226 0-603 0-294 0-145 0-075 + 0-025 + 0-020 + 0-015 + 0-004 -0-005 124 MR J. Y. BTJOHANAN ON THE Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TEIAD OF BEOMIDES. Table IV. POTASSIUM BROMIDE. KBr= 119-1. T = 19-5°C. 1/4 1-690 1/8 4-314 7 1/16 2-153 6 5 4 3 2 1/32 1/64 1/128 1/256 1/512 1-081 0-554 0-278 0-139 0-074 1 1/1024 Sub-table a. Vn+l-Vn — dA A-1000 = 'D dA~v 8-857 8-690 + 0-167 4-376 4-314 + 0-062 2-161 2-153 + 0-008 1-072 1-081 -0-009 0-5-27 0-554 -0-027 0-276 0-278 -0-002 0-139 0-139 0-000 0-065 0-074 -0-009 Sub-table 'i'n+l - -"n-i 4(fn+l - I'n-l) v'„+i-v'n = dA' ">l-l + M^'i+l - '"n-lj dA' - v' 8-725 13-233 6-537 3-233 1-599 0-803 0-415 0-204 4-411 2-179 1-078 0-533 0-268 0-138 0-068 4-393 2-173- 1-072 0-541 0-269 0-135 0-068 4-332 2-159 1-087 0-546 0-277 0-142 0-074 + 0-061 + 0-014 -0-015 -0-005 -0-008 -0-007 -0-006 Sub-table !-"n+l - v"n = dA" v' + v_ ,, dA" - v" 8-840 8-707 + 0-133 4-384 4-323 + 0-061 2-167 2-156 + 0-011 1-072 0-534 0-273 0-137 0-066 1-084 0-550 0-277 0-140 0-074 -0-012 -0-016 -0-004 -0-003 -0-008 Table V. RUBIDIUM BROMIDE. RbBr = 165-5. T = 19-5°C. Sub-table a. Vn+l -Vn = dA A-1000 = 'i) dA-v 10-279 9-983 + 0-296 5-042 4-941 + 0-101 2-485 2-456 + 0-029 1-234 1-222 + 0-012 0-595 0-627 - 0-032 0-319 0-308 + 0-011 0-119 0-189 -0-070 0-099 0-090 + 0-009 0-008 0-082 -0-074 Sub-table Vn+l - Vn-l i{v„+i - Vn-l) v'n+l-v'n = dA' ■'>n-l + i{l>n+l-Vn-l)=v' dA' - v' 10-048 15 321 5 107 5 083 4 965 + 118 7-527 2-509 2-503 2-462 -0-041 3-719 1-829 0-914 0-438 0-218 1-240 0-610 0-305 0-146 0-073 1-225 0-624 0-278 0-172 0-045 1-237 0-613 0-335 0-163 0-118 -0-012 + 0-011 -0-057 + 0-009 -0-073 0-107 0-036 0-036 0-082 -0-046 Sub-table c. 1-230 0-609 0-299 0-145 0-072 1-229 0-620 0-321 0-176 0-104 + 0-001 -0-011 -0-022 -0-031 -0-032 0-022 0-082 -0-060 Table VI. CJilSIUM BROMIDE. CsBr = 213-0. T=19-5°C. Sub-table a. Vn+l-Vn = dA A -1000 = '!) dA-v 11-894 11-756 + 0-138 5-954 5-802 + 0-152 2-929 2-873 + 0-056 1-407 1-466 -0-059 0-771 0-695 + 0-076 0-302 0-393 -0-091 0-169 0-224 -0-055 0-116 0-108 + 0-008 0-045 0-063 -0-018 Sub-table b. V„+i - Vn-L i(l'n+l - V«-l) v'n+1 - v'„ = dA' ■Wn-l + J(l)n+1 - Vn-l)=v' dA' - v' 17-848 5-949 5-917 5-834 + 0-083 8-883 2-961 2-923 2-911 + 0-012 4-336 2-178 1-073 0-471 0-285 1-445 0-726 0-358 0-157 0-095 1-490 0-670 0-370 0-178 0-086 1-421 0-751 0-381 0-203 0-117 + 0-069 -0-081 -0-011 -0-025 -0-031 0-161 0-054 0-054 0-063 -0-009 Sub-table c. v"n+l-1>"n = dA" 2 dA" - v" 11-897 11-753 + 0-144 5-935 6-818 + 0-117 2-926 2-892 + 0-034 1-449 1-443 + 0-006 0-720 0-723 -0-003 0-336 0-387 -0-051 0-174 0-213 -0-039 0-101 0-112 -0-011 0-049 0-063 -0-014 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 125 Tables of Class F, illustrating the Method of arriving at the Volumetric Bflect produced by changing the Concentration of a Solution. TRIAD OF IODIDES. Table VIL POTASSIUM IODIDE. £1 = 166-1. T = 19-5°C. n m V 9 1/4 11-281 5-574 7 1/16 2-772 1/32 1-395 5 1/64 0-69E 4 1/128 0-347 1/256 0-168 2 1/512 0-089 1 1/1024 0-040 Sub-table a. Vn+l- Vn = d^ A-1000=:U dA-v 11-497 11-281 + 0-216 5-707 5-574 + 0-133 2-802 2-772 + 0-030 1-377 1-395 -0-018 0-700 0-695 + 0-005 0-348 0-347 + 0-001 0-179 0-168 + 0-011 0-079 0-089 -0-010 0-049 0-040 + 0-009 Sub-table b. Vn+l - 1>n-l JC-Wn+l - ■Wn-l) v'n+l-v'n = dA' "n-l + Ul>n+1 - -Wn-l) = 1)' dA' - v' 11-309 17-204 5-735 5-701 5-608 + 0-093 8-609 4-179 2-077 1-048 0-527 0-258 2-836 1-393 0-692 0-349 0-176 0-086 2-820 1-401 0-691 . 0-352 0-169 0-092 2-788 1-387 0-696 0-344 0-175 0-083 0-032 + 0-014 -0-005 + 0-008 -0-006 + 0-009 0-128 0-043 043 0-040 -0-003 Sub-table c. v"„+i-v"n = dA" v' + v_ 2 dA" - v" -v" 11-483 11-295 + 0-183 5-704 5-591 + 0-113 2-811 1-389 0-696 0-350 0-174 0-085 2-780 1-391 0-695 0-345 0-171 0-086 + 0-031 -0-002 + 0-001 + 0-005 + 0-003 -0-001 0-048 0-043 0-000 Table VIIL RUBIDIUM IODIDE. RM = 212-5. Sub-table a. T = 19-5° C. V„+i~Vn=dA A -1000=11 dA-v 12-969 12-836 + 0-133 6-412 6-424 -0-012 3-221 3-203 + 0-018 1-601 1-602 -0-001 0-789 0-813 -0-024 0-391 0-422 -0031 0-204 0-218 -0-014 0-075 0-143 -0-068 0-082 0-061 + 0-021 Sub-table b. 1>n+l-1>n-l 4(»n+l - Vu-l) ^ v'n+l-v'n = dA' ■»»-! + i{Vn+l - V„-i) = v' dA' ~v' 12-884 19-381 6-460 6-470 6-414 + 0-056 9-633 3-211 3-205 3-209 -0-004 4-822 1-607 1-599 1-610 2-390 0-797 0-795 0-815 1-180 0-393 0-399 0-416 0-595 0-198 0-180 0-236 0-011 -0-020 -0-017 -0-056 +0-010 -0-009 0-279 0-093 0-123 0-113 0-157 0-052 0-052 0-061 Sub-table c. v"n+l-'V"„ = dA" t±JL=v" 2 dA"-v" 12-945 12-860 + 0-085 6-441 6-419 -0-022 3-213 1-600 0-792 0-395 0-192 099 3-206 1-606 0-814 0-419 0-227 0-128 0-007 -0-006 -0-022 -0-024 -0-035 -0-029 0-067 0-061 + 0-006 Table IX. CESIUM IODIDE. Csl = 260-0. T=19-5°C. Sub-table u. 'I'n+l — -Wn = dA A -1000 = '!) dA-v 14-893 14-788 + 0-105 7-445 7-343 -0-102 3-668 3-675 -0-007 1-S61 1-814 + 0-047 0-875 0-939 -0-064 0-456 0-484 -0-029 0-207 0-277 -0-070 0-042 0-235 -0-193 0-082 0-153 -0-071 Sub-table b. 1>n+l - 1>n-l JCn+l - '"n-l) v'n+\-1l'n = dA' ^»-l + 4(^n+l - V„-i) = v' dA' - v' 14-789 22-338 7-446 7-410 .7-379 11-113 3-704 3-722 3-657 5-529 1-843 1-806 1-851 + 0-031 +0-066 -0-046 -0-003 -0-069 -0-138 2-736 0-912 0-924 0-927 1-330 0-443 0-429 0-498 662 221 180 318 0-249 0-083 0-124 0-194 -0-070 0-124 0-041 0-041 0-163 -0-112 Sub-table c. i^"n-n--!'"n=rfA" 'i±l=^v" 2 dAl'-v" 14-893 14-788 + 0-105 7-427 7-361 + 0-066 3-695 3-666 + 0-029 1-834 0-899 0-442 0-194 0-083 1-832 0-933 0-491 0-297 0-214 + 0-002 -0-034 -0-049 -0-103 -0-131 0-061 0-163 -0 092 126 MR J. Y. BUCHANAN ON THE 52. Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TRIAD OF CHLORATES. Table X. POTASSIUM CHLORATE. KC103 = 122-6. T=19-5°C. 1/4 11-352 1/8 5-632 7 6 5 4 3 2 1/16 1/32 1/64 1/128 1/256 1/512 2-786 1-337 0-661 0-324 0-158 0-057 1 1/1024 Sub-table A-1000 = i) dA ~v 11-352 5-720 5-632 + 0-088 2-847 2-785 + 0-062 1-448 1-337 + 0-111 0-676 0-661 + 0-015 0-337 0-324 + 0-013 0-166 0-158 + 0-008 0-101 0-057 + 0-044 StTB-TAELE 6. A{r„+i -■!!„_,) ^''n+i-v'n-dA' Vn-l + J(i;„+l-D„_i) = dA' - v' 11-352 5-711 5-641 + 0-070 8-567 4-295 2-124 1-013 0-503 0-267 2-855 1-432 0-708 0-338 0-168 0089 2-872 1-400 0-707 0-336 0-180 0-089 2-769 1-369 0-662 0-326 0-146 0-057 + 0-103 + 0-031 + 0-045 + 0-010 + 0-034 + 0-032 Sub-table c. V „+i - ■» ', v' + v_ ,, ~2 ^ dA'' - v'' = dA" 11-352 5-716 5-636 + 0-080 2-859 1-424 0-692 0-336 0-173 0-095 2-777 1-353 0-661 0-325 0-152 0-057 + 0-082 + 0-071 + 0-031 + 0-011 + 0-021 + 0-038 Tablb XI. RUBIDIUM CHLORATE. RbC103= 169-0. T = 19-5°C. Sue-table «,. Vn+l-Vn = dA A-1000 = y dA -V 12-726 6-373 6-353 + 0-020 3-170 3-183 -0-013 1-599 1-584 + 0-015 0-809 0-775 + 0-034 0-375 0-400 -0-025 0-200 0-200 0-000 0-089 0-111 -0-022 Sub-table 6. ■"n+i - ■».■-! i(»n+l- ''ii-l) v'„+i-v'„ = dA' l + Ufn+l-Vn-i)- dA' - v' 12-726 6-364 -0-002 9-543 3-181 3-190 3-174 + 0-016 4-769 2-408 1-184 0-575 1-590 0-803 0-395 0-192 1-596 0-783 0-403 0-185 1-578 0-795 0-392 0-207 + 0018 -0-012 + 0-011 -0-022 0-289 0-096 0-096 0-111 -0-015 Sub-table c. 6-368 6-353 + 0-010 3-180 1-597 0-796 0-389 0-193 0-092 3-178 1-581 0-785 0-396 0-203 0-111 + 0-002 + 0-016 + 0-011 -0-007 -0-010 -0-019 Table XII. C/ESIUM CHLORATE. Sub-table i CsC10j = 216-5. T=19-5°C. v„+i ~ v„ = dA A-1000 = w dA -V 14-515 7-282 7-233 + 0-049 3-564 3-669 -0-105 1-865 1-804 + 0-061 0-833 0-971 -0-138 0-495 0-476 + 0-019 0-184 0-292 -0-108 0-080 0-212 -0-132 Sub-table b. «n+l - V„-i i(('n + l-'!)n-l) 1''h+1- 0'n = dA' Vn -1 + i{l)n+l - V„-i) - v' dA' -v' 7-231 7-284 -0-053 10 3 3 3 + -846 -615 -670 -614 -056 5-429 1-810 1-744 1-870 -0-126 2-698 0-899 0-951 0-919 h 0-032 1-328 0-443 0-401 0-618 -0-117 0-679 0-226 0-218 0-300 -0-082 Sub-table c. v"n+\-v"n=dA" v' + v_ ,1 dA"-v" 14-515 7-267 7-258 -0-001 3-617 3-641 -0-024 1-804 0-892 0-448 0-201 0-084 1-837 0-945 0-497 0-296 0-212 -0-033 -0-053 -0-049 -0-095 -0-128 SPECIFIC GEAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 127 Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TRIAD OF BROMATES. Table XIIL POTASSIUM BROMATE. KBrO, = 167-L T = 19-5°C. 7t m V 9 1/4 11-290 8 1/8 5-576 7 1/16 2-761 6 1/32 1-370 5 1/64 0-688 4 1/128 0-347 3 1/256 0-176 2 1/512 0-089 1 1/1024 Sub-table a. Vn-\-\ — l/'n = dA A -1000 = 11 dA-v 11-290 5-714 5-576 -[-0-138 2-815 2-761 -HO-054 1-391 1-370 -1-0-021 0-682 0-688 -0-006 0-341 0-347 -0-006 0-171 0-176 -0-005 0-087 0-089 -0-002 Stjb-tablb 6. Vn+l - 'i'n-l J(ll„+1 - Vn-l) v'n+l--l>'n = dA' 1>»-\ + i{rn+l-Vn-l) = v' dA'-v' 11-290 5-686 5-604 4-0-082 8-529 2-843 2-832 2-772 -1-0-060 4-206 1-402 1.393 1-379 •fO-014 2-073 0-691 0-691 0-688 -1-0-003 1-023 0-341 0-341 0-347 -0-006 0-512 0-171 0-172 0-175 -0-003 0-258 0-086 0-086 0-089 -0-003 Sub-table c. v"„+i-v"n = dA" 2 dA"-v" 11-290 5-700 5-590 -HO-110 2-824 2-766 -fO-058 1-392 1-374 -1-0-018 0-686 0-688 -0-002 0-341 0-347 -0-006 0-172 0-175 -0-003 0-086 0-089 -0-003 Table XI^ ". EUBI] DIUM BROMATE. Sub-table a EloBrC )3 = 213-5. T=19-5°C. Vn+l-Vn = dA A- 1000 = 1! dA-v 3-057 1-516 1-541 -0-025 0-774 0-767 4-0-007 0-360 0-407 -0-047 0-216 0-191 4-0-025 0-095 0-096 -0-001 Sub-table b. ■Kn+l - «n-l J(d„+i - ■i;„-i) v'„+i-v'„ = dA' ■"n-l -1- i( Wn4-1 -V„-i) = v' dA' - v' 3-057 1-527 1-530 -0-003 2-290 0-763 0-745 0-785 -0-040 1-134 0-378 0-402 0-383 4-0-019 0-576 0-192 0-183 0-200 -0-017 0-311 0-104 0-104 0-096 4-0-008 1 SUB-TABLB C. v"n+i-v\ = dA" 2 dA" - v'' 3-057 1-522 1-535 -0-013 0-759 0-776 -0-017 0-381 0-395 -0-014 0-200 0-195 -i- 0-005 0-099 0-096 4-0-003 Table X^ V. C^S] [UM BROMATE. Sub-table a CsBrOj- = 261-0. T=19-5° C. 1V-|-l-'!'n = 'n=-dA' dA' - v' 8-832 4-429 4-403 -1-0-026 6-643 2-214 2-226 2-177 + 0-049 3-243 1-081 1 -058 1-119 -0-061 1-605 0-535 0-574 0-545 + 0-029 0-827 0-276 0-266 0-279 -0-013 0-457 0-152 0-151 0-128 + 0-023 0-212 0-071 0-071 0-057 + 0-014 Sub-table u. v"n+i-v"n = dA" ■»'+^-^'. 2 dA" -v" 8-832 4-461 4-371 -(-0-090 2-188 2-183 -1-0-005 1-076 1-107 -0-031 0-543 0-564 -0-021 0-290 0-274 + 0-016 0-147 0-127 + 0-020 0-070 0-057 + 0-013 Table X"V 11. EUi ilDIUM lODATE. Sub-table a EblOj = 260-5. T = 19-5'' C. ■i)n+l-Vn = dA A-1000=1) dA-v 2-576 1-300 1-276 + 0-024 0-615 0-661 -0-046 0-317 0-344 -0-027 0-154 0-190 -0-036 0-118 0-072 + 0-046 Sub-table 6. ^(Vn+l - Vn-l) v'n^X-v'n = dA' dA' - -b' 2-576 1-277 1-299 -0-022 1-915 0-638 0-644 0-655 -0-011 0-932 0-311 0-308 0-347 -0-039 0-471 0-157 0-184 0-163 + 0-021 0-272 0-091 0-091 0-072 + 0-019 Sub-table c v"„+i-v"n = dA" ■"' + ■" -v" 2 dA"-D" 2-576 1-289 1-287 + 0-002 0-629 0-658 -0-029 0-313 0-345 -0-032 0-169 0-176 -0-007 0-104 0-072 + 0-032 Table X :viii. c ^SIUM lODATE. Sub-table c CsIOg t. = 308-0. T = 19-5° C. Vw+l - V/i = ^A A-1000 = u dA-v 2-903 1-432 1-471 -0-039 0-685 0-786 -0-101 0-329 0-457 -0-128 0-185 0-272 -0-087 0-120 0-152 -0-032 Sue-table •). ■"'n+l- v'n = dA' '»n-l + l(Vn+l-Vn-l) = v' dA' - v' 2-903 1-411 1-492 -0-081 2-117 0-706 0-697 0-795 -0-098 1-014 0-338 0-352 0-443 -0-091 0-514 0-171 0-189 0-254 -0-065 0-305 0-102 0-102 0-152 -0-050 Sub-table e. lf'n+l-1>"n = dA" 2 dA"-v" 2-903 1-422 1-481 -0-059 0-691 0-790 -0-099 0-340 0-450 -0-110 0-187 0-263 -0-076 0-111 0-152 -0-041 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 129 Summary. § 53. Voluvietric Effect produced on changing the Concentration of a Solution. n m 9 1/4 8 1/8 7 1/16 6 1/32 5 1/64 4 1/128 3 1/256 2 1/512 1 1/1024 MR d^" -v". KCl RbCl CsCl + 0-159 + 0-185 + 0-209 + 083 + 0-090 + 0-102 + 0-037 + 0026 + 0-044 + 0007 + 0-017 + 0-025 - 0-008 + 0020 + 0020 + 0-002 + 0-009 + 0-015 -0-001 -0-035 + 0-004 -0-022 - 0-008 - 0-005 KBr RbBr CsBr + 0-133 + 0-232 + 0-144 + 0-061 + 0109 + 0-117 + 0011 + 0-035 + 0-034 -0-012 + 0001 + 006 -0-016 -0-011 - 0003 - 0-004 -0-022 -0-051 -0-003 -0031 -0039 - 0-008 ■-0-032 -0-011 -0-060 -0-014 KI Rbl Csl + 0-183 + 0-085 + 0-105 + 0113 + 0-022 + 0066 + 0-031 + 0-007 + 0029 -0-002 -0-006 + 0-002 + 0-001 - 0022 -0034 + 0-005 - 0024 -0049 + 0-003 - 0-035 -0-103 -0-001 -0-029 -0-131 0-000 + 006 -0-092 MRO3 d^"-v". KCIO3 RbC103 CSCIO3 + 0080 + 0-010 -0-001 + 0-082 + 0002 -0 024 + 0071 + 0-016 -0-033 + 0-031 + 0-011 - 0-053 + 0011 - 0-007 - 0-049 + 0-021 -0-010 -0095 + 0-038 -0-019 -0-128 KBr03 Rbl*-03 CsBr03 + 0-110 + 0-058 + 0-018 -0013 - 0-001 - 0-002 -0-017 + 0-022 -0-006 -0-014 + 0-001 -0-003 + 0-005 -0 031 -0003 + 0-003 -0-036 KIO3 RblOs CsIOg + 0-090 + 0-005 -0-031 + 0-002 -0-059 -0-021 -0-029 -0-099 + 0-016 -0-032 -0-110 + 0-020 - 0-007 -0-076 + 0013 + 0-032 -0-041 § 54. Solutions of the Salts of the Ennead MR. — The notes deal principally with the character of the change in the value of c?A — v with changes of the value of m in the dijGferent solutions. Table I. : — KCl. — This salt is the subject of the specimen table, § 50, and it has been commented on in connection with that table. Table II. : — RhCl. — In all three sub-tables the change of sign occurs between m= 1/128 and m= 1/256. There is a steady decrease in the positive values from m=l/4 to m= 1/128 in all three cases, excepting sub-table a at to =1/64, when an increase over the previous value occurs. The solutions of this salt show a regular decrease from high positive values of dA — i; to small negative values at low concentrations. Table III. :— CsCl. — The series of values of cZA — -u in the three sub-tables shows a very regular decrease in magnitude from m = 1/4 to to = 1/256 ; change of sign occurs between to= 1/256 and 1/512 with a small negative value. Table IV. : — KBr. — There is a rapid decrease in the value of dA — v from to= I/4 to TO =1/1 6, and between to =1/16 and to =1/32 there is change of sign to a small negative value, which persists right on to to =1/512, and which is the characteristic feature of the three sub-tables. TRANS. EGY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 17 130 MR J. Y. BUCHANAN ON THE It would seem to indicate that in the solutions of any concentration less than m= 1/64 the dissolution of a small quantity of salt produces the same increment of displacement. Table V. : — RhBr. — In sub-table a the value of d^ — v decreases very rapidly from 0"296 at m = 1/4, and changes to a negative value between m = 1/32 and m = 1/64, and then oscillates between alternate high negative values and low positive values. In sub-table c there is a regular increase in the negative values from m = 1/64 to m = 1/512. We have here definite evidence of expansion on dilution. Table VI.: — CsBr. — -The character of the decline in positive values for di^ — v is the same as that observed in the case of KBr and RbBr, and change of sign occurs between m= 1/16 and m= 1/32. After this there is an irregular oscillation between high positive and high negative values in sub-table o. In sub-table c the positive values persist to r/i= 1/32, after which change of sign occurs, and the negative sign remains for all values down to m= 1/512. The negative values reach a maximum at m= 1/128 and then decline. Here agaut. we have definite evidence of expansion. Table VII.: — KI. — A rapid decrease in positive values occurs between m=\jA. and ??i= ]/16. Then, with the exception of the small negative values of '01 8 and O'OIO at m = 1/32 and m = 1/512 respectively, there are small positive values for dA — v. This holds also in sub-table c, only that the positive and negative values foi' values of m below 1/32 are less. The final note for KBr applies with greater force in the case of KI. Table YIII. : — RhI. — In sub-table a there is a sudden fall from a high positive value of 0'133 for m.= l/4 to a negative value of 0'012 at m=l/8. and then a reversion to positive at 1/16 ; after this, the values are negative, except where m= 1/1024. In sub-table c there is a more progressive decrease in positive values from m = 1/4 to m = 1/16, and between this and «t = 1/32 there is change of sign. The negative values increase gradually to a maximum of 0-035 at i/256 and then decrease, and we have a positive value of 0-006 at 1/1024. The evidence of expansion is conclusive. The character of these values is com- parable with those of CsBr. Table IX. : — Csl. — In sub-table a, with the exception of the sudden fall to a negative value of 0-007 at m= 1/16, there is a progressive decrease to m= 1/32, where chano-e of sign occurs between m= 1/32 and m= 1/64, and an increase in magnitude of negative values to a maximum of 0-193 at m= 1/256, and then a slight fall. In sub-table c there is a progressive decrease in positive values to m = 1/32 ; then change of sign, and progressive increase in negative values to 0-131 where ot = 1/512, a slight decrease occurring at m= 1/1024. The character of values for di^-vm all three sub-tables is the same. This is the most marked instance where expansion occurs. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 131 § 55. Solutions of the Salts of the Ennead Ifi^Og.— The reason for the small number of results in the cases of RbBrOg, RblOg, GsBrOg, and CsIOg is the very sparing solubility of these salts in water. Table X. : — KCIO^. — The values of dA — t; in all the sub-tables are positive. In sub-table a they are oscillatory in character, the maximum value being O'lll at m = l/32; the minimum of 0-008 at m= 1/256 rises to 0-044 at m= 1/512. In sub-table c the maximum occurs at m=l/l6, while the minimum is at m= 1/128. The nature of the oscillation is the same, but less pronounced. Table XL : — RhClO^. — There are somewhat irregular alternations between positive and negative values oid^ — v'va. the sub-table a. They are also of appreciable magnitude, and in sub-table c the oscillations are still apparent, although a definite change of sign occurs at m = 1/128, when the values of c?A — v for higher values of m are positive, and the lower values of m are negative. In the table for MR = RbCl the same character is observed as here in the sub-table c ; see note above. Table XII. : — CsClO^. — There are exhibited here regular alternations between com- paratively high positive values and high negative values for dA - v in sub-table a, except at m= 1/250 and m= 1/512, both of which are negative. The maximum positive value is at m = 1/32, while the maximum negative value is at TO= 1/64. Owing to the greater magnitude of the negative values than the positive ones in the sub-table a, we obtain a complete series of negative values of comparatively high magni- tude in sub-table c, and with the exception of a slight diminution in the negative value at m= 1/128 below that where m= 1/64, there is a progressive increase of the negative values from the beginning to the end, giving distinct evidence of expansion on dilution. Table XIII. : — KBrO^. — The character of changes in the values for dA — vm all three sub-tables is the same : a rapid fall in the positive values from 0-138 at m=l/8 to 0-021 where m= 1/32, the negative values from m= 1/64 onwards being negligible. This is observed in all three tables, although in sub-tables 6 and c the high magni- tude of the positive values for dA — -y is slightly modified. This feature of the steady fall in positive values to a series of negligible negative values is also to be seen in the series for ME = KBr, with the exception that there are two negative quantities of appreciable magnitude in the values for d^ — v, where m= 1/32 and m= 1/64 in sub-table c for KBr. Table XIV. : — RhBrO^. — In sub-table a there is a regular alternation between rather high negative values and positive values, while in sub-table c there is a regular transition from negative to positive values, the change of sign occurring at m= 1/256, the general character being that of commencing with a negative value and rising to a positive quantity. This is the only instance in these tables of the occurrence of contraction from the highest concentration, m— 1/32, to the lowest, m= 1/512. 132 MR ,T. Y. BUCHANAN ON THE Table XV. : — CsBrOg. — Here an irregular feature is observed in that there is a negative value of 0-023 at m=l/32, which changes to a positive value of 0-039 at m= 1/64, then a diminution in a positive value at m= 1/128 to the maximum negative value of the series of 0-049 at m= 1/256, with a slight diminution at m= 1/512. In sub-table c a similar series of values for dA — v is seen, except that they are more regular. Table XVI. ■.—KlO^.—ln sub-table a the high positive value of 0-154 for dA-v at m= 1/8 is changed to a negative value of 0-039 at m= 1/16, and with a diminution of the negative value to 0-003 at 1/32 the maximum negative value of 0-072 is reached at 771 = 1/64 ; then a transition occurs at m = 1/128 to a positive value of 0-046. After- wards the positive value falls away. There is thus a change from a high positive value to a high negative value, and then reversion to moderately high positive value. The same feature is observed in sub-table c, but it is of a more undulatory character. Table XVII. :— igfc/Og.— The positive value of 0-024 at m= 1/32 gives place to the maximum negative value of 0-046 at m= 1/64 ; then there is a diminution in negative values leading to a positive value of 0-046 at 1/512 in sub-table a. The same character is observed in sub-table c, only more regular, the maximum negative value of 0-032 occurring at to = 1/128. Table XVIII. : — Cs-JOg. — The values for dA-v in each of the three sub-tables constitute the most regular of all the series. All the values are negative and reach a maximum value at m= 1/128 in all three sub-tables, and fall away regularly for higher and lower values of m. The character of the values for CSIO3 somewhat resembles those for RblOg. Section IX. — Notes on the Values of v for the Enneads MR and MRO3. § 56. The increment of displacement produced in 1000 grams of water at 19-5° C, when 1/2 gram-molecule of potassium chloride is dissolved in it, is 14-001 Gj ; when a molecularly equivalent amount of potassium bromide is dissolved in the same quantity of water, the increase in the displacement is 17-547 Gt; when the salt in solution is potassium iodide, the number is 22-778 Gj. Replacing, therefore, the chlorine by bromine increases the displacement by 3-546 G.j^. ; and if the bromine be now replaced by iodine, there is a further increase of 5-231 Gt in the displacement; or, replacing the chlorine by iodine causes an increment of displacement of 8-777 Gj. Proceeding in a similar manner with the other salts of the ennead MR and tabulating the results, we obtain Table I. An inspection of the table shows us that the differences for Br — CI when equivalent quantities of the salts of K, Rb, and Cs are dissolved in the same quantity of water are of the same order of magnitude till m = 1/32. The same characteristic is observed between the same limits of m when bromine is replaced by iodine, but the differences for the same gram-molecular weight of the salt are in these three series greater than those observed when chlorine is replaced by bromine. In the third section SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 133 of the table, when chlorine is replaced by iodine, the numbers expressing the differences of the increments of displacement for the same value of m are the sum of the differences for Br— CI, I— Br. Turning now to Table II., we have the increase in the increment of displacement produced when the metal in combination with the same acid is varied. Here again it will be found that the numbers on the same line in each section are, inter se, of the same order of magnitude till m= 1/32, after which they vary more or less irregularly. Table I., giving the corresponding Differences between the Values of the Increments of Displacement, v, caused by the Dissolution of in gram-molecule of MBr and MCI; Ml and MBr; MI and MCt (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. ENNEAD MR. R = BROMI DE -CHLORIDE. IODIDE-BROMIDE. IODIDE-CHLORIDE. M = K. Eb. Cs. K. Rb. Cs. K. Rb. Cs. in. 1/2 3-546 3-625 3-249 5-231 5-543 6-031 8-777 9-168 9-280 1/4 1-791 1-781 1-690 2-591 2-853 3 032 4-382 4-634 4-722 1/8 0-898 0-884 0-813 1-260 1-483 1-541 2-158 2-367 2-354 1/16 0-469 0-436 0-398 0-619 0-747 0-802 1-088 1-183 1-200 1/32 0-240 0-216 0-241 0-314 0-380 0-348 0-554 0-596 0-589 1/64 0-131 0-138 0-091 0-141 0-186 0-244 0-272 0-324 0-355 1/128 0-061 0-070 0-102 0-069 0-114 0-091 0-130 0-184 0-193 1/256 0-041 0-067 0-080 0-029 0-029 0-053 0-070 0-096 0-133 1/51? 0010 0-017 0-029 0-015 0-053 0-127 0-025 0-070 0-156 1/1024 -0-021 0-090 Table II., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of RbR and KE; CsR and RbR; CsR and KR (where R = C1, Br, or I) in 1000 grams of Water at 19-5° C. ENNEAD ME. M = RUBIDIUM— POTASSIUM. CESIUM— RUBIDIUM. CESIUM— POTASSIUM. R = 01. Br. I. CI. Br. I. CI. Br. I. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 2 636 1-303 0-641 0-336 0-155 0066 021 0-024 0009 2-715 1-293 0-627 0-303 0-140 0073 0-030 0-050 0-016 3-027 1-555 0-850 0-431 0-207 0-118 0-075 0050 0-064 0-021 3-764 1-864 0-932 0-455 0-219 0-115 0-053 0-022 0-006 3-388 1-773 0-861 0-417 0-244 0-068 0-085 0-035 0-018 -0-019 3-876 1-952 0-919 0-472 0-212 0-126 0-062 0-059 0-092 0-092 6-400 3-167 1-573 0-791 0-374 0181 0074 0-046 0-015 6-103 3-066 1-488 0-720 0-384 0-141 0-115 085 0-024 6-903 3-507 1-769 0-903 0-419 0-244 0-137 0-109 0-146 0-113 134 MR J. Y. BUCHANAN ON THE § 57. Tables III. and IV. deal with the salts of the ennead MRO3, and correspond in arrangement with Tables I. and II. respectively ; and what has been said of the two previous tables holds good, in general, with these two tables, but the agreement of the values is not so close, nor is the number of values tabulated so great. In Table III. the differences of the increments are nearly all negative quantities ; in Table IV. they are all positive. Table V. gives the differences of v between the oxyhalides and the halides of the same metal for the two enneads, MEO3 and MR, and here also the same characteristic agreement is noticed between the numbers on the same line in each section of the table. Having thus briefly explained the contents of the tables and the chief characteristics of the numbers in them, we will proceed to more fully discuss the effects produced on the displacement of 1000 grams of water at 19 '5" C. when the constituents of the salts dissolved in it are changed ; and in order to compare the results of the halides with those of the oxyhalides, we shall confine our attention to the numbers for >n= 1/16 and less. Table III., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of MBrOg and MCIO3 ; MIO3 and MBrOg ; MIO3 and MCIO3 (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. ENNEAD MRO,. R0.,= BROMATE— CHLORATE. lODATE— BROMATE. lODATE— CHLORATE. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. m. 1/2 1/4 -0-062 -2-458 -2-520 1/8 - 0-056 -1-137 -1-193 1/16 -0-024 -0-126 -0-158 -0-572 -0-481 -0-608 -0-596 -0-607 - 0-766 1/32 + 0033 -0-043 -0-037 -0-274 -0-265 -0-296 -0-241 -0-308 -0-333 1/64 + 0-027 - 0-008 -0-107 -0-104 -0-106 -0-078 -0 077 -0-114 -0-185 1/128 + 0-023 + 0-007 - 0-055 -0-078 -0063 + 0-036 -0055 -0-056 -0-019 1/256 + 0-018 -0 009 -0-057 -0-049 -0001 + 0-037 -0-031 -0-010 - 0-020 1/512 + 0-032 -0-015 -0-078 -0 032 -0-024 + 0-028 0-000 -0-039 -0-050 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 135 Table IV., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of RbROg and KRO^ ; CsROg and RbROg ; CsROg and KRO3 (where RO3 = CIO3, BrOg, or IO3) in 1000 grams of Water at l^'b" C. ENNEAD MRO,. M = RUBIDIUM— POTASSIUM. CAESIUM-RUBIDIUM. CESIUM— POTASSIUM. R03 = CIO3. BrOa. IO3. CIO3. BrOs. IO3. CIO3. Br03. IO3. m, 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1-374 0-720 0-398 0-247 0-114 0-076 0-042 0-054 0-296 0-171 0-079 0-060 0-015 0-007 0-387 0-180 0-077 0-075 0-063 0-015 1-789 0880 0-486 0-220 0-196 0-076 0-092 0-101 0-454 0-226 0-097 0-014 0-044 0-038 0-327 0-195 0-125 0-113 0-082 0-080 3-163 1-600 0-884 0-467 0-210 0-152 0-134 0-155 0-750 0-397 0-176 0-074 0-059 0-045 0-714 0-375 0-202 0-188 0-145 0095 Table V., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of MCIO3 and MCI ; MBrOg and MBr ; MIO3 and MI (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. MEO J— ME. R03- R= CHLORATE— CHLORI DE. BROMATE— BROMI DE. lODATE- IODIDE. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. m. 1/2 1/4 4-453 4-524 4-449 2-600 -2-449 1/8 2.-216 2-296 2-244 1-262 -1-235 1/16 1-101 1-163 1-194 0-608 0-601 0-638 -0-583 -0-727 -0-772 1/32 0-496 0-578 0-579 0-289 0-319 0-301 -0-299 - 0-326 -0-343 1/64 0-238 0-286 0-367 0-134 0-140 0-169 -0-111 -0152 -0-253 1/128 0-107 0-162 0-185 0-069 0-099 0-028 -0-078 - 0-078 -0-027 1/256 0-060 0-038 0-148 0037 002 0011 -0-041 - 0-028 - 0-005 1/512 - 0-007 0-038 0133 0-015 0-006 0026 -0032 -0-071 -0-083 § 58. If, in a solution containing I/I6 grm.-mol. KCl in 1000 grams of water at 19"5' C, we imagine the chlorine to be replaced by bromine, the process is accompanied by an increase of P"469 G^, in the displacement of the original solution. If the operation be performed upon an equivalent solution of RbCl, the increase in the displacement is 0"436Gt; if the salt in solution be I/I6 grm.-mol. CsCl, the increase is 0'398 Gt. Therefore, it appears that, when we replace CI by Br in 1/16 grm.-mol. solutions of the 136 MR J. Y. BUCHANAN ON THE chlorides of K, E,b, and Cs, approximately the same increment of displacement is produced. Commencing again with our solution of KCl, and replacing the potassium by rubidium, causes an increase m the displacement of 0-336 Gj ; when rubidium is replaced by caesium, the increase is 0'455Gt; replacing potassium by caesium produces an increase of 0'791 G^. If we now consider a solution of 1/16 grm.-mol. of KBr, and replace the potassium by rubidium, there is an increase in the displacement of 0'303 G^ ; replacing the rubidium by caesium causes a further increase of 0'417 Gt ; or if potassium be replaced by caesium, the increase is 0720 Gj. Setting out the numbers in the manner shown below gives a clearer view of the various changes that take place when one element in a compound is replaced by another : — K. Diff. Rb. Diff. Cs. V. f. V. CI . 1-684 + 0-336 = 2-020 + 0-455 = 2-475 Br . . 2-153 + 0-303 = 2-456 4-0-417 = 2-873 Diff. 0-469 0-436 0-398 It will be seen that the difference between RbCl and RbBr is nearly the same as that between KCl and KBr, because the increase in the increment of displacement produced when K is replaced by Rb in KCl is about the same as that produced when Rb takes the place of K in KBr. Therefore, when in solutions containing 1/16 grm.- mol. of KCl or KBr the potassium is replaced by rubidium, approximately the same increase in the increment of displacement is produced ; further, when CI is replaced by Br in KCl and RbCl, the increase is nearly the same in each case, but of a higher value than when the change is made in the metals. The difference between the atomic weights of CI and Br is 44'5 ; between K and Rb it is 46'4. The atomic weight of CI is less than that of K ; so, also, is the atomic weight of Br less than that of Rb ; yet there is a greater diflference of displacement produced by changing the acid than by changing the base. Turning our attention now to the chlorides and bromides of rubidium and caesium, we find that replacing CI by Br in RbCl causes an increase in the displacement of RbCl which is the mean of the increases produced when Cs replaces Rb in RbCl and RbBr, and is greater than when Br replaces CI in CsCl. There is a greater effect produced by changing the metals when CI is the acid than when Br is the acid ; also, when the acid united with the same base is changed, the variation is greatest for the lightest metal, and least for the heaviest. Proceeding on the hues set forth above, we will next consider the changes caused by replacing bromine by iodine, when combined with the same three metals : — IC. Di(f. Kb. Diff. Cs. «'■ !'. 11. Br . . 2-153 + 0-303 = 2-156 + 0-417 = 2-873 I . . 2-772 + 0-431 = 3-203 + 0-472 = 3-675 Diff. 0-619 0-747 0802 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 137 Replacing Br by I in KBr, RbBr, or CsBr produces increases in the displacements which become greater as the atomic weight of the metal increases. There is a greater increase produced by replacing K by Rb in KI than that produced when Rb takes the place of K in KBr; a similar effect is seen with the corresponding salts of rubidium and caesium, but in both instances the replacing of one metal by another causes a smaller change than when iodine takes the place of bromine in the bromide of the metal. The exchange of iodine for bromine produces increases in the values of v which rise with the increase of the atomic weight of the metal in combination ; as was previously observed, the replacement of chlorine by bromine caused changes in the increase of v which diminished with the increase in the atomic weight of the metal. We may summarise the foregoing observations by saying that tha replacement of the acid in a salt of the general formula MR (where M = K, Rb, or Cs, and R = CI, Br, or I) by another acid causes a greater change in the value of the displacement of a solution containing 1/16 grm.-mol. of the salt in 1000 grams of water at 19 '5° C. than the replacement of the metal by another metal. The only exceptions to this are when Cs takes the place of Rb in RbCl, and when Br replaces CI in CsCl, this latter being the smallest change produced when one acid is replaced by another. The values of the differences of the displacements for 1/16 grm.-mol. solutions of the salts of the halides are given in the table below. K. Diff. Rb. Diff. Cs. Ditr. (K by Cs). CI DiflF. Br DifF. I Diff.Clbyl 0-469 0-336 0-436 0-455 0-398 0-791 0-619 0-303 0-747 0-417 0-802 0-720 1-088 0-431 1-183 0-472 1-200 0-903 In the table, differences on the same line are, inter se, comparable ; the differences in the same column headed " Diff." are also comparable. § 59. The salts of the oxyhalides will now be dealt with in a manner similar to that of the halides. K. Diff. Eb. Diff. Cs. ClOg BrO, V. V. V. 2-785 + 0-398 = 3-183 + 0-486 = 3669 2-761+0-296 = 3057 + 0-454 = 3-511 Diff. -0024 -0-126 -0-158 If, in a solution containing 1/16 grm.-mol. KClOg per 1000 grams of water at 19'5°C., we replace the chlorine by bromine, the process is accompanied by a decrease in the displacement of the solution by an amount equal to — 0*024 G^ ; if the operation TEANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 18 138 MR J. Y. BUCHANAN ON THE be performed on an equivalent solution of RbClOg, the decrease is — 0"126 Gt; if the salt in solution be CsClOg, the decrease is —0-158 G^. Therefore, when we replace the chlorine by bromine in 1/16 grm.-mol. solutions of the chlorates of K, Rb, and Cs we observe that the change produces a decrease in the displacement of the solution, and this decrease becomes greater as the atomic weight of the metal increases. Confining our attention next to the changes produced in the displacement by varying the metal combined with the same acid, we find that when K is replaced by Rb in KClOg the displacement of the solution increases, as it also does when Rb is replaced by Cs in RbClOg. There is a similar increase when we consider the bromates of the same three metals ; but replacing K by Rb in KBrO^ produces a smaller increase than when the same change is made in KClOg. Similarly, the replacement of Rb by Cs in RbBrOg is less than when Cs replaces Rb in RbClOg. In the four cases where an exchange of metals takes place the corresponding changes in the displacements are positive ; with the three changes obtained by replacing CI by Br the changes in the displacement are negative, and numerically less than when the metals are changed. K. Diff. Rb. Diff. Cs. BrOs 10, v. V. 3-057 + 0-454 = 3-511 2-761+0-296 2-189 + 0-387 = 2-576 + 0-327 = 2-903 Diff. - 0-572 -0-481 0-608 With the bromates and iodates of the same three metals we find that replacing the bromine by iodine causes a reduction in the displacement of — 0'572 Gt in the case of KBrOg ; with RbBrOg the change in the displacement is — 0'481 Gt ; and with CsBrOg it is — 0'608 Gt. When we compare the results obtained by changing the metal combined with the same acid, we find that the iodates have positive values for the change in the displacement, just as the bromates and chlorates had, but that, whereas the replacement of Rb by Cs in RbClOg and RbBrOg gave an increase in the displace- ment which was greater than that produced by the exchange of Rb for K in KClOg and KBrOg, the replacement of Rb by Cs in RblOg causes an increase in the displacement which is less than that caused by replacing K by Rb in KlOg. The results of the changes produced in the displacement by the replacement of one constituent by K. Diff. Rb. Diff. Cs. Diff. (K by Cs). C103 Diff. BrOg Diff. IO3 DiffiClOgbylOg -0-024 0-398 -0-126 0-486 -0-158 0-884 -0-572 0-296 -0-481 0-454 -0-608 0-750 -0-596 0-387 -0-607 0-327 -0-766 0-714 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 139 another in the salt dissolved is given in the preceding table. We do not here find so close an agreement between the numbers in a line, nor between those in the same column, but the agreement is still near enough to prevent any ambiguity as to which line or column a series belongs. Moreover, the columnar differences are all positive, while the line differences are all negative. We may further note that with the replace- ment of Eb by Cs and K by Cs the columnar differences decrease with an increase in the molecular weight of RO3, while replacing K by Rb causes irregular changes in the displacement. With the line differences the replacement of CIO3 by BrOj and ClOg by IO3 causes an increase with an increase of the atomic weight of the metal ; but with the replacement of BrOg by IO3 the changes in the displacement are irregular. § 60. The next effect to consider is that produced by the addition of the three oxygen atoms to the salts of the halides to form the corresponding salts of the oxyhalides. K. Kb. Cs. CIO3— CI . . MOl 1-163 1-194: BrOg— Br . . 0608 0-601 0-638 IO3— I . . -0-583 -0-727 -0772 in order to do this the above table has been constructed, in which the differences between the corresponding salts of the halides and oxyhalides for the same metal are entered in vertical columns. If we imagine that in a solution of 1/16 KCl-l- 1000 grams of water at 19-5° C. we add sufficient oxygen to the chloride and so produce KCIO3 in solution, the operation is accompanied by an addition to the displacement of I'lOl Gtt ; if the same operation be performed on a I/I6 grm.-mol. solution of the bromide of the same metal, the increase in the displacement is only 0'608 G^; and if we treat a solution of the iodide in the same way it produces a diminution in the dis- placement of —0-583 Gj. An inspection of the changes occurring when the three corresponding salts of rubidium and caesium are similarly treated shows us that they behave not only in an analogous manner, but that the amount of the change in each case is almost the same as that observed with the potassium salts, increasing slightly with the atomic weight of the metal. This action of the three atoms of oxygen upon the displacements of solutions of I/I6 grm.-mol. of the halides in 1000 grms. of water at 19-5° C. is peculiar, since in each case we have added the same weight of oxygen, namely, 3 grams, and the effects produced by it are similar in the salts with the same acid but different bases, but differ when the acid in combination with the same base is varied. §61.^ General Comparison and Summary of the Variation in the Values of the Mean Increment of Displacement for Dilute Solutions of Salts of the two Enneads MR and MRO^ {where M may he K, Rb, or Cs, and R may be CI, Br, or I). — This comparison includes: — (a) The variation produced by successive dilutions of a solution of an individual salt. (b) The character of the variation in the case of the whole series of solutions of salts of the two enneads. (c) The variation with the molecular weight. 140 MR J. Y. BUCHANAN ON THE The first point has been adequately dealt with in the immediately preceding section, and the two remaining ones will now be considered. The diagram on next page clearly shows the relations pointed out above, and the following are the more distinctive features which are illustrated. All the halide salts, with the possible exception of KI, have the property of causing expansion with dilution of their respective solutions, this expansion, in the case of the chlorides, being nearly proportional to the rise in the atomic weights of the base, as shown by the almost parallel march of the curves. In the case of the bromides the march is not so regular, the solutions of the rubidium and csesium salts inducing a greater relative expansion on dilution than is the case with the potassium salt, the change being greatest in the case of the rubidium salt. With the iodides, this increased effect of expansion which occurs on dilu- tion of solutions of the salts of rubidium and caesium over that of potassium is considerably enhanced, the solutions of potassium iodide showing practically no expansion. Thus, summarising the effects, the mutual relations of halogen and base in the cases of halide salts of potassium and the chlorine compounds of rubidium and csesium produce normal effects, as shown by only slight changes in the values of vim as the solutions decrease in concentration, while the remaining salts show expansion on dilution of solutions of them, which increases in magnitude with increase in molecular weight, reaching a maximum with csesium iodide. This is interesting when it is considered that csesium is the most electro-positive element, and seems to point to the expansive effect produced by both csesium and iodine independently, while mutual interference occurs in the other cases. The oxyhalides are not comparable in any sense with their respective halide compounds, which have been treated above. The most obvious feature of the incorporation of the oxygen atoms is, that the values for vjm decrease with the increase in molecular weight when triads of the salts having common base and the same concentration are compared, the only exception being the case of potassium bromate ; and this feature is the reverse of that in the case of the halide salts. Also in the case of KCIO3 and KIO3 contraction occurs on dilution of their respective solutions ; and where expansion occurs on dilution, the general order is that of proceeding from the iodates to the chlorates, where the greatest expansive effect is seen in the case of csesium chlorate. This is the reverse of the order which is seen in the case of the halides. The chlorates show the greatest variations in the values of -u/m with dilution of solutions of the salts, and least with the bromates, the iodates being intermediate. Thus the effect of the inclusion of the oxygen in the molecule of the halides is to greatly increase the expansion effect when solutions of the chlorates of rubidium and csesium are diluted, to exert very little if any effect in the case of the bromides, and to diminish the effect of expansion in the case of the iodides, the general effect in the SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 141 % CO I 5 o" 3 a: o" 3 o: o -* 1 1/ \ j A f \ \ 03 /> X 1 v^ ' \ - ^ X A CO t^ to in ■* o o to IM ' 1. OQ (A o O 1. CO cs: 9 m S li / to ^ A rx - // / N k^ K (0 in --• ^^ 3 )\ / -5 2 I g § S S O o O m CN ( / o" O d o o £1 o j J CO cs ^ \ \ ^ \ / \ ID - — ■ ^ y >^ < ^ r- o o a O O) 0, 60 ■a e 11 .2t3 13 rt •43 Ms 142 MR J. Y. BUCHANAN ON THE cases of potassium and rubidium iodates being that of contraction on dilution, while the iodate of csesium simulates the character of the iodide of the same base, though to a modified degree ; as though the dominating influence were the expansive effect of the basic radical. § 62. If we consider the solutions of the salts of the double ennead MR, MRO3, we have eighteen solutions for each value of m. Owing to the sparing solubility of some of the salts of the ennead MRO3, the highest value of m available for all the salts is 1/16. The eighteen salts can be divided into three hexads, the members of each hexad containing a common metallic element, K, Rb, or Cs, and into three other hexads having a common metalloidal element, CI, Br, or I. The values of v ( = A— lOOO) for the solution of 1/16 gram-molecule of each of the salts in the three hexads having the common elements K, Rb, Cs are arranged in the tables, and the graphic effect is illustrated in the diagram of § 38. When we wish to compare the solutions having different values of 7n, it is convenient to use the values of v/m, that is, the increment of displacement (A — 1000) reduced to the value which it would have if m= 1. This is found in the general tables of Class E (§ 30) ; and for the solutions of 1/32 gram-molecule salt and under, with nucleus CI, Br, or I, the values of v/m are represented graphically in the diagram § 61, in which the ordinates are values of v/in, and the abscissae values of m. When this diagram is studied, it is seen that the arrangement of the curves is different in each of the three compartments which correspond to the solutions of salts having as common elements the metalloids CI, Br, I respectively, and that their differences are not altogether irregular. In the first diagram, the common element being CI, the values of v/m follow the same order as that of the arrangement for m = 1/16 in the tables, namely, KCl, RbCl, CsCl, KCIO3, RbClO,,, CsClOg. This order is maintained for m= 1/64, 1/128, 1/256. When the common element is Br or I, the arrangement of the salts with respect to the values of v/m is different. The values of v/m recorded in the general tables of Class E, with the curves in the above diagram, furnish the means of appreciating the changing characters of the different solutions with change of concentration, having regard to the numerical values of the constant v/m for the different salts for the different values of m. § 63. It is instructive to consider the order in which the salts of each hexad follow each other when arranged in ascending order of values of v/m, without paying particular attention to their actual numerical values. For this purpose it is convenient to represent each hexad of salts by a hexagon, the centre of which is occupied by the common clement, metal or metalloid, as nucleus. The angles of the hexagon are then supposed to be occupied by the residues of the respective salts after abstraction of the common element, arranged in ascending order of magnitude of v/m, the lowest value occupying the lowest angle on the paper, and the other values of v/m occupying the other angles seriatim in ascending order of magnitude, and going round from left to right. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 148 In the figure we have a hexagon the corners of which are numbered on this plan from 1 to 6. Inside the hexagon we have the common element M or E, and above it the value of m for the particular solution. The residue corresponding to the lowest value of vjm is entered at the corner numbered 1, the next higher at 2, the next at 3, and so on, the residue corresponding to the highest value of v/m occupying place No. 6. For concentrations higher than m=l/64, the arrangement of residues is the same as that given for m=l/64 in the six hexagons corresponding to the common elements CI, Br, I, K, Eb, Cs. In the accompanying figures we have the three hexagons 1/64 [CI], 1/64 [BrJ, 1/64 [I] corresponding to the nuclei CI, Br, I, and to the value of 7^=1/64. The salts corresponding to the first hexagon are CIM and ClMOg, and their residues after abstraction of CI are K, Eb, Cs, KOg, EbOg, CsOg. Entering these at the corners, on the plan above explained, in ascending order of magnitude of v/m, the residue corre- sponding to the lowest value of vjm being entered at place 1 , we find that the order in which the residues follow each other is that of the salts of the two triads CIM and Cs Rb K0„ 1/64 CI K RbO, CsO, KO, Rb Cs 1/64 Bp K RbOj CsO, RbO„ CsO, K / ^/g^ > Rb KO, Cs ClMOg, and following the ascending order of molecular weight in each triad. When the nucleus is Br, the order differs from that corresponding to CI in that the neigh- bouring residues Cs and KOg change places. When the nucleus is I, the arrangement seems to be quite diff'erent, but it is derived from that with the nucleus Br by replacing at each corner the residues M by MOg and MOg by M. If we arrange the residues in parallel lines we have : — Hexagon. Residues in ascending order of magnitude of v/m. 1/64 1/64 1/64 [01] K K KO3 Rb Rb RbOg Cs K0„ KO3 Cs CsO^ RbOj RbOg Rb CsOg CsOs Cs When the metals act as nucleus, we have the hexagons in the figures on p. 144. In each of these hexagons CI occupies place 1, Br place 'Z, and IO3 place 3. The 4th place is occupied in the consecutive hexagons by CIO3, BrOg, BrOg ; the 5th by BrOg, CIO3, I ; and the 6th by I, I, CIO3. The hexagon 1/64 [K] is derived from 1/64 [CI] by an exchange of place between I and IO3, which correspond to Cs and CsOg ; when 144 MR J. Y. BUCHANAN ON THE CIO3 and BrOg change places, we get 1/64 [Rb] ; and when CIO3 further changes places with I, we get 1/64 [Cs]. C10„ BrO, BrO. lOa ^ 1/64 ^'^° Br K I0„ Br 1/64 Rb C10„ io„ Br 1/64 Cs C10„ CI CI CI The expressions 1/64 [Cs], 1/64 [CI], etc., are used as abbreviations to mean the hexagons corresponding to the nuclei Cs, CI, etc., and the solutions containing 1/64 grm.-mol. salt per thousand grams of water. The general expressions m [R] and m [M] indicate the hexagons corresponding to salts with a metalloidal or a metallic nucleus respectively, the solutions of which contain m grm.-mol. of the salt per thousand grams of water. § 64. It has already been pointed out that the hexagonal arrangement of residues in ascending order of magnitude of vjm is the same for each nucleus at all concentrations for which m,>l/64, and we have shown how the arrangements expressed by 1/64 [R] and 1/64 [M] are derived from that corresponding to 1/64 [CI]. We now proceed to consider the case of m [R] and m [M] when m= 136-69884 + 23-25860 = 159-95744 grams. The specific gravity would therefore be : — W + ifl 159-95744 W 136-69884" : 1-170144. On admitting air into the hydrometer (Experiment No. 3), the result would be to cause the instrument to be immersed to C = 32-2 mm. in distilled water. This is arrived at in the following manner : — The internal volume occupied by the air is 112-493 c.c, and the density of the air was 0-001208 gram per cubic centimetre. The weight would therefore be a = 0'13592 gram. Since 0-1 gram added weight produces an immersion of 10-69 mm. of stem, and as the weight of air admitted is distinctly an added weight, the immersion produced by 0-13592 gram would be 10-69 X 0-13592 ..^ — = 14-5 mm. Whence 17-7 + 1 4-5 = 32-2 mm. Total weight after admission of air to hydrometer is : — Weight of shot + glass + air = W + a= 136-69884 + 0-13592 = 136-83476 grams. On immersing the hydrometer filled with air into the experimental liquid with a similar adjustment as in the first experiment ( W + w), the hydrometer would be immersed to a point short of C, since the air represents the same added weight in this case as when the hydrometer is immersed in distilled water, and the same added weight would not produce so great an immersion of the stem in the experimental liquid as in the distilled water of lower density. Hence an addition must be made to the original added weight {w) to cause the hydrometer to float at C, the 32-2 millimetres division, when immersed in the experimental liquid, and the value of this addition is the difference between the weights of the same volume of experimental liquid and distilled water represented by the volume of the portion of stem immersed when air was admitted into the hydrometer while experimenting in distilled water. Then we have seen that the weight required to increase the displacement in distilled water from C to C is the weight of the air filling the hydrometer, namely, 0-13592 gram. When the distilled water is displaced by the experimental solution. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 161 of specific gravity 1 ■170144, then the air admitted depresses the hydrometer in the solution from C to a point lower than G'. The total weight required to increase the immersion of the hydrometer in the solution from C to C is 0'13592 x ri70144 = "15 9 05 gram. Therefore, in addition to the weight of the air, we require a supplementary weight = 0'15905- 0-13592 = 0-02313 gram. The total weight of the hydrometer is : — Glass + shot =W = 136-69884 grams. Air =a = 0-13592 „ Total added weight = w' = 23 -28 1 73 „ 160-11649 „ =W + a + w'. In this case 23-25860 + 0-02313 = 23-28173 grams = the total weight added to the top of the stem. The specific gravity under these conditions is : — W 4- a + w' _ 160'11649 _ i.-,jq-,aa W + a ""136-83476" When air is admitted generally (Experiment No. 5), the line of flotation will be at another point, C", for distilled water, and, as explained above, may be represented as a deduction from the added weight, the amount being equal to the weight of air displaced by the non -immersed portion of the stem ; let s denote the value of the weight of air displaced. The volume of the non-immersed portion of stem is 0-9 c.c, and the weight of 1 c.c. air = 0-001208 gram. Therefore the weight of air displaced is s = 0-00109 gram. Now an added weight of 0-1 gram produced an' immersion of 10-69 millimetres, when the hydrometer was immersed in distilled water, so an alteration of immersion of the stem will occur, the amount being 10-69 X 0-00109 „.,, -— = 0"11 mm. Hence the final position of the hydrometer when immersed in distilled water will be C" = 32-09 mm. ; and the total weight : — Glass + shot + air=W + a= 136-69884 + 0-13592 =136-83476 grams. Less correction for non-immersed portion of stem = s = — 0-00109 ,, W + a -5=136-83367 „ In the case of the experimental liquid, the final position is nearly that of C", the actual correction for the non-immersed portion of the stem being arrived at in the same manner as above, since 0-1 gram added weight produced an immersion of the stem of 9-17 millimetres, and the volume of air displaced being the same as above, as also is the weight, the alteration of immersion will be 9-17x0-00109 „,„ jfPj = 0*10 mm. TRANS. EOY. SOO. EDIN., VOL. XLIX., PART I. (NO. 1). 21 162 MR J. Y, BTJOHANAN ON THE The scale reading would therefore be 32"10 millimetres, and as the two readings are such that the difference on the millimetre scale is imperceptible, they are taken as identical. The final weight is therefore : — Shot + glass + air + added weight = W + a + i(;'= 136-69884 + 0-13592 + 23-28170 = 160-11649 grams. Correction for non-immersed portion of stem = s = — 0-00109 ,, W + a + w'-s = 160'11540 ,, Q --c -^ 160-11540 T.,w^,,, Specific gravity = ^^^.q^^q^ = 1 170 1 44. C" is then the final position at which the surfaces of the water and of the experimental liquid cut the stem when the added weight is nothing for water and w' for the experimental liquid, and the experiment is made in air. The eff"ective downward vertical pressures are represented by the true weights W + a-s and W + a + w' - s respectively. It should be noted that in the example here given the value of the weight added to the stem of the hydrometer to cause it to float at C" = 32 09 mm. is so very nearly the same as that which caused it to float at C' = 32-2 mm., that no alteration has been made in the value of this weight, and we have, therefore, used the symbol w' in this first experiment instead of w", as given in Experiment No. 5. We have imagined that the open hydrometer was actually weighed in a vacuum, when it contained no air. In practice the hydrometer is weighed full of air and in air. When to this weight we apply the vacuum correction, that is, the weight of air displaced by the whole hydrometer and closed with its weightless cover, we obtain the value of W + a which is the working weight in vacuo of the hydrometer. In this expression, for any particular load, W is constant, it is the sum of the weights of glass and shot alone. The weight of air, a, contained in it will vary Avith the density of the atmosphere at the time. § 83. The open hydrometer consists of G,, grams (true) of glass and L„ grams (true) of shot and A,, grams (true) of air, as when weighed in vacuo. In order to obtain these constants, we first weigh the glass instrument empty as it comes from the glass-blower, and find that it weighs G grams in air of given density. Taking the specific gravity C of the glass to be 2-5, we obtain —^ as the volume (in cubic centimetres) of the glass. The weight of -^ cubic centimetres of air of the given density is a^ grams, and when added to G gives the weight in vacuo of the glass of the instrument : G„ = G + ag. Similarly, the weight of the shot added as load is found to be L grams in air, and SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 163 if we take its specific gravity to be 11 "35, the volume of air which it displaces is c.c, the weight of which at the observed density is ai grams, whence the weight in vacuo of the lead is L„ = L + a,. If the load L has been so adjusted that at the temperature, T, fixed for the experiments the hydrometer floats in distilled water at the top of the stem, then the weight of distilled water displaced by the hydrometer when so floating is in vacuo G„ + L„ + A„, whence the external volume of the whole instrument is obtained ; let this volume be V, then we have ~2-5 11'35 ^' where (p is the density of the air expressed in grams per cubic centimetre if A„ is expressed in grams. In this equation V, G„, and Lo are known, therefore J- VF5 + Tr35J" " whence In any locality

44'1 „ 9 none none A 0'97 ,, 73'0 ■'5 , 62-2 ,, r 0^7570 gram. 14^72749 grams. A 1-07 ,, 83-5 -85 , , 59^3 ,, s 0-13508 ,, 0^13028 U 1-17 ,, 94-0 •95 , , 66-8 „ t .t. /•lo 15^06 , , 74-4 ,, u 199-53624 grams. f^^ ■15 , , 81-5 ,, V 137 •00340 grams. 137-00340 ,, f^■' ■25 , , 89^1 ,, w 1-456433 /,s ■35 , , 95^5 ,, The weight 137'0034 grams entered in line v includes that of the air contained in the hydrometer. Its value is obtained in the following manner : — As the result of many determinations, of which the example in § 84 is an instance, the mean added weight necessary to immerse the hydrometer to 50 mm. at 19-50° C. was found to be 075471 gram. Hence weight of hydrometer and added weight = 136"86603 grams. Density of distilled water at 19-50° C. = 0-99834. Therefore volume of distilled water displaced ■■ 0-99834 = 137-093 c.c. SPECIFIC GEAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 169 By subtracting from this the volume of glass and shot ( = 24"6 c.c. ; see § 83), the resultant volume, 112-493 c.c, is that of the enclosed air. (The internal volume of the stem above the 50-mm. division is here disregarded.) The weight of this volume of air is obtained as follows : — Weight of 1 c.c. air under the atmospheric conditions during the experiments = 0"001208 gram. Weight of 112-493 c.c. air = 0-13592 gram. These numbers give the amount of the air contained in the hydrometer when it carries an internal load of 95-6 grams of lead shot. If this load is altered, the residual volume of air experiences a corresponding alteration. § 87. Correction for the non-immersed Portion of Stem. — When the hydrometer is floating at 50 mm. in distilled water, there is a length of stem of 75 mm. in air — namely, 50 mm. to the end of the scale, and 25 mm. to the open end of the stem. By line g of the table in § 86, we see that 10-69 mm. of scale are immersed by 0*1 gram, and 75 mm. are immersed by 0-7 gram, whence the volume of the non-immersed portion of the stem may be taken as 0-7 c.c. By the Archimedean principle the non-immersed portion of the stem displacing this volume of air loses weight equal to that of the air so displaced ; so that, were the air removed from the surface of the liquid, the hydrometer would sink into the liquid and the scale reading would be higher. The value of this difference of scale reading is the weight of air displaced by the non-immersed portion of the stem. The weight of 0-7 c.c. of air, under the atmospheric conditions quoted above, is 0-00084 gram. We have then, for the total weight which immerses the hydrometer to the 50-mm. division : — Weight of loaded hydrometer in vacuo =136-11132 grams. Weight of enclosed volume of air = 0-13592 „ Added weight to immerse stem to 50 mm. = 0-75471 „ 137-00195 Correction for exposed portion of stem = — 0-00084 Sum= 137-00111 „ This number represents the weight of distilled water displaced by the hydrometer up to the 50-mm. division when immersed in it at 19*5° C. The determination of the weight of any experimental solution displaced by the hydrometer up to the 50-mm. division is determined in a precisely similar manner. If any adjustment of the internal load of the hydrometer is made, its volume must be taken into account in estimating the volume of enclosed air. § 88. The degree of accuracy attainable by the use of the hydrometer is best TEANS. EOY. SOC. EDIN., VOL. XLIX., PAET I. (NO. 1). 22 170 MR J. Y. BUCHANAN ON THE illustrated by quoting the results of five series of observations, each series consisting of eleven independent observations made in a solution of calcium chloride containing 6 '3 gram-molecules of CaClg in 1000 grams of water. The table includes, by the method of least squares, the estimation of the probable error r of a single observation, and Tq that of the arithmetical mean of each series. It will be seen from the example given in § 86 that we obtain a series of differences between the consecutive readings corresponding to added weights of O'l gram, and, to take the first case, O'l gram immerses 10'50 mm. of stem, an added weight of 0'0095 would be required to immerse 1 "0 mm. of stem. When a series of readings has been made in the experimental solution with the hydrometer whose constants are known, the weight of solution displaced to a given scale division, which is one of the actual readings, is known, and the total weight of the hydrometer when floating at the same division in distilled water is obtained. With these data the calculation of the specific gravity of the solution is made. An example will illustrate this method : — Taking the first reading in series No. 1, using hydrometer A : 1st Reading — 4"0 grams added weight immersed 13 "9 mm. Corrected weight of hydrometer = 188'53748 grams. "Volume of enclosed air = 108'56 c.c. Weight of enclosed volume of air = 0'12880 ,, Added weight = 4-00000 „ 192-66578 Correction for exposed stem (weight of 0*9 c.c. air) = — 0*00106 Weight of solution displaced to 13-9 mm. = 192-66472 Weight of distilled water displaced to 13-9 mm. Corrected weight of hydrometer Weight of enclosed volume of air Added weight to immerse 13-0 mm. -9 mm. Stem correction (weight of 0-9 c.c. air) = 136 = 136 = = 136 -0 11132 orams. 13592 „ 24724 41042 00837 66603 00110 Weight of distilled water displaced to 13-9 mm. = 136-66493 ^ .. . 192-66472 Specific gravity = iggTgg^gg = 1-409760. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 171 The table in § 90 includes three series obtained with hydrometer A, and two obtained with hydrometer B. The values of the mean specific gravity (S) furnished by each series, and its probable error (±To), expressed in units of the sixth decimal place, are collected in the following table : — Hydrometer. S. +r„. A 1-409752 3-1 1-409746 3-5 1-409746 3-6 B 1-409727 4-5 1-409753 6-4 It will be seen that the uncertainty of the means of each series lies entirely in the sixth decimal place. The mean of the five means tabulated is 1 '409744, and its probable error is ±3*16 in the sixth decimal place. § 89. In order to reap the full benefit of the precision of which the hydrometric method is capable, the operations must be carried out with attention to every pre- caution, and the experimental data must be recorded according to strict method. Scrupulous cleanliness is of the first importance, and the operations must be carried out with attention to all the precautions usually observed in laboratories from which exact work is expected to proceed. It is important that the room in which the observations are made should have a north light and be entirely under the control of the experimenter, who is its only occupant. This is essential, because the management of the temperature of the room, which must be that which the experimenter has found by his own experience to be the one which maintains the experimental liquid constantly at the selected standard temperature while the observations are being made, is the most important element of success and the most diflicult of achievement. The conditions are similar to those which have to be observed in the room in which gas analysis is made by Btjnsen's original method, only they are rather more stringent. For myself, when I begin hydrometric observations I always lock the door, a practice which I adopted on board the Challenger and have adhered to ever since. The conclusion arrived at from the discussion on temperature conditions which is given in Section IV. on the closed hydrometer applies with equal force in the use of the open hydrometer. An interesting diiference occurs in experiments on strong solutions, since they have a lower specific heat, which may fall as low as 0'5, as in the case of most concentrated solutions of CaClg, so that the thermal mobility of these solutions is greater, and this condition may be met by allowing a somewhat increased margin of diflference between air and solution temperature when the compensating luminous flame is used. \72 90. MR J. Y. BUCHANAN ON THE Table of Specific Gravities calculated from Single Observations made with Hydrometers A and B when floating in a Solution of Calcium Chloride con- taining 6 '3 gram-molecules in 1000 grams of Water. Hydrometer A. Added Weight in Grams for Hydro- meter B. Hydrometer B. Added Weight in Grams for Hydro- meter A. Series 1. Series 2. Series 3. Series 1. Series 2. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions 4-0 4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 5-0 13-9 21-8 29-6 37-2 44-6 52-2 59-8 67-1 74-7 82-2 89-7 1-409760 735 731 730 744 749 762 776 764 762 761 14-1 21-7 29-7 37-2 44-9 52-1 59-8 67-2 74-9 82-4 89-9 1-409741 745 722 730 722 765 768 772 750 748 747 14-0 21-5 29-5 37-4 44-8 52-1 60-1 67-5 74-8 82-6 89-7 1-409750 764 741 711 731 765 741 744 760 730 767 2-05 2-15 2-25 2-35 2-45 2-55 2-65 2-75 2-85 2-95 3-05 7-1 15-9 24-5 33-5 42-8 50-8 60-0 67-9 77-8 86-0 94-8 1-409740 732 744 725 683 751 723 725 694 740 739 7-0 15-8 24-7 33-8 42-0 50-9 59-0 68-1 76-9 86-0 94-8 1-409750 742 724 696 760 742 818 790 782 740 739 Mean Specific Gravity. S 1-409752 1-409746 1-409746 1-409727 1-409753 Probable error, ex- pressed in units of the 6th decimal place of a single observation ±r. 10-3 3-1 11-6 11-9 14-8 20-1 of the arith- metical mean +r„. 3-5 3-6 4-5 6-4 The hydrometer A, constructed on the above specification, has proved itself, in use, to be an excellent model. Its volume, about 137 c.c, is very suitable, being safficiently great to secure precision without rendering it necessary to use extravagant quantities of very soluble salts, which, in the case of costly preparations, might be prohibitive. It is very steady, and this is principally due to the fact that the ballast is all contained in the bulb at the lower extremity. The position of the centre of gravity of the instrument is thus kept very low, and in the spherical bulb the ballast cannot shift. Section XIII. — On the Specific Gravity and Displacement of Solutions of Salts op the Ennead MR which have nearly the same Molecular Weight and may be looked on as " Isomeric." § 91. There are three such groups of salts in the ennead, namely, KBr and RbCl ; KI, RbBr, and CsCl ; and Rbl and CsBr. Experiments have been made on strong solutions of the first group, KBr and RbCl. To these " natural isomers " we have added SPECIFIC GRAVITY AND DISPLACEMENT OP SOME SALINE SOLUTIONS. 173 an (artificial) isomer consisting of a mixture which contains KCl and KI in equal mole- 01 + T cular proportions, so that it may be represented by the formula K — —~^ This mixture contains 3 TOO per cent, of KCl and 69-00 per cent. KI. It was found that at 19'5°C., the temperature used in these experiments, 702*25 grams of this mixture saturated 1000 grams of water. No more could be dissolved without leaving a residue. This amount was made up of 21 7 "65 grams of KCl and 484"60 grams KI, representing 2'917 gram-molecules of each salt. From the tables of solubility of these well-known salts we find that 217"65 grams of KCl saturate 632"26 grams of water at 19"5°C. ; and if we imagine that this quantity of water is wholly taken possession of by 217"65 grams of KCl, there remains 367'74 grams of water to accommodate the 484'60 grams KI. But, at 19"5° C, 36774 grams of water require 530*28 grams KI to produce saturation. Therefore, though saturated with the mixture, the 1000 grams of water is not saturated with both the individual salts. 92. Table giving Results of Specific Gravity Determinations tnade upon Solutions of Rubidium Chloride, Potassium Salt of mixed Halides, and Potassium Bromide, of different Concentrations. m. 1. W. 2. S. 3. dm i. log A. .5. d log A dm 6. A. 7. dA dm 8. V m 9. logA^-3. ^. log Ai - 3 "" 10. RbCl= 121-0. T= 19-50° C. 7 6 5 4 3 2 1 1847-000 1726000 1605-000 1484-000 1363-000 1242-000 1121-000 1-456464 1-406075 1-351760 1-292983 1-229-284 1-159851 1-083782 0050389 0054315 0-058777 0-063699 0-069433 0-076069 31031672 30890324 3-0745755 3-0598410 3-0448789 3-0297194 3-0146637 0-0141348 0-0144569 0-0147345 0-0149621 0-0151595 0-0150557 1268-140 1227-531 1187-341 1147-733 1108-865 1070-827 1034-341 40-609 40190 39-608 38 868 38-038 36-486 38-306 37-922 37-468 36-933 36-288 35-413 34-341 7-035 6-072 5-086 4-081 3060 2-027 1-000 k'^' + I- 120-35. T-19-50°C. 1j 5 4 3 2 1 1601-75 1481-40 1361-05 1240-70 1120-35 1-336904 1-280510 1-219453 1-152989 1-080182 0-056394 0-061057 0-066464 0-072807 3-0784945 3-0632893 1 0-0152052 3-0477089 0-0155804 3-0318418' 0-0158671 3-0158567 0-0159851 1198-104 1156-880 1116-115 1076-073 1037-186 41-224 40-765 40-042 38-887 39-620 39-220 38-705 38 036 37-186 4-950 3-991 3-009 2-008 1-000 KBr= 119-1. T= 19-50° G. 5 4 3 2 1 1595-500 1476-400 1357-300 1238-200 1119-100 1-343255 1-285584 1-223113 1-155257 1-081211 0-057671 0-062471 0-067856 0-074046 3-0747383 3-0601036 3-0452092 30301122 3-0149585 0-0146347 0-0148944 0-0150970 00151537 1187-786 1148-428 1109-709 1071-796 1035-043 39-358 38-719 37-913 36-753 37-557 37-107 36-569 35-898 35-043 4-996 4-018 3 022 2-013 1-000 174 MR J. Y. BUCHANAN ON THE § 93. Solubility. — The molecular solubility of each of these salts, that is, its solu- bility expressed in gram-molecules salt per thousand grams of water at 19-5° C, is : — Salt. RbCl. ^Gl + I. 2 KBr. Molecular weight .... Gram-molecules in 1000 grams water . 121 7-77 120-35 5-83 119-1 5-7 The discussion will, however, be confined to the relation of solutions of these salts which contain, per thousand grams of water, 5 or a smaller number of gram-molecules of salt. Considering the change of specific gravity over a range of concentration varying from 5 to 1 gram-molecules per thousand grams of water, that of rubidium chloride varies from i-351760 to 1-083782, that of the potassium salt of the mixed halides from 1-336904 to 1-080182, and that of potassium bromide from 1-343255 to 1-081211. Although potassium bromide has the lowest molecular weight, there is a closer agreement in the specific gravity of the solutions of this salt with those of rubidium chloride than with those of the potassium salt of the mixed halides. At the same time the nature of the change of values with change in concentration of solution, as indicated by the numbers representing the differences of consecutive specific gravities given in the column dS/dm of the tables, shows that in this respect the potassium salts exhibit a closer relationship among themselves than either of them does with rubidium chloride. Also the nature of the decrease in this value with increasing concentration seems to indicate the fact that the increase in specific gravity becomes more nearly proportional to the increase in concentration in the strongest solutions. It will be observed that the actual weight of each salt per thousand grams of water in each solution is slightly different, and if the specific nature of the salts were the same in each of these solutions, and the masses of them present in the solution were equal, as their molecular weights would in that case be, the specific gravities of these solutions and the constants derived from them would be different from those in table § 92. § 94. For comparison in this sense the specific gravities have been adjusted to the value which they would have if their gram-molecules had the uniform weight 121, which is the actual molecular weight of the heaviest of the three, namely, rubidium chloride. The following table gives the specific gravities adjusted in this sense : — Multiples of 121 grams of Salt per 1000 grams Water . Observed speoilic gravities for solutions of RbCl . CI 4- 1 Calculated ,, „ ,, K — ^ — 5 1 11 1) n -t\.jjr 1-351760 1-338724 1-292983 1-282025 1-348731 1 1-290140 1-229284 1-220131 1-226672 1-159851 1-083782 1-153815 1-157734 1-080575 1-082507 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 175 It will be observed that the adjustment of the molecular weight does not materially affect the relations of the solutions as regards their specific gravities. Returning to the consideration of the data obtained from the original experiments, the comparison of the displacements for the same concentrations in the case of solutions of each of the three salts shows a close agreement to exist between the values for rubidium chloride (which are lower in each case) and potassium bromide, while the values for the potassium salts of the mixed halides stand quite apart and are much higher than the corresponding values for the other two salts. If we compare the differences of displacements of equivalent solutions of RbCl and KBr for m = 5, thenAabci" Akbi = 0'445, and for 'm = l it is 0"702. The differences of displacements between corresponding solutions of K Cl + I and KBr are, for m = 5, A g-Cl+I ~ A KBr = 10-318, and form =1, A^ci+i- AKBr = 2-143. 2 The molecular displacement of each of these salts in crystal, as given in § 127, is RbCl = 44-710, K^^^ = 46-406, KBr =44-460, and if the sum of the displacements of the constituent materials forming the solution, i.e. 1 gram-molecule and 1000 grams of water, are compared with the displacement of the solution obtained from the constituents, the following results are arrived at : — RbCl. K^l + I. 2 KBr. Sum of displacement of constituents Displacement of solution Difference 1044-710 1034-341 1046-406 1037-186 1044-460 1035-043 10-369 9-220 9-417 Here, with regard to the change in displacement when solution is effected, the potassium salts are quite comparable, while the rubidium chloride shows a much greater change, although in the case of values for the sum of the displacements of the con- stituents, rubidium chloride and potassium bromide are the more comparable. §95. Difference of Displacement, dA. — dA gives the increment of displacement of a mass of 1000 grams of water produced by successive additions of 1 gram-molecule of salt to that already in solution. The values of v/m represent the mean increment of displacement of 1000 grams of water per gram-molecule of salt when m gram- molecules have been dissolved in iti The values of c?A from 1 to 4 gram-molecules for each salt show that, with the exception of that for the 1 gram-molecule, they are lowest in the case of potassium bromide, and the values for corresponding concentrations of rubidium chloride very closely approximate to them, while those for the potassium salt of the mixed halides show a considerable divergence. 176 MR J. Y. BUCHANAN ON THE Thus the value of dA for a 4 gram-molecule solution of potassium bromide, which is 39-358, diminishes to 36753 for the 1 gram-molecule solution, while that for rubidium chloride diminishes from 39'608 to 36"486 for the same range of con- centration, and for the potassium salt of the mixed halides the two values are 4r224 and 38-887. If we express these pairs of values as ratios, the following values are obtained : — RbCl. 2 KBr. Actual values = 39-358 : 36-753 41-224:38-887 39-608 : 36-486 Ratio = 1 : 0-9212 1 : 0-9433 1 : 0-9338 While, therefore, the values of dA closely approximate in the case of rubidium chloride and potassium bromide, yet the ratios given above show that the rate of decrease in the value of c^A for potassium bromide lies between those for the other salts, but closer to that for the potassium salt of the mixed halides. An inspection of the values of v/m shows that all the values for EbCl are lower than the corresponding values for the other two salts, although the values for potassium bromide approach very close to them, while those for the potassium salt of the mixed halides are much higher. The values of v/m for the 5 and 1 gram-molecule concentrations for each of the salts are 37'468 and 34-341 for rubidium chloride, 37-557 and 35-043 for potassium bromide, and 39-620 and 37-186 for the potassium salt of the mixed halides; and expressed as ratios, as in the case of the values for dA, we have for RbCI. K 2 - KBr. Actual values = 37-468 : 34-341 37-557 : 35-043 39-620: 37-186 Ratio = 1 : 0-9165 1 : 0-9386 1 : 0-9331 Here, the similarity of the ratios for the potassium salt of the mixed halides and potassium bromide shows a similar rate of decrease of this value v/m for these two salts, while that for rubidium chloride shows a considerable departure from either of them. The agreements which exist, when the values -, — and — for the three salts are dm m compared, seem to indicate that the molecules of rubidium chloride and potassium bromide exert almost equal effects in the displacement of solution, but the nature of change of displacement with change of concentration shows that the potassium salts are more allied in this respect. § 96. Tlie Displacement of Solutions of the Potassium Salt of the Mixed Halides when considered in reference to the Displacement of Solutions of the Constituent Salts. — The following table gives full data relating to the displacement, difference of displacement, and mean increment of displacement of solutions of different concentra- tions of potassium chloride, potassium salts of the mixed halides, and potassium iodide. The experiments were made with the open hydrometers A and B (see § 82) at the constant temperature 19-50° C. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 177 Conoen- tration in gram- molecules per 1000 grams of Water. KCl. ^ 2 • KI. Displace- ment. A. Difference of Dis- placement. dA dm Mean Incre- ment of Displacement. V m Displace- ment. A. Difference of Dis- placement. dA dm' Mean Incre- ment of Displacement. V m Displace- ment. A. Difference of Dis- placement. dA dm Mean Incre- ment of Displacement. V m' 5 4 3 2 1 1/2 1123-005 1090-533 1059-617 1028-904 1014-001 32-472 30-916 30-713 29-806 30-751 30-178 29-808 28-904 28-002 1198-104 1156-880 1116-115 1076-073 1037186 1018-343 41-224 40-765 40-042 38-887 36-308 39-620 39-220 38-705 38-036 37-186 36-686 1240-334 1190-788 1141-787 1093-384 1046-189 1022-778 49-546 49-001 48-403 47-195 46-822 48-067 47-697 47-262 46-692 46-189 45-556 The composite salt was prepared by mixing the component salts KCl and KI in the proportion of their molecular weights, 74-6 : 166"1, so that 1 gram-molecule of the salt, which weighs 120 '35 grams, would contain |- gram-molecule of each of the salts, namely 37"3 grams of KCl and 83'05 grams of KI. When 1 gram-molecule of this salt is dissolved in 1000 grams of water, the displacement of the resultant solution may be compared with the mean of the displacements of the solutions KCl-MOOO grams of water and Kl-t- 1000 grams of water. The following table gives the results of such a comparison : — § 97. Table of Values of Displacements of Solutions of Potassium Salts of the Mixed Halides which have been obtained — A, by experiment. B, calculated by the method detailed above. B — A, the difference of calculated and observed results. Concentration in gram-molecules per 1000 grams Water. m. A. B. B-A. 5 4 3 2 1 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1198-104 1156-880 1116-115 1076073 1037-186 1018-343 1009071 1004-474 1002-213 1001-122 1000-535 1000-262 1000-117 1000-044 1156-896 1116-160 1076-500 1037-546 1018-389 1009-090 1004-495 1002-228 1001-118 1000-559 1000-282 1000-133 1000-076 0-016 0-045 0-427 0-360 0-046 0-019 0-021 0-015 - 0004 0-024 0020 0-016 0-032 This table shows that, with the possible exception of the 1/32 gram-molecule solution, the mixture of mKCl-|- 1000 grams of water and mKI -|- 1000 grams of water is accompanied by contraction. TRANS. BOY. SOC. EDIN,, VOL. XLIX., PART I. (NO. 1). 23 178 MR J. Y. BUCHANAN ON THE Section XIV. — The Specific Gravity and the Displacement of Solutions OF the Chlorides of Beryllium, Magnesium, and Calcium. § 98. For the purpose of determining these constants, hydrometric observations were made on solutions of the three salts the concentrations of which ranged from 1/2 to 1/1024 gram-molecule per thousand grams of water, the experiments being made with the closed hydrometers Nos. 3 and 17. Experiments were also made on strong solutions of calcium chloride and magnesium chloride, using the open hydrometers A and B ; the concentrations of these solutions varied from 1 gram-molecule per thousand grams of water to the highest attainable degree of supersaturation. It was when the experi- ments on a supersaturated solution of calcium chloride were in progress that the observations were made which revealed the remarkable state of unrest in that solution which preceded its partition into crystals and mother-liquor with liberation of heat. The details of this experiment are given in Section XV., and from them it will be seen that the range of supersaturation which can be explored hydrometrically when the salt in solution is chloride of calcium is considerable. The solution of magnesium chloride which is saturated at 19"5°C. contains 5918 gram-molecules (564"123 grams) of MgCla in 1000 grams of water. A supersaturated solution, containing 5'982 gram- molecules of salt per thousand grams of water was cooled to 16"5° C, at which tempera- ture the saturated solution contains 5'853 MgClg per thousand grams of water; yet, with this small degree of supersaturation, the slightest disturbance, such as lifting the beaker, induced crystallisation in the solution. This shows that the limits of super- saturation are restricted, and that it would certainly be discharged by an attempt to make hydrometric observations in the solution. This difference in the behaviour of the supersaturated solutions of these two salts is interesting. On the one hand we have the calcium chloride, which produces a high degree of supersaturation with great absorption of heat, and offers great resistance to crystallisation ; while magnesium chloride can produce solutions attaining only to a moderate degree of supersaturation with very moderate absorption of heat, and the salt crystallises from such solutions on the slightest provocation. With a view to a com- parison with the thermal behaviour of chloride of calcium, some observations were made on the heat of solution of magnesium chloride in water, while experiments were being made to determine the concentration of solutions saturated with the salt at difl'erent temperatures. It was found that when the quantities of the crystallised salt MgCl2,6H20 and water used were such as to produce a solution the concentration of which was about 2'0 gram-molecules of JMgClg per thousand grams of water, the dissolution of the salt was accompanied by an appreciable liberation of heat. When the conditions of the experiment were such that a saturated solution was formed, some of the crystals remaining undissolved, the dissolution of the salt was accompanied by absorption of heat. When the saturated solution was produced by fractions, it was observed that during the dissolution of the first fraction the thermometer indicated a SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 179 § 99. Table giving Specific Gravity Values obtained from Experiments made upon Solutions of the Chlorides of Beryllium, Magnesium, and Calcium. m. W. S. log A. dlog A dm A. dA. V m logA„-3_^ logAi-3 a; -TO. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. BERYLLIUM CHLORIDE = BeC]a=80-00. T=19-60°C. 1/2 1040-0000 1-025620 3-0060468 1014-0208 28-04 1 X 2-000 1 _1 m X 0-000 1/4 1020-0000 1-013055 3-0029671 0-0123188 1006-8555 7-1663 27-42 4-076 -0076 1/8 1010-0000 1-006599 3-0014618 0-0120181 1003-3785 3-4770 27-03 8-256 -0-256 1/16 1005-0000 1-003347 3-0007149 0-0119995 1001-6745 1-7310 26-37 16-916 -0-916 1/32 1002-5000 1-001587 3-0003957 0-0102144 1000-9115 0-7360 29-17 30-562 + 1-438 1/64 1001-2500 1-000742 3-0002204 0-0112192 1000-5076 0-4039 32-49 54-870 + 9-130 1/128 1000-6250 1-000325 3-0001302 0-0115430 1000-2999 0-2077 38-39 92-872 + 36128 1/256 1000-3125 1-000083 3-0000996 0-0078259 1000-2296 0-0704 58-75 121-362 + 134-638 1/512 1000-1562 0-999957 3-0000865 0-0067225 1000-1992 0-0303 101-99 139-778 + 372-222 1/1024 1000-0781 0-999906 3-0000747 0-0120832 1000-1720 0-0272 176-13 166-854 + 862-146 MAGNESIUM ( DHLORIDE = MgCl2 = 95-32. T=19-50°C. 5-9820 1570-2050 1-338895 3-0692097 1172-7345 28-87 X 7-638 x-m 1-656 5-9182 1564-1230 1-336101 3-0684316 0-0121959 1170-6623 2-0722 28-84 7-453 1-535 5-5 1524-2600 1-317763 3-0632219 0-0124574 1156-7032 13-9591 28-49 6-886 1-386 50 1476-6000 1-295011 3 0569894 0-0124650 1140-2-220 16-4812 28 04 6-207 1-207 4-0 1381-2800 1-246666 30445317 0-0124577 1107-9793 32-2427 26-99 4-850 0-850 3-0 1285-9600 1-193986 3-0322282 0-0123035 1077-0310 30-9483 25-68 3-510 0-510 2-0 1190-6400 1-136425 3-0202398 0-0119884 1047-7070 29-3240 23-86 2-204 0-204 1-0 1095-3200 1-072407 3-0091814 0-0110584 1021-3660 26 3410 21-37 1-000 1 0-000 1 1 1/2 1047-6600 1-037385 3-0042803 0-0098020 1009-9047 11-4613 19-81 2-146 TO X -0-145 1/4 1023-8300 1-019096 3-0020127 0-0090705 1004-6453 5-2594 18-58 4-662 -0-562 1/8 1011-9150 1-009675 3-0009624 0-0084024 1002-2185 2-4268 17-75 11-982 -3-982 1/16 1005-9575 1-004893 3-0004598 0-0080422 1001-0693 1-1592 16-96 19-968 -3-968 1/32 1002-9787 1-002461 3-0002242 0-0075385 1000-5164 0-5429 16-52 40-948 -8-948 1/64 1001-4893 1-001244 3-0001063 0-0075411 1000-2450 0-2714 15-68 86-299 -22-299 1/128 l('00-7446 1-000639 3-0000458 0-0077516 1000-1055 0-1395 13-50 200-336 -72-336 1/256 1000-3723 1 -000299 3-0000318 0-0036865 1000-0732 0-0323 18-74 288-542 -36-642 1/612 1000-1861 1-000172 3-0000066 0-01-29587 1000-0150 0-0682 7-68 1410-353 -898-353 1/1024 1000-0930 1-000082 3-0000047 0-0017715 1000-0110 0-0040 11-26 1920-796 -896-795 CALCIUM CH LORIDE = Ca Clj = lll-00 T = 19-50 °C. 6-627 1735-620 1-424183 3-0858888 1218-6775 33-00 X 8-279 x-m 1-652 6-613 1734-043 1-423500 3-0857023 0-0133214 12181540 0-5233 32-99 8-261 1-648 6-6 1732-600 1-422871 3 0855327 0-0130461 1217-6787 0-4753 32-98 8-246 1-645 6-5 1721-500 1-418572 3-0840556 0-0147710 1213-5441 4-1346 32-85 8-102 1-602 6-4 1710-400 1-414247 3-0825725 0-0148310 1209-4069 4-1372 32-72 7-959 1 559 6-3 1699-300 1-409741 3-0811308 0-0144170 1206-3988 4-0081 32-60 7-820 1-5-20 6-2 1688 200 1-405270 3-0796641 0-0146670 1201-3349 4-0639 32-47 7-697 1-497 6-1 1677-100 1-400460 3-0782883 0-0137580 1197-5352 3-7997 32-38 7-546 1-446 6-0 1666-000 1-395919 3-0768148 00147350 1193-4791 4-0561 32-24 7-421 1-421 5-0 1555-000 1-342961 3-0636673 0-0131475 1157-8899 35-5892 31-68 6-165 1-165 4-0 1444-000 1-284536 3-0508210 0-0128463 1124-1413 33-7486 31-03 4-899 0-899 3-0 1333-000 1-2-27685 3-0357431 0-0150779 1085-7832 38-3581 28-69 3-445 0-445 2-0 1222 000 1-160139 3-0225612 0-0131819 1053-3221 32-4611 26-66 2-175 0-176 1-0 1111-000 1-084776 3-0103741 0-0121871 1024-1745 29-1476 24-17 1-000 1 0-000 1 1 1/2 1055-5000 1-043739 3-0048663 0-0110155 1011-2681 12-9064 22-54 X 2-132 m X -0-132 1/4 1027-7500 1-022253 3-0023290 0-0101489 1005-3773 5-8908 21-50 4-454 -0-454 1/8 1013-8750 1-011231 3-0011340 0-0095604 1002-6146 2-7627 20-92 9-148 -1-148 1/16 1006-9375 1-005660 3-0005513 0093233 1001-2703 1-3443 20-32 18-817 -2-817 1/32 1003-4687 1-00-2763 3-0003055 0-0078656 1000-7037 0-5666 22-62 33-954 -1-964 1/64 1001-7343 1-001423 3-0001349 0-0109145 1000-3109 0-3928 19-90 76-851 -12-861 1/128 1000-8672 1-000729 3-0000599 0-0096038 1000-1380 0-1729 17-66 173-017 -45-017 1/256 1000-4336 1-000378 3-0000241 0-0091699 1000-0556 0-0824 14-23 429-747 -163-747 1/512 1000-2168 1000179 3-0000163 0-0039680 1000-0378 0-0178 19-35 632-963 -120-963 1/1024 1000-1084 1-000093 3-0000066 0-0099430 1000-0154 0-0224 15-77 1553-009 -529-009 180 MR J. Y. BUCHANAN ON THE rise of temperature. On adding further fractions of salt this ceased, the thermal effect was reversed, and when saturation had been effected the temperature of the solution had fallen below the initial temperature of the water used. No experiments have been made on solutions of beryllium chloride of greater con- centration than 1/2 gram-molecule per thousand grams of water. The preceding table contains all the experimental results and the deductions there- from. The form and the symbols used have been already explained. § 100. Before discussing the data of the tables, attention must be directed to the distinctive characters of the three salts. While the bases BeO, MgO, and CaO give an alkaline reaction with litmus paper, the chlorides of magnesium and of calcium are neutral, while that of beryllium is acid. In order to obtain, if possible, a neutral solution of BeCl2, the method adopted was to proceed by way of the sulphate and double decomposition with chloride of barium. A solution of pure crystallised sulphate of beryllium, containing exactly 1 gram-molecule of BeSO^ in 1000 grams of water, was made, and with it was mixed a quantity of a solution of barium chloride containing exactly 1 gram-molecule of BaClg in 1000 grams of water. The barium sulphate was precipitated completely, and the supernatant liquid contained exactly 1 gram-molecule of BeCla in 2000 grams of water, or, at the rate of 1/2 BeClj in 1000 grams of water. This solution, which still had an acid reaction, was used for the preparation of the less concentrated ones by exact dilution. It is impossible to produce solutions in this way for which m>l/2, on account of the bulk of the barium sulphate produced. Solutions of the highest attainable degree of concentration were prepared in the case of magnesium chloride and calcium chloride, the concentration being determined by the usual chemical methods, and the solutions of a lesser degree of concentration were prepared from these. In all cases the solutions were prepared by diluting the more concentrated solution immediately preceding it, a method capable of a high degree of precision, which is shown by the fact that, after the experiments on strong solutions of MgClj were com- pleted, a single determination of the concentration of the 1 gram-molecule solution of MgCla gave a result of 0'9991 gram-molecule of salt in 1000 grams of water. The result was obtained by a determination of the chlorine content. Chlorine found . . . . . . . 6'62 per cent. ,, ealoulated ...... 6'63 DifF. 0-01 The specific gravity experiments were carried out by the use of the open hydro- meters A and B in the case of strong solutions of the salts, magnesium chloride and calcium chloride ; and by the use of the closed hydrometers Nos. 3 and 17 in the case of the solutions of each of the three salts where the concentrations were less than 1 '0 gram-molecule of salt in 1000 grams of water. The constant experimental temperature was 19 "50° C. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS, 181 Concentration of the Solutions (m). — The highest concentrations were those of slightly supersaturated solutions in the case of magnesium and calcium chlorides. The solution of magnesium chloride which is saturated at 19 "50° C. contains 5 "9 182 gram- molecules of salt in 1000 grams of water, and is the second of the series of strong solutions of this salt. The solution containing 5*5 gram-molecules of salt was prepared from this solution, and then solutions were experimented on having a common difference of 1 gram-molecule, and ranging from 5'0 to TO gram-molecule. The 6 "6 27 gram-molecule solution of calcium chloride is supersaturated, and the 6 "6 13 gram-molecule forms a solution which is saturated with CaClg at 19*50° C This solution is of interest as being the mother-liquor obtained after crystallisation from the solution which showed the condition of unrest described in Section XV. The experi- ments on this solution were made at a much earlier date than the others included in this table, but the results are included here in order to give a complete list of the experiments made. As will be seen, the solutions for which ?n = 6"6 to 6'0 decrease regularly in concentration by O'l gram-molecule. They were made in order to trace the changes of displacement due to small changes of concentration in nearly saturated solutions. For m. = 6 "0 to 1 "0 gram-molecules the common difference of concentration of consecutive solutions is 1 "0 gram-molecule. Discussion of Results. Specific Gravity. — With regard to the agreement of the individual results among themselves for a particular series, the analysis of the specific gravity results in the case of the calcium chloride solution containing 6'3 gram- molecules of salt in 1000 grams of water (see § 90) affords a fair criterion, and the usual number of series of observations made for each concentration was six, three with each hydrometer. In all the experiments the results of which are included in these tables, the temperature of the solution remained constant at 19'50° C. Comparing the specific gravities of solutions of the three salts, having the same molecular concentration, and m being less than 1"0, the values in all cases increase with increasing molecular weight. Thus, for m=l/2 the specific gravities of the solutions rise from 1 "025620 for BeCla to 1-037385 for MgCla and to 1-043739 for CaCl2, and the same feature is observed in comparing the values for all concentrations down to m = 1/1024. It is interesting to compare the increments of specific gravity (S— 1), (which for this purpose are conveniently multiplied by 1000), of the solutions with the molecular weights of the salts dissolved in them. We have them in the following table, for solutions for which m — 1/2 : — MR = BeCl^. MgCla. CaCla. 1/2 MR = 40 47-66 55'5 1000 (S-1) = 25-620 37-385 43739 1000 (S-1) ^ Q.g^Q Q.^g^ Q.;j.g^ 1/2 MR When m= 1/16 and 1/128 we have the following values : — 182 MR J. Y. BUCHANAN ON THE ■MR = BeCla. MgCl2. CaCls. ^^?n}t~J^ = 0-669 0-821 0-815 1/16 MR \T.1^Jt!^ = 0-520 0-858 0-841 1/128 MR From this table we see that the increment of specific gravity produced by dissolving 1/2 ME in 1000 grams of water is exactly proportional to the molecular weight of the salts in the case of MgClj and CaClj, and that this proportionality is maintained for values of m=l/l6 and 1/128. In the case of BeClg, however, the proportionality fails. It will be remarked that the specific gravities of the solutions of beryllium chloride for which m = 1/512 and 1/1024 fall below unity, and the values are quite authentic. It follows that the displacements of these two solutions must be greater than the sum of the displacements of the salt and the water which they respectively contain. A similar feature is observed in the saturated solutions of caesium salts, § 127, Table III. Comparing the values of c?S for concentrations greater than 1/2 gram-molecule, they diminish from 0"064018 for MgClj at 1"0 gram-molecule concentration to 0'048345 at 4*0 gram-molecules, while in the case of CaCL the values are 0-075363 at 10 gram- molecule, and 0-058415 at 4-0 gram-molecules concentration. The variation in the values of dS for solutions of CaClj between m = 6-0 and m = 6-6 does not exhibit itself in a regular decrease but an oscillatory one, for the value at m = G'O is 0-004541, rising to 0-004810 at m = 6-l, with a fall to 0-004471 at to = 6-2, rising slightly again at ?)i = 6"3 to 0'004506, then decreasing to 0"004325 at m = 6'4: and to 0-004299 at7H = 6-5, the general tendency being to decrease in value with increasing concentration. S 101. Values of -^ — and — . — The features of the displacement of the solutions are dm m best exhibited by discussing the values of ^ — and — . The values of -,— are obtained dm m dm from columns 7 and 1. The solutions of the salts with concentrations less than 1 gram-molecule give values for -^ — which are highest in the case of beryllium chloride, while those of magnesium chloride are lowest, those of calcium chloride being intermediate. cZA The value of -^ for beryllium chloride solution when m=lj2 is 28-66, and this decreases to 23-55 when •hi=1/32, rising to 26-58 at m= 1/128. There are two low values, namely, 18"02 and 15"51 at m= 1/256 and 1/512 respectively, with a value of 27-85 at TO =1/1024. In the case of magnesium chloride the value of -y— at m= 1/2 is 2292, and the value decreases with succeeding concentrations to the value 17'37 at m= 1/32, which SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 183 The value The is also the value at m= 1/64. There is a slight rise to the value 17'86 at m= 1/128, and a sudden fall to 8-27 at m= 1/256, with an equally sudden rise to 29-80 at m = 1/512. The value at 7n= 1/1024 is 4-10. In the case of calcium chloride there is a steady decrease from the value of 25 '81 at m=l/2 for -=i— to 8'13 where m, = l/32, with a rise to 25-14 at m=l/64. decreases to 21 '09 at m= 1/256, where there is a sudden fall to 9-11 at m = 1/512 value at m= 1/1024 is 22-94. The values for vjm for concentrations below m = 1 are on arithmetical grounds more regular in all three cases than the corresponding values for -=— . The value for beryllium chloride at m = l/2 is 28 '04, and this value decreases regularly to 26 '37 at m= 1/16, where there is a rise to 3839 at m= 1/128, after which the rate of increase is greatly augmented, and reaches a value of 17fi'13 at wi= 1/1024. The value of vjm for magnesium chloride at m = 1/2 is 19'81, decreasing to a value of 13-50 at m= 1/128, and rises to 18-74 at m= 1/256, with a sudden fall to 7-68 at m= 1/512, rising to 11-26 at m= 1/1024. Calcium chloride shows the least tendency to sudden variations in the values of vim, since the maximum amplitude is between 22-54 and 14-23 at m=l/2 and m= 1/256 respectively. With the exception of the value 22'52 at m= 1/32, there is a fairly regular decrease between the two values quoted above, the rate of decrease taking place in two phases, the rate being greater between m= 1/32 and 1/256 than between TO = 1/2 and 1/32. There is a rise to a value of 19-35 at to= 1/512, and this decreases to 15-77 at m = 1/1024. It is seen that the value of vjm at m=l/2 is highest in the case of beryllium chloride and lowest in the case of magnesium chloride, while that of calcium chloride more nearly approaches that of magnesium chloride. The rise in the value of vjm for calcium chloride, where m — 1/2, over that of magnesium chloride is almost exactly proportional to the rise in molecular weight. § 102. The values of (dA — v) have been treated in the way fully set forth in Section VIII. for the solutions of the salts of the enneads MR and MR'Oj. It is there- fore sufficient to give here a table of the values of (dA — v) in the case of solutions of mBeCla, wMgCli, and mCaClz in 1000 grams of water, for which mm. Considering the solutions of BeClj, we see that the values of {l/m — 1/x) change sign for a value of m lying between 1/16 and 1/32. The behaviour of the solutions of BeClj is, in this respect, quite remarkable. If column 6 be referred to, it will be seen that for 1/128. 0-2999 1/256. 0-2295 1/512. 0-1992 1/1024. 0-1720 A - 1000 SO that for these very different concentrations the displacements are very nearly the same. This depends on the remarkably low specific gravities of these solutions, which was commented on in § 100. In the following table, which is constructed on the same scheme as Table VIII., § 45, the solutions of each salt are taken in successive pairs. The numbers in it represent the values & ^ = x, or the exponent of the displacement A^ when the exponent of log ^-A^ 2" A^ is taken as unity. If the solutions conformed to the logarithmic law, the value of X should be 2. Table giving the Values of ^ ™ for the three Salts, Beryllium Chloride, "2 Magnesium Chloride, and Calcium Chloride. ?». 6-0. 4-0. 2-0. 1-0. 1/2. 1/4. 1/8. 1/16. 1/32. 1/64. 1/128. 1/256. 1/512. BeClg MgCl^ CaClg 2-154 2-149 2-200 2-253 2-204 2-175 2-145 2-132 2-038 2-127 2-089 2-025 2-091 2-054 2-049 2-093 2-057 1-807 2 051 1-804 1-795 2-107 2-263 1-692 2-321 2-251 1-307 1-440 2-484 1-152 4-888 1-473 1-158 1-362 2-454 Here again the radical changes which take place in the properties of the solutions when the values of m fall below 1/16 are apparent, and particularly so in the case of the solutions of BeCh. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 185 Section XV. — On a Remarkable State of Unrest in a Supersatdrated Solution oe Calcium Chloride before Crystallising. § 104. The primary purpose for which the open hydrometer was designed was to investigate the specific gravity and the displacement of solutions having concentra- tions in the neighbourhood of that of saturation. In § 90 we have seen the satisfactory result of experiments made for this purpose with solutions of chloride of calcium containing 6 '3 grm.-mols. CaClg per 1000 grams of water. Experiments in the same direction were made with solutions of chloride of calcium of still higher concentration. A parent solution was made, which, on the basis of published data relative to the solubility of the salt, should be supersaturated at 19 "5° C. With it, it was intended to produce the solution saturated at this temperature, and to study its specific gravity and that of solutions formed by diluting it with small quantities of water. As the solution showed no inclination to crystallise, although every opportunity was offered to it to do so, it seemed to me to be an example of a supersaturated solution peculiarly adapted to closer study. Its composition was determined, and it was found to contain 7 "225 grm.-mols. of chloride of calcium dissolved in 1000 grams of water. Its specific gravity was determined with the hydrometer exactly as if it had been a non-saturated solution. Two hydro- meters were used for this purpose. They are designated A and B respectively. That designated A is the hydrometer whose constants have been set out in detail in Section XI. The hydrometers were made at different dates and on different specifica- tions, though possessing the same general characteristics. In Table I. are given the constants of both these instruments when loaded so as to float with small added weight, (a) in distilled water, and (6) in a supersaturated solution of calcium chloride, respectively. The entries opposite " weight of glass " and " weight of lead shot " in these tables are the approximate weights in air of these substances, which are required for the estimation of the corresponding volumes. The entries opposite "weight of the loaded hydrometer" are the exact weights, as in iiacuo, of the glass -t- lead forming part of each instrument. To each of these weights has to be added that of the air contained in the instrument. The external volume of the hydrometer is independent of the internal load which it carries. It is entered only in (a), line 6. The " internal space occupied by air" is arrived at by subtracting the sum of the volumes of glass and of lead from the external volume of each hydrometer respectively. The mass of the air which fills this space depends not only on the volume of that space, but also on the density of the air which forms the atmosphere of the laboratory at the time of the experiment. TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 24 186 MR J. Y. BUCHANAN ON THE Table I. Constants of Hydrometers A and B when loaded so as to float with small added Weight, {a) In Distilled Water, and (b) In a Supersaturated Solution of Calcium Chloride. (a) Distilled Water. Hydrometer A. Hydrometer B. Weight of glass ........ grams Volume ,,.... . . . c.c. Weight of lead shot used for internal load . grams Volume „ „ ,, . c.c. Weight of the loaded hydrometer as in vacuo . grams External volume of hydrometer . . c.c. Internal space occupied by air . . ■ c.c. Volume of stem from zero scale division to the top of the stem c.c. 40-5 16-2 95-6 8-4 136-1113 137-09 112-49 1-2 38-11 15-24 78-00 6-87 115-1026 118-09 95-98 1-0 (b) SUPERSATUEATED CaLCIUM ChLOEIDB SOLUTION. Weight of glass . . . ... grams Volume ,, . . . ... . c.c. Weight of lead shot used for internal load . , . grams Volume ,, ,, ,, . . c.c. Weight of the loaded hydrometer as in vacuo grams Internal space occupied by air . . . c.c. 40-5 16-2 148-3 13-1 188-8312 107-79 38-11 15-24 125-4 11-05 163-5755 91-80 The use of these constants in arriving at the volume of air enclosed in the hydro- meter, and in the reduction of the -weight of the hydrometer in air to its value in vacuo, has been described in Section XL A little consideration and experience enables the experimenter to adjust the internal load so that the greatest possible range of specific gravity may be covered without altering it. The inferior limit of this range corresponds to a solution of such density that the hydrometer floats in it, immersed up to the highest division in the scale, with- out the addition of any external weight. The superior limit of the range corresponds to a solution of such density that the external weight to be added in order to immerse it to the lowest division on the scale begins to endanger the stability of the hydrometer as a floating body. § 105. Experiments and Observations tvith Hydrometers A and B. — The first set of determinations of the specific gravity of the supersaturated solution (7 "225 CaCla-l- 1000 grams of water) was made on 11th May 1910 in one of the smaller rooms of the Davy -Faraday Laboratory. The room has a northerly exposure, which is essential, and in other respects it is well suited for this class of investigation (§ 24). A series of observations had been made with each hydrometer, and further observa- tions were proceeding, when it was noticed that discrepancies between successive SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 187 readings and corresponding ones in the earlier experiments made with the same added weights were occurring, and that these were far greater than any which could be attri- buted to errors of observation. They persisted while four series of observations were made — two sets with each hydrometer — and were so great that in the fifth series of observations it was necessary to reduce the initial added weight in order that the complete series of observations might be made. Throughout each series of experiments the temperature of the solution remained absolutely constant at 19 "50° C. After the removal of hydrometer A from the experi- mental solution, on the completion of the fifth series of observations, the solution was stirred carefully with the standard thermometer, and its temperature was found to be 19"50° C, that of the air being 19'30° C. It was not until after these observations had been made that a cloudiness indicating the commencement of crystallisation appeared in the solution. It increased rapidly, and the temperature rose smartly to 23"16° C and remained constant from 1.10 p.m. to 2.35 p.m. — a period of 85 minutes — when the temperature began to fall. A careful record of the thermal and other observations throughout the whole experiment was kept, and the following is a resume of these data : — Weight of solution + cylinder =1270'190 gram s. Weight of cylinder = 463-580 „ Weight of solution taken for observations with the hydrometers = 806 '6 10 ,, This solution was 7'225 CaClg+lOOO grams of water, and contained 44*48 per cent. CaClg. § 106. Thermal Data. — When the hydrometer A had been removed from the solution after the fifth series of observations, the time was 1.5 p.m. The solution was stirred with the thermometer, gently, and the temperature noted at 1.8 p.m. It was at this time that the crystals appeared in the solution, and its temperature rose in less than one minute to 23'16° C. arid then rem^ained stationary until 2.35 p.«i., while that of the air in the room varied only between 19 '2° and 19 "4° C. When the tempera- ture of the crystals and the solution had fallen somewhat the cylinder was placed in water of 19'3° C. and cooled to 19'5° C, when the mother-liquor was found to have the specific gravit}^ 1*423500 and to contain 42'33 per cent. CaCl2. § 107. Rate of Cooling of Original Solution. — The crystals, together with the mother-liquor in the cylinder, were then heated to a temperature of 30° C. by placing the cylinder in a water-bath of that temperature and keeping it there until the crystals were re-dissolved. The system was then allowed to cool in the air, the temperature of which remained constant at 19 '3° C, and the temperature of the cooling liquid was taken at intervals of 30 seconds. The series of observations extended over 41 minutes, during which the temperature 188 MR J. Y. BUCHANAN ON THE 0-0 +0-5 +1-0 +1-5 +2-0 23-16° 23-14° 23-12° 23-09° 23-07° fell from 23-82° C. to 21-99' C. and the solution remained liquid to the end. The cooling had proceeded for 13 minutes before the temperature fell to 23-16° C, and the loss of heat was taking place quite regularly. The following are the temperatures observed at each half-minute for two minutes before and two minutes after the temperature 23-16° C. was passed : — Time in minutes : -2-0 -1-5 -TO -0-5 Temperature: 23-23° 23-21° 23-19° 23-17° During the four minutes the temperature fell 0-16° C, whence 0-04° C. per minute represents the mean rate of fall of temperature when the system has the temperature 23-16° C. and is cooling in air of constant temperature 19-30° C. § 108. Calculation of Heat liberated during Crystallisation. — The first thermal effect observed was when crystallisation began. The temperature of the system rose in less than a minute from 19-5° to 23-16°. During this phase the glass cylinder, as well as its contents, was warmed 3-66°. The heat liberated in this act depends on the weight of the solution, on its specific heat, and on the rise of temperature. In determining the thermal exchange which has taken place, we have to take account of the capacity for heat, which is generally represented by the " water-value," of the cylinder. The numerical data required in this calculation are the following : — Weight of CaCla solution Its specific heat (Regnault) . Whence, water-value of solution . Weight of cylinder Specific heat of glass . Whence, water-value of cylinder Rise of temperature . Whence, heat liberated in first act (513-00 -I- 92-72)3-66 = 2217 gr.° C. After the first minute, when the temperature had become constant at 23-16°, the rate of liberation of heat was exactly equal to its rate of dissipation, which we have found to be represented by a fall of temperature of 0-04° per minute. This state was maintained for 85 minutes, which requires a liberation of heat, in the second act, of 85 X 605-72 x 0-04 = 2059 gr.° C. Adding the 2217 gram-degrees liberated in the first act, we find the total heat evolved during the interval of 85 minutes to be 2059 + 2217 = 4276 gr.°C. § 109. In order to verify the state of unrest above described, the experiment was repeated with a 7-196 CaCl2 solution (§ 113), and after crystallisation was completed, the crystals were removed and freed as far as possible from adherent mother-liquor, and their composition ascertained by estimation of the chlorine contained in a weighed quantity. The results of duplicate determinations gave the composition of the crystals 806 61 grams. 636 513 00 grams. 463 58 5) 2 92 -72 grams. 3 66^ C. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 189 SO obtained as CaClaG-SHaO and CaCl26'4H20 respectively. It is obvious, therefore, that the crystals which were deposited had the composition CaClaGlIaO, and that the excess of water indicated by the analyses was due to some adherent mother-liquor, from which it is almost impossible to free the crystals. That the crystals deposited in the first experiment had the composition CaClsSHgO is confirmed by the thermal data already set forth. The weight of original calcium chloride solution which crystallised in the cylinder was 806"61 grams. It contained 44'48 per cent. CaClg. The mean of the first series of specific gravities — 1 "44601 9 — is taken as the specific gravity of this solution when at rest. The concentration of the solution is therefore : — Per Cent. By Weight. CaClg . . 44-48 359-0 grams. Water . . 55-52 447 6 „ Total . . 100-00 806-6 „ i After the crystallisation was ended, and with the solution at a temperature of 19 '5° C, one determination of the specific gravity of the mother-liquor gave the result 1-423.500. The concentration of the mother-liquor determined by analysis was 42'B3 per cent., equivalent to 734'0 grams, or 6'613 gram-molecules CaClj per 1000 grams water. The crystals (CaClgSHaO) contain 50 '6 8 5 per cent. CaClg. The cooling observations showed that the heat evolved in the act of crystallising was 4276 gr.° C. According to Thomsen, the heat of solution of CaClaeHaO is - 4340"0 gr.° C. ; there- fore on thermal evidence alone 215"5 grams, or 0'984 CaClaSHaO, has separated out. But, on the basis of the analytical estimations made on the supersaturated solution and the mother-liquor, we find that 210"3 grams of crystals separated out of 806'61 grams of solution, or 96 gram-molecule CaCl26H20. The agreement of these two computed values is excellent. We accept then as the quantities of crystals and mother-liquor 210"3 grams and 596 '3 grams respectively. § 110. The nature of the experiments having been indicated, and the general character of the thermal change and the alterations in specific gravity mentioned, the following table, IIa., gives a complete account of the individual observations of specific gravity made, together with the corresponding displacements calculated from them. Table IIb. gives a similarly complete account of the individual observations of specific gravity in five series made in the solution 6*3 CaCl2-l- 1000 grams of water at 19'5° C, with the corresponding displacements calculated therefrom. The solution of calcium chloride saturated at 19'5° C. is 6 613 CaClj-f-lOOO grams of water; therefore the 6*3 CaCla solution, though of high concentration, is. sufficiently removed from saturation to exhibit the tranquillity of a dilute solution. 190 ME J. Y. BUCHANAN ON THE Table II a. Table of Observations made with Hydrometers A and B when floating in the Supersaturated Solution 7"225 CaCl^ + 1000 grams of Water at 19'5" C. before Crystallisation. Hydrometer A. Hydrometer B. Series 1 (10.45 a.m.-11.5 a.m.). Series 2 (11. 3C a.m.-11.45 a.m.). Added Weight in Grains. Scale Reading in Millimetres. Specific Gravity calculated from Single Observations. Displace- ment. Added Weight in Grams. Scale Reading in Millimetres. Specific Gravity calculated from Single Observations. Displacement. 8-65 13'7 1-445961 1245^71 6^1 7^8 r445905 1245-7.6 8-75 20-9 5972 •70 6^2 16^9 5826 •83 8-85 28-1 6034 •64 6^3 25^3 5837 •82 8-95 35-6 6044 •63 6^4 34^0 5828 •83 9-05 42-8 6033 •64 6-5 42^1 5880 •78 9-15 50-4 6015 •66 6-6 50-7 5895 ■77 9-25 57-8 6039 •64 6^7 58-3 5962 ■72 9-35 65-0 6049 •63 6^8 67-1 5948 ■71 9 '45 72-4 6037 ■64 6-9 75-8 5936 •64 9-55 79-9 6001 •68 7-0 83^6 5998 •67 965 87-1 6028 •65 7-1 9r3 6076 •61 Hydrometer A. Hydrometer B. Hydrometer A. Series [ 5(12.10 p. m.-12. 25 p.m.). Series 4 (12.35 p.m.-12.49 p.m.). Series 5 (12.55 p.m.-1.6 p m.). Added Weight Scale Reading Specific Gravity calculated Displace- Added Weight Scale Reading Specific Gravity calculated Displace- Added Weight Scale Reading Specific Gravity calculated Displace- m Milli- from Single ment. m Milli- metres. from Single ment. in Milli- metres. from Single ment. Grams. metres. Observa- tions. Grams. Observa- tions. Grams. Observa- tions. 8-65 16-0 1-445741 1245'90 6^1 7^8 1^445905 1245-76 8^6 12-5 1-445719 1245-92 8-75 23-9 5780 ■87 6-2 16-9 5826 •83 8-7 201 5703 •93 8-85 31-6 5686 •95 6-3 25^3 5837 •82 8^8 27'9 5681 •95 8-95 39-1 5663 •97 6-4 34^3 5796 -86 8^9 36-9 5525 1246^09 9-05 46'5 5711 •93 6-5 42^7 5820 •84 9-0 45^1 5448 ■16 9-15 53-6 5831 •82 6^6 51-8 5794 •88 9-1 53^9 5313 ■27 9-25 61-0 5717 •92 6^7 60^0 5852 •81 9-2 62-9 5165 •40 9-35 68-1 5732 •91 6-8 68^1 5855 -80 9^3 70^5 5133 •43 9-45 75-3 5768 •88 6^9 77^1 5805 •79 9^4 78-2 5096 •46 9-55 82-6 5796 •85 7^0 85^2 5838 •82 9-5 86-8 4959 •58 9-6.5 89-9 5824 •83 7^1 94-5 5759 •89 9^6 94^7 488 6 •64 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 191 Table 11b. Table of Observations made with Hydrometers A and B when floating in the Solution 6'3 CaCZa + lOOO grams of Water at 19'5° C, for Comparison with the Results given in Table IIa. Hydrometer A. Hydrometer B. Series 1. Series 2. Added Weight in Grams. Scale Reading in Millimetres. Specific Gravity calculated from Single Observations. Displacement. Added Weight in Grams. Scale Reading in Millimetres. Specific Gravity calculated from Single Observations. Displacement. 4-0 13-9 1-409760 1204-94 2-05 7-1 1-409740 1204-96 4-1 21-8 735 ■97 2-15 15-9 732 -96 4-2 29-6 731 •96 2-25 24-5 744 •95 4-3 37-2 730 -96 2-35 33-5 725 -97 4-4 44-6 744 -95 2-45 42-8 683 120500 4-5 52-2 749 -95 2-55 50-8 751 1204-95 4-6 59-8 762 -94 2-65 600 723 -97 4-7 67-1 776 -92 2-75 67-9 725 ■97 4-8 74-7 764 -93 2-85 77-8 694 ■99 4-9. 82-2 762 ■93 2-95 86-0 740 ■96 5-0 89-7 761 •94 3-05 94-8 739 -96 Mean . . 1-409752 MeaE L 1-409727 Probable error of mean expressed in " units of the sixth decimal place / ±r„=3^11 4-46 Hydrometer A. Hydrometer B. Hydrometer A. Series 3. Series 4. Series 5. Added Weight in Grams. Scale Reading in Milli- metres. Specific Gravity calculated from Single Observa- tions. Displace- ment. Added Weight in Grams. Scale Reading in Milli- metres Specific Gravity calculated from Single Observa- tions. Disp me lace- nt. Added Weight in Grams. Scale Reading in Milli- metres. Specific Gravity calculated from Single Ob.serva- tions. Displace- ment. 4-0 14-1 1-409741 1204-95 2^05 7^0 1-409750 120' 1-95 40 140 1-409750 1204-95 4-1 21-7 745 •95 215 15^8 742 -95 4^1 21-5 764 •94 4-2 29-7 722 ■97 2-25 24^7 724 ■97 4-2 29-5 741 -95 4-3 37-5 730 -96 2-35 33^8 696 ■99 4-3 37-4 711 -98 4-4 44-9 722 •97 2-45 42-0 760 ■94 4-4 44-8 731 -96 4-5 52-1 765 -94 2-55 50^9 742 ■95 4-5 521 765 -94 4-6 59-8 768 -93 2-65 59^0 818 ■89 4-6 610 741 -95 4-7 67-2 772 -93 2-75 68^1 790 ■92 4-7 67-5 744 -95 4-8 74-9 750 -95 2^85 76^9 782 ■92 4-8 74-8 760 •94 4-9 82-4 748 -95 2^95 86^0 740 •95 4^9 82-6 730 ■96 5-0 89-9 749 ■95 3^05 94^8 739 •96 5-0 89^7 767 •93 Mean . . 1-409746 Mean. . r409753 Mean . 1-409746 Probable error of mean \ expressed in units of the j- ± r^ = 3-49 sixth decimal place j 6 35 3-6 192 MR J. Y. BUCHANAN ON THE Table lie. Table of Observations made with Hydrometers A and B in the Supersaturated Solutions, 7-196 CaC4+ 1000 grams of Water, a« 19'50° (7. Index of Hydro- meter used. Time Interval in Series of Minutes of Successive Added Weight Reading in Corresponding Correspoiidincr Observa- Observations from in Grams. Millimetres. Specific Gravity. Displacement. tions. iirst Observation. 1-4 8-65 13-4 1-443843 1245-81 2-7 8-75 20-5 876 •78 4-1 8-85 28-0 884 •78 5-5 8-95 35'6 868 •79 6-8 9-05 43-1 859 •80 1st A 8-2 9'15 50-9 824 •83 9-6 9-25 58-2 851 •80 10-9 9-35 65-8 825 •83 12-3 9-45 73-0 831 -82 13-6 9-55 80-3 832 •82 15-0 9-65 87-5 843 •81 Time interval of 8 minutes between experiments. 24-5 6-1 lO'O 1-443941 1245-73 25-9 6-2 18-8 911 -75 27-4 6-3 27'3 912 -75 28-8 6-4 36-7 839 -82 30-3 6-5 45-0 867 -79 2nd B 31-7 6-6 54-2 806 -84 33-2 6-7 62-6 830 -82 34-6 6-8 711 830 -82 36-1 6-9 79-9 807 -84 37-5 7-0 88-0 844 •81 39-0 7-1 96-6 838 -82 Time interval of 8 minutes between experiments. 48-5 8-65 13-9 1-443793 1245-85 501 8-76 21-3 799 -85 51-6 8-85 28-2 865 -79 53-2 8-95 36-6 769 •88 54-7 905 43-8 800 •85 3rd A 56-3 9-15 51-5 767 •88 57-8 9-25 58-3 841 ■81 59-4 9-35 66-2 784 -86 60-9 9-45 73-8 752 -89 62-5 9'55 81-0 762 -88 64-0 9-65 88-7 724 •92 SPECIFIC GKAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 193 Table III. Giving Details of the Order of Succession of the Experiments, of their Duration, and of the Temperatures of the Solutions and the Air respectively during the Experiments made on the Solution, 7'22,b CaGl^+ 1000 grams of Water. Number of Experiment. (1) Time of Com- mencement of Experiment. (2) Time of Com- pletion of Experiment. (3) Duration of Experiment. (4) Time Interval between Successive Experiments. (6) Initial and Final Solution Temperatures. (6) Initial and Final Air Temperatures. (7) Hydrometer. (8) 1 10.45 a.m. 11.5 a.m. 20 minutes 25 minutes 19'5°C. 19-5° C. 19'3°C. 19-1° G. A 2 11.30 a.m. 11.45 a.m. 15 minutes 25 minutes 19-5° C. 19-5° C. 19-3° C. 19-3° C. B 3 12.10 p.m. 12.25 p.m. 15 minutes 10 minutes 19-5° 0. 19-5° C. 19-3° C. 19-4° G. A 4 12.35 p.m. 12.49 p.m. 14 minutes 6 minutes 19'5°C. 19-5° C. 19-4° C. 19-3° C. B 5 12.55 p.m. 1.5 p.m. 10 minutes 19'5°C. 19-5° C. 19-3°C. 19-35° C. A § 111. Comparison of Results obtained with Hydrometers A and B when floating in the Supersaturated Solution of Calcium, Chloride with those obtained when the Hydro- meters are floating in a Solution containing 6 '3 gram-molecules of Calcium, Chloride in 1000 grams of Water. — We will first draw attention to Table III., which gives the dura- tion of each experiment, the initial and final solution temperatures, and the air tempera- tures before and after each experiment, in connection with the observations and results recorded in Table IIa. Table III. also affords a fair criterion of the usual duration of these experiments, and it gives suitable relief to the constancy of the temperature, both of the experimental liquid and of the atmosphere of the laboratory, which can, and must be secured, if the full precision of which the hydrometric method is susceptible is to be achieved. It will be observed that the temperature of the air was generally 0'2' C. lower than that of the experimental liquid, and that, in these conditions, the temperature of the experimental liquid remained perfectly constant during the time of the experiment. The absolute degree of constancy covered by this statement depends on the specification of the thermometer used. It was a standard instrument, divided, on the stem, into tenths of a Centigrade degree, and the length TKANS. ROY. SCO. EDIN., VOL. XLIX., PART I. (NO. 1). 25 194 MR J. Y. BUCHANAN ON THE of a whole degree was 12 millimetres. On such an instrument variations of one- hundredth of a degree are easily appreciated by the practised eye. It must, however, never be forgotten that ivhat is directly observed is, at the best, the most probable value of the temperature of the bulb of the thermometer. The legitimacy of the conclusion that this is the temperature of the medium, in which the therm^ometer is immersed depends on the expertness and experience of the experimenter. The use of an instrument of the degree of delicacy above specified is justified only when all the precautions have been taken which are required in order to justify the experi- menter in concluding that he has the temperature of the system under such control that its uncertainty is not greater than ±0'005" C. Nothing short of first-rate work secures this. In the work which Mr S. M. Bosworth has been doing under my direction, upwards of 3000 hydrometer observations have been made during the last twelve months, and the temperature conditions have been controlled with such skill that only three of the series showed a sensible variation of the temperature of the solution from the standard temperature during the time the experiment lasted. Their results were rejected, not because they were not very good, but because in this respect the others were perfect. We will now proceed to a comparison of the figures in Tables IIa. and IIb. § 112. It would be useless to take the means of each series of specific gravity results in Table IIa. and compare them with the mean results given in Table IIb. But these numbers show the progressive character of the alteration of the specific gravity in each consecutive series, as well as the considerable differences of these numbers inter se, when contrasted with the agreement which holds among the mean results set out in the other table, IIb. The mean results are given in the following table : — Table IV. Giving the Mean Specific Gravities calculated from the Series in Table IIa. Series. Hydrometer. llean Specific Gravity. 1 2 3 4 5 A B A B A 1-446019 1-445917 1-445750 1-445826 1-445330 Taking the five mean results given above, we find that the maximum amplitude of variation is 689 units in the sixth decimal place. If we turn to Table IIb., we find the maximum amplitude of variation to be only 26 such units. Although the consideration of the mean specific gravities shows clearly that there is an unstable condition in the supersaturated solution as contrasted with the stable condition of the 6 "3 CaCl2 solution, this is made more evident if we compare, as in 1 2 3 4 5 A B A B A 88 250 168 146 833 46 68 50 66 56 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 195 the following table, the greatest amplitude of the variation in each series given in Table IIa. with those occurring in series made with the same hydrometer, as given in the other table, IIb. Series ...... Hydrometer ..... Amplitudes of Variation [ ^^^^'^ ^^"^^ ^ I Table IIb. In series 4 of Table IIb. there are two extreme values of the specific gravitv, namely, 1'409696 and r409818, giving an amplitude of 122, but they are quite ex- ceptional, and if they are omitted the greatest amplitude in the series is 66, so that the mean maximum amplitude in the series made with hydrometer B is 67, while that in the series made with hydrometer A is 50. On examining the figures for the supersaturated solution, their irregularity when compared with those of the G'3 CaClj solution is at once apparent; moreover, the irregularity increases very rapidly in each consecutive series, so that the amplitude of variation is in the first series 88, rising to 250 in the second, then falling to 146, and reaching 833 in the last series, immediately after which crystallisation commenced. The rate of increase is not regular, for in the fourth series the variation amounts to 146, which seems to show that the solution was for the time being in a state of com- parative calm. This table, therefore, serves the useful purpose of indicating the fluctuating character of the alteration of the specific gravity, while Table IV. shows that in spite of these fluctuations there is a definite decrease in specific gravity from the first to the fifth series. § 113. Displacement. — The displacement of the 6 '3 gram - molecule solution throughout the series is for all practical purposes constant, as might be expected, since the solution is quite stable and no disturbing influences, such as the imminence of crystallisation, are present. But the displacement in the case of the supersaturated solution is subject to variations corresponding to those of the specific gravity. These afford evidence of considerable and, to some extent, spasmodic acts of expansion and contraction, unaccompanied by any change of temperature of the solution or of the external pressure to which it urns subjected. These spasmodic changes of volume exhibit a veritable species of labour, going on in the solution in its efforts to become a mother-liquor. In this it is finally successful, but not before it has succeeded in forcing the door which confined its store of heat. The birth of the crystal ivas synchronous with, and dependent on, the libera- tion of heat. If we consider the mean specific gravities of the five series given in Table IIa., we find a progressive decrease in them from the first to the fifth, with an interruption in the fourth, where a slight increase is observable over that of No. 3. This resultant decrease of the mean specific gravity of the solution is accompanied by a series of 196 MR J. Y. BUCHANAN ON THE fluctuations in the results of the single observations of each series -which indicates a condition of unrest in the solution, which is most accentuated in the fifth series of observations, during which the specific gravity fell from 1'445719 to 1"444886. The most remarkable feature of these changes is that they occurred without being ac- companied by any change in the temperature of the solution. Confirmation of the occurrence of this remarkable condition of unrest was furnished by a repetition of the experiment, made with a solution containing 7 '196 gram-molecules CaClg per 1000 grams HgO, recorded in Table lie, and in it similar fluctuations of density, although not quite so pronounced, occurred as the forerunner of crystallisation. When the temperature of the solution had been observed after completion of the third series, the side of the cylinder was accidentally rubbed by the thermometer and crystallisation took place; but the behaviour of this solution and that of the 7'225 CaClj solution, in the case of the first three series, exhibit similar features of unrest. § 114. It is interesting to inquire into the nature of the changes of displacement which have occurred in the transition of the solution from a condition of supersaturation to that of a mixture of saturated solution and crystals at the same temperature, 19 "5° C. They are clearly shown in the accompanying table. We commence with 806"61 grams of a solution having a specific gravity 1444886, the displacement of this weight of solution being therefore .558'25 grams, and this re- solves itself into 596'3 grams of mother-liquor with a specific gravity of 1 "423500, giving a displacement of 418"89 grams, and 210-3 grams of CaCl26H20 crystals with a specific gravity of r654 (Landolt's Tables), giving a displacement of 127'15 grams, from which we see that the displacement of the mixture of crystals and mother-liquor is 12-21 grams, or 2-2 per cent less than that of the original volume of supersaturated solution. The following table shows this clearly : — Weight in Grams. Displacement in Grams of Water. Volume in o. o. at 19-5° C. Percentage Displacement. Original solution Mother-liquor . CaClaGHsO Total Difference . 806-6 558-25 558-75 100-00 596-3 210-3 418-89 127-15 419-48 127-36 75-03 22-83 806-6 546-04 546-84 97-86 12-21 11-91 2-14 §115. When we compare the behaviour of the chlorides of magnesium and calcium in supersaturated solution, it seems strange that the salt which has the greater amount of heat to lose by crystallising should be the more difficult to bring to crystallisation. The difiiculty, however, lies only in the starting of crystallisation ; there is none in its continuation. To start crystallisation in any solution, no matter how supersaturated SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 197 it may be, is an operation which has some of the elements of an act of creation — some- thing appears where there was nothing o? the kind before. The actions and reactions which take place before the first element of crystal appears are withdrawn from our sight, but their existence has been revealed by the hydrometer, which faithfully reports to him who can use it the dilatations and contractions which precede the crystal's birth. They are illustrated in the accompanying diagram. In it the ordinates represent displacements of the solution and the abscissae intervals of time, dating from the first observation of the first series. The lowermost curve. No. 1, represents graphically the data of displacement relating to the supersaturated solution 7 '225 CaClz+lOOO grams of water given in Table IIa. The uppermost curve, No. 2, represents those relating to the non-saturated solution 6'3 CaCla-l- 1000 grams of water given in Table IIb. ; and the intermediate curve, No. 3, represents the data relating to the supersaturated solution 7-196 CaCl2+ 1000 grams of water given in Table lie. The displacements are plotted in the order in which they were observed, and the series follow each other in chronological order. The letters A, B designate the hydro- meter which was used for the series represented under each respectively. The time intervals between successive series of observations are included in the diagram and are traced by dotted lines. The interval of time which separated two consecutive series of observations was on an average seventeen minutes, and the duration of each series of experiments was about fifteen minutes. The diagram shows at a glance the contrast between the tranquillity of the 6 '3 CaCla solution and the unrest indicated by the curves for the two supersaturated solutions. The curve No. 2 for the 6 "3 CaCla solution pursues an even course, the displacements oscillating between the extremes 1205 '00 and 1204 '89. Otherwise the curve differs little from a straight line, and there is perfect agreement between the last result in one series and the first in the succeeding series. This is shown by the horizontality of the four dotted lines connecting the successive serial curves. Curve No. 1 for the 7 "225 CaClj supersaturated solution is in striking contrast with No. 2. There is little agreement between the displacements in any of the corresponding series, and the oscillations of the serial curves are very marked, culminating in the continuous expansion shown in series 5, after which crystallisation took place. This is also well shown by the difference between the last displacement of one series and the first displacement of the following series. It is evident that the state of unrest con- tinued when the solution was left to itself in the cylinder. The slight contraction shown in passing from the third to the fourth series indicates an efi'ort on the part of the solution to regain a more stable condition. It is, however, clear that the state of unrest continued during the whole of the 140 minutes represented by the line of abscissae in the diagram, and it suggests the possibility, and indeed the probability, that the super- saturated solution, even when confined in a closed vessel, may never be at rest. § 116. If we consider attentively what took place before the supersaturated solution of calcium chloride was brought to shed its salt as crystals, it is seen that it difi'ers very 19S8 MR J. Y. BUCHANAN ON THE <15 oc >o "t CN o( oc( nc 'J- -o NO -<5 -c ■« NC y; lO -* 't t "^ M- ^ f ^ c^ CN CNl CN CJ CN eJ £io «o — H - u^ — UJ (- -___^_^ K D ' — 3 5to < "^ Z o - W2 o -^ > o c>« Os i o o A o CN ^ (. •n* o / ~ o o < i o o f y < ( X o > <^ o 1 I > o 09 1 o 00 \ o^ t-> s » LO lO \ QQ \ ^ t <" CnI c< O \ o 1 o >o 1 > o 1 <^ I 00 S < ; < / o ' <■ J O . o I O •s» d I" \ X \ o X g 1 I o g « \ ^ g j 00 c o o to o o 133 \ o o o -l o o \ \ o to o \ ■*■ 4 "^» + + ) ^~f I N ^ 1 o o ^-^ 1 iH ' d * o CN o ( o o \ o •) o 1 1 •o / CM s n \ I CNl ^1 •O \ IV ] r^ o ) (, ( o oi / lO < \ Oi Z < / 0( z < ^ 2 / o v. /■ 1 o O o> <£. o o- op N 00 •o 't <1^ "3 "3 t ^ ■a lO ^ lO •o "3 'h 1 o C O c ^ "t ^ d M So oi C O o O T3 ta ^ S c3 nj o <'a a s +-> bo SPECIFIC GEAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 199 little from what takes place when its non-saturated solution is brought to shed part of its water as crystals of ice. In each case considerable depression of the temperature of the solution below that of crystallisation is required before crystallisation sets in. When it does set in, an immediate rise of temperature takes place in the solution, and it stops only when the ordinary temperature of crystallisation has been reached. The same sequence of events is observed when water, containing no salt, is brought to crystallisation ; it also rises to its ordinary temperature of crystallisation. Unless these experiments are made in conditions which are unusual in chemical laboratories, none of these liquids begins to crystallise immediately when its temperature has been lowered exactly to the crystallising point. The extent to which any particular solution can be cooled below its crystallising temperature, and the amount of mechanical disturbance which it can withstand when in this condition, vary with the nature of the solution. We have seen that the resistance so offered by a supersaturated solution of calcium chloride is considerable. But even that offered by pure water to the starting of crystallisation is greater than is generally believed to be the case. When the mass of water used is small, and the capacity for heat of the vessel which contains it is large, it is possible, with care, to reduce the temperature of the system so far that, when crystallisation takes place, the whole of the water is transformed into ice and its temperature does not rise so high as 0° C. An instance of this is given in the following passage quoted from a lecture on " Ice and its Natural History " which I delivered before the Royal Institution on 8th iMay 1908 : — * "Evidence of the uncertainty which exists regarding the temperature at which ice begins to form in water, when it is cooled in contact only with a solid other than ice, is furnished by the wet-bulb thermometer when it is being prepared for use at tem- peratures below 0° C, by freezing on it the quantity of water which is supported, against gravity, by the perfectly clean bulb. When this is rotated in air of — 10° to —20° C, ice never begins to form until the temperature of the bulb of the thermometer has fallen to —2° or —3° C, and rarely before it has fallen to -4° C. In many cases I have observed it fall to temperatures as low as — 8° or — 9° C. ; and in such cases, when freezing begins, the whole of the water is frozen without its being able, by the liberation of latent heat alone, to raise the temperature of the bulb of the thermometer to 0°C." Whether, when in this unstable state, it would stand the mechanical disturbance which is resisted by a supersaturated solution of calcium chloride, can only be determined by experiment. This I have not as yet attempted. All that is required is to set about determining the specific gravity of pure water hydrometrically in a laboratory having the constant temperature — 4° or - 5° C, and using at least equal precautions with those observed in the case of supersaturated solutions at ordinary room temperatures. If water, in these conditions, is sufficiently unsensitive to mechanical disturbance, it will undoubtedly do its part in manifesting its unrest ; it will then be the part of the * Proceedings of the Boyal Institution of Great Britain, 1909, xix.. Part I. p. 248, 200 MR J. Y. BUCHANAN ON THE experimenter to receive the message, and if he succeeds he will have done a very fine piece of work. § 117. In considering the dilatation of the 7"225 CaCla solution before crystallisation, we may pass over the first four series, although the oscillations of displacement which they exhibit would be remarkable enough if they stood alone, and confine our attention to the expansion in the fifth series which is continuous from the first to the eleventh observation. The displacement at the first observation was 1245'92, and at the eleventh 1246 '64, corresponding to an increase of 0'72 gram in ten minutes. But the absolute minimum displacement observed was 1245'61 in the second series, so that the extreme amplitude of expansion was 103 gram. While these changes of displace- ment were going on, the liquid was perfectly homogeneous and its temperature was absolutely constant. Therefore the dilatations were not of thermal but of mechanical origin. We can apply no mechanical power which would produce such a stretching efi'ect on a liquid, but we can easily arrive at the mechanical power which could efi'ectually counteract it. Drecker * gives 0'0000217 as the coefficient of compressibility of a 40"9 per cent, solution of CaCli, and we may take this as the compressibility of our 7 '225 solution, although it would be rather less. On this basis we obtain 38 atmospheres as the pressure required to reduce the volume of the solution 7 '225 CaCl2+ 1000 grams of water from 1246 '64 to 1245 '61 cubic centimetres, and we conclude that, if we could place the solution in conditions such that its internal pressure should be increased hy S8 atmo- spheres, the extreme dilatation observed would he mechanically p)rovided for. These isothermal oscillations cease immediately when the first element of crystal appears in the solution and aff'ords an outlet for its latent heat, after which crystallisation proceeds in perfect tranquillity at a rate proportional to that at which heat is removed from the solution. It is stopped if heat is supplied at this rate to the solution from without. § 118. There is a remarkable resemblance between the state of unrest preceding the crystallisation of a supersaturated solution and that preceding the liquefaction of a gas, under a pressure not inferior to its critical pressure, when its temperature is reduced slightly below its critical temperature. Andrews, in reporting his discovery of the critical state of liquids and gases, in- cidentally describes this state of unrest as follows : — " On practically liquefying carbonic acid by pressure alone, and gradually raising at the same time the temperature to 88° Fahr. (31 "1° C), the surface of demarcation between the liquid and gas became fainter, lost its curvature, and at last disappeared. The space was then occupied by a homogeneous fluid which exhibited, when the pressure was suddenly diminished or the temperature slightly lowered, a peculiar appearance of moving or flickering striae through- out its entire mass. At temperatures above 88° Fahr. no apparent liquefaction of CO2 or separation into two distinct forms of matter could be efi'ected, even when a pressure of 300 or 400 atmospheres was applied " [Pldl. Trans. (1869) vol clix. p. 575). * Wied. Ann., 1888, vol. xxxiv. p. 955. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 201 When a gas such as carbonic acid, under a pressure which is not inferior to its critical pressure, is confined in a tube as in Andrews' experiment and has a temperature ever so little higher than its critical temperature, it fills the tube as a homogeneous fluid which no pressure, however high, can liquefy. If, by removal of heat or by sudden relief of pressure, its temperature is reduced ever so little below its critical temperature, the homogeneous fluid begins to exhibit the peculiar appearance of moving or flickering strise throughout its entire mass, as described by Andrews. These moving or flickering striiB indicate oscillations of density accompanying the effort on the part of the homo- geneous fluid to shed a portion of its mass in the liquid state before there is a liquid nucleus for it to condense on and to afford the first outlet to the latent heat, the escape of which is an essential condition of liquefaction. § 119. We do not know the temperature at which the dry gas can condense on the dry walls of the envelope, but there can be little doubt that it is lower than that at which it condenses on its own liquid. It is only in the conditions of Andrews' experiment that we can witness a substance persisting in the gaseous state under a greater than the critical pressure and having a temperature lower than the critical temperature, because it is only when the gas and the envelope which contains it have been maintained at a temperature higher than the critical temperature of the gas that the inner walls of the envelope have a chance of being perfectly dry. By "perfectly dry" I mean free from every and any trace whatever of the liquid substance. If the cooling process as specified above be then carried out, the temperature may be reduced slightly below the critical temperature, and yet the substance may persist in the gaseous state because there is none of itself in the liquid state for it to begin to condense on. I have defined * the boiling point of a substance, under a particular pressure, to be the temperature at which it as a liquid evaporates into itself as a gan, and as a gas or vapour condenses on itself as a liquid. When the gas condenses on any other substance, or in a space filled only by itself, the temperature at which liquefaction commences is uncertain. In the moment, however, that the first, even the minutest trace of liquid appears, whether in the gas or on the walls, the temperature of condensation is defined, because the gas is then condensing on itself as a liquid. How, in such an experiment, the first element of liquid appears, we do not know. We say, it is by accident ; but we may with equal right say, it is by an act of creation — because in the process some- thing appears where there was nothing of the kind before. We thus see that there is a close analogy, in all important particulars, between the state of unrest which exists in a supersaturated saline solution before crystallisation commences and that indicated by the fiickering strise in a supersaturated gas before liquefaction takes place. * "Chemical and Physical Notes," by J. Y. Buchanan, F.R.S,, The Antarctic Mcmual, 1901, p. 97. TRANS. ROY. SOC. BDIN., VOL. XLIX., PART I. (NO. 1). 26 202 MR J. Y. BUCHANAN ON THE Section XVL — The Determination of the Specific Gravity of the Crystals of A Soluble Salt by Displacement in its own Mother-Liquor, and the Volumetric Relations between the Crystals and the Mother-Liquor WHICH ARE established BY THE EXPERIMENT.* § 120. The work on the specific gravity of dilute solutions at 19 "5° C. reported in the early part of this memoir was interrupted by the arrival of the great anticyclone or heat- wave of the summer of 1904, during which observations at a temperature of 19 '5° were quite impossible. Indeed, the temperature of the laboratory, whether by night or day, hardly ever fell below 23° C. or rose above 25° C. It persisted over Northern Europe for nearly six weeks, and produced tropical conditions, which were evidenced alike by the high temperature of the air and by its insignificant diurnal variation. In these circumstances I decided to make use of the time by putting into practice a method of determining the specific gravity of soluble salts which I had long intended to try. I took it up at first merely as a tour de force in experimentation with which to occupy myself during the hot weather, but it turned out to be a valuable method of research, and the duration of the spell of hot weather enabled me to prove and to use it. The specific gravity of an insoluble substance is determined by the amount of distilled water which a known weight of it displaces. In the case of soluble salts it has been the custom to replace the water by a hydrocarbon or mineral oil. The objections to the use of this liquid are numerous, especially when the salt, the specific gravity of which it is desired to determine, is rare or costly. Moreover, to judge by the want of agreement among the values of the specific gravity of the same salt found by difierent chemists, there is greater uncertainty about the numerical results than there should be. One reason for this may be that the salts are not insoluble, but only sparingly soluble in the oil, and that sufficient attention has not been given to this point. There is one liquid in which every soluble salt is quite insoluble, and that is its own mother-liquor at the temperature at which the one parted from the other. By immersing the salt in its own mother-liquor at the temperature of what we may call its birth, and by making the maintenance of this temperature a conditio sine qua non of every manipulation during which the two are brought together again, errors due to uncertain solubility are eliminated, and contamination of valuable preparations is avoided. It is therefore by the immersion of each salt in its own mother-liquor that I determined its displacement ; and this, combined with the weight of the salt and the specific gravity of the mother-liquor, gave the specific gravity of the salt. * This formed the subject of a paper which was read at the meeting of the Chemical Society of London on 6th April 1905, but it was not published by the Society. I owe it to the courtesy of Professor E. S. Dana that the hospitality of the pages of the American Journal of Science was extended to it. It appeared in the January number of 1906, vol. xxi. p. 25, under the title :— " On a Method of Determining the Specific Gravity of Soluble Salts by Displacement in their own Mother- Liquor ; and its Application in the case of the Alkaline Halides. By J. Y. Buchanan." SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 203 It is obvious that the method is applicable only to salts which have a mother- liquor, such as KCl ; RbBr ; Q&G[1 "-16 "'ir '"is "■ho ©2 «'21 D« D CsGl= 168-5 23-r C. 38-8900 gms. 89-2399 „ 50-3499 „ 135-0620 „ 96-1720 „ 1-9101 1-0334 gms. 41-21 c.c. 0-6944 gms, 0-3390 „ 12-1563 22-1229 gms. 146-5514 „ 85-5385 „ 44-7828 „ 5-5671 „ 3-9739 26-6220 gms. 48-7449 „ 160-4249 „ 72-7900 „ 38-1085 „ 12-2414 „ 3-9820 6-6743 gms. 3-9890 3-982 For weighing out the salt and passing it directly into the specific gravity bottie a special and convenient form of weighing tube was used. It was made out of a stoppered specimen tube with an internal diameter of 2 centimetres and a length of 7 or 8 centi- metres. The lower end of this tube was opened and a piece of narrower glass tube joined to it before the blowpipe. This tube, which had a length of about 3 centimetres, had an external diameter such that it could just pass freely through the neck of the 206 MR J. Y. BUCHANAN ON THE specific gravity bottle. The wide end was closed with a glass stopper, and the narrow end with a small india-rubber cork. It was the custom to work so as to have about 15 c.c. of dry salt to be added in two charges to the specific gravity bottle. These charges were intended to be nearly, though not quite, equal. The available supply was distributed between two weighing tubes by approximate weight, after which the exact weight of each portion was deter- mined in the usual way. The two portions of caesium chloride weighed respectively 22'1229 and 26"6220 grams, so that in the first determination of specific gravity 22"1229 grams and in the second 487449 grams were concerned. It is not immaterial whether the first portion is charged into the empty specific gravity bottle and the mother-liquor poured over the dry powder, or is charged into the bottle which is already about half full of mother-liquor. In the former case the elimination of the entangled air is difficult and takes time, during which it is not easy to prevent the temperature getting out of hand. By the latter process very little air is carried past the surface of the liquid and very little stirring with the thermometer, which is required on other grounds, suffices to eliminate it. § 124. Owing to the readiness with which these salts crystallise and to the slowness with which all salts dissolve in an almost saturated solution, the temperature of the mixture of salt and mother-liquor, during the adjustment of level in the specific gravity bottle, must on no account be permitted to fall below T by even 001", nor should it be allowed, even momentarily, to rise above it by more than O'l". The regulation of temperature was effected entirely with a standard thermometer divided into tenths of a degree, each tenth occupying a length of rather more than one millimetre on the stem. The thermometer which forms part of the specific gravity bottle is used chiefly as a stopper of convenient form. So soon as the level of the liquid has been adjusted in the bottle, it is weighed. The temperature and pressure of the air are kept account of for the reduction of all weights to the vacuum. When the first weighing has been completed, about 20 or 25 c.c. of the clear mother- liquor are drawn off and the second charge of dry salt is added and mixed, after which the level is adjusted, and the weight determined. In the absence of experience it might be thought that it would be difficult to draw ofi' so much of the liquid without some of the solid salt ; but no matter how much they may be stirred up, these crystallised salts settle at once and completely to the bottom when immersed in their saturated solutions, and the operation presents no difficulty. It was at first intended to make a series of three determinations with each salt, but two were found to be sufficient. During all these manipulations the temperature of the air in the laboratory never differed from that of crystallisation (T = 23"l°) by more than one or two tenths of a degree, and, when the solubility of the salt is great, it is only in such conditions that operations of this kind can be carried out successfully. Before bringing the crystals together with the mother-liquor in the specific gravity bottle, the operator must realise that their common temperature when mixed is to be SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 207 exactly that of crystallisation or equilibrium (T) ; and he must take such measures as his experience dictates to arrive at this end. Preliminary experiments on a some- what extensive scale are absolutely necessary, and the success of afi operation depends almost entirely on the operator and the trouble that he is prepared to take. § 125. Table II. gives for each salt, MR, the temperature, T, of equilibrium between crystals and mother-liquor, and, in condensed form, the experimental data of the determination of S, the specific gravity at T of the mother-liquor, that of water at the same temperature being unity, of m, the concentration of the mother-liquor in gram- molecules salt per 1000 grams of water, and of Di, Dg, Ds, the three observed values, as well as D, the finally accepted value, of the specific gravity of the salt, all at T, and referred to that of water at the same temperature as unity. Table II. — Experimental Results regarding each Salt in the Ennead. Salt : Formula MR Salt : Mol. weight . Temperature, T Specific Gravity. "Weight taken, gms. Wj Displacement, gms. w^ Specific gravity, — 5 = S Concentration. Gm.-mols. p. 1000 gm. H^O, ni Specific Gravity. A. Weight of first portion of salt, gms. ?»!() . Displacement, gms. w-^^^ Specific gravity J£ = Dj B. Weight of both portions of salt, gms. Wjg . Displacement, gms. Wjo Specific gravity —^ = 1)^ C. Weight of second portion of salt, gms. ?Cj, . Displacement, gms. jw^q - w-^^ Specific gravity. ^ = D, Accepted specific gravity, D KCl. 74-6 23-4° KBr. 119-1 23-4° KI. 166-1 24-3° EbCl. 12'l-0 22-9' RbBr. 165-5 23-0° Rbl. 212-5 24-3° CsCl. 168-5 23-r CsBr. 213-0 21-4° Csl. 260-0 22-8' Mother-Liquor. 59-4068 34-3044 85-9636 74-7356 81-3282 46-2696 96-1720 42-3756 50-3524 24-95.54 49-9140 49-9188 49-9196 24-9478 50-3499 24-9744 1-1798 1-3746 1-7222 1-4971 1-6292 1-8548 1-9101 1-6968 4-7619 5-7250 8-9344 7-7670 6-7l'29 8-2307 12-1563 5-3057 78-0087 50-3658 1-5488 3-5454 Salt in Crystal. 13-3684 7-3271 1-8245 27-4258 14-5322 1-887 14-0574 7-2051 1-951 36-7928 13-7498 2-676 52-5142 19-6005 2-679 15-7214 5-8501 2 688 1-951 2-679 27-1751 8-9703 3-0295 52-1768 17-1465 3-043 25-0017 8-1762 3-058 3-043 19-0112 7-0256 2-706 43-7750 15-9627 (2-74) (24-76) 8-9371 (2-77) 2-706 27-0906 8-4700 3-198 51-5438 16 0568 3-210 24-4532 7 5868 3-223 3-210 26-4777 7-7248 3-428 50-6025 14-7658 3-428 24-1248 7-0410 3-426 3-428 22-1229 5-5671 3-974 48-7449 12 2414 3-982 26-6220 6-6743 3-989 3-982 27-8926 6-2453 4-466 57-5390 12 9466 4-455 29-6464 6-7013 4-424 4-455 26-3890 5-8545 4-5075 533916 11-8423 4-5085 27-0026 5-9878 4-509 4-508 208 MR J. Y. BUCHANAN ON THE The letters and suffixes have the same significance as in Table I. The numbers in line T show how uniform the temperature was during the period over which the experiments were spread. All the experiments were made between the 12th and 22nd of July 1904, with the exception of those on csesium bromide, which were made on 10th August. By that time the anticyclone had begun to break, and the value of T for this salt is 2r4°. For all the other salts, T lies between 22-8° and 24-3°. During the whole of the period the barometer was very steady, varying between 758 and 761 millimetres, and the relative humidity of the air in the laboratory varied between 40 and .50 per cent. Of the three values Dj, Dj, D3 for the specific gravity of the salt, Di is obtained directly from the first portion of the salt, Dg from the sum of the two portions, and D3 is derived from Dj and Dj by subtraction. D2 represents very nearly the mean of Dj and Dg, and is the accepted value for the majority of the salts. It is expressed to three places of decimals, of which units in the second place are exact. It will be noticed that in the case of rubidium chloride the value of Dj is accepted. The second determination depends on the approximate weight of the second portion of salt when the tube was being filled, the exact weighing on the balance of precision having been accidentally omitted. The operation was however completed, and the calculation made with the approximate weight was used as a control. The result shows that the value of Dj may be safely accepted. In the case of potassium chloride the value of D3 (r951) is accepted, and the reason for this is as follows: The first portion of salt was in very coarse powder, and in mixing it with the mother-liquor numerous crystalline particles were observed which contained gaseous enclosures, easily per- ceptible by the naked eye. As was expected, the observed specific gravity proved to be low. The second portion was much more finely powdered and the specific gravity resulting from the two was higher (1'887). But this result is afi'ected to the full extent by the gaseous enclosures in the first portion. We therefore calculate the specific gravity from the second portion alone, which gives 1-951 for the specific gravity. It is an advantage of the method just described that it furnishes more than the mere determination of the specific gravity of the salt. Thus, by ascertaining almost simultaneously the specific gravity of the mother-liquor and the displacement in it of the crystals, both being at the temperature of equilibrium, data are obtained for the determination of the relation between the displacement of the salt in crystal and the increment which it produces in the displacement of 1000 grams of water when it is dissolved in this mass of water and forms a saturated solution with it at that temperature, it has not hitherto been permissible to make exact comparisons of this kind, owing to the independence of the observations on the salt and on the solution which have been available. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 209 § 126. In discussing the results of observation it is convenient to arrange them in a more articulate form than that of Table II. The group of salts which forms the subject of these experiments is one of the most remarkable in nature. The salts are nine in number and include all the possible binary combinations of the members of the electro-positive triad K, Rb, Cs with those of the electro-negative triad CI, Br, I. The two triads of simple bodies make three triads, or one ennead, of binary compounds. The relations of the different members of the ennead are shown in Table III., in which the diiferent features of the salts are exhibited in separate sub-tables. In these sub-tables the data referring to salts of the same metal (M) are found in the same column under the symbol for the metal (K, Rb, Cs), and those relating to salts of the same metalloids (R) are found in the same line opposite the symbol for the metalloid (CI, Br, I). The symbol MR is used to represent both the formula and the molecular weight of the salt. Sub-table (a) of this, table contains the formula and sub-table (c) the molecular weight of each salt. The latter is the fundamental attribute of a substance, on which all its properties depend. The molecular weights of the salts which occur in one column differ by the amount of the difference of the atomic weights of the metalloids which they contain, that is, by 44"5 or 47 Similarly, contiguous salts in one line have molecular weights which differ by 46 "4 or 47 '5. If we consider the two diagonal triads in the ennead, we see that they are characterised by the fact that both the elements in each unit are different from those in either of the other units. Further, along the diagonal KCl-CsI the molecular weights of the units differ as much as possible from each other, while the atomic weights of the components of each unit are as nearly as possible identical, being close neighbours in the atomic series. On the other diagonal, KI-CsCl, the molecular weights of the units agree with each other as nearly as possible, while the atomic weights of the constituents of the units differ from each other as much as possible. In sub-table (6) we have the values of T, the temperature at which the crystals and mother-liquor of each salt were in equilibrium, and that at which the various displacements were observed. Under the experimental conditions, which have been minutely described above, it is impossible to fix in advance the exact temperature of equilibrium of the crystallising liquid. This is given by the meteorological conditions, modified by the structural features of the laboratory and of the apartment or enclosure where crystallisation takes place. § 127. The Crystal. — In compartment (g) we have the values of D, or the specific gravity of the salt in crystal at T, referred to that of distilled water of the same temperature as unity. The data in this compartment are in most cases for different, but always neighbouring, temperatures. The differences of the values of T are, how- ever, so small and those of D are so great that we may discuss the specific gravities as if they had been made at one common temperature. TRANS. ROY. SOC. EDIN., VOL. XLIX., PART L (NO. 1). 27 210 MR J. Y. BUCHANAN ON THE Table III. — Table giving Numerical Relations between the Crystallised Salts of the Ennead MR and their Mother-Liquors. K. Rb. Cs. K. Rb. Os. K. Rb. Cs. (J) The common temperature at which the determinations of the {a) Formula of each salt. specific gravity of the crystals (c) Molecular weight of each salt. and the mother-liquor respect- ively were made. MK. T. MR. CI. KCl. RbCl. CsCl. 23-4 22-9 23-1 74-6 ■■ 121-0 168-5 Br. KBr. RbBr. CsBr. 23-4 23-0 21-4 119-1 ' 165-5 213-0 I. KI. Ebl. Csl. 24-3 24-3 22-8 166-1 212-5 260-0 {d) Weight of salt per 1000 grams of («) Concentration of the mother- (/) Weight of the mass of the water in eao i solution. liquor expressed in gram-mole- mother-liquor which contains cules salt dissolved in 1000 1000 grams of water. grams of water. w. MR = ™- 1000-f«)=W. CI. 355-24 939-81 2048-34 4-7619 7-7670 12-1563 1355-24 1939-81 3048-34 Br. 681-85 1112-64 1130-11 5-7250 6-7229 5-3057 1681-85 2112-64 2130-11 I. 1484-00 1749-02 921-80 8-9344 8-2307 3-5454 2484-00 2749-02 1921-80 {g) Specific gravity of the crystal at (A.) Specific gravity of the mother- (i) Displacement of W grams of T, referred to that of distilled liquor at T, referred to that of mother-liquor at T, expressed m water at the same temperature distilled water at the same grams of water at T. as unity. temperature as unity. W D. S. ^ = ^- CI. 1-951 2-706 3-982 1-1798 1-4971 1-9101 1148-70 1295-71 1595-90 Br. 2-679 3-210 4-455 1-3746 1-6292 1-6968 1223-52 1296-73 1255-37 I. 3-043 3-428 4-508 1-7222 1-8548 1-5488 1442-34 1482-11 1240-83 1 (Z) Mean increment of displacement {j) Displacement of one gram-molecule [k) Increment of displacement of 1000 of mother-liquor per gram-mole- ed in 1000 of the crystal at T, expressed in grams of water caused by the dis- grams of water at T. grams of water at T. solution in it of TO . MR. MR A -1000 V A-1000 = u D m m CI. 38-233 44-710 42-310 148-70 295-71 595-90 31-223 38-069 49-021 Br. 44-460 51-553 47-820 223-52 296-73 255-37 39 038 44-131 48-137 I. 54-580 61-986 57-670 442-34 482-11 240-83 49-506 58-576 67-907 (n) Difference of the molecular dis- (m) Displacement of one gram- molecule of crystal, expressed in gram-moleoules of water at T. placement of the salt in crystal from the mean molecular incre- ment of displacement of the water in the mother-liquor. (o) Ratio. MR MR V MR m 18D' D VI D ' v' CI. 2-124 ' 2-489 2-350 7-010 6-641 - 6-711 1-225 1-175 0-863 Br. 2-470 1 2-864 2-657 5-422 7-422 - 0-317 1-139 1-168 0-993 I. 3-032 1 3-444 3-204 5-074 3-411 -10-237 1-103 1-059 0-849 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 211 On examining the values of D, we see that they increase with those of MR, but the increase is not continuous, it is remittent. It takes place triadwise; and this holds whether we take the triads in column or in line. Comparing salts in the same line, we see that replacing Kb by Cs causes a rise of specific gravity which is twice as great as that caused by the substitution of Rb for K. Comparing salts in the same column, the replacement of CI by Br causes more than double the rise caused by the substitution of I for Br. However we regard it, we see that the specific gravity of the salts is a periodic function of their molecular weight, within the ennead. MR in compartment (j) we have the values of =- or the displacement of one gram- molecule (MR) of salt stated in grams of water, and in compartment (m) the same constant is stated in gram-molecules of water ( — ^)- In dealing with the specific gravities, we saw that, whether we follow the columns or the lines, they increase with increase of molecular weight. In the case of the molecular displacements this holds for the columns but not for the lines. In these the salts of rubidium have the greatest molecular displacement, the potassium salts have the least, and the caesium salts occupy an intermediate position. As we shall see later, this irregularity is due to a specific peculiarity of the csesium salts. Meantime it may be noted MR that the values of — ^^, which may be called the volumetric equivalent of one gram- molecule of any of the salts of the ennead, varies from 2-124 H2O to 3-204 H2O, the iodides having the highest and the chlorides the lowest equivalents. The average difference between the volumetric equivalents of the iodides and bromides is 0-563 H2O, and that between those of the bromides and chlorides is 0-343 H2O. § 128. The Mother-liquor. — The values of T are the same for the mother-liquor as for the crystals, and are presented in (6). In (e) we have the values of m or the molecular concentration of the mother-liquor. This is expressed in gram-molecules salt per 1000 grams of water, its equivalent iv in grams is given in sub-table {d), and the total weight in grams (W) of the solution is given in sub-table (/). The concentration, m, of the mother-liquor represents with great exactness the molecular solubility of the salt at T, and we shall consider it for a moment from this point of view. The least soluble, molecularly, of the nine salts is caesium iodide, which has the highest molecular weight, and potassium chloride, which has the lowest molecular weight, comes next to it. Next to caesium iodide, in molecular weight and in solubility, we have caesium bromide ; and, similarly, next to potassium chloride, in molecular weight and in solubility, we have potassium bromide. In the latter case the solubility increases with the molecular weight, while in the former it decreases with it. But, if sub-table (c) be referred to, it will be observed that, as regards molecular weight, KCl and Csl occupy singular positions in the ennead. On the other hand, KBr (11 9-1) and RbCl (121) have almost identical molecular weights, as have also CsBr (213) 212 MR J. Y. BTJGHANAN ON THE and Rbl (212-5), yet the solubilities in each pair respectively are very different. The lowest solubilities are on the diagonal KCl- Csl, and the highest solubilities on the diagonal KI-CsCl. RbBr, which occupies the middle place on both these diagonals, is also in the middle of the middle column and of the middle line, and is the centre of the ennead. Its solubility, besides being nearly the average of the group, has a symmetrical position with respect to those of the other salts. On one diagonal the solubility of its neighbours is lower, on the other higher, than its own. In its column the solubilitj^ of its neighbours is higher, in its line it is lower, than its own. Turning from the molecular solubilities in sub-table (e) to the ordinary solubilities given in sub-table (d), we see that the positions of Csl and KCl are reversed ; the least soluble salt of the ennead is KCl, with 355 '24 grams, and next to it comes Csl, with 921 '80 grams per 1000 grams of water. Other great differences occur which are obvious on inspection and need not be further referred to here, because in the research only the molecular weights of the salts are taken into account. In compartment (h) we have the values of S, the specific gravity of the mother- liquor at T, referred to that of distilled water of the same temperature as unity. These numbers cannot, as they stand, be compared with each other because they refer to solutions of such different concentrations. They enable us, however, to arrive at the increment of the displacement of 1000 grams of water caused by its being saturated with the particular salt at T. Thus, taking again caesium chloride as an example, we have for the weight of salt dissolved in 1000 grams of water 10 = OT.CsCl = 2048-34 grams. Adding 1000 grams to this, we have for the weight of the solution W = 1000 4- !« = 3048-34 grams. The specific gravity (S) being r9101, the displacement of the solution is W A = — = 1595-90 grams of Avater, whence the increment of displacement of the water by its «aturation with the salt is V = \- 1000 = 595-90 grams, and the mean increment of displacement per molecule is _ = 49-021 grams. m m.MR+1000 ,. , . , ,. -' -^ = A = displacement of the mass ot mother-hquor containing 1000 grams of water. A- 1000 = y = increment of displacement due to dissolution of ?)i.l\IR iu 1000 grams of water. In compartment (I) we have the value of — for each member of the ennead. m § 129. Before commenting on the numbers in the table, it is important to form a clear conception of their physical meaning. We shall best arrive at this by returning to our detailed example of chloride of cfBsium. As the quantity of saturated solution which contains 1000 grams of water weighs 3048'34 grams and displaces 1595'90 o-rams SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINB SOLUTIONS. 213 of water, we may imagine it to have been prepared in the following way: — 1595-90 grams of water are taken, and caesium chloride is dissolved in it so that each portion, as it is added, forms a saturated solution with the exact quantity of water which it requires for this purpose, and the remainder of the water remains uncontaminated. Parallel with the dissolution of the salt, pure water is removed at such a rate as to keep the displacement or bulk of the liquid always the same. When no more salt will dissolve, we have a saturated solution which contains 1000 grams of water. The weight of csesium chloride which has entered the solution is 2048 '34 grams, and the weight of water which has left it is 595 '90 grams, whilst the displacement of the liquid is the same at the end of the operation as it was at the beginning. In thus describing the preparation of the saturated solution, we have described an operation of substitution. It is therefore permissible to regard saturated solutions as products of substitution. If we give to the above numbers their molecular interpretation, we see that the mean increment of displacement produced by the presence of one molecule of caesium chloride in its saturated solution at 23'1° is equal to that of 2'723 gram-molecules of free water, and therefore, that, in these conditions, CsCl is, in a sense, volumetrically equivalent to '2-7'33 H^O. If we study sub-table (l), we see that the average molecular increment of dis- placement produced by the salts increases with their molecular weight, whether we follow the columns or the lines. The only exception is furnished by caesium bromide, the increment produced by which is very slightly lower than that of caesium chloride. The greatest increment is that due to caesium iodide, which has the highest molecular weight ; and the least increment is that due to potassium chloride, which has the lowest molecular weight. The pair, potassium bromide and rubidium chloride, which have almost equal molecular weights, cause also almost equal molecular increments of displacement. The same is true of the pair, potassium iodide and caesium chloride, but rubidium bromide causes a markedly lower increment of displacement. Finally, the pair, rubidium iodide and caesium bromide, which have almost identical molecular weights, present no resemblance in the increment of displacement which they produce. § 130. Comparison of the Displacement of the Salt in Crystal and the Increment of Displacement luJdch it produces in the Water of its Mother-Liquor. — The molecular displacement -p- of the salts in crystal is given in sub-table {j ) in terms of grams of water ; that of — , the salts in mother-liquor, is similarly given in sub-table (I), m, If we compare these two tables, we find the remarkable result that while in the case of the potassium and the rubidium salts the numbers for the displacement in crystal are greater than those for the increment of displacement in mother-liquor, in the case of the caesium salts the reverse is the case. In sub-table (n) we have the difference ( ^ j of the molecular displacement of 214 MR J. Y. BUCHANAN ON THE the salt in crystal from its mean molecular increment of displacement of the water in the mother-liquor. In compartment (o) we have the ratio ( ^f^ . — j of these quantities. Taking the figures in compartment {n), we see that in the case of the salts of potassium and rubidium crystallisation is accompanied by considerable expansion, and this is what is usually met with. In the case of the caesium salts the reverse is the case, and very decidedly so in that of the chloride and of the iodide, but much less so in the case of the bromide, which, in this, as in other particulars, maintains its singular position. /MR m\ In this connection it should be noted that among the ratios ( ^j=r- , — j given m com- partment (o), the two which are nearest to unity are those for Rbl (r059) and for CsBr (0"993) respectively; and their molecular weights are almost identical. Further, the salts situated co-diagonally to them, namely RbBr and Csl, have ratios whose differences from unity are, numerically, almost equal, namely + 0'168 for EbBr and — 0'15i for Csl. Taking a general view of the numbers in (o) which give the ratios of displacement in crystal and in mother-liquor, we see great diff'erences. The most striking examples are, as in the case of solubility, the extreme members of the ennead, KCl and Csl. The former expands by more than 25 per cent., and the latter contracts by 15 per cent, on crystallising. These figures accentuate the peculiarity of the caesium salts, that crystallisation is accompanied by contraction. An interesting conclusion can be drawn from the behaviour of the different salts in this respect, namely, that the crystallisation of the potassium and rubidium salts of the ennead must be hindered by increased pressure, ivhile that of the csesium, salts must be helped by the same agency. § 131. Extension of the Research to the Salts of the Ennead MRO^, oi- the Oxyhalides of Potassium, Rubidium, and Cwsium. — It appeared to be interesting to extend this work so as to include the salts of the ennead of the oxyhcdides, having the general formula MROg, in which J\I may be K, Rb, Cs, and ROg may be ClOg, BrOg, IO3. In contrast with the salts of the ennead MR, which are very soluble, the oxyhalides are only sparingly soluble. The determination of the specific gravity of the crystals in their mother-liquors is therefore much easier, and was efi'ected quite successfully by my assistant, Mr H. F. Fermob. The results so obtained are given in Table IV., which is identical in form with Table II., dealing with the salts of the halides, which has already been explained. § 132. The results of the discussion of the observations made with the salts of the ennead MRO3 are given in Table V., which is constructed on the same plan as Table III. It consists of a number of sub-tables, («), (6), (c), etc., and the nature of each is specified in its title. The molecular weight of each salt, represented by the general formula MRO3, differs from that of the corresponding salt of the general formula MR by O3 = 48. Therefore the differences between the molecular weights in the same SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 215 column and between those in the same line in sub-table (c) are the same as those between the molecular weights of the corresponding salts of the ennead MR to be found in sub-table (c) of Table III., and what was said in this respect about the linear, columnar, and diagonal relations of the molecular weights of the salts of the ennead MR applies equally in the case of the ennead MRO3. The concentration, m, of the mother-liquor, given in sub-table (e) is derived from its specific gravity. § 133. In sub-table (g) we have the values of D, the specific gravity of the salt in crystal at T, referred to that of distilled water at the same temperature as unity. If we examine the values of D, we see that they rise triadwise and parallel to the values of the molecular weight. In order to study their differences the accompanying table has been constructed : — Table giving the Specific Gravities, D, of the Salts of the Ennead MRO^, and their Differences. K. Diff. Rb. Diff. Cs. C103 . . 2-319 0-857 3176 0-406 3-582 Diff. . 0-900 0-505 0-527 BrOg . 3-219 0-462 3-681 0-428 4-109 Diff. . 0-705 0-655 0-740 IO3 . . 3-924 0-412 4-336 0-513 4-849 i In this table we have the nine entries of the specific gravity of the crystals, and these furnish six entries of independent diff"erences taken column-wise, and an equal number taken line-wise. The difi"erences occurring in the lines correspond to pairs of salts having the same acid and difi"erent bases ; those occurring in the columns correspond to pairs of salts having the same base but different acids. In the upper left-hand corner we have in the top line 0'857, which is the excess of the specific gravity of RbClOg over that of KCIO3, and 0'406, which is the excess of the specific gravity of CsClOg over that of RbClOg ; so that 0'857 is the increase of the specific gravity of the salt MCIO3 when the substitution of Rb for K as the value of M is efi"ected. Similarly, the increase of specific gravity caused when the substitution of Cs for Rb in MCIO3 is effected, is 0-406. Replacing CI by Br as R in KRO3 produces a rise of 0'900 in the specific gravity, while the replacement of K by Rb as M in MCIO3 produces a rise of 0'857. When Rb is replaced by Cs as M in MCIO3 and MBrOg the efiects are similar, namely, a rise of 0'406 and 0'428 respectively. The replacement of Br by I as R in KRO3 and CSRO3 causes a rise of 0'705 and 0"740 respectively, while the replacement of Rb by Cs as M in MCIO3 is very close to that produced by the replacement of K by Rb as M in MIO3, namely, 0'406 and 0-412 respectively. These examples illustrate the similarity of the substitution effect produced by elements having nearly identical atomic weights but antagonistic chemical and physical properties. 216 MR J. Y. BUCHANAN ON THE Table IV. Experimental Results regarding each Salt in the Ennead MRO^. Salt : Formula MRO3 . ( Salt : Mol. weight . \ Temperature, T . . Specific Oravity. Weight taken, gms., w^ . Displacement, gms., w.^ . . ! KCIO3 122-6 14-8° KBrOg 167-1 19-2° KIO3 214-1 18-6° EbClOg 169-0 16-2° RbBrOj 213-5 16-0° RblOg 260-5 15-6° CsClO,, 216-5 16-0° CsBrOg 261-0 16-0° CsIOg 308-0 15-4* MoTHEE-LlQUOR. 52-2451 50-4321 52-7937 50-3973 53-9820 50-4135 52-1316 50-4209 51-2751 50-4223 51-6035 50-4258 52-4-185 50-4235 51-4449 50-4219 51-3776 50-4274 Specific gravity, — 5 = S W3 1-0360 1-0475 1-0708 1-0339 1-0169 1-0233 1 1-0402 1-0203 1-0188 Concentration. ! i Gm.-mols. p. 1000 gms. HgO, m Specific Gravity. A. Weight of first portion of salt, gms., !«!„ Displacement, gms., -Wj^ 0-4764 0-3990 0-4027 0-2938 0-1029 0-1072 0-2596 0-0995 0-0720 Salt in Crystal. 6-5566 2 -82 11 23-5976 7-2897 38-2490 9-7153 29-0782 9-1539 32-6042 8-8402 39-0514 8-9315 290122 8-0905 25-4094138-9291 6-1773: 8-0102 1 Specific gravity, -i2 = Dj 2-3-241 3-2371 3-9370 3-1766 3-6882 4-3723 3-5860 4-11341 4-8600 B. Weight of both portions of salt, gms., ?fi|3 Displacement, gms., w^^ 12-3282 5-3153 53-0730 '79-6206 16-4973 120-2904 58-0266 18-4619 68-1770 18-5218 78-6761 18-1460 64-9130 18-1219 60-7122 14-7769 83-3354 17-1872 Specific gravity, ^^ = D^ . 2-3192 3-2171! 3-9240 3-1755 3-6809 4-3360 3-5820 4-1086 4-8487 C. Weight of second portion of salt, gms., w'l., Displacement, gms., JWjg - ?rj^ = ?»2i . ! 5-7716 '29-4754 2-4942 : 9-2076 41-3716 10-5751 29-5484 9-3080 35-5728 9-6816 39-6247 9-2135 35-9008 10-0314 35-3028 8-5996 44-4063 9-1770 Specific gravity, —^ = Dg . 2-3140 3-2012 3-9122 3-1745 3-6743 4-3008 3-5789 4-1052 4-8389 Accepted specific gravity, D 2-319 3-219 3-924 1 3-176 3-681 4-336 3-582 4-109 4-849 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 217 Table V. Table giving Numerical Relations between the Crystallised Salts of the Ennead MRO^ and their Mother -Liquors. K. Rb. Cs. K. Rb. Os. K. Rb. Cs. (6) The common temperature at (a) Formula of each salt. which the determinations of the specific gravity of the crystals (c) Molecular weight of each salt and the mother-liquor respect- ively were made. MRO3. T. MRO3. CIO,. KCIO3. EbCIOj. GSCIO3. 14-8 16-2 16-0 122-6 169-0 216-5 BrO,. KBrOj. EbBrOj. CsBrOs. 19-2 16-0 16-0 167-1 213-5 261-0 lo; KIO3. EblOg. CsIOj. 18-6 15-6 15-4 214-1 260-5 308-0 {d) Weight of salt per 1000 grams of (e) Concentration of mother-liquor (/) Weight of the mass of the mother- water in each solution. expressed in gram-molecules salt liquor which contains 1000 dissolved in 1000 grams of water. grams of water. w. MR03~'"' 1000-f«) = W CIO,. 58-41 49-65 56-20 0-4764 0-2938 0-2596 1058-41 1049-65 1056-20 BrO,. 66-67 21-97 25-97 0-3990 0-1029 0-0995 1066-67 1021-97 1025-97 iOs- 86-22 27-92 22-18 0-4027 0-1072 0-0720 1086-22 1027-92 1022-18 (g) Specific gravity of the crystal at (A) Specific gravity of the mother- (i) Displacement of W grams of T referred to that of distilled liquor at T, referred to that of mother liquor at T , expressed water at the same temperature distilled water at the same tem- in grams of water at T. | as unity. D. perature as unity. S. 1- ClO,. 2-319 3-176 3-582 1-0360 1-0339 1-0402 1021-63 1015-24 1015-38 BrO,. 3-219 3-681 4-109 1-0476 1-0169 1-0203 1018-21 1004-98 1005-56 IO3. 3-924 4-336 4-849 1-0708 10234 1-0188 1014-40 1004-42 1003-31 [l) Mean increment of displacement (J) Displacement of one gram-mole- {k) Increment of displacement of 1 000 of motl ler-liquor per gram-mole- cule 01 the crystal at T, ex- pressed in grams of water at T. gi-ams of water caused by the dis- solution in it of m . MRO3. grams jf water at 1 MRO3 A-1000=». A - 1000 V 7n 7n CIO5. 52-867 53-212 60-441 21-63 15-24 15-38 45-399 51-858 59-264 BrO,. 51-910 58-001 63-519 18-21 4-98 5-56 45-629 48-444 55-849 10. 54-603 60-078 63-518 14-40 4-42 3-31 35-756 41-251 44-634 {11) DifiTerenoe of the molecular dis- (m) Displacement of one gram-mole- placement of the salt in crystal cule of crystal, expressed in i'rom the mean molecular incre- (0) Ratio. gram-molecules of water at T. ment of displacement of the water in the mother-liquor. MRO3 MRO3 V MROs m 18D" D m D v' CIO3. BrOj. 2-937 2-956 3-358 7-467 1-354 1-177 1-164 1-026 1-020 2-884 3-222 3-530 6-281 9-557 7-670 1-137 1-197 1-137 103^ 3-033 3-337 3-529 18-847 18-827 18-884 1-527 1-456 1-423 TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 28 218 MR J. Y. BUCHANAN ON THE § 134. In sub-table (j) is given the molecular displacement, MEO3/D, of the crystal in grams of water, and in sub-table (m) the same constant MRO3/I8D is given in molecules of water. In the potassium salts the values of this constant is least for KBrOg, and greatest for KIO3. In the rubidium salts there is a progressive increase from the chlorate to the bromate and the iodate. In the caesium salts the values for the bromate and iodate are identical, and that for the chlorate is only very little lower. § 135. Sub-tables {d), (e), and (/) give the concentration of the mother-liquor for each salt, expressed in three different ways. In (e) it is expressed in gram-molecules, m, of salt per 1000 grams of water, and for none of them is the value of m as high as 0'5. Therefore, although saturated, they cannot be called concentrated or strong solutions. As was pointed out in § 132, these values of the concentration of the mother-liquor are derived from its specific gravity by extrapolation from the ratios of concentration to specific gravity in the most concentrated solutions of the salts, as given in § 26, Tables 16 to 24. This course was adopted owing to the difficulty of determining analytically the concentration of solutions of the salts of the ennead MRO3 and the uncertainty of the results obtained by desiccation. The dependence of the value of the concentration on that of the specific gravity of the mother-liquor excludes certain lines of discussion which were followed in the case of the solutions of the salts of the ennead ME. It will be remarked that the specific gravities of the non-saturated solutions were all determined at 19"5° C, and are referred to that of distilled water at the same temperature as unity, while those of the mother-liquors are determined at temperatures inferior to 19 '5° C, but the specific gravity of each solution is referred to that of distilled water of the same temperature as unity. This almost completely eliminates any error in the determination of the concentration of the solution which might accrue from the difference of temperature at which the specific gravities were determined. If Table 66 in § 28 be referred to, the value of possible error due to this cause can be ascertained for the two temperatures 19 '5° and 23° C. The concentration of the KCIO3 solution would be given too low by 2 per cent. ; in the case of the other solutions the error would be less than 1 per cent. But the specific gravities of the mother- liquors were determined at temperature lower than 19 '5°, and the error would be less and in the opposite sense. S 136. In sub-table (m) we have the values of — ^^ . They are all positive ; Dm' therefore in every case crystallisation is accompanied by expansion. This is small in the case of EbClOg and CsClOa, considerable in that of KCIO3 and the bromates, and very high in that of the iodates. It is remarkable that the crystallisation of each of the three iodates is accompanied by identical expansion. § 137. Finally, attention must be called to the effect on the molecular displacement in crystal of the salts of the ennead MR by the addition of O3 so as to form the corresponding salts of the ennead MRO3. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 219 In the following table we have in the first line the values of MR, in the second and third lines the molecular displacements MRO3/D and MR/D respectively, in the fourth line their difi'erences, in the fifth line their ratios, and in the sixth line the corresponding ratios MRO3/MR of their molecular weights. Salt. MR = MRO 3 D MR D MRO3 MR D D MRO„ /MR D MRiQ mr' ,/MR / D KCl. KBr. KI. RbCl. RbBr. Rbl. CsCl. CsBr. 52-86 51-88 54-60 53-31 58 00 60-07 60-44 63-52 38-23 44-46 54-58 44-71 51-55 61-99 42-31 47-82 14-63 7-42 0-02 8-60 6-45 -1-92 18-13 15-70 1-38 1-17 1-00 1-19 1-12 0-97 1-43 1-33 1-64 1-40 1-28 1-39 1-29 1-41 1-28 1-22 Csl. 63-52 57-67 5-85 1-10 1-18 § 138. Concluding Remarks. — These will be very short. The paper has already expanded to an unexpected length, and yet, owing to the enormous amount of ex- perimentally established material, the discussion of it which has been possible is far from adequate, but an end must be made somewhere. The Table of Contents has been drawn up in a form which constitutes it really a recapitulation of the principal features of the paper, with reference to the paragraph and page where they are to be found, so that the reader has no difficulty in making himself acquainted with the matters dealt with in the paper, or in studying those which more particularly interest him. This being so, I will content myself by indicating here the points about the research which present the greatest interest or novelty. Two methods of determining specific gravities are used. Neither of them is new in principle, but there are innovations in the details of both. To take the case of the determination of the specific gravity of a soluble salt in its own mother-liquor, the principle is not new, because, if the common practice of determining the specific gravity of a salt in petroleum is adopted, the liquid in which it is weighed is, or ought to be, a saturated solution of the salt from which, as a mother-liquor, crystals of the salt can be obtained ; but it is obvious that this is a very diff"erent case from determining the specific gravity of chloride of caesium in its mother-liquor, which contains in solution something like two parts of salt to one part of water. To carry out correctly this opera- tion, the experimenter must be a trained and very experienced chemist ; but it is not necessary to be an experienced chemist to perceive the experimental difficulties of the operation ; it is therefore unlikely to be attempted by unsuitable hands. The principal method used, namely, that in which the very ancient instrument, the hydrometer, is used, also requires to be practised by a trained and experienced chemist if it is proposed to obtain results of the exactness recorded in this memoir. But to most 220 MR J. Y. BUCHANAN ON THE people the hydrometer is associated with a rough-and-ready method of ascertaining the specific gravity of liquids in public works, and in other similar places, where its use is commonly entrusted to a workman ; and the idea of readiness, if not of roughness, is, it may be said, habitually associated with the instrument and its use. An important part of this paper is devoted to showing how the hydrometer has to be used if the best results of which the instrument is capable are to be obtained from it. It will be seen that experimental skill and perseverance, and constant attention to many minute pre- cautions, are necessary. If this care is taken, the results will be good ; if it is not taken, they will be bad. When the hydrometric method is practised in the manner here specified, it is possible to obtain the specific gravity of liquids with greater accuracy than by any other means. Hence, in the case of saline solutions it is possible with it to carry the exact determina- tion of the specific gravity of the solutions of a salt to much higher dilutions than is possible by other methods. It was to experiment on solutions of such high dilution that their specific gravities have hitherto escaped experimental determination, that this systematic research was originally undertaken. It will be seen that the results obtained fully justify the time and labour expended on them. It has hitherto been the general experience that, when two equal quantities of a salt are dissolved seriatim in a quantity of water, the diminution of the total volume of the salt and the water produced by the dissolution of the first quantity is greater than that produced by the further dissolution of the second quantity. It has been proved in this memoir that for the solutions of many salts there is a concentration below which this law is reversed. It is the first time that this has been unequivocally demonstrated. In the case of some salts which, when dissolved so as to furnish solutions of moderate concentration, exhibit considerable contraction, they at high dilutions exhibit an expansion, which may cause the volume of the solution to exceed the sum of the volumes of the salt and the water. A similar and very remarkable feature of saturated solutions is shown in the case of the salts of the ennead MR. In the saturated solutions of the salts of potassium and rubidium the sum of the volumes of the salt and water is greater than that of the solution produced, while in the case of the solutions of the caesium salts the reverse is the case. From this it follows that increase of pressure must assist the crystallisation of the solutions of the caesium salts, and hinder that of the solutions of the potassium and rubidium salts. The main purpose of this investigation was to determine the specific gravity of solutions of moderate concentration and of high dilution. In order to use the same hydrometer for these diff'erent classes of solutions, its weight was altered by the use of accessory weights attached to the top of the stem. It occurred to me during the course of the investigation that, by carrying this principle further, the use of the hydrometric method, in all its delicacy, might be extended to solutions of any degree of concentration by increasing the additions made to its weight. It was found that for our hydrometers, SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 221 closed at the top, solutions having a specific gravity of 1 '2 could be experimented on, but the accessory weight required was so great as almost to disturb the equilibrium of the instrument. In order to meet this difficulty, the stem of the hydrometer was left open, so that the internal weight or ballast could be varied at will. With the open hydrometer so constructed, saturated and even supersaturated solutions of very soluble salts have been experimented on, and results of the highest interest have been obtained. The most noteworthy case is that of calcium chloride in supersaturated solution. In it a very remarkable state of unrest was observed before crystallisation took place. When the crystallisation of this solution is finished, the sum of the volumes of the crystals and the mother-liquor is less than that of the original supersaturated solution. The state of unrest which precedes the actual appearance of the first crystal consists in a rhythmic series of isothermal expansions and contractions, which cease the moment the first crystal appears and heat is liberated. The supersaturated solution exhibits veritable symptoms of labour before giving birth to the crystals and becoming itself a mother-liquor. The details of this remarkable phenomenon are to be found in Section XV. It now only remains for me to discharge the pleasant duty of acknowledging my obligations to the gentlemen who have acted as my assistants in the experimental work and in the preparation of this memoir. The work has been hard and continuous, having extended to nearly ten years, and it is impossible for me adequately to express my thanks to these gentlemen for the intelligence, skill, and perseverance with which they have all devoted themselves to it. The secretarial work connected with it has been very heavy, and it has been managed with great ability and success by Mr W. G. Royal-Da wsoN, to whom my best thanks are due. The pages of Tables in the memoir will suggest to anyone who is familiar with such work the amount of labour which has been expended in their preparation and verification. The experimental work has for nearly three years been in the hands of Mr S. M. BoswoRTH, B.Sc, who has carried it out in a room in the Davy-Faraday Laboratory, which was admirably suited to the purpose. My thanks are especially due to Sir James Dewae and the Managers of that Institution for their generosity in putting it at my disposal. Mr Bosworth's name appears several times in the text in connection with some of the more remarkable features chronicled, more particularly in connection with the state of unrest occurring in the supersaturated solution of calcium chloride before crystallisation. It was owing to his confidence in the exactness of the readings of the hydrometer which he observed in this solution, and in the reality of the discrepancies which he observed, that the state of unrest was not only noticed but measured. Mr BoswoRTH was preceded as my assistant by Mr H. F. Fermor, now of the Metro- politan Water Board, to whom a large part of the experimental work recorded in the Tables is due. His work was of the highest order, and justified his selection for the responsible office which he now holds. Before him, my laboratory assistant was Mr H. Royal-Dawson, brother of Mr W. G. Royal-Da wson, and he, like all the gentlemen whom 222 MR J. Y. BUCHANAN ON THE I have been fortunate enough to have as assistants, attained the same high degree of exactness in his experimental work, so soon as he perceived that, when he took the necessary trouble with the work, it was rewarded by increased accuracy of results. This has been my invariable experience. Comparisons of work done on solutions of the same concentration of the same salt by Mr Eoyal-Dawson, and afterwards by Mr BoswoRTH, are quoted in the memoir, and they furnish evidence of the excellence of the work put out by both these chemists. Nearly the whole of the experimental work of this memoir has been done by the gentlemen just mentioned. It would, however, be unjust if I did not refer to the great and valuable work with the hydrometer done for me at an earlier date by my old and valued friend and former assistant, Mr Andrew King of the Heriot-Watt College, Edinburgh. The exactness of his work is of the highest order, and his intimate know- ledge of, and sympathy with, my work for many years has been of the utmost value to me, and I wish to take this occasion to make public acknowledgment of the debt of gratitude which I owe to him. APPENDIX A. Densities of the Solutions at T. In the following tables the specific gravities of the solutions have been reduced to their value when referred to that of distilled water at 4° C. as unity. The factors used for this purpose are : — for T = 15-0° 19-5° 23-0° 26-0° factor = 0-999173 0-998372 0-997614 0-996879 For example, 15.S15. of | NaCl is 1 -020564. Therefore its density 4.S15. = 0-999173 ^.S^y ■■ 1-019720. CHLOEIDES. MCI. M = Na. K. K. Rb. Cs. K. Rb. Cs. t= m. 1/2 15-( °C. 19-5° C. 23-0° C. 1-019720 1-022321 1-021312 1-041446 1-060842 1/4 1-009597 1-011063 1010023 1-020204 1-030059 1/8 1-004427 1-005080 1-004251 1-009377 1-014340 1/16 1-001821 1-002123 1-001340 1-003903 1-006395 1-000531 1-003086 1-005549 1/32 1-000494 1-000659 0-999859 1-001139 1-002400 1/64 0-999827 0-999888 0-999112 0-999770 1000396 1/128 0-99949.5 0-999538 0-998736 0-999078 0-999395 1/256 0-9985G5 0-998721 0-998885 1/512 0-998454 0-998535 0-998620 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 223 BROMIDES. MBr. M = K. Rb. 1 Cs. K. Rb. Cs. T = 19-6° 0. 23-0° C. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1-039583 1-019241 1-008883 1-003642 1-001006 0-999676 0-999023 0-998696 0-998530 i 1-059519 1-029411 1-013935 1-006227 1-002310 1000326 0-999354 0-998828 0-998605 0-998450 1-079175 1-039316 1-019040 1-008764 1-003545 1-000999 0-999640 0-998978 0-998679 0-998517 1002907 1-013316 1-005490 1-001597 0-999577 0-998598 1-018237 1007975 1-002847 1-000242 0-998943 IODIDES. MI. M = K. Rb. Cs. K. Rb. Cs. Cs. T = 19-5° C. 23-0° C. 26-0°C. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1-057205 1-028229 1-013451 1-005948 1-002156 1-000268 0-999220 0-998851 0-998607 0-998494 1-076665 1-038085 1-018349 1-008402 1003404 1-000873 0-999607 0-998923 0-998644 0-998518 1-096000 1-048131 i-023304 1-010880 1-004661 1-001487 0-999915 0-999108 0-998644 0-998472 1-056113 1027260 1 012568 1-005140 1001366 0-999528 0-998562 0-998100 1-017641 1-007682 1 002645 1000163 0-998878 0-998265 1 022635 1-010221 1-003940 1-000769 0-999206 0-998526 1-009463 NITRATES. M'NOa and M"(N03)2. M' or M" Na. K. Sr". Ba". Li. Na. Ba". Pb". Rb. ' Cs. T = 15-0° C. 19-5° C. 23-0° 0. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 1-002623 1-000887 1-000036 0-999604 1-030021 1-014860 1-007140 1-003136 1-001145 1-000157 0-999663 1004513 1-001844 1-000523 0-999838 0-999502 1-005886 1-002547 1-000865 1-000008 0-999595 0-999391 1-018047 1-008389 1-003395 1-000916 0-999660 0-999025 0-998707 1-026137 1-012472 1-005479 1-001954 1-000171 0-999271 1-011652 1-005058 1-001734 1-000079 0-999227 0-998804 0-998577 1-016131 1-007304 1-002869 1-000618 0-999498 0-998948 0-998672 1-023143 1-010648 1-004182 1-000960 0-999341 0-998567 0-998017 1-015514 1-006672 1-002139 0-999897 0-998797 0-998193 224 MR J. Y. BUCHANAN ON THE Tables giving a Summary of the Densities of the Solutions of different Salts at different Temperatures. TRIADS OF NITRATES, CHLORATES, BROMATES, AND lODATES. MRO3. EO, M= 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 ijie NO,. Rb. Cs. 19-5*0. -028886 013880 006232 002334 000382 999374 998880 048924 024028 1 011314 004958 001721 000119 999290 998829 -043933 ■016304 •007397 -002950 -000615 ■999516 -998975 ClO,. K. Rb. BrO.. 10,. Gs. Rb. Rb. Cs. 19-6° C. and;?S-0°C. 19-5° C. a,nA 23-0° C. 19-5° C. and ;S5-0°C. ■017422 007994 ■003227 ■000758 ■999623 999004 998691 998554 ■027478 ■013027 005716 ■002057 000232 999289 998830 99859010 0373511 0180261 0081811 003317-1' 0007771' 999586 0- 9989230- 99858l!0' ■030146 ■013570 ■006022 002-212 000290 999328 998847 998609 l-00Jf927\l ■00747e\l-006164. 1-008609 1-003487 1-000934 0-999630 0-999013 0-998691 1-007752 ■011107 ■004739 ■001578 999986 999245 998746 1-010343 1-042602 1-020662 1-009523 1-003952 1-001128 0-999773 1-012027 1-005215 1-001771 1-000059 0-9990800-999198 0-998732|0-998807 ■014644 ■006501 ■002388 ■000317 999300 ■998820 1 -0087S4 1-011206 1 -013801 STRONG SOLUTIONS (Pyknometer). Tables giving a Summary of the Densities of the Solutions of different Salts at different Temperatures. Ror R03= 01. Br. L NO3. M = T = K. Rb. Cs. K. Rb. Cs. K. Rb. Gs. Rb. Li. Na. 19-5° 0. 19 -5° 0. 21-4° C. 19-6° 0. 23-1° C. 19-5° 0. m. 1/2 1 3 4 5 6 7 8 9 10 1-0432 1-0835 1-1204 1-1543 1-0409 1-0814 1-1573 12263 1-2915 1-3519 1-4061 1-4562 1-0599 1-1060 1-2250 1-3223 1-4090 1-4931 1-5644 1-6447 1-6997 1-7561 1-0790 1-1526 1-2-200 1-2832 1-3403 1-0596 1-1175 1-2261 1-3250 1-4155 1-4985 1-5746 1-1467 1-3015 1-4297 1-5516 1-6590 1-1128 1-2157 1-3097 1-3959 1-4766 1-5458 1-6115 1-6722 1-0753 1-1469 1-2814 1-4003 1-5077 1-6055 1-6944 1-7676 1-1718 1-3431 1-4887 1-0488 1-0964 1-1842 1-2654 0372 0730 1063 1373 1665 1940 2194 2437 2663 2885 1-0525 1-1012 1-1459 1-1871 1-2247 1-2592 1-2918 1-3231 1-3517 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 225 APPENDIX B. Table giving the Number of Series as well as the Number of Single Observations made with the various Hydrometers, from which the results recorded in this Memoir were obtained. Hydrometer. Number Number of of Single Series obtained. Observations Type. Designation. made. Closed No. 3 394 3,546 „ 17 1287 11,583 n „ 21 511 4,599 Open A 207 2,183 )» B 164 1,616 1910, No. 3 22 198 23,725 Total 2585 TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 29 226 MR J. Y. BUCHANAN ON THE INDEX. Accessory weights, Increase of weight of hydro- meter by means of JIultiple observations Ijy means of Preparation of Andrews, Reference to experiments made on the critical temperature and pressure of gases by Archimedes, Principles of . 21 27 29 201 17 Beryllium chloride, Comparison of specific gravity and displacement of solutions of . . 179-184 Expansion on dilution of solutions, of low concentration, of . . . 182 Specific gravity and displacement of solu- tions of 179 Calcium chloride, Comparison of specific gravity and displacement of solutions of Concentration of supersaturated solutions of Constitution of crystals of ... Rate of cooling of supersaturated solution of Remarkable state of unrest in a super- saturated solution of . Tables of specific gravities of solutions of 179 185 189 187 185- C'/iaHoigcr, Hydrometer used on board the . Laboratory on board the Concentration, Change of displacement pro- duced in a solution by change of . Crystallisation, Analogy between formation of ice and Heat liberated during Ri-markable state of unrest in a solution of calcium chloride preceding . Displacement, Difference of 61 Discussion on the values of increments of . Hypotheses used in the discussion of the increments of Increments of . 102, 10."), Mean increment of Statistics of solution . Summary of inciements of . Summary of mean increments of Values for difference between increment of displacement and difference of 123- 196 171, 179, 190-192 20 24 116-131 199 188 185-196 -72, 102 132- -144 108 135, 139 105, 139 6] -72 84-88 89-93 129, 183 Ennead, Tables giving relations of the molecular displacements of salts of the double . 219 Tables giving data relating to salts and mother-liquors of the double . . 210, 217 Exponents, Discussion of relation between. 113-116, 184 Hydrometei', Accessory weights used at the top of the stem of Determination of true weight of . Determination, in distilled water, of dis- placement of . . . Determination of specific gravity of solids lighter and heavier than water by means of . . . Example of degree of accuracy attainable by the use of Principle and construction of closed Principle and construction of open Study of mineral waters with Use of accessory weights with Use on board the Challenger of the Hypotheses, Agreement of values of increments of displacement for a particular salt with one of two . Ice, Analogy between the deposition of crystals from a solution, and the formation of . Isomer, Discussion of displacement of solutions of the artificial Isomeric salts, Ditt'erences of displacement Solubility of Specific gravity of bolutions of Use of the term Lal^orator)', LlmUfiiijer Control of room temjierature in Privacy of . 21 32 33-44 17 172 26 155 19 20 20 108-116 197 177 175 174 173 172 24 53 24, 171 Magnesium chloride. Behaviour of super- saturated solution of . 178, 196 Comparison of specific gravity and displace- ment of solutions of . 179-184 Specific gravity and displacement of solu- tions of . . 179 Thermal effects of the dissolution of crystals of . . . 179 Meniscus, Influence, on the determination of specific gravity, of . . 46 Mineral waters, Use of hydrometer in the study of . 19 ^1 other-liquors. Concentration of certain . 187, 207, 217 Determinatiim of the specific gravity of salts by displacement in their own . 202-219 Discussion relative to . . . 209, 218 Numerical relations between crystallised salts and tlieir . 209, 218 Specific gravity of . 187, 207, 217 Tables of displacements of . 207, 216 Observations, Sclieme for logging 38, 167 SPEOIEIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS, 227 Salts, Determination, by displacement in their own mother - liquor, of the specific gravity of soluble 203-:219 Solubility of certain 174-204 Use of open hydrometer in determining the specific gravity of " isomeric " . . 173 Sodium chloride, Specific gravity and displace- ment of solutions of . . . 1 48-154 Solids, Hydrometer for the determination of specific gravity of any . . . 17 Solids lighter than water. Hydrometer for determination of specific gravity of 17 Solution, Behaviour of a supersaturated . . 185-196 Control of temperature of . . . 55-60 Determination of the specific gravity of a saline .... . . 49 Solutions, Displacement of 107 Increment of displacement of . 84-89 Methods of preparation of . . . 120, 149 Series of observations made with hydro- meter in . . . . 44 Statistics of displacements of 61-72 Specific gravity, Determination of . . . Discussion of exactness of results of . Discussion of results of ... . Exactness of determination of Influence of menisou.'! on the determination of Summary, in the case of solutions of different salts at different temperatures, of State of unrest. Large and rapid variations of specific gravity in a supersaturated saline solution indicating a . Phenomena accompanying a . . . Supersaturated solution exhibiting a . A^alue of hydrometer to indicate a Tables, Displacements of hydrometer in distilled water, as given in . . Temperature, Example of control of room . Importance, in hydrometric work, of con- stancy of . . . Maximum departure of solution Mean range ot solution Statistics of range of variation of 1>AGB8 46 103 104 73-79 46 81-83 85- -201 85 -201 196 36-44 55- -193 23 51 51 51 r % v-/i. W y / "^''■ '-_> \W E •« ^1 '^^ / IJPSifi^ si ' t«'<-''l |*^v'' / y * >U ^- ^-^,"'~'A«8 •r -s^^ N^r. -^- \ .^^ >vV y*. V'^S -^J /A*, ' f v,f ^- ^. .tv V ^aV >.* u -:A<"^. ■A-. ''^ i>?'. V^"' h^ •S^k-i '^ t*^ f » i •-.s:. VT St^i- 'i .f .-.■¥'. \ "irM '^ Jf-f *A.. _,*^ ,•"'>- A^"- 'V^ )l' '^ ^ >,*f . ^ f% -<. i~ /' Vr- ■''^'^^* ^\ Vn jr^*w/ ■^ li i -IS ^* >-i:'ii .^;r::^^ u^ 'J* '.I «. SH: ifA'Arf 'f < ■^•: ,^^/- ^^; :a. iijl ^V •\; '^1 w>-. mmmm^ 3L^ ^BS r^. Ji.f >:^ •j5iu :'i ''^m ■^t yS.r^;S.P^ U j; ^ 1^ ^P^^^: '^^m^'' i^ ^m M SiWi'^'' ij^-i^ 15^vv' i^C. V^ , ft^ ,'f/ m ',';•: Tt, "^^■^ i^ t^v./: i'V, "M ■ill' '}u4 t J*^:^ . -T kV".!^ :\V 'r'r''j. .^^^.^•^l^ h'r4r:cA-^,. ■;:*ir: ^