102 MK 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 Gj , in 

 which G is the unit of weight and T or Ms 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 tons, that is, tons of water of ordinary 

 atmospheric temperature. In this research the units of displacement used are expressed 

 by the symbols Gja-, G19.5., and Gis-. If the adopted value of T were 4° C, then the 

 unit of displacement would be G40, and this is the gravimetric symbol for the standard 

 cubic centimetre. 



In the fifth column we have the values of d^, 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^^g and 

 \ii, the increment of displacement produced by dissolving 1/8 MR in 1000 grams of 

 water is A^^^j— 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 Aj^^, is c^A = Aj,^ — Aj,8. 

 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 {A^^ — A,„) — 

 (A„^— 1000) is positive for values of m= 1/16 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 of 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 



