SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 119 



When, however, we consider the values of v, ( = A-1000), or those of cIA, the 

 probable error has a close relation to the concentration. Thus, when the value for A is 

 1000-064, this effect of an error of ±3 in the third decimal place, which corresponds 

 to the sixth place of decimals in the value of the specific gravity, is insensible ; but 

 when we consider the value of v = 0-064, a diiference of ±0-003 gives the values 0-061 

 and 0-067 as possible values, and this is equivalent to an uncertainty in the value of v 

 . having a range of 0-006, which is 94 per cent, of 0-064, the mean value of v. 



If we consider a solution of greater concentration, e.g. that of 1/128 KCl in 1000 grams 

 of water, the value of v is 0-217, which, when affected by a probable error of ±0-003, 

 gives a possible range of uncertainty of 0-006, and this is only 2-75 per cent, of the 

 mean value oft', which is 0-217. 



We have considered the case of KCl, which has a low molecular weight, and its 

 solutions have a comparatively low specific gravity. Salts of higher molecular weight, 

 such as KI or the salts of rubidium and caesium, form solutions which have higher 

 specific gravities for an equivalent concentration. In these cases the range of un- 

 certainty of the values of v and d^ is relatively less considerable than that in the 

 case of KCl. 



§ 49. The following table furnishes evidence of the possible uncertainty of the 

 value of the displacement of a solution which is due to the accumulation of the errors 

 affecting the preparation of the solution and those affecting the determination of its 

 specific gravity when practised by different experimenters. 



POTASSIUM CHLORIDE. KCl=74-6. 

 T = 19-5°C. 



m. 



Weight of 

 Solution. 



Specific Gravity obtained by 



Corresponding Displacement. 



D. 



B. 



D. 



B. 



1/8 



1/16 



1/32 



1/64 



1/128 



1/256 



1/512 



1009-325 

 1004-662 

 1002-331 

 1001-166 

 1000-582 

 1000-291 

 1000-146 



1-005889 

 1-002973 

 1-001489 

 1-000741 

 1-000365 

 1-000193 

 1-000082 



1-005911 

 1-002972 

 1-001473 

 1-000740 

 1-000376 

 1-000195 

 1-000073 



1003-416 

 1001-684 

 1000-841 

 1000-423 

 1000-217 

 1000-098 

 1000-064 



1003-394 

 1001-685 

 1000-857 

 1000-424 

 1000-206 

 1000-096 

 1000-073 



The numbers in the columns headed D are abstracted from Table No. ] , Class A. 

 The experiments were made by Mr H. Royal-Dawson in May 1904, using hydrometers 

 Nos. 17 and 21. The scheme for the preparation of the various concentrations of the 

 solutions in this series was that of diluting a known quantity of the stronger solution 

 with the quantity of water necessary to produce the solution whose strength was one- 

 half that of the solution from which it was made ; thus providing a series of solutions 

 whose strengths diminish in a geometric succession. 



