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's W - s^ + to^ - dio^ 

 ''' H,- W-s, 



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 v-^^ is added which immerses the hydrometer until it floats exactly 

 at 15. Let % be the weight of air displaced by the exposed stem above the 15th 

 division, and let dv^^ be the weight of air displaced by the small weight v-^^. 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 



^1 1; — T^ — -:;^^ ; . 



■'IS' 



^15 W-Sis + U^s-C^Vis 



Now H5 and H'5 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 



TT/ TT/ 



=j^ and ==^ we have two independent values of the specific gravity of the heavier liquid 

 under identical conditions, namely, 



S, = ll^ and S,, = |l^ 



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. 



