SPECIFIC GKAVITY AND DISPLACEMENT OF S01V1E 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 C The total weight required to increase the 

 immersion of the hydrometer in the solution from C to C is 013592 x ri70144 

 = 0'15905 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' = 23-28173 „ 



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 + a + w>' _ 160-11649 _^.^^^^^^ 

 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 5 = 0-00109 gram. 



Now an added weight of O'l 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 



10-69x0-00109 rt.,, 

 — = 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 + 0-1 3592 = 136-83476 grams. 

 Less correction for non-immersed portion of stem = s=— 0-00109 ,, 



W + a-s=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 ^,^ 

 Ty. =0'10 mm. 



TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 21 



