204- Improvement i?i Say 's Instrument/or taking Specific Gravities* 



Lastly, the depths of M and C, the extremities of the columns 

 of mercury in the tubes, below the mark at P, are to be mea- 

 sured by means of the scale and sliding-index. 



Let v be the volume of the substance examined, u the space 

 occupied by the air between E and P before the substance is 

 placed in the cup, h the atmospheric pressure expressed in 

 the height of the column of mercury, of the same temperature 

 as the mercury in AB, which it supports. 



At the commencement of the observation, when the surface 

 of the mercury was at P and the cup B closed, the air be- 

 tween E and P occupied a space = u — v 9 and its pressure 

 was measured by // ; when the extremities of the columns of 

 mercury in the two tubes are at M and C, the air which was 

 in B occupies a space = u — v + vol. PM, and its pressure is 

 measured by h — MC. 



Hence, by Hooke's law, 



u — v + vol. P M h 



u — v ~ h- MC 



h - MC , . '^L 

 •'• v = u MC~ ( )# 



When the bore of the longer tube is very uniform, and the 

 area of a perpendicular section of it = K, we have 



h -UQ 

 v =: u ^j£- K . PM. 



The value of u may be found by a similar process, the cup 

 being empty. K is readily deduced from the weight of a 

 column of mercury of known length contained in the longer 

 tube. 



If the weight of the substance be also known, its specific 

 gravity can of course be easily calculated. 



The advantages which the instrument here described pos- 

 sesses over that of M. Say, appear to be: (1.) It is only half 

 the length of Say's, and requires no complicated frame- 

 work for its support. (2.) The heights of the columns of mer- 

 cury may be measured with great accuracy with the vernier. 

 In Say's, the fractions of a division on the scale can only be 

 obtained by estimation. (3.) By making both tubes of the 

 same diameter, the effect of capillary depression is completely 

 eliminated ; while in Say's its amount, more especially in the 

 space between the tubes, can never be accurately allowed 



for. 



W. H. M. 



