the Measurement of the Specific Gravity of Liquids. 117 

 For a floating hydrometer properly wettedj we have, thou, 



and the effect of this force must obviously be the same as if the 

 weight of the instrument had been increased by G. Let^ then, /* 

 denote the increased distance to which the hydrometer sinks in 

 the liquid when loaded with the weight G ; then, if m and T are 

 determined by observation, h may be calculated as follows : — Let 

 V be the volume of the part of the hydrometer immersed in the 

 liquid in consequence of its own weight P, dv the increased 

 volume immersed by the additional weight G ; then 



dv.M::G:V; 

 and since 



^ k' 



^ PG G 

 '^"^IP^T' 

 but 



dv='rrr'^.h, 



•• "-'rrr'^k' 



and if the value for G above determined, namely ^irmrk, be sub- 

 stituted, we get 



h=^-^ (6) 



r 



If the constant m has different values for different liquids, it 

 follows from this that an hydrometer, the scale of which is cor- 

 rect for a given liquid, will be incorrect for others. 



Should the scale of an hydrometer be divided according to 

 Brisson's method, it will sink either too deep, or not deep enough 

 in the liquid for which it is designed, according as for that liquid 

 m is greater or less than for water. Let, then, h' express in the 

 case of the liquid in question the same as h does for water, then 

 the error in the position of the division of the scale caused by 

 capillary attraction will be expressed by A— /i'. 



In order to determine how far the observed differences in the 

 readings of hydrometers mentioned at the beginning of this 

 paper could be explained on the above grounds, I made a large 

 number of measurements which appear to confirm completely 

 the correctness of my hypothesis. For the purposes of compa- 

 rison I made use of the following instruments : — 1st, an hydro- 

 meter, No. 53, by Ch. F. Gcissler of Berlin ; 2nd, an hydrometer 

 of J. G. Greiuer of Berlin ; 3rd, another instrument by the same 



