Hydrometers of Total Immersion. 505 



without sensible error by the formula 



Yt^Yt-O-OOitdit-h) (I) 



Assuming that the volume of the hydrometer may be 

 expressed as a function of the time in the form 



Yt A =Y tl + aA + bA% (2) 



when Y tlA is its volume at temperature t x and A is the time 

 in days, then on some other day A : at the same temperature 

 its volume will be 



Vt lA =Y tl + aA 1 + bA^; (3) 



subtracting equation (3) from equation (2) we get 



V, lA -V, lA =a(A-A 1 )+^(A 2 -A 1 2 ). . . (4) 



Calculated by the method of least squares from every expe- 

 riment which permitted the use of equation (4), the most 

 probable value. of a is 



-0 000,008,262,84, 

 and of b 



+ 0-000,000,016,286. 



Further, assuming that the volume of the hydrometer for 

 any temperature t can be found by the formula 



Y t = Y + xt+yt*, 



and by means of the above values of a and b reducing all 

 observations to the day on which the first experiment was 

 made, the most probable values of V , x, and y are 



V = 161-929816, 



x =+0-003,839,9, 



y =+0-000,001,881; 

 which gives 



V,=V [1 + (23,714 + 11-620 10- 9 *]. 



According to Thiesen and Scheel (JZeitsclirift fur Instrh. xii. 

 p. 294, 1893) the linear coefficient of expansion of normal 

 Jena glass is 



(7797 + 3-64/) 10- 9 , 



which would, give a cubical coefficient of expansion of 



(23,391 + 10-92010- 9 . 



In Table III. the figures given in the last column but one 



