§ 8 OF ARTS AND SCIENCES. 389 



Hence for any three temperatures, t„ f^ and A, at which 

 the two formulae are assumed to agree, we can find the 

 difference between C and c, and hence by substitution in 

 (10) or (11) the value of B — b, which again, substituted 

 in (7), (8) or (9), will give the excess of ^ over a. 



If, however, the three temperatures, ^',, t^ and t^^ are 

 chosen at equal distances, as we presume in absence of con- 

 trary evidence that they are, we have 4 = 2^, and t^ = 3/1 ; 



C= c ^6dt ^ 2sef' + etc. ] 



B = b — iidf — Goefi + etc. V I. 



A=z a -\- 6df' + 2>^et^ + etc. J 



where i is the lowest of the three temperatures at which 

 the formula is exactly fulfilled. 



Table IV. was constructed to show the different values 

 of y4, B and C corresponding to values of e from .0001 

 to .0020, which must be chosen to represent correctly the 

 volume at the extremes of three adjacent intervals of tem- 

 perature, each equal to the figure at the head of the col- 

 umn, the lowest extreme being (strictly) zero. The 

 table shows that the values of B and C may be very dif- 

 ferent according to the range of temperature chosen, and 

 that A cannot be relied upon to represent the true coeffi- 

 cient of expansion at zero. As a practical confirmation of 

 this indication of the theory, I will quote three different 

 values of A for butyrate of eth}!, namel}', .001202790, 

 from 13^ to 99'', and .000632742, from 99° to ii9°.4, ac- 

 cording to Pierre, while Kopp gives .001 178 17, probably 

 for the whole range of temperature. It would seem, at 

 first sight, impossible that two such careful observers could 

 have difiTered by 50% in their estimation of the coefficient 

 A from 99° to 119", but if wc compare the volumes indi- 

 cated in each case, taking into account the other coeffi- 

 cients as well, we shall find differences which may easily 

 be attributed to errors of observation.* The fact remains 



*See Table VII. 



