Heat by the Method of Mixtures. 267 



Second, W. This may be determined in two ways. 



(a) By calculation from the formula 



w M'c' + MV 



W = 



c 



where M' and M" are determined by weighing, and c' and c" 



either determined by experiment (best) or taken from tables. 



(b) By experiment in the usual manner (introducing known 

 quantity of hot water). 



Its effect on s and the limiting error will be discussed under 

 effect of M. 



Third, M. To find the error in s, due to error in observing 

 the weight, M, we have, by differentiation, 

 ds _ c(6—t) s 



d(M + W) ~ w(T-0) ~ M + W 

 Suppose M+W = 300 grms. Then in order that the error of 

 s should be within 0*1 per cent, the weight must be taken to 

 0*3 grms. ; with 200 grms. to 0*2 grm. But with the degree of 

 accuracy ordinarily obtainable in reading temperatures to -fa 

 (see below), the weight need not be taken closer than 0*5 grm. 

 for a weight of 200 grms. ; so that unless the error in observ- 

 ing temperatures can be reduced there is no necessity for cor- 

 recting for evaporation, for loss of weight in air, etc., etc. For 

 the same reason it is not necessary to obtain the weight of w 

 closer than *05 grm. for a weight of 50 grms. 



ds ds 



Fourth, c. Likewise to find — , we have — =s/c; or since 



(XG CLG 



0=1, it must for an accuracy of 0*1 per cent be correct for the 

 interval employed to *001. But the extreme variation of c, 

 for 10° (from 4° to 14° C), is 0*00033, which makes it apparent 

 that all correction for c is entirely unnecessary, although Kohl- 

 rausch makes note of the fact that such a correction should be 

 applied. 



Fifth. Effect of errors in observing temperatures. 



(A) Error in t. 



From equation (2) we have 



c^ (M + W), = _^_. 



dt ^ w(T-6) 6-t K ' 



From the first of these values we see that in order to diminish 

 the effect of the error in t upon s, we must make M+W as 

 small and T — 6 as large as possible, conditions which conflict 

 with each other ; for the larger ut, and the smaller M + W, is, 

 the smaller will be T — 6. But the condition of things for 



which — — — tt- will be a minimum, will evidently be M+W 



= 0, a condition which cannot be realized, but which shows 



