CONTINUOUS ELECTRIC CALORIMETRY. 
143 
doubtful whether the advantage gained would be worth the extra complication, and 
the possible confusion caused by changing a formula already published and widely 
distributed. 
Dr. Barnes (‘ Roy. Soc. Proc.,’ vol. 67, p. 242) has proposed the following :— 
From 5° to 37°‘5, 
5 = -99733 -f -000,0035 (37-5 - tf + ‘000,000,10 (37’5 - if . . (9). 
From 37°'5 to 55°, 
.s- = -99733 + -000,0035 (37'5 — tf — -000,000,10 (37'5 - tf . . (10). 
From 55° to 100°, 
6- = "99850 + -000,120 (t — 55) -f ‘000,000,25 (t — 55) 2 . . . . (11). 
The first two formulae differ only in the sign of the third term. They are not 
quite so simple and convenient for calculation as (5) above. The first formula does 
not represent the observations below 10 quite so accurately as formula (6), but both 
are probably within the possible limits of error. The mean divergence of the 
observations between 37°‘55 and 5° from the second formula is about 3 parts in 
10,000, and is rather greater than the mean divergence of the observations from the 
old formula (5). The agreement with the latter would be greatly improved if we 
reject the discordant observation No. XXII., in series 2 at 54°"61 (Barnes, p. 244), 
giving greater weight to the later observations, No. XXXII. in series 3 at 54°"57, 
and No. XLVIII., in series 6 at 51°"02. On the whole, the balance of probability 
appears to me to be in favour of retaining the older and simpler formula in preference 
to that since proposed by Dr. Barnes. 
The third of the above formulae, from 55° to 100°, does not fit with the second at 
55°, the respective values being, (L0) "99893, and (11) '99850. This is shown by the 
difference in Table XIY. between the values at 55° and 60° in the column headed 
“Barnes, Roy. Soc., 1900,” which is only "00016. The corresponding differences for 
five degrees on either side are 50° to 55°, "00087 ; 60° to 65°, "00061. There is also 
a considerable change of slope from "000216 to "000120 at 55°. It is, of course, necessary 
that the values should fit accurately at the point where the formulae meet, and it is 
further desirable that there should not be a sudden change of slope. The first 
condition is accurately and the second very approximately satisfied by the old 
formulae (5) and (7) at 60°. 
The following table contains a comparison of the formula of Ludjn and those of 
Barnes, with those previously published in the B.A. Report, 1899. 
