HEAT OF WATER, WITH EXPERIMENTS BY A NEW METHOD. 5 
particular type of empirical formula chosen. The formula given hy Ludin for the 
actual specific heat s was as follows* :—■ 
.s = 1-0-OOU76668^ + 0-000019598^'-0-00000011G2^' .... ( 4 ) 
±0-0000025 ±0-0000040 ±0-000000030. 
The probable errors of the several coefficients, as calculated by Ludin, are given in 
the second line below the coefficients to which they apply. It would appear that this 
type of formula is unsuitable for representing the variation of specific heat of water 
from 0° C. to 100° C., because the coefficients come out relatively large and of 
opposite signs. For instance, the value of the specific heat at 100° C. is made up as 
follows, according to Ludin’s formula :— 
.s- = 1-0-076668 ±0-00025 
+ 0-19598 ±0-040 
-0-1162 ±0-030 
Sum = 1 + 0-0031 ± ? 
The small difference 0-0031, representing the required variation of the specific heat, 
is less than 1 per cent, of the sum 0-388848 (taken without regard to sign) of the 
MEAN SPECIFIC HEAT FROM 
0“ TO t° C 
w 
Li/D/f 
GROL 
/'S OBSBRVf 
IP MEANS 
^TtONS * 
-© 
DIETERICI 
MEANS <S) 
.UOIN’S FOR 
■t ^ 
vlULA. ^ 
LUDIN'S FOB 
MULA^ 
CA 
-LENDAR'S 
--- +•. 
-ORMULA 
+' 
% 
-- 
--- +4 
MDAR'S 
/lULA'x^ 
_0_ 
_0"^ 
-^ 
1010 
1-006 
I-000, 
10 * 
20 ° 
30 ° 
40 ° 50 ° 
Fig. 2. 
60 ° 
70 ° 
80 ° 
90 ° 
100 ° 
terms by which it is represented, and is only a tenth of the probable error of either of 
the last two terms. It is obvious d 2 ^nori that a measurement of the mean specific 
heat between 18° C. and 89° C., combined with a measurement between 18° C. aiid 
* Ludin’s results have since been corrected by reference to a comparison made by Thiesbn, Scheel, 
and Sell between the French “Terre Dur” and the Jena 16^^^ glass thermometers. This reduction is 
somewhat uncertain, and does not affect his values materially except in the neighbourhood of 0° C. His 
original formula has been retained for purposes of discussion, because it is more nearly correct between 
0° C. and 20° C., and because it was employed by Messrs. Bousfield in their comparisons. There is an 
obvious misprint in Ludin’s corrected formula as cpioted in the ‘Fortschritte der Physik,’ 1900, IL, p. -304, 
but the tables appear to be correct. Ludin’s ratio of the mean specific heat from 0° C. to 100° C. to the 
specific heat at 20° C. is reduced from 1 • 0063 to 1 • 0058. His value for the specific heat at 90° C. is 
reduced from 1'0136 to 1 ’0127 in terms of the specific heat at 20° C. 
