HEAT OF WATEE, WITH EXPERIMENTS BY A NEW METHOD. 
29 
Explanation of the Tables. 
The most useful table in practice is that of the variation of the total heat, which 
also permits the mean specific heat between any limits to be readily calculated. The 
corresponding curve, representing the variation between 0° C. and 100° C., has been 
given in fig. 6, but the scale of fig. 6 does not permit the values to be read with 
sufficient accuracy from the curve as reproduced. It should be observed that it is 
important to tabulate the variation in terms of the specific heat at 20° C. taken as 
unity, and not in terms of the specific heat at 15° C., which is so often taken as the 
standard, l)ecause in the latter case the values of dh from 42° C. to 92° C. would all 
be negative, which would be inconvenient in using the table. If, on the other hand, 
the miiiimum value of s, or the value at 30° C., were taken as the standard, the 
values of dli would be inconveniently large. 
The table gives the values of dh for each degree, and a column of differences is 
added to facilitate interpolation if desired, but the differences are so small for the 
greater part of the range 0° C. to 100° C. that this is seldom required. Above 
100° C. the differences are larger, but the values are here so uncertain that it could 
seldom be worth while to interpolate. The method of using the table is fairly 
obvious, but the following examples may make it clearer. 
To find the total heat h from 0° C. to any point t ; add to the exact value of t, 
expressed to 0°'001 C., the corresponding value of dh for the nearest whole degree 
taken from the table, interpolating for fractions of a degree if great accuracy is 
required in a problem depending on small differences. Unless t is known to 0°‘001 C., 
interpolation is unnecessary. 
To find the change of total heat between and t .^; find from the table the corre¬ 
sponding values of dh, namely, d/q and d/q, and add the difierence dl^—dhi to the 
difference with due regard to sign. 
To find the mean specific heat from 0° C. to ^; divide the corresponding value of dh 
by t and add unity. 
To find the mean specific heat between q and q! fbe difierence d/q—d/q, divide 
by the difierence q—q, and add unity. Thus, if the given values are q = 25°'442 C., 
q = 56°'452 C., we find d/q = 0‘073, d/q = 0’037, whence d/q—d/q = —0'036, 
^ 1,2 == 1 —0‘036/31'0 = 1 —O'OOllG = 0’99884. The result will be correct to 1 in 
10,000, if q—q is not less than 10° C. If the range is less than 10° C., the specific 
heat at the mean point of the range, taken from the table of specific heat at t, is a 
sufficiently close approximatioii in most cases. 
The values of the entropy of water cp i-eckoned from 0° C. are sometimes required, 
and are generally given in steam-tables. Assuming that 0° C. is 273°'10 C. from the 
absolute zero, the formula for the entropy obtained by integrating from 0° C. to t 
formula (6) for the specific heat divided by ^-l-273‘l is as follows ; 
0 = 2-36602 logi, (^ + 273-l)/273-U-0-004586 logio (^ + 20)/20 
-0’01618 (^/l00)-h0-0045 (^/lOO)". 
