CONTINUOUS ELECTRIC CALORIMETRY. 
141 
(46.) Empirical Formula. 
The usual method of representing the results of a series of observations like the 
present is to adopt an empirical formula of the type, 
s = 1 -f- at bt~ + cfi -f dd + &c.,.(3), 
and to calculate the values of the coefficients a, b, c, d, &c., by the method of least 
squares. This was, in fact, the method adopted by Ludin. It has the advantage of 
providing a simple and ready rule, which is very generally recognized and applied ; 
but it appears to me that it is in reality liable to several objections. Too much 
weight is given to the observations at higher temperatures, which are necessarily less 
accurate than the rest. The results obtained are in a great measure dependent on 
the particular type of formula assumed, which is frequently inadequate to represent 
the phenomenon, and is generally quite unsuitable for extrapolation. Moreover, the 
method gives a fictitious appearance of completeness and accuracy, which is quite 
misleading, as the calculated values of the probable errors contain no reference to 
possible sources of constant error. It also generally happens that the terms of the 
empirical formula are large and of alternate sign, so that the small variation required 
is given as the difference between large quantities, which must be calculated to 
several figures in applying the formula. The following formula of Ludin supplies a 
good illustration of some of these points :— 
s = 1 - •000766Gffi + -000019598^ - -000,000,1162^ 
± -0000025 ± -000004 ± ’000,000,03 
The probable errors of the several coefficients, as calculated by Ludin, are given in 
the second line below the coefficients to which they apply. The value of the specific 
heat at 100° C. on Ludin’s formula is made up as follows :— 
s - 1 - -076668 ± ‘00025 
+ -19598 ± -040 
- -1162 ± -030 
1 + -0031 
It is at once obvious that a formula of this type is quite unsuitable for the 
representation of the variation of the specific heat over the whole range 0° to 100° C. 
Moreover, since the maximum divergence of the specific heat from its mean value 
over the range 10° to 70° is only 2 parts in 1000, according to the present series of 
