Diurnal Variation of Temperature. 217 
great advantage must certainly be derivable from a general 
expression which absolutely represents such observations as 
exist, even though it might not be demonstrably correct for | 
intermediate moments. Objections may be urged against the 
abuse or improper application of such a formula, but there is 
certainly a legitimate use for it. An empirical periodic fune- 
tion can be made to represent any number of observations of 
any periodic fluctuation, provided the number of constants be 
equal to that of the independent data. Whether it does or does 
not, at the same time represent the true law throughout its extent 
1S a separate question. But surely the attainment of a general 
expression which represents the available observations is most 
important, since the higher terms serve to make manifest the 
degree of confidence to which the lower ones are entitled. 
, however, with an inferior number of constants, a satisfac- 
tory representation can be obtained, we have an argument toa 
corresponding extent, that the periodic variation does in fact 
follow the law expressed by the formula. This ceases to be 
18 the only basis for a legitimate application of Bessel’s formula 
© the diurnal variation of temperature. If it represents the 
true law, it ought to be used, since it affords the most general 
and convenient expression. 
The monthly means of the hourly observations of tempera- 
e have thus the evidence that the formula represents” 
the true law of nature with close approximation; and the de- 
Stee of approximation is furthermore attested by the character 
of the residuals, irrespective of their magnitude. If the mental 
