116 B. A. Gould—Algebraic Expression of the 
non. Cases are by no means infrequent in which the highest 
temperature of the day occurs as early as 8 A. M., or as late as 
8 P.M. Sudden changes of wind, or in the amount of cloudi- 
ness exert so great an influence that great care is often needful 
average times for the daily maximum, differing by many 
minutes, whether the interval considered be one of 5, 7, 10, or 30 
days, or the entire year. The next following would, in its turn, 
generally differ from both the previous ones; indeed the dura- 
tion of the observations needed for obtaining a value, which 
should be essentially unchangeable by their longer continuance, 
is such that it has certainly been obtained for few, if indeed 
for any, places on the earth’s surface. This certainly does not 
absolve us from the duty of investigating and remedying the 
sources of constant errors which would not probably disappear 
mean of a larger number of observations ; but none 
the less is it futile to attempt to fix the epochs within limits 
which nature has not prescribed. To these considerations is to 
be added the independent one that, in many places, the diurnal 
curve of temperature varies so slightly at certain seasons in 
the vicinity of its extremes that a point of maximum or min- 
imum value has scarcely more than a theoretical existence ; 
so that small, and often inevitable, errors of observation woul 
suffice to change the epochs by an amount relatively very large. 
If determinations of the average times of the epochs are to be 
made within narrow limits of error and in such a way as to be 
serviceable for scientific ends, they must either be separately 
they are modified by influences analogous to those just men- 
tioned. : 
The distinguished physicist, to whose criticisms and strong 
denunciations of the employment of the general mathematical 
formula we have alluded, has repeatedly asserted that errors 10 
the times of daily maximum and minimum are produced by 
the employment of Bessel’s formula; and that this places the 
