110 B. A. Gould—Algebraic Expression of the 
It is manifest that the trustworthiness of this method must 
process, employing an assumed epoch for the daily minimum ; 
or, what amounts essentially to the same, by comparing the 
epoch resulting from the determinations already made with that 
which is made probable by other considerations. In the case 
that observations of the minimum temperature exist, these will 
afford a more delicate criterion than those of the maximum, ~ 
since the epoch of minimum is during most of the year far 
more distant from our hour of morning observation, than is that 
of maximum from 2 P. M. 
It has been already stated that the earlier stages of the com- 
putation can be greatly facilitated by graphical processes, but 
in this place we are only considering the regular numerical 
routine available under all circumstances. 
append three examples, to illustrate the mode of computa- 
tion. These are selected from among those places for which 
hourly observations are on record, because, while they are 
markedly diverse in their geographical relations, they also be-— 
ong to the class most difficult to determine, namely that for 
which we can derive no indication regarding the form of the 
diurval curve from a knowledge of that which pacing ee to 
any place in the vicinity or even similarly situated. us we 
have a severe test of the degree of approximation to the true 
law which is attainable by means of the daily observations at 
7®, 14% and 21", without any other data whatsoever. The dis- 
cordances, between the hourly temperature thus inferred and 
those derived from actual observation, represent the sum-total 
of the various errors due to inaccuracies in determining the con- 
stants, and to the disregard of all terms of the general formula 
beyond that which depends on twice the time. It has been 
already mentioned that in practice the determinations may be 
much facilitated by the use of graphical methods for the first 
approximations; but we will dispense with them in our exam- 
ples, and likewise with the various indirect processes which may 
often be advantageously employed; and begin in each case by 
assuming the mean of the three daily observations for the first 
approximation to the true daily mean, and 14" for the hour of 
maximum. For readily perceiving the general form of the 
curve, a rough drawing is of course always desirable. 
1. First, let us take the observations made in the month of 
January during five successive years at the island of St. Helena, 
and published in degrees of Réaumur’s scale by Dove in his 
second series. Here we have T,=18°05, T,,=16-02, T,,=1374, 
the mean of which is 14°27. 
