Diurnal Variation of Temperature. 111 
Putting this mean for M and 14% for H,, the equations (1) to 
(4) give a=1:09, A=225°, b=0°71, B=41°. The resultant 
curve has a strongly marked secondary minimum at 21" with 
its corresponding maximum at about 1", showing this value of 
to be inadmissible. 
A second supposition, M=1421, gives a=1:27, A=227°, 
6=059, B=44° and this curve also exhibits a contrary flexure 
analogous to the former although less pronounced. 
third supposition, M=1415, gives a=146, A=229°, 
_ 6=0°47, B=48°, and since in this curve there is no secondary 
maximum, the question arises as to the value of etween 
14:21 and 14:15 for which this disappears. It will quickly be 
perceived on trial that this value is very near to 14718 for 
which a=136, A=228°, b=0°58, B=46°. 
Inspecting now the corresponding curve and comparing it 
with straight lines drawn to connect the point for 14" with 
those for the other two observations, it becomes evident at a 
glance that the hour of maximum was assumed too early, and 
that a better assumption would have been 14°30". This latter 
_ gives the equation 
T=14'18 + 1°385 sin (A+ 224° 24’) + 0°508 sin (2/ + 26° 41’) 
There is in this curve no indieation of any failure to fulfill 
all the conditions of our problem; and in the total absence of 
other data, the equation may be regarded as a sufficient repre- 
Sentation of the diurnal curve. Some slightly more probable 
values for the constants might be obtained by new trials, 
which would fix better limits for M with 14" 30™ and better 
limits for H, with M=14:18; inasmuch as each of these de- 
terminations js quite close enough to render quantities of the 
second order negligible. Nevertheless any such additional eal- 
culations would imply a minuteness scarcely appropriate to the 
character of the problem. But did we possess any one of the 
not unfrequently available additional data which are afforded 
Sy an approximate knowledge of the time or value of the 
daily maximum or minimum, we should thus be enabled to fix 
the constants with much greater precision ; while a knowledge 
of all of them would permit us to deduce with considerable 
accuracy those of an additional term in the formula. 
The hourly values of the temperature which correspond to 
the curve just deduced are given below, side by side with those 
actually observed. The grouping of the algebraic signs in the 
residuals, and the relative magnitude of these, show how large 
Is that part of them due to the omission of the term depending 
upon 8h, 
