108 B. A. Gould—Algebraice Expression of the 
effected is the determination of a sufficiently accurate value of 
, the daily mean. hen we know the epochs of maximum 
and minimum or the corresponding temperatures within narrow 
values for M, m,, an 
us to congruous values of all three which will accord with the 
facilitated by graphical methods. 
or a first approximate value of M, the mean of the temper- 
atures observed at 74, 14" and 21" will usually suffice, although 
it is always too high, its value being 
M+0-16 asin (A +14") +0:24 d sin (B+ 16*) + 0°80 csin (C +18") 
40°67 dsin(D +8") 
but when the constants of either the first or second variable 
term are approximately known, a much closer estimate may be 
made by taking in the former case + (T;+2Ty+Tx) which 
gives 
M+0-37 asin (A +14") +0-07 b sin (B +4") + 0°85 ¢ sin (C + 18") 
dsin (D +8") 
+0°72 dsin ( 
or in the latter case } (2T;+7T,,+2Ty) which gives 
M+0-01 asin (A+2") +049 dsin (B+ 16*) +.0°77 esin (C +18") 
+0°60 dsin(D+8") 
and substituting the numerical values of the known constants. 
In practice it is almost always possible to estimate the magn!- 
tude of the unknown constants with sufficient correctness to 
deduce a very close approximation to the true values. 
But, in the absence of any knowledge of the constants, a very 
near approach to the true daily mean may be generally ob- 
tained for this country from the combination +, (6T;+5Tut 
6T.,); this being equal to 
M+0-11 asin (A +14‘) +0°32 } sin (B+ 16") + 0°79 esin (C +18’) 
+0°65 dsin (D +8") 
and the relations between the constants of the different terms 
being in this region such that the several variable terms in this 
formula nearly cancel one another. 
With the preliminary value of M, obtained by any of these 
devices, is to be combined the approximate time H, of the daily 
maximum. This epoch, as also that of the minimum, Is SO * 
variable on account of the large effect exerted upon it by dis- 
turbances of the casual class, that a very long series of years 
