114 B. A. Gould—Algebraic Expression of the 
3. As a third and last example we will take the important 
series of observations made at Upsala in Sweden during the 
ten years 1869-1879, and consider the mean diurnal variation 
mum in the curve; and decreasing the assumed daily mean 
more perceive that the epoch of maximum is probably later 
than 14°. 
Supposing then this epoch to be 14" 36", we find for M=4°70, 
a=2.29, A=228°, b—0°52, B=20°, with an evident tendency 
to a secondary maximum and a very flattened curve for the 
night-hours. Even for M= 
recognizable. But for M=4-60, for which the curve appears 
satisfactory in all other respects, we find the improbable epoch 
2» 42™ for the minimum. 
It is furthermore readily seen that either an increased value 
of M, or an earlier value of H, will give a later epoch of mini- 
mum. Thus we have for 
M=4°65 H,=—145 36™ a=2-45 A—228° 55’ 6=0°43 B=18° 17’ H,=3* 3 
4°60 14 36 2°60 229 43 0°33 1 at | 2 42 
4°60 14 24 2°60 230 41 0°32 3L 28 3 15 
4°60 14 12 2°58 231 34 0°33 45 19 3 24 
4°58 14 24 2°66 230 56 0°28 32 40 3 20 
Plotting these curves, it is clear that either of the last three 
will give satisfactory results, although the general form of the 
last but one seems the more probable. : 
Comparing the observed values with those deduced from this 
system of constants, we find 
, Temperature. Temperature. 
2, ee r—C. Hoar to ee 
; Observed. | Computed. Observed. | Computed. 
yh 2°55 2°-55 0°-00|; 134 77-28 7°29 —0°01 
g “30 2°36 —0°06 14 748 7-43 0°00 
3 2°10 2°27 O17 745 7-41 + 0°04 
4 2°02 2-28 —0°26 16 720 7-08 +012 
5 2°19 2:43 94 17 6°78 6°59 +0719 
6 2°60 2°75 —O015 18 615 597 +0718 
7 3°25 3°25 0:00 19 5:46 5°31 +015 
8 4°61 3°90 OK 20 4-15 4°66 +0°09 
9 4°84 4°65 +0719 21 4:07 4-07 0°00 
10 56-4 547 +017 22 3°54 3°67 —0°03 
11 6°36 6°23 +0°13 23 313 3°15 —0°02 
1 6-91 6°86 + 0:05 24 2°82 2°82 0 
The true value of M, as determined by the hourly observa 
tions, is 4°62, the maximum being at 14° 10™ and the minimum 
