30 J.D. Everett on Reducing Observations of Temperature. 
sin = sin 
¥n=Ao+4, —— sin (e-+E,)+a, =" sin (27--E,). 
Let m = 2 and we have for the mean temperature of a half year 
Ys oe = sin (7 + E,), 
the third term vanishing, since sin ps Hence the half yearly 
term produces no effect upon the mean temperature of a hal 
year (as is also obvious from general considerations), and the 
riot of the half yearly means is to that of the annual 
term fi y means, as the radius of a circle is to a quad- 
rantal a ! 
The sais of the half yearly means, being | wget of the 
amplitude, i 18 @,. — which being divided by a, . ne the am- 
2 FP) 
' plitude of the annual term for monthly means, gives as a quo- 
tient 
— the numerical value of which is 1-2879. Hence if 
SID 75 
the amplitude A, deduced from monthly means be multiplied 
by this number, the product will be the difference between the 
temperatures of i warmest and coldest halves into which the 
year can be divi 
Lastly, let the sey for instantaneous temperatures take 
the general form : 
y=A,+a,sin (t+E,)+a,sin(2e+E,)+ . . . . +a,sin (na+E,) 
It will be found by proceeding as in the preree cases, that — 
the expression for the mean temperature of the + th of a year is 
sin= sin = 2 
Yn=Ao+@, -—— sin (e+-E,)-+-a, —> sin (22-+-E,)+ 
m « 
4 
ah F sin (37-+-E,)+..... +a, a sin (nw-+E,). 
Hence if A, i: x . A, denote the seit deduced 
from monthly means, we have | 
sin 15° sin 30° n 45° j 
"are 15°’ Ag 030"? Ay=a, = oe $3 
sin n< 15° 
aren 15°" : 
A,=4, 
and generally Aa, ‘ 
