34 Professor J. D. Everett’s Description of a Method 
. T 
sin — 
mm ° 
m 
Hence the amount by which the mean temperature of any th 
part of a year differs from that of the whole year, is always 
less than the amount by which the temperature of its middle 
day differs from the mean temperature of the year, in the 
: ae ae 
Fatio OF Gin — *°—. 
m°>m 
This proves the second note of my paper. 
Next, let the equation to the annual curve of temperature be 
y =a, + a, sin (@ + ¢,) of a, sin (2% + @,) 
The mean temperature of any = th part of a year will be, as in 
the previous case, the integral of ydw from # — ¢ tow + ¢, 
T 
where ¢ =-. 
m 
yde = a, dz + a, sin (« + e,) dw + a, sin (2% + €,) da. 
yde = a, — a, cos (a+e,)— 4 a, cos (2 + @,), 
which between the limits is 
ay { @+ c)—(a — °)} — 4, { 208 (2 + ¢ + e,)—cos (a — e+e) | 
— ha, { c0s (22 + 2c + e,) — cos (24 — Qe + “.) | 
= 2a,c + 2a, sin (a + ¢,) sin¢ + a, sin (2u + ¢€,) sin 2c. 
The mean temperature is the quotient of this by 2c, which is 
STAG. sees = sin 2c , za 
a, + 4, ~~ Sin (@ + @,) + a. 3, sm (Qe + €); 
or substituting for c its value — 
alt dae ra “074 
sin — ain Be 
mM” . (w mM . D7 
faye a sin ® + 6) + a, .—>-— sin (2a + ¢,). 
mM 1% 
If m = 2, we have for the mean temperature of the half-year 
whose centre is w, the expression 
