of Reducing Observations of Temperature. 30 
ada eR! I 
sin — 
: sing , 
a, +a, sin (@ + a) + a, > sin (2a + Cs) 
2 
2 
=a, + = sin (@ + é,) 
since sin 4 = land sin «= 0. 
Hence the mean temperature of a half year is independent 
of a, and ¢,, and is completely determined by finding a,, a,, 
and e,. 
Bide i 
In the expression Corea, BM (z + ¢), 
the coefficient = a, 1s the difference between the mean tem- 
perature of the warmest or coldest half-year and the mean of 
the year; hence its double, or =a, is the difference between 
the mean temperatures of the warmest and the coldest half- 
year. 
Since the amplitude for monthly means is less than a, in 
DT T 
| 12 12 ° ° 
| the warmest and coldest half-year will be obtained by multi- 
T 
_ plying this amplitude by = — , OF 3 Cosec or which is 
sinz5 
| the ratio of sin , it follows that the difference between 
| 1-2879, as stated in my paper. 
To prove the concluding note. 
| Let the expression for the temperature at time w be 
a, +a, sin (@ + ¢,) + a sin (2% + Eo) Gears ete sin (nv + ¢,). 
It may be proved in the same manner as before, that if y and 
| 
as 
ithe M 
th parts of a year, a being the centre of the parts, 
2a 
sin sal sin: —= 
mm. m . 
— sin (Qz 
ean (7 +¢,) + a, ae (2¢ + €,) 
m 1) 
then y=a,+ a, 
