of Temperature for unequal length of Months, 375 
ity in the climate of Greenwich, I have computed the equa: 
tions for three other places whose climates are widely different, 
taking from the Army Meteorological Register the monthly 
means derived from 33 years’ observations at Fort Columbus, 
New York Harbor, from 1822 to 1854, and those derived from 
36 years’ observations at Fort Snelling (St. Paul), Minnesota, 
and from 28 years’ observations at Fort Moultrie, Charleston 
Harbor, South Carolina, from 1823 to 1854. But not having ae- 
cess to any concise table of daily temperatures for every day in 
the year at those places, I have been led to adopt the following 
method for finding the means for mean mouths directly from the 
means for calendar months, avoiding the use of daily means al- 
together. 
We may assume that the portion of the curve which belongs 
to any three consecutive calendar months will coincide very 
closely with a curve of the 2nd degree whose equation is 
yor A+Ba+Cr?. 
If we take the middle ordinate of the middle month as the 
axis of Y, and let n, n, m, represent the number of days i 
each month respectively, their mean temperatures will be 
aie 
1 1 1 
me = [yte= a P(t +2) +7504" ft6nn,+3n?), 
—}no-n, 
8 1n 
+$% 
mya [yea Z0ng, 
—}n2 
$ng+ns ; 
m= [vie Dt Brats) + GG0Un ge fOngnypIng), 
These three equations enable us to determine the three constants 
A, B, C, as follows: 
5 bi seen =F (Carte aU tee a Ot iea bala) 
i sigs (24-+M2)(M2-F5)( 1+ M2-bNs) ‘ 
p—(M2+Ng)(mo+2n4)(mz —™ 1)-H(% M2) (Ma 2m, )(m, — my) 
ce (2, -rg)(Mo-ng)(m, Fog) ’ 
a +(n,-+-n,)m, — (mF2ny-fng)my\ 
(2, #m2)(22-bM5)(m1 Fra T"s) } 
Now let 2, represent the time, in days, from the middle point 
of the middle month to that of the corresponding mean month, 
and let ¢ represent the number of days in the mean month; 
then its mean temperature will be 
