16 
kirwan's formula. 
elevation. With two exceptions, the reduced temperatures decreased, though not uni¬ 
formly, as you go north from New-York. The exceptions were, that Newburgh showed 
a lower temperature than Poughkeepsie, and Kinderhook than Albany. 
The mean latitude of the places compared was 42° 13 7 ; the mean temperature reduced 
to the standard of Albany, and to the level of the sea, 48°.95 ; and the mean difference 
for 1° of latitude, 1°.6. Applying Kirwan’s formula* to these data, we obtain results 
which correspond very nearly with the observed temperature, after making a proper 
allowance for elevation; as appears from the following table. The sixth column was 
computed as follows : Adding and subtracting to and from the mean latitude, and also 
adding and subtracting half of 1°.6 to and from the mean temperature, we obtain 49°.75 
for the temperature in lat. 41° 43 / , and 48°. 15 for the temperature in lat. 42° 43k Let 
p = the polar temperature of the earth, and d = the difference between the equatorial and 
polar temperatures ;t then by Kirwan’s formula, 
p + (cos 2 41° 43 ') d — 49°. 75, 
and p + (cos 2 42° 43') d = 48°. 15. 
Reducing these equations, we get p = — 1°.78, and d = 92°.49. 
Now let <p be the latitude of any place, and t its temperature; then, 
t — — 1°.78 + 92°.49 x cos 2 <p. 
To verify the law, I have applied it to a number of other places beyond the limits of 
the State under examination, allowing also for the elevation of the place above tide water 
at the rate of 1° for 350 feet; and the results are seen in the table below. 
It would seem that the formula would be more correct, if in place of the square of the 
cosine of the latitude we should substitute the square of the sine of the sun’s meridian 
altitude; for, 1st, the number of rays of the sun that fall upon any place at noon, is 
proportional to the sine of the altitude; and 2dly, the intensity of those rays is also nearly 
proportional to the same4 Hence from both united, the heating power must be nearly 
proportional to the square of the sine of the meridional altitude. In the temperate zones 
it would evidently make no difference which we use, as the complement of the latitude 
and the sun’s mean meridian altitude are the same; but in the torrid and frigid zones, 
* Dr. Brewster’s formula is. 
Mean temperature = 86°.3 x sin D — 3|°, 
in which D represents the distance of the place from the nearest isothermal pole; but the results obtained by it do 
not correspond so well with those obtained by observation in the State of New-York, as those which we shall deduce 
from Kirwan’s. 
f By the terms equatorial and polar temperatures we are to understand not the temperature actually existing there, 
but that which would exist if the sun were constantly over the equator. 
J See Abstract of Prof. Forbes’s Report on Meteorology, at the Meeting of the British Society for the Advancement 
of Science (Am. Journal. Vol. 40, page 319). 
