10 kirwan's formula. 



elevation. With two exceptions, the reduced temperatures decreased, though not uni- 

 formly, as von go north from New-York. The exceptions were, thai Newburgh showed 

 a lower temperature Mian Poughkeepsie, and Kinderhook than Albany. 



The mean latitude of the places compared was 42 13 ; the an temperature reduced 



i<> the standard of Albany, and to the level <>f the sea, 4S°.95; and the mean difference 



for lo of latitude, I i ; . Applying Kirwan's fi ula" to these data, we obtain results 



winch correspond verj nearl] 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 ohtain 49°. 75 

 for the temperature in lat. 41° 43', and 4S D .15 for the temperature in lat. 42° 43'. Let 

 srsthe polar temperature of the earth, and rf = the difference between the equatorial and 

 polar temperatures :t then by Kirwan's formula, 



p + (cos* 41° 43') d = 49°. 75, 

 and p + (cos* 42° 43') d = 48°. 15. 

 Reducing these equations, we get p = — 1°.78, and d = 92°. 49. 

 Now let ; be the latitude of any place, and t its temperature ; then, 



t = — 1°.78 + 92°. 49 X cos*<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 he 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 Bine of the altitude ; and 2dly, the intensity of those rays is also nearly 

 proportional to the same.} Hence from both united, the beating 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. 



t By the terms tijualorial 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. 



Abstract of IV f. Forbes'a Report on Meteorology, at the Meeting of the British Society for the Advancement 

 ace (Am Journal, Vol. -10, page 319). 



