16 - . kirwan's formula. 



elevation. With two exceptions, the reduced temperatiiies 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' ; 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 

 wliich 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 sulilracting ^° 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° 43'. Let 

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

 polar temperatures ;t then by Kirwan's formula, 



p + (cosMl°43')f^ = 49°.75, 

 and p + (cosM2°43')c? = 48".15. 



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

 Now let (p be the Lntiliide of any place, and t its temperature; then, 



t = — V'.IS + 92". 49 X cos" cp. 



To verify the hiw, 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 tiie fornuda would he more correct, if in place of the square of the 

 cosine of the latitude we siiould 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 same.| 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 witli those obtained by observation in the State of New- York, as those which we shall deduce 

 from Kirwan's. 



t By the terms cqtuiiorial 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 cipiator. 



X See Abstract of Prof, t'orbes's Report on Meteorology, at the Meeting of the British Society for the Advancement 

 of Science (Am. Journal, Vol. 40, page 319). 



