658 Mr W. HOPKINS, ON THE EXTERNAL TEMPERATURE OF THE EARTH, 



A = 31°,65 70°, 



A = 30°,30 80°, 



A = 31°,75 90°. 



In the expression for w , (Art. 19) the first periodical term gives nearly the whole amount 

 of the annual variation when the latitude (/u) is not too small, the value of Q, being small. 

 At the equator it is 0,04152, and in the latitude of Paris only 0,00253, and it decreases with 

 the increase of latitude. Restricting ourselves, then, to the principal inequality in u , and 

 denoting by A the difference between the greatest and least values of its coefficients, we have 



A = 32°,88 sin jti, (Art. 20), 

 and hence 



A, = 5°,69 (C) in latitude 10°, N. 



A 2 = 11°,24 20°, 



. A 3 = l6°,44 30°, 



A 4 = 21°,11 40°, 



A 5 = 25°,18 50°, 



A 6 = 28°,47 60°, 



A 7 = 30°,90 70°, 



A 8 = 32°,31 80°, 



A 9 = 32°,88 90°. 



Comparing the corresponding values of D and A, it will be observed that, in the higher 

 latitudes, they are nearly the same, but that the former are considerably less than the latter 

 in the lower latitudes. This will necessarily be the case wherever there are causes which 

 tend especially to an equalization of temperature. Such is the case, as I have shewn, near 

 the equator. It seems probable that, in the absence of such causes, there would be little 

 difference between the annual variations of temperature in the surface of the Earth, and 

 those of the contiguous portion of the atmosphere. The latter probably approximate to the 

 former as their limit. 



27. It will be observed, that the annual inequality in the expression for w is multiplied 

 the factor — , a 

 (Art. 17), we have 



by the factor — - , and the semi-annual inequality by the factor — ; and from the equations 



Z> 2 = 6 2 + 2VV - + %, 



a a 2 



A 2 = b 2 + 2 v/^r" - + ~ ; 



a a 2 



D 2 r- 1 2,r 



b 2 ab a*b 2 



A 8 /— 1 *t 



— = 1 + 2 V27T -r + -jrr, 

 b 2 ab a 2 b 2 



