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



Hence the above expression 



= 32°,88 sin fx. 



At places sufficiently near the equator y. becomes so small that this term in the 

 expression for u becomes of no more importance than the next term, which is small 

 on account of Q,. Its period is half a year. 



21. The whole effect of the solar heat on the mean temperature of the Earth's 

 surface is not expressed by hQ, for there is also, as above explained, the effect of the 

 higher temperature of the atmosphere superinduced by the higher temperature of the 

 Earth's surface, and by the direct absorption of a certain portion of the solar heat in 

 passing through the atmosphere. Tholigh we have no sufficient data for calculating 

 mathematically the amount of the effect thus produced, we may still form an estimate of it. 



It has been above explained that P depends on the interchange of heat between the 

 Earth on the one hand, and the atmosphere and stellar space on the other. Let \|/ 

 denote the value which £ would have if it depended only on radiation from stellar space 

 and the atmosphere in the state in which it would exist if the solar heat were absent ; 

 and let s denote that part of P which depends on the higher temperature of the atmo- 

 sphere arising from the existing solar heat. We shall then have 



If we suppose the radiation of heat to the Earth from stellar space to be the same 

 in all directions, the temperature of the atmosphere, in the absence of the Sun, would 

 be the same in all latitudes. Consequently \^ would be constant, as I shall here suppose 

 it to be, while s will be a function of the latitude, and will also be affected by any local 

 causes brought into action by the difference of temperature in different latitudes. Ocean 

 currents, for instance, which would produce no effect on local temperature if the general 

 temperature were the same for all latitudes, do actually produce very considerable effects. 

 We shall, however, eliminate in some degree these local irregularities in the values of 

 s if we take its mean value for any proposed parallel of latitude, instead of its value for 

 any particular place situated upon that parallel. In such case the values of s will only 

 be affected by local causes so far as those causes may affect the mean of the temperatures 

 for a whole parallel of latitude, and not merely the temperature of one particular part 

 of it. Taking only that part of the expression for w which gives its mean value, 

 we have 



u = \f/ + s + hQ. 



The value of u might be ascertained by observing the mean annual temperature 

 of the surface of the Earth at each particular place, but very few observations of this 

 kind have hitherto been made. We can only take, therefore, instead of them, observations 

 on the mean temperature of the atmosphere. If we take for u the mean annual temper- 

 ature for a whole parallel of latitude, the corresponding value of s will be referred likewise 

 to the whole of the same parallel, for which also the corresponding value of Q can be 



