jS^ Atatheituitiea) anl Ph'ikfophtcal Correfpondenee. 



produced by the dircft adion of the fun, is as the fine of the fun's altitude \ fo that if the 

 earth were equally heated at the equator and poles, the quantity to be added to the polar 

 heat would be ti X fine of the fun's altitude, radius being I. But it has been afcertained 

 from obfcivation, that the heat on the earth's furfacc (cctirit paribus), and confequently 

 the heat emitted by the earth itfelf, is always proportional to the dircd folar heat; 

 whence the quantity to be added muft be it X the fquare of the fine of the fun's ahltude : 

 or, fince the mean annual altitude of the fun, in any latitude, is equal to the complement 

 of that latitude, the quantity to be added to the polar heat (»« — «) will he n X cof. =// 

 but cof. / = V 1 — fine-V; confequcntly, >« — « + « X cof. =/=/» — « + «—» X fine »/ 



— m /) X fine '/. Hence, if the mean temperature of any two latitudes be known, the 



temperature under the equator, at the pole, and in every intermediate latitude, may be 

 readily afcertained. 



The mean temperature of lat. 40° is found to be 62.1, and of lat. 50° to be 52.f^; but 

 the fquare of the fine of 40'' is "413, and the fquare of the fine of 50° is "586 ; whence 



m — '4131 = 62'i 



m — -jBdw = 52'9 > 

 From which equations « is found = 53 nearly, and m = 84. So that, the mean annual 

 temperature at the equator being 84", that of the pole mull be 84 — 53 = 3 i» j and the 

 mean annual temperature of every intermediate latitude will be 84 — 53 X the fquare of 

 the fine of that latitude. 



NEjr MATHEMATICAL QUESTION. 



Question X. Sy iP'. Tikmson. 



IT is required to find at what time of the longeft day it is the hottcfl in London, fup- 

 pofing the heat to be as the fine of the fun's altitude, and the time of its continuance above 

 the horizon. 



PHILOSOPHICAL QUESTION. 



THERE is an optical appearance fo frequent, that it is rather furprifing that writers oti 

 that fciencc have never mentioned it. Whenever the fun fhines upon agitated water not 

 abfolutely loaded with opake matter, and the fpe£lator is fo placed that the fbadow of his 

 head may be projccled upon the furface of the fluid, he will fee an innumerable quantity 

 of divergent rays within the water, of which that fhadow is the centre. They are inceflantly 

 ihifting their place laterally ; and if more perfons than one arc prefent, each fees a fyftem 

 of radiations or glory round his own head, but no fuch appearance round the fhadows of 

 the other perfons, though thefe alfo are very vifible to him. As this phenomenon has a 

 flriking effect when obferved, and may be accounted for upon the common principles of 

 optips and pcrfpeftirt, it is ofiered to correfpondents as an objeft for explanation. 



T» 



