Royal Society. 77 
is vifibly greater than the other area HZ G H, by as much as the 
area H G Q^is greater than the area Z G O ; which,^ that it is fo, 
is vifible to light, by a great excels • and i'o much in proportion 
does the heat of twenty four hours fun~fhine under the Tole^ ex- 
ceed that of the twelve hours under the EquinoSiial 3 whence CdPteris 
'Paribus^ it is reafonable to conclude, that were the fun perpetu- 
ally under the Tropic, at the Pole it would be at leaft as warm, 
as it is now under the Line itfelf: But whereas the nature of 
heat is to remain in the fubjeft, after the caule that heated it is 
removed, and particularly in the air 5 under the EquinoElial, the 
12 hours abfcence of the fun does very little abate the motion 
imprefled by the pall aftion of his rays, wherein heat conlifts, 
before he rife again 5 but under the (Pole-, the long ablence of 
the fun for fix months, wherein the extremity of cold obtains, 
does fo chill the air, that it is as it were frozen up, and cannot, 
before the fun has got far towards it, be any way fenlible of his 
prefence, his beams being obftrufted by thick clouds, and perpe- 
tual fogs and mifts^ and by that atmofphere of cold, as the 
honourable Mr. Soyle exprcfles it, proceeding from the ever- 
lading ice, which in immenie quantities docs chill the neighbour- 
ing air, and which the too fudden retreat of the fun leaves un- 
thawed, to inercafe again, during the long winter that follows 
this fhort interval of fummer : But the different degrees of heat 
and cold, in different places, depend in a great roeafure on the 
accidents of the neighbourhood of high mountains, whole height 
exceedingly chills the air brought by the winds over them 5 and 
of the nature of the foil, which vanoully retains the heat, parti- 
cularly the fandy, which in Africa and Arabia, and generally 
where iuch fandy defarts are found, do make the heat of the 
fummer incredible to thole that have not felt it : In prolecution of 
this nrft thought, Mr. i/^//rjV' has folved the problem generally; 
viz. to give the proportional degree of heat, or thelum of all the 
fines of the fun's altitude, whilit he is above the horizon in any 
oblique fphere, by reducing it to the finding of the curve furface 
of a cylindric Ungula or hoof, or of a given part thereof: Now 
this problem is not of that difficulty, as appears at firffc fight 3 for 
in Fig. 5. let the cylinder A BCD be cut obliquely by the 
ellipfe BKDI, and by the centre thereof H, delcribe the circle 
I K L M 3 I fay the curve furface 1 K L B is equal to the re6]:angle 
of I K and B L, or of H K, and 2 B L or B C ; and if there De 
fuppofed another circle, as NQJPO, cutting the fame ellipfe in 
the points P, Q.; draw P S, CLR parallel to the axis of the 
cylinder, till they meet the aforefaid circle IKL«/ in the points 
