VOL. XVII.] PHILOSOPHICAL TRANSACTIONS. 57t 



sines of the sun's altitude under the equinoctial, erected on the respective hours 

 from sun-rise to the zenith ; and the area 25 H H 25 is in the same proportion 

 to the heat for the same 6 hours under the pole, on the tropical day ; and 



H H Q is proportional to the collected heat of 12 hours, or half a day, under 

 the pole, which space H H Q. is visibly greater than the other area H Z G H, by 

 as much as the area H GQ is greater than the area ZG ; which, that it is so, is 

 visible to sight, by a great excess ; and so much in proportion does the heat of 

 the 24 hours sun- shine under the pole exceed that of the 12 hours under the 

 equinoctial : whence, caeteris paribus, it is reasonable to conclude, that were 

 the sun perpetually under the tropic, the pole would be at least as warm as it 

 is now under the line itself. 



But whereas the nature of heat is to remain in the subject, after the cause 

 that heated it is removed, and particularly in the air ; under the equinoctial the 

 12 hours absence of the sun does very little abate the motion impressed by the 

 past action of his rays, in which heat consists, before he arise again : but under 

 the pole, the long absence of the sun for 6 months, while ihe extremity of cold 

 obtains, has so chilled the air, that it is as it were frozen, and cannot, before 

 the sun has got far towards it, be any way sensible of his presence, his beams 

 being obstructed by thick clouds, and perpetual fogs and mists; and by that 

 atmosphere of cold, as Mr. Boyle terms it, proceeding from the everlasting 

 ice, which in immense quantities chills the neighbouring air, and which the too 

 sudden retreat of the sun leaves unthawed, to increase again during the 

 long winter that follows this short interval of summer. But the different de- 

 grees of heat and cold, in different places, depend in a great measure on the 

 accidents of the neighbourhood of high mountains, whose height exceedingly 

 chills the air brought by the winds over them ; and of the nature of the soil, 

 which variously retains the heat, particularly the sandy, which in Africa, Arabia, 

 and generally where such sandy desarts are found, make the heat of the sum- 

 mer incredible to those that have not felt it. 



In prosecution of this first thought, I have solved the problem generally, 

 viz. to give the proportional degree of heat, or the sum of all the sines of the 

 sun's altitude while he is above the horizon, in any oblique sphere, by reducing 

 it to the finding the curve surface of a cylindric hoof, or of a given part of it. 

 Now this problem is not of that difficulty, as appears at first sight : for, in 

 fig. 4, let the cylinder ABCD be cut obliquely with the ellipse B K D I, and 

 through its centre H describe the circle IKLM; I say, the curve surface 



1 K L B is equal to the rectangle of I K and B L, or of H K and 2 B L or BC: 

 and if there be suppo?e(l another circle, as NQPO, cutting the said ellipse in 

 the points P, Q ; draw PS, Q R, parallel to the axis of the cylinder, till they 



VOL. in. 4 E 



