But that this Matter may the better be understood, I have exemplified it by a Scheme, (_Tab. 4. Fig. 2_) wherein the _Area ZGHH_, is equal to the _Area_ of all the _Sines_ of the Sun's Altitude under the Æquinoctial, erected on the respective Hours from Sun-rise to the Zenith; and the _Area ♋HH♋_ is in the same proportion to the Heat of the same 6 Hours under the Pole on the Topical Day; and _⨀HHQ_, is proportional to the collected Heat of 12 Hours, or half a Day under the Pole, which space _⨀HHQ_, is visibly greater than the other _Area HZGH_, by as much as the _Area HGQ_ 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 Æquinoctial: Whence, _Cæteris paribus_, it is reasonable to conclude, that were the Sun perpetually under the Tropick, the Pole would be at least as warm, as it is now under the Line it self. But whereas the Nature of Heat is to remain in the Subject, after the Cause that heated is removed, and particularly in the Air; under the Æquinoctial, the 12 Hours absence of the Sun does very little still the Motion impressed by the part Action of his Rays, wherein Heat consists, before he arise again: But under the Pole the long absence of the Sun for 6 Months, wherein the extremity of Cold does obtain, has so chill'd 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 the late Honourable Mr. _Boyle_ was pleased to term it, proceeding from the everlasting Ice, which in immense Quantities does chill the Neighbouring Air, and which the too soon retreat of the Sun leaves unthawed, to encrease again, during the long Winter that follows this short interval of Summer. But the differing Degrees of Heat and Cold, in differing Places, depend in great measure upon 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, do make the Heat of the Summer incredible to those that have not felt it. In the 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 of the Curve Surface of a Cylindrick Hoof, or of a given part thereof.