whole 24, higher than 'tis there, and is 15 Hours lower. Now the simple Action of the Sun is, as all other Impulses or Stroaks, more or less forceable, according to the Sinus of the Angle of Incidence, or to the Perpendicular let fall on the Plain, whence the vertical Ray (being that of the greatest Heat,) being put Radius, the force of the Sun on the Horizontal Surface of the Earth will be to that, as the Sinus of the Sun's Altitude at any other time. This being allow'd for true, it will then follow, that the time of the continuance of the Sun's shining being taken for a Basis, and the Sines of the Sun's Altitudes erected thereon as Perpendiculars, and a Curve drawn through the Extremities of those Perpendiculars, the Area comprehended shall be proportionate to the Collection of the Heat of all the Beams of the Sun in that space of time. Hence it will follow, that under the Pole the Collection of all the Heat of a tropical Day, is proportionate to a Rectangle of the Sine of 23½ gr. into 24 Hours, or the Circumference of a Circle; that is, the Sine of 23½ gr. being nearly 4 Tenths of Radius; as 3⁄10 into 12 Hours. Or the Polar Heat is equal to that of the Sun containing 12 Hours above the Horizon, at 53 gr. height, than which the Sun is not 5 Hours more elevated under the Æquinoctial.
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,