Miscellanea Curiosa, Vol. 1 / Containing a collection of some of the principal phaenomena in nature, accounted for by the greatest philosophers of this age

by Unknown

I had one of these Barometers with me in my late Southern Voyage, and it never failed to prognostick and give early notice of all the bad Weather we had, so that I depended thereon, and made provision accordingly; and from my own Experience I conclude that a more useful Contrivance hath not for this long time been offer for the benefit of Navigation.

These Instruments are made according to the Direction of Dr. Hook, by Mr. Henry Hunt, Operator to the Royal Society, who will furnish any Gentlemen with them, and give them Directions how to use them.

A Discourse concerning the Proportional Heat of the Sun in all Latitudes, with the Method of collecting the same; as it was read before the Royal Society, in one of their late Meetings. By E. Halley.

THere having lately arisen some Discourse about that part of the Heat of Weather, simply produced by the Action of the Sun; and I having affirmed, that if that were considered, as the only Cause of the Heat of the Weather, I saw no Reason, but that under the Pole the solstitical Day ought to be as hot as it is under the Æquinoctial, when the Sun comes vertical, or over the Zenith: For this Reason, that for all the 24 Hours of that Day under the Pole, the Sun's Beams are inclined to the Horizon, with an Angle of 23½ Degrees; and under the Æquinoctial, though he come vertical, yet he shines no more than 12 Hours, and is again 12 Hours absent; and that for 3 Hours 8 Minutes of that 12 Hours, he is not so much elevated as under the Pole; so that he is not 9 of the 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, 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.

Now this Problem is not of that difficulty as appears at first sight, for in Tab. 4. Fig. 3. let the Cylinder ABCD be cut obliquely with the Ellipse BKDI, and by the Center thereof H, describe the Circle IKLM; I say, the Curve Surface IKLB is equal to the Rectangle of IK and BL, or of HK and 2 BL or BC: And if there be supposed another Circle, as NQPO, cutting the said Ellipse in the Points P, Q; draw PS, QR, parallel to the Cylinders Axe, till they meet with the aforesaid Circle IKLM in the Points R, S, and draw the Lines RTS, QVP bisected in T and V. I say again, that the Curve Surface RMSQDP is equal to the Rectangle of BL or MD and RS, or of 2 BL or AD and ST or VP; and the Curve Surface QNPD is equal to RS × MD----the Arch RMS × SP, or the Arch MS × 2 SP: Or it is equal to the Surface RMSQDP, substracting the Surface RMSQNP. So likewise the Curve Surface QBPO is equal to the Sum of the Surface RMSQDP, or RS × MD, and of the Surface RLSQOP, or the Arch LS × 2 SP.

This is the most easily demonstrated from the Consideration, That the Cylindrick Surface IKLB is to the inscrib'd Spherical Surface IKLE, either in the whole, or in its Analogous Parts, as the tangent BL is to the Arch EL, and from the Demonstrations of Archimedes de Sphæra & Cylindro, Lib. I. Prop. XXX, and XXXVII, XXXIIX. which I shall not repeat here, but leave the Reader the pleasure of examining it himself; nor will it be amiss to consult Dr. Barrow's Learned Lectures on that Book, Publish'd at London, Anno 1684, viz. Probl. IX. and the Corollaries thereof.