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9) Page 7. continued. [[Right margin]] Atmosphere. [[underlined]] V.p. [[/underlined]] 54. & 56. [[/margin]] Corollary 1. (from the 1. [[supersript]] st [[/superscript]] Solution) [[Left margin]] Application to Solar Elipses. [[/margin]] [[Right margin]] Why least at the Equator & the great dews there. [[/margin]] Hence if D, represent a given place on the surface of the earth, considered as a sphere, and the right line AH. be supposed to be the axis of the moon's shadow (in a solar eclipse) falling the place D in a given direction, the solution of this problem, affords a method of determining the position of the place F, on the surface of a Spheroid (whose section is the ellipsis B G F C,) where the eclipse will be central at the same instant of time: and by the help of this problem, I constructed the map of the ensuing eclipse, (on Apr.1. 1764) which I lately published. [[Right margin]] Exhalations have a determinate height, but [[underline]] pure [[/underline]] air may reach to the fixed Stars. Refraction greatest from Hills. [[/margin]] [[Left margin]] And to the Eclipses of Jupiter's satellites. See p. 134. [[/margin]] [[Right margin]] Principles of H's Philosophy. [[/margin]] Corollary 2. (from D. [[supersript]] o [[/superscript]]) If the body of any primary planet, should deviated so far from a sphere, as to affect the form of his shadow, the curve of the section of the shadow (made by a plane perpendicular to its axis) at a small distance from the primary, will not be sensibly different from an ellipsis; and, by the means of this problem, we may determine the duration of an eclipse of a satellite, passing through such a section of the shadow. _____ That excellent astronomer, Dr. [[underlined]] Bevis [[/underlined]], was the first person who suspected that some irregularities, observed in the eclipses of [[underlined]] Jupiter's [[/underlined]] satellities, resulted from this cause; this he mentioned to me, in a conversation upon that subject, about three years ago; and sometime after, I presented to him a paper, containing a general investigation of the nature of the curve, which arises from the section of such a shadow. This is the paper mentioned by [[underlined]] M. de la Lande; vide Connoissance des mouvemens célestes, pour l'annee [[/underlined]] 1765, p. 177. [[right margin]] 1. [[superscript]] st [[/superscript]] All actions in Nature are Mechanical see the margin p.97. 2. [[superscript]] d [[/superscript]] The Universe is a Plenum. 3. [[superscript]] rd [[/superscript]] This [[underlined]] Plenum [[/underlined]] is the three etherial fluids, Fire, what. Light, what. and Air, what. 4. [[superscript]] th. [[/superscript]] Fire, light & air can't be supported or increased, but from one another. 5th. This fluid is the [[underlined]] cause [[/underlined]] of all motion in Nature. [[/margin]] [[Left margin]] Ratio of the θ's Diameters & that it ought to be a Spheroid from Solar Eclipses. In 2 [[superscript]] d. [[/superscript]] Edit. of Chamber's Dict. under Earth, the last and best ratio is as 1 to 0,9953467 or 230 to 228,92974, which is very nearly as 216 to 215, being as 1 to 0,9953708. In Mayer's Tables. p. LXXV. it is taken as 1 to 0,99[[strikethrough]] 10515 [[/strikethrough]] ^[[insertion]] 5666 [[/insertion]], or as 230 : 229,00[[strikethrough]] 0845 [[/strikethrough]] ^[[insertion]] 32 [[/insertion]] or as 216 : 215,063859 [[strikethrough]] [[?]] [[/strikethrough]] Dimensions of the θ deep. [[?]] 136. [[/margin]] The ratio of the earth's diameters has been found to be as 178 to 179; but later observations make the figure of the earth to approach nearer to a sphere, and that the ratio of its diameters is nearly as 215 to 216 which best corresponded to the observations of the solar eclipse on April 1. [[superscript]] st [[/superscript]] 1764. from which observations as well as the calculations, it appears that the deviation of the figure of the earth from that of a sphere, will produce a very considerable effect, with respect to the passage of the shadow, no less (in this example) than thirty-two geographical miles, by which means, if the calculation had be made in the usual manner, the limit, instead of passing over [[underlined]] Rochester [[/underlined]], would have scarce reached [[underlined]] Canterbury [[/underlined]], and the eclipse would not have been annual in any part of [[underlined]] Essex [[/underlined]], [[underlined]] Suffolk [[/underlined]], or [[underlined]] Norfolk [[/underlined]]; it is therefore absolutely necessary to have regard to the spheroidal figure of the earth in the calculation of solar eclipses, and, as I (G. Witchell) do not know that any author has given sufficient precepts for that purpose,I intend to treat particularly upon it, in a treatise, which I am now publishing by subscription. [[Left margin]] Dimensions of the θ [[See?]] p.136. [[/margin]] By many observations given under the word EARTH in the complete Dict. of Arts & Sciences: the polar diameter is [[strikethrough]] give [[/strikethrough]] deduced from a long process = 7863,2 Miles, & the Equatorial = 1/92 x 7863,2 + 7863,2 = 86,8 + 7863,2 = 7950 Miles. And 7863,2 : 215 :: 7950 : 217,386; :. ^ [[insertion]] greater [[/insertion]] in Ratio than [[underlined]] Witchels [[/underlined]] 215 : 216. Also 7863,2 : 178 :: 7950 : 179,965 fevè: :. greater than 178:179, the Ratio he rejects: being nearly as 89 to 90.
Transcription Notes:
Have transcribed all right and left hand margins are transcribed as they appear along main text.
