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39) [[Right margin]] My objection to the 1.[[superscript]]st[[/superscript]] account. A consequence from both, contrary to all Nature. Gamaches shows that the motion of the Earth & Moon will always be Retrograde upon the Newtonian Principles. S.[[superscript]]r[[/superscript]] I. Newton's Projection & Attraction will not account for the motion of Planets & Comets. [[/margin]] If the velocity with which a body would describe a Circle at the point of Projection, be an unit, or 1, then the least velocity that would throw a body or a Planet quite off through the ambient space, describing a curve which does not return upon itself, nor inclose Space, but runs out still to a greater distance ^ [[insertion]] will be [[/insertion]] [[strikethrough]] as [[/strikethrough]] as 1,4142 &c. so that with the velocity 1 a body describes a circle, but with more than 1, and less than 1,4142 (or one & nearly an half) it describes an ellipse, and with more than [[strikethrough]] 1,4142 [[/strikethrough]] ^ [[insertion]] 1,4142 [[/insertion]] it flies quite off. [[underline]] Baxter's [[/underline]] C.P. Vol. II. p.152. Ed. 12.[[superscript]]mo[[\superscript]] (*) i.e. [[underline]] the attraction of the ^ [[insertion]] New [[/insertion]] Moon upon the Sun is as (,36)3833076, at Full as (,36)3787915; the attract of the Moon upon the earth is as (,22)4340279, and that of the earth upon the Sun is as (,16)152416. [[/underline]] I have since very carefully calculated the Attraction of the Sun, Earth, & Moon upon each other, and find them stand thus; [[Table with three columns, column two headed Logarithms, column three headed Natural Numbers. Each line of column is separated by dash above and below logarithm number]] [[heading]] Logarithms Natural Numbers [[/heading]] √S upon E -- 89,5400114 = (,10)346746 S upon New M -- 89,5425888 = (,10)34881 S upon Full M -- 89,5374416 = (,10)34470024 √E upon S -- 84,1830300 = (,15)152416 √E upon M -- 89,2395776 = (,10)1736112 Full M upon S -- 64,5784002 = (,35)3787915 New M upon S -- 64,5835474 = (,35)3833076 √M upon E ---- 78,6375176 = (,21)4340279 *87, [[/table]] [[curly bracket encapsulating table data, text written sideways]] Supposing each of the same density. but some authors say they all differ very much in density. V. [[underlined]] Prin[[superscript]]c[[\superscript]]ipia [[/underlined]]. [[/curly bracket]] [[start table]] ^[[The point of equal Attraction between the]] Miles from the S Miles from the E [[**transcriber's note: there is a vertical line between the (neither column has text)]] S & E= S & New M= S & Full M= S & N.M+E= S & F.M+E= E & M= [[end table]] [[start table]] ^[[The Distance of the Center of Gravity between]] Miles from S Miles from E [[**transcriber's note: there is a vertical line between the (neither column has text)]] S & E = S & New M= S & Full M= S & N.M with E= S & F.M with E= E & M---= [[margin]] * This is evidently a mistake; for while E goes forward in the order of the signs [[symbols for Aries, Taurus, and Gemini]], &c. from right to left, the earth at [[bold]] a [[\bold]] goes in the same direction from [[bold]] a [[\bold]] to E, and the moon at b, in a contrary direction, from b to M, while the point b from [[bold]] a [[\bold]], or line [[bold]]ab [[\bold]], will appear to pass through all the signs of the ecliptic in a direct order [[/margin]]