72 



MATHEMATICAL and 



peuds upon a feries of propofitions, with long and difficult:^ 

 demonflratious: fo that the rules of calculation are not 



very obvious, without a coniklerable knowledge of geo- 

 metry, in general, and a particular acquaintance with his 

 very ufeful and ingenious treatife. I was defirous of fee- 

 ing what agreement there was between the refult of his 

 method of calculation, and the obfervations made on the 

 tranfit of Venus; and therefore amufed myfelf in a leifure 

 hour with the comparifon. As it may be agreeable tofome, 

 who have not time to read over the book, and to others, 

 whofe acquaintance with the mathematics will not admit 

 of it, to have the pradical rules of computation deduced 

 from his propofitions; 1 fhall annex them to the foregoing 



calculations, together with the determination of the Sun's 

 parallax and diftance derived from them. 



A Cahidation of the horizontal ParallaH and ihjlanct of the Sim, according to Mr. Stuart* s m-dhod fram 



the princijjhs of gra'v'italiQn, ■« 



Let i'^^the periodical time of the earth round the Sun=365,. 3156417824 

 /^the periodical time of the Moon round the carth== 27. 32162036 

 fisher revolution from apogee to apogee in time, 27. 554J35 



iw=:=:hcrmeandift. from theearth, infemidi. oftheearth^^ 60. ia^ 

 /~=the tangent of the Sun's horizontal Parallax, at his mean diftance. 

 £'=:the diltiincc of the Sun from the earth. 



Then according to Mr. Stuart's method, 



P a 



X 



4—/ 1 



a-V 1—9^2^2 



J « 1-3/1 



^m'^t^ y/ l-i)m'^f^ 



Nov/ if 



P2 



5 ^l-3/l 



\c\ then S 



^mXi^i.Sc 



a-i/i-.jcXi-i-aff 



nearly 



And 5 



3otX34-<: 



a-/i-.j6-X3+i.5£ 



Nearly. S is greater than the iirll, and Icfs than the leafl: 

 in thefc theorems. 



a 



27,3216^036^ 



27,554535! 



a 



But the parallax and diftance of the Sun, may he found nearly, in a fhorter method, by the 

 following rulrs, derived from the forcgoinjr; hy faying, 

 I, As the cube root of theftjuare of the Moon's periodic revolution round"? 



the Earth, viz. S 



Is to the cube root of the ftjuare of her revolution from apogee to 



apogee, viz. 



So is I to a fourth number, which call A=i.oo56748l64. 



a. As 5 A — 3 : A I : ; I : a fourth number, which call B.:=:.ooa797833=the mean dillurb- 

 ing force of the Sun; the 3)'s forco=i. 



3. Asthe ret^langle of B and tlie f(^uarc of the periodic time of the Earth? _ % 

 round the Sun, viz. 5 BX 3 65,2^6^4 

 Is to the fc[uaro of the periodic time of the moon round the Earth,? ^ 



viz. 



So is I, to a fourth number, which call C^:=I, 999^40899. 



4. As C — il : l^ : : C : to a fourth number; to which add 1, and from thefquare root of 

 that fum fubtra6t i, and multiply the remainder by the half of C — I, or 0,49997,04495, and 

 call that produ6l 0^1,9999715505. 5. Subtrad 



5 ^7,3ai 



6ao3 





