-^ . . .C . . 



E 



r 



I' 



146 



MATHEMATICAL and 



fo found, take the angle correfponding out of Dr. Halieyh 

 table abovementioned, which angle being added to or fub- 

 trafted from the place of the perihelion, as the time pro- 

 pofed is after or before Auguft 8th, 19/7. 36', gives the 

 heliocentric place of the comet in its orbit; and, as that 

 is fo nearly parallel to the plane of the ecliptic, 1 have, for 

 the more eafy calculation, negleded the reduction entirely, 

 which could fcarcely exceed 50" at any time. Likewife, 

 to the mean motion, take out of the table aforefaid the 

 Logarithmus pro dijlantia (ifole\ from which fubtratSt the 

 compliment of the log. of the perihelion diftancc, viz. 

 2023347 always, and you have the log, of the comet's 

 diftance from the Sun. The inclination and geocentric 

 place may then be found by the fame method we ufe for 

 the planets. 



Example. Let the vifiblc place of the Comet for June a7th, <)h, be required. 

 iTom Auguil 8. 80CJ65 

 Subtract June %';, $TS 

 Remain days 4t. 43465 log. 1.6277207 

 Log. daily motion add - - • 0.3636300 



r 



Mean motion before perihel, 77.86^54. 1. 8913507 

 Angle correfponding 80^; 5'. la''. Log. pro diftantla 



Sub. from perihelion K 26''. 19'. %Z", 



lains the Co-^ 



tet's hcliocen- S- J^, 6°.,I4'. 



ic longitude j 



Remains the Co- 

 met' 

 trie 

 Sub. from longitude Q^j". 6^. j(/. 



16" 



7 



// 



Compliment log, perihelion? 

 dift, fubtraa 5 



Comet a 107082,2 

 © a 101678,* 



Comet k f^ 



5404 



Dificrence 5=*i'. 51" Tangent 6.7308977 



Add the Log. of© diftance a 5,0072280 



5.2320440 



.2023347 



^g- 5-f5^97o<;3 

 Log. 5.00722^0 



Log- $'lZ%n5o 



Subtra(5fc the Log. of the Comet a © 



Sum 



ir.7381257 

 3-7327153 



Remains Tangent 

 Which fub. from 



^ 



Remains 

 plate of the node 



Argument of lat. 

 -^Sinc inclin. of orbit 



34'. 48/' 8.0054104 



VS. 6°. 14'. 16" The heliocentric longitude, 



VS' 5°- 39'. 28'' The Comet's vifible place. 

 . T4°- 21'. 45'' Defcending. 



if 





38°. /. 29" 

 I". 49'. 5'' 



.Rad.— Sine heliocent. lat. i*^. 7'. ao" 



Tangent ditto 

 4-Log. Comet a 



Log. Comet a ©=3 

 j^ Secant 34'. 48^' — Rad 



•7327153? 



ad. =5 15 5 



Sine 9^7905493 

 8.5014111 



8.2919604 



8 'Xi)%QAH 

 5.0297093 



Sum 13.3217527 

 Sub. 3- 73*7^68 



Remains Tangent vifiblc lat. 21°. I3^ 



9.5889859 



Obfcrrcd 



