08 GEKARDr PiEGNETlIFOCKENS 



« 90 tUal : taU' ^ = — ( • — e' ) cotan ( t — y ) 



« bul: (1 — «") = sin. ;.^ 



« and by equation ( 1 ) : — tan. $ = sin. / . cotan. (Q — 

 « Hence subslilutiag , we gel : 



sin. A" . tan. (O — = «in- ^ tan. {tt — 7) ; (2) 



« This equation gives at once the value of Q , the sun's longitude , and therefore ( by 

 <f Consulting an epliemeris ) the time of year souglit , by an eiceedingly simple proccss 

 « adapled to logarithtnic computation. 



« Tlie actual advantage or disadvantage in point of Situation in the case of any parti- 

 « cular slai- , is expressed by the maguitude of the whole change in the angle of position 

 « produced by parallax , i. e. by the angle subtended by the ellipse at the smali star , or 

 (( (calling the distanse of the latler from its centre S) oo the original suppositioa of the 

 « whole effect being small , by the exprcssioQ 



P = y . sin. (<?'— 0). 



(. Now if WC Substitute for ?' and sin. ((P' — Cp) their values in terms of <J), or «■ — «,■ 

 « deduced from the eqnations already slated , by proper eliminalioas , we find : 



P = ^ . 1/(1— COS. A»cos.(!r — <r)») (3) 



o 



« whence the maximum effect of parallax on the angle of position of any double star ig 

 « readily compuled ; the espression is inconvenient for logarithmic computation, bat 

 « this inconvenience is obviated by the very obvious subslitutioa 



2a 

 cos. A cos. (r — s-) = COS. M P =z —- sin. M (4) 



« we also have : 



sin. M sin. M 



« from which we may deduce the value of 2a the maximum of parallax when the total 



« effect (?) on the angle of position is kuown. 



sin 30' 

 « If we take . . ; . P = 30', we have ... 2a = 5'. ■■ . ■ -„ (6) 



sin. In 



«which expresse» the amount of annual parallax in any proposed star which will be in- 

 « dicated by a periodical Variation of 30' in the angle of position, The smallness of 

 « this amount is a criterion (matliematically speaking) of the favourable or unfavou- 

 « rable nature of the individual star for reaearches of this kind. " 



Subjungit his seriem duplicium maxime huic investlgationi aptarum , cujus structuram 

 exemplo iudicat 35" Piscium. 



Sc 



