06 «ERARDI REGNER! FOCKENS 



« and by Tar ihe grealest proper molions knowu belong to stars low in tlie Scale of 

 « magniludcs. " 



Methodi autem virtutes ita exponit: 



« It is liardly necessary to insist on the great advantagcs presented by llie method here 

 « proposcd , in ils complcte excmption from those instrumental errors depending on un- 

 « sleadincs , erroneous graduation and expansion, and from all tliat uncertainly on the 

 <( score of refraction , and any doubls still remaiuing as to the magnitudes of the con- 

 « stants of aberration , nutation etc. , wliich do rauch embarras aslronomers. A good 

 <( telescope and a good micrometer arc all the instrumenta required. Tliis advantage is 

 « really incaiculable. Instead of confiuing our attention to one or two principal stars, 

 « it puls an almost unlimited ränge of objects in our power , by enabüng us to employ 

 « in ihis research the largest telescopes, and llius easily obtain measures of Ihose stars, 

 « wliicli, from their faintness, must present iusuperable difficulties with instruments of 

 V ordinary apertures. " 



Quaerit cöndiliones , quibus maximo cum fructu melhodus possit inslitui , et ipsum in- 

 dicat valorem mutali anguli positionis hoc modo ; 



« Let / represent the longitude , and 4- A the N. latitude of the slar , a ils angle o/ 

 « siiua/irtn , or the angle included at the slar by great circles joining it and tlie north 

 <( poles of the equinoctial and ecliplic respectively , a- being considered positive for slars 

 « in the vveslern hemispbere (or that whose pole is the point V) and negative for 

 « Stars in the eastern, whose pole is tu. Let also Q represent the suns longitude at 

 « any time , and call a the maximum semiannual parallax or the angle ( expressed in 

 '< seconds) which the radius of the earth's orbit would subtend if perpeudicularly pre- 

 « seuied to an eye at the dislance of the slar. It is obvious, then, that a will represent 

 « the major semiaxis of the slar's parallaclic ellipse , and a sin. A the minor, so that its 

 « eccenlricily t= ^(«^ — «= . sin. a= ) = « cos. A, which if we call ae , we have 

 <i e= cos, A. The oiar will appear lo describe thisellipsin the direction "npsf. Ils motiou 

 <( in it will howeyer not be uniform , but equal areas will be described in equal times 

 « about ils cenire (or the slar's mean place): ^his is evident because the area described 

 <i by the slar in the parallaclic ellipse round ils centre is the Orthographie projeclion on 

 « the surface of the heavens of that described by the earth round the sun in ils orbit. 

 « This considcration gives us at once the cquation 



tan. ^ ■=. — sin. / . cotan. ( Q — / ) ( I ) 



« where ^ represenls ihe elongaliou of the slar in its ellipse from the eastern extremily 

 « of ils major axis reckoned in ihe direction npsf. 

 « Let X be the angle of position of Ihe sraall star , ^ being reckoned from a parallel 



« to 



V 



I 



