54 ABERRATION of the STARS, &c. 



will be the apparent diftance of the ftar from its true place. 

 From 1 1 draw up perpendicular to the meridian of the ftar, 

 and that diftance will be the aberration in right afcenfion, which 

 is always at right angles to the meridian, and the diftance E/i, 

 on the meridian will be the effeft in declination. — The firft mea- 

 fured on the fcale by which the projeftion was made, will give 

 1 8 ".62, and the latter about y'.ia : But the firft niuft be re- 

 duced to the equator, which may be done various ways, but 

 the moft expeditious is by multiplying it into the natural lecant 

 of the ftar's declination, which will give 24 .34, the elFefi: of 

 aberration in right afcenfion anfwering to 2* and 8" of the Sun's 

 place ; but with contrary figns of application*. If the pro- 

 jedion fliould be large, this method will aufwer for common 

 purpofes, but when great accuracy is required, the quantities 

 muft be determined by calculation. For this purpofe, draw the 

 diameter RS, at right angles to the meridian, and cutting the 

 ellipfe in the point m. Then in the right angled fpherical 

 triangle ;;/E/^t, right angled at E, it v/ill be neceffary to find 

 the arcs mF, Fw, and the angles muY., tniiE. — The angle 

 ?««E muft be firft obtained by folving the right angled fpherical 

 triangle EF//, right angled at F. — the arc EF being 22° 28' the 

 latitude of the ftar, and the angle FE?/ 18'^ 11'. From thefe 

 data, the angle F;^E will be found 73'' 21' — the arcFw y° g' — 

 the angle F/iiF. 28° 31', and the arc Ym 49® 21 . — To find the 



aberration in right afcenfion anfwering to 2' and 8', 3^ and 



9% 4' and 10' &c. in the projeftion, add to the log. fine of 



the angle 'Eu¥rzyy 21' the log. of 20, and from that fum 

 deduft I o for a conftant log. to the conftant log. add feparately, 

 the log. fines of the arcs U2, ?^3, 1/4., &c. from each of thefe fums, 

 deduft 10, and the numbers anfwering to the log. remainders, 

 will be the values of 2 b, 3/, 10^, &c. Each of thofe values 

 being multiplied by the natural fecant of the ftar's declination, 

 will give the effect in right afcenfion, as in the following ex- 

 amples. 



* The algebraic figns of -|- plus, and — minus. 



f An ellipfe may be confidered a circle in the onhogrnphical projeflion of 

 the fpliere, the femi-conjugate being the co-fine of the circle's elevation above 

 the piiraJuve^ 



Angle 



