282 On some neiv Tables 



from the commencement of the year, expressed in the decimal 

 part of the year. 



In order to render these expressions more convenient for 

 computation, let us pursue M. Bessel's plan, and make 



^«-^= 0,3334 



20,0436 ' 



^'^^^^ - 0,0265 



20,0436 



whence we shall have 



46-0175 X0-3334. = 15-3412 = 15-3958 --0546 

 46-0175x0-0265= 1-2212= 1-2255 — -0043 



and by proper substitution the preceding expressions may be 



reduced to the following ones: 



Right Ascension. 



4- (/^--3334 sin ft --0265 sin 2 O) x 

 (46,0175 + 20,0436 tan D. sin M) 



— ( 8,9771 cos S3 +-5799 cos 2©) tan D. cos M 



— 18,5837 cos ©. cos M. sec D 



— 20,2550 sin ©. sin M. sec D 

 -•0546 sin ft- -0043 sin 20. 



Declination. 



+( if- -3334 sin ft- -0265 sin 2©) 20,0436 cos M 

 + ( 8,9771 cos ft + -5799 cos 2©) sin M 



— 18,5837 cos © (tan «3. cos D— sin M. sin D) 



— 20,2550 sin ©. cos M. sin D. 



It is evident that the two quantities, in the last line of the ex- 

 pression for the right ascension, are too minute to affect the 

 residt in any sensible manner, and may therefore be safely 

 omitted. Whence, if we make 



A = + it- -3334 sin ft — -0265 sin 2© 



B = -8,9771 cos ft--5799 cos 2© 



C =-18-5837 cos © 



D = -20-2550 sin © 



a = + 46-0175 + 20-0436 tan D. sin M 



6 = + tan D. cos M. 



c = + cos M.. sec D 



d = + sin JR. sec D 



fl' = + 20-0436 cos M. 



b' =r — sin jR 



c = + tan w. cos D— sin M.. sin D 



rf' = + cos ill. sin D 

 we shall have the total correction for 



Rt, As. = Aa +B6 +Cc +T>d 



Dec. = Aft' + B/y + Cc' + D./'. 



It 



