208 Royal Astronomical Society. 



5. Errors of the Ephemeris in R.A. from differential transits at 

 the mural circle. 



6. Errors of the Ephemeris in N.P.D. from differential observa- 

 tions only. 



7. Computation of the index errors in N.P.D. of the equatoreal. 

 8 Errors of the Ephemeris in N.P.D. from the data of the last 



section. 



9. A tabular collection of all the previous results, with remarks. 



On a proposed Alteration of Bessel's Method for the Computation 

 of the Corrections by which the Apparent Places of Stars are derived 

 from the Mean Place. By the Astronomer Royal. 



After mentioning the great superiority in uniformity and sim- 

 plicity of Bessel's method over those previously in existence, the 

 Astronomer Royal remarks, that the strict attention to sign required 

 both in the partial additions and in collectin^j the sum is exceedingly 

 troublesome, and that more errors in observatory business arise from 

 oversight liS to sign than from any other cause. He has therefore 

 been led to consider the possibility of avoiding changes of sign, and 

 suggests the following method as probably an improvement in giving 

 the data of the corrections in the Ephemeris and Catalogue. 



On examining the maximum values of the quantities A, B, C, D 

 in the Nautical Almanac, and of a, b, c, d, a', b', c', d' in the British 

 Association Catalogue, it will be seen that A, B, and D can never 

 be equal to 25, that c' is always less than 25, and that up to a north 

 polar distance of 3° 45', c must also be less than 25. All the other 

 numbers are less than \'2. 



Let E=A+25 Let e=a+ 1-2 Let e'=a'+ 1-2 



F=B+25 f=b+ 1-2 f'=b'+ 1-2 



G=C+ 1-2 g=c-|-25 g'=c'+25 



H=D+25 /i=d+ 1-2 h'z=zd'+ 1-2 



All the introduced symbols are necessarily positive. 

 Arranging and multiplying 



Aa=Ee—l-2E— 25^+30 

 Bd=F/— 1-2F— 25/+30 

 &c. &c. 



And 



Aa'=Ee'— l-2E-25e'+30 

 &c. &c. 



Hence, collecting and arranging, it will be found that the sums of 

 the corrections in R.A. and in north polar distance will be respect- 

 ively, — 



InR.A. =120-()+Ee+Ff+Gg+Hh 



-(1-2E+1-2F+25G+1-2H) 

 —(25e+25f + \-2g+25/t) 

 In N.P.D.=120-0 + Ee'+F/'+Gg'-^HA' 



-(1-2E+1-2F+25G+1-2H) 

 —(25 e' +25/'+ ] ■2g'+25/i') 



where the numbers are seconds of time in the first group, and se- 

 conds of space in the latter. 



