39] ON DR MORRISON'S PAPER (ON KEPLER'S PROBLEM). 299 



By comparing Schubert's result with that of Dr Morrison, we see that 

 there are the following errata in the latter : viz. the coefficient of e w sin 8M 

 in the equation of the centre should be 



4745483 . 1182827 



~ mstead of -*' 



and the coefficient of e l ~ sin 1 M should be 



76972457 . 769805651 



rf " 



*. . 7T ' 



In Schubert's expression for in p. 231, which is also carried as far as 



e, there are the following errata, which are evidently merely typographical : 

 viz. in the coefficient of cos 3g, instead of 



3M1 3". 11 



- 



and in the coefficient of cos 1 2g, instead of 



e l - should be -=r e l . 



5 2 .7.11 5 2 .7.H 



Oriani's formula for the radius vector has been examined and found 

 correct. 



A very good investigation of the general term of the expansion of the 



true anomaly in terms of the mean is likewise given in a paper by 



Mr Greatheed, in the first volume of the Cambridge Mathematical Journal, 



p. 208 (p. 228 in the second edition). 



The approximate expression for the eccentric anomaly in terms of the 

 mean given by Dr Morrison in the latter part of his paper coincides with 

 the first two terms of the series found in Keill's Astronomical Lectures, 

 p. 291 (5th edition, .1760), and the method of correcting an approximately 

 known value which Dr Morrison quotes from Encke is identical with Newton's 

 method for the same purpose, which is also explained in Keill's Lectures, 

 p. 296 et seq. 



On this subject reference may also be made to my paper in the Monthly 

 Notices for December 1882, p. 43 (see p. 289 above). 



382 



