490 Mr. H. Holt on a Method of Calculating 



brightness of the sun was considerably subdued by proximity to 

 the horizon. I suspect the ray I am in search of is but feebly 

 transmitted through glasses so coloured. 



Having communicated the substance of the above letter to my 

 friend Professor Stevelly, I received a reply (dated Belfast, No- 

 vember 29, 1866), from which I extract the following: — "I am 

 myself convinced it is the vera causa, and I have for more than 

 thirty years taught it as my own conviction, both in my optical 

 and astronomical lectures. What led me to it was exactly your 

 own mode of observing; viz., I made with a needle a fine hole in 

 a piece of sheet-tin lead, laid on a smooth iron, small enough to 

 give me distinct vision of very small print at 1^ inch distance ; 

 this I found brought the setting sun on a very frosty evening to 

 its ordinary apparent size. 



" I am also convinced that your opinion as to the cause of the 

 twinkling of the fixed stars is the true one. You mentioned it 

 to me in the year 1828 when we were working together, and I 

 have ever since given it to my class as yours. 33 



LXVIII. On a Method of Calculating the Coefficients of the Lunar 

 Inequalities. By Henry Holt*. 



THE method of undetermined coefficients, the application of 

 which to the calculation of the lunar inequalities was first 

 suggested by D'Alembert (see his Theorie de la Lune, p. 107), has 

 been adopted by most writers on the subjects both of the lunar and 

 planetary theories. It is certainly (as D'Alcmbert himself states) 

 " sans comparaison la plus courte et la plus facile de toutes, puis- 

 qu'elle demande ni integration ni aucune adresse de calcul." It 

 is obvious, however, that, whether the method of undetermined 

 coefficients be employed or not, much of the facility of the com- 

 putation must depend on the choice of the coordinates and on 

 the selection of the differential equations on which the calcula- 

 tion is to be based. Two different sets of coordinates and equa- 

 tions have been used for this purpose. In one, the coordinates 

 employed are the true values of the moou's longitude, the reci- 

 procal of her curtate radius, and the tangent of her latitude ; 

 and the differential equations are functions of these coordinates, 

 the forces P, T, and S, and the time t. In the other, the coordi- 

 nates employed are the mean values of the longitude, radius vec- 

 tor, and latitude ; and the differential equations are functions of 

 these mean values, the time t, and the disturbance-function R. 

 The latter is the method usually adopted in the planetary theory ; 

 but it has been applied also to the computation of the lunar in- 



* Communicated by the Author. 



