[ 283 ] 
XVI. Researches in Physical Astronomy. By John William Lubbock, Esq. 
V. P. and Treas. R.S. 
Read June 9, 1831. 
I PROPOSE in this paper to extend the equations I have already given for 
determining the planetary inequalities, as far as the terms depending on the 
squares and products of the eccentricities, to the terms depending on the 
cubes of the eccentricities and quantities of that order, which is done very 
easily by a Table similar to Table II. in my Lunar Theory ; and particularly 
to the determination of the great inequality of Jupiter, or at least such part 
of it as depends on the first power of the disturbing force. That part which 
depends on the square of the disturbing force may I think be most easily 
calculated by the methods given in my Lunar Theory ; but not without great 
care and attention can accurate numerical results be expected. I have how- 
ever given the analytical form of the coefficients of the arguments in the 
development of R , upon which that inequality principally depends. 
It is I think particularly convenient to designate the arguments of the 
planetary disturbances by indices. The system of indices adopted in this paper 
is given as appearing better adapted for the purpose than that used in my 
former paper on the Planetary Theory ; but it is not advisable to make use 
of the same indices in this as in the Lunar Theory. 
I have also given analytical expressions for the development of R to the 
terms multiplied by the squares and products of the eccentricities inclusive, 
and for the terms in r (^7) multiplied by the first power of the eccentricities, 
which are I believe the simplest that can be proposed. 
The following are the arguments which occur in the Planetary Theory. 
