MATHEMATICAL SECTION. 133 
ness of the objects measured. The price to be paid for this ad- 
vantage is a greatly increased complexity in the computation; for 
the elements of both orbits now enter into each equation of con- 
dition, and there are therefore twelve normal equations instead 
of six to solve. The comparative difficulty may be estimated by 
the number of auxiliary quantities that must be computed in the 
solution of 2 equations, namely : 
Zn (n+1) (n+), 
which amounts to 77 for n = 6, and to 442 for n = 12; a value 
nearly six times as great. But it is worth while to bear in mind 
that the twelve equations, by giving the elements and mean distance 
. of each satellite, give two values of the planet’s mass. 
Mr. Harkness called attention to the advantage of substituting 
an accidental error, be it even a large one, for an unknown constant 
error. 
Mr. Taytor criticised the designations usually given to the 
apsides of satellites orbits as being particular when they should be 
general. He suggested the terms peri-apsis and apo-apsis, or aphapsis. 
Remarks were also made by Messrs. KUMMELL and HI Lt. 
Before adjournment the Chairman replied to some questions as 
to the new object glass for the Imperial Observatory at Pulkowa; 
and gave a short explanation of the difficulty of calculating the 
true anomaly in elliptic orbits, 
4TH MEETING. May 9, 1883. 
The Chairman presided. 
Present: twelve members and one guest. 
The report of a committee appointed by the General Committee 
of the Society to consider matters pertaining to Sections was read. 
Mr. DooxitrLeE read a paper entitled 
INFINITE AND INFINITESIMAL QUANTITIES. 
[ Abstract. ] 
An infinitesimal may be defined as the result of infinite division ; 
