( 1H3 ) 
i 
UPON THE FOUETH ORDEE PEETUEBATIONS IN THE 
MOTIONS OF SATELLITES IIL AND IV. OF JUPITEE. 
By E. T. A. Innes, F.E.A.S., F.R.S.S.Af. 
(Eead March 15, 191L) 
In addition to the well-known relations amongst the mean-motions of 
the three inner great satellites of Jupiter, there is the approximate 
relation — 
77^^-37^,3 = 0°•0448 
between the mean-motions of III. and IV., which gives rise to inequalities 
of the fourth order of the eccentricities. These inequalities are largely 
increased by the motions of the lines of apsides which are of the same 
order of magnitude as In^ - ^n.. The period of the largest coefficient is 
about twenty-seven years. 
In the Bulletin Astronomique, vol. ix., de Haerdtl called attention to 
these inequalities, and computed their effect so far as the longitude of III. 
is affected. M. E. de Haerdtl combines all the terms into one, viz. — 
3/3 = + 6"-49S(7/4 - 3/3 + 114°-8), 
[See postscript on notation at end of paper] 
in which the suffix 3 applies to Satellite III. and ^ to IV. This combina- 
tion of the various terms into one is, however, illegitimate, because of the 
rapid motions of the apsides. 
In his new tables of the great satellites Professor Sampson states that 
he has included every inequality which he found amounted to 1", but 
none of the above-mentioned inequalities is shown, so that it would appear 
from Professor Sampson's calculations that they are all under 1". I have 
therefore made a new calculation, of which the details are presented. 
The inequalities in question are given in seconds of arc by the 
following equations : — 
