March 15, 1872.] 435 [ Kirkwood. 
Library, the Franklin Institute, the Penn Monthly, the Li- j 
brarian of Congress, the Chief of U.S. Engineers, Senator 
Charles Sumner, and Prof. F. V. Hayden. 
The death of Christian Olrik, of Denmark, a member of 
the Society, was announced by the Secretary. 
The committee to which was referred the paper of Prof. 
Stevenson, on West Virginia Coal Measures, reported in fa- 
vor of its publication in the Transactions, which on motion 
was so ordered. 
: A. communication entitled, On some remarkable relations 
between the mean motions of Jupiter, Saturn, Uranus, and 
Neptune, received by letter from Prof. Daniel Kirkwood, 
dated Bloomington, Monroe County, Ind., March 11, 1872, | 
was read by the Secretary. 
On soME REMARKABLE RELATIONS BETWEEN THE MnAn Morions oF 
JUPITER, SATURN, URANUS, AND NEPTUNE. 
By Pror. Danie Kirkwoop. 
i 
(Read before the American Philosophical Society, March 15th, 1872.) 
It was noticed by the writer several years since, that 85 periods of 
Jupiter are nearly equal to 12 of Uranus,* and that 149 periods of Uranus 
If, therefore, nV, mvi, nvii and 
are approximately equal to 76 of Neptune. 
PI ‘ I 
i nviii denote the respective mean motions of Jupiter, Saturn, Uranus, and | 
| Neptune, these relations are expressed as follows : i 
i te ry +s see ti 
J 12nv -—85vii — 76vii — 149 vill, nearly ; ah 
J : ne 2 , : : yy 
| or, 12nv —161nvii + 149nvili -—y, . .. . . (fh). 
i 
With Neweomb’s value of nviii and the values of nv and nvii adopted hi 
| 
in the American Ephemeris, we find y = 390/’.. The equation, i 
MS. Z2nvi — 153nvii + 121nvili — — 7 f , OQ), 
| was obtained by a process somewhat similar. Subtracting (2) from (1), i 
| and dividing by 4, we have / 
: 
| Snv — Snvi — anvil + Tnviii — 0, ‘ : i : (8).4 
i 
. : : L at oF © dees ¥ . i 
This equation, like that which exists between the mean motions of i 
Jupiter’s first three satellites, is doubtless exact. The mean motion of 
d Neptune is less accurately known than those of the old planets. If we 
assume, then, that the received values of nv, nvi, nvii, are correct, 
* Runkle’s Mathematical Monthly, January, 1860, 
+ Equation (3), without any account of its discovery, was given in Silliman’s Journal, 
March, 1872, ! 
t 
