10 On Kirkwood’s Analogy. 
Thus out of the ¢en primary bodies (counting the Asteroids as 
one) there are no less than seven, in which the Analogy is either 
indeterminate or fails: and we have only three left, Venus, the 
rth, and Saturn, from which to obtain ¢wo coincidences that 
shall establish a law universal in its claims, 
The following values are those given in the Annuaire du 
Bureau des Longitudes, for 1851, being the latest authoritative 
table of whose publication I am aware. 
Planet. oe gah tear Mean distance. "ip, é Senta. %\ Rotation. 
Mercury, 0:3870985 | systsis 
Venus, 224°70080 0°7233317 ZUTBET 23h Q]m 
Earth, 365'25637 1-0000000 Bsaoss 23h 56m 
Mars, 1:523691 ZesesaT 
Ju piter, 5°202767 rosu 
Saturn, 10759°2198 9-588850 apo 10h 30m 
ranus, 19-1824 Sid00 
From these I deduce the following table— 
| Planet. n | D k | 
Venus, 230-9558 3666685 1082025: 
Earth, 366-2738 "5265920 918732: 
Saturn, 24592:50 8513061 980276- 
The values of & do not, I think, agree with sufficient nearness 
to establish the Analogy: in fact, the difference betwen the values 
for the Earth and Venus would cause an error of two hours in 
the rotation of the latter. 
Lastly, suppose that a change in density and volume of one of 
the planets were to take place; then, since the mass and mean 
distance are unaltered, D remains the same; and since the side- 
iod is not affected, it would follow, if the analogy were 
true, that the time of rotation would remain unchanged, which 
is contrary to the mechanical principle of the conservation of 
areas 
From these reasons I feel compelled to reject Kirkwood’s 
Analogy as “the expression of a law of nature,” and must agree 
with Prof. Loomis in considering it not established as a “ phys- 
ical fact.” 
University of Toronto, U. C., April 10, 1852. 
