TRANSACTIONS OF THE SECTIONS, 27 
the explanation of many eruptive or upheaving phenomena, which the earth’s crust, 
and especially that of the moon, present, namely, that on the approach toa the 
point of solidification molten mineral substances then beneath the solid crust of the 
earth must, in accordance with the above-stated law, expand, and tend to elevate or 
burst up the solid crust,—and also express upwards, through the so cracked surface, 
streams more or less fluid of those mineral substances which we know must have 
been originally in a molten condition. Mr. Nasmyth stated, that the aspect of the 
lunar surface, as revealed to us by powerful telescopes, appeared to him to yield 
most striking confirmation of the above remark. He ccncluded by expressing a hope, 
that the facts which he had brought forward might receive the careful attention of 
scientific men, which their important bearing on the phenomena in question 
appeared to him to entitle them to. 
On certain Planetary Perturbations. By the Rev. W. G. PENNY. 
It appears that there are in the motions of several of the planets inequalities 
arising from the product of the disturbing forces of two planets, which inequalities 
appear to have been but little noticed hitherto, but which seem to be much larger 
than might have been expected, owing to the length of time during which they 
are accumulating. The most remarkable is one which exists in the motions of 
Mars and the earth. Its period is about 1800 years, or about twice that of the 
long inequality of Jupiter and Saturn. In the case of the earth it appears to amount 
to about 7”, and is owing to the product of the disturbing forces of Jupiter and 
Mars ; and in the case of Mars it seems to amount to about 451", and is owing to 
the product of the disturbing forces of Jupiter and the Earth. It arises from the 
fact, that four times the mean motion of the earth is very nearly equal to eight times 
that of Mars minus three times that of Jupiter. Its value for the earth is repre- 
sented by the following equation :— 
602=7'°293 sin (8n3t —4 nyt — 3ngt+ 8e5—4€,—3e4+75° 14’); 
and for Mars by the equation 
00;= —45'-684 sin (Sngt— 4ngt — 3ngt-+ Bes — 4¢)—3e,+73° 34); 
where mg, ™3, m are the mean motions of the earth, Mars, and Jupiter. This 
inequality is remarkable as being, if the work is correct, larger, and in the case of 
Mars very considerably so, than any which arise from the simple perturbation of a 
single planet,—the largest hitherto known in the case of the earth amounting to only 
7°15, and in the case of Mars to 25’""5. Also, there will be a corresponding inequality 
in the motion of the moon, which I have not yet examined, but which may, perhaps, 
be sensible ; for, according to the investigations of M. Hansen, the inequality in the 
motion of the earth discovered by Prof. Airy, amounting to 2':04, with a period of 240 
years, produces one of not less than 23” in the motion of the moon, so that, judging 
by analogy, there ought to be a sensible inequality in the present case also. Again, 
there seems to bean inequality in the motions of Jupiter, Saturn, and Uranus, witha 
period of somewhat more than 1700 years, and amounting in the case of Jupiter to about 
10” ; and in the case of Saturn toabout 40”; and in that of Uranus to 43”. It arises 
from the fact, that six times the mean motion of Saturn is nearly equal to twice that 
of Jupiter plus three times that of Uranus. There are several others besides these of 
_ less importance, arising from the product of two disturbing forces; and thereis even one 
which results from the product of three.forces, and appears to amount to nearly 7”. 
There are also several inequalities of the same kind in some of the asteroids, which are 
very much larger than any in the motions of the principal planets; but as the theory 
of the asteroids is considered to be of comparatively little interest, I have not sent 
them. 
On Transit Observations of the Moon. By the Kev. T. R. Rozinson, D.D. 
Dr. Loomis’s remarks on longitudes, deduced from the method of moon culmi- 
nating stars, reminded him of the results which he had formerly obtained by it. 
The high praise given to it by the German astronomers, and his valued friend the 
late Mr. Baily, had induced him to attend to it particularly when determining the 
longitude. of the Armagh Observatory. He found it very unsatisfactory. The longi- 
tudes, deduced by comparison on the same night with Dublin, Greenwich, Paris, and 
Konigsberg, all first-rate Observatories, were very discordant; and those deduced 
