GENERAL MEETING. 45 
A subsidiary point deserving of notice is the certainty that the 
inner portions of the bright ring (and still more those of the dusky 
ring) are revolving in periods three or four hours shorter than that 
of Saturn himself. When Professor Hall made his brilliant discov- 
ery of the satellites of Mars, and announced that the inner satellite 
(Phobos) was found to have the short period of 7h. 38m. (or less 
than one-third of that of Mars) the fact was at once proclaimed by 
some as incompatible with the “nebular hypothesis.” Everybody 
knows that the rotation periods of the’sun and planets do not con- 
form to the third law of Kepler. Our own moon has an actual 
velocity in its orbit more than double that of our terrestrial equator. 
And had the moon a little less than one-third its present distance, 
(that is, were its radius-vector less than 70,000 miles,) its angular 
velocity would exceed that of the earth, or its period would be less 
than 24 hours. Or, stated in another way, our earth, if expanded 
to the orbit of the moon, (under the most favorable disposition of 
form and of homogenous density,) would occupy considerably more 
than a year in completing its rotation. The supposed nebular diff- 
culty is therefore just as pertinent to our own satellite as to those 
of Saturn or of Mars. The obvious solution is, that all the planets 
(without exception) have lost a very large amount of rotatory 
energy ; and this may be largely or chiefly ascribed to the retarding 
effects of internal friction resulting from solar tides. And, given 
time enough, the rotation of every planet should be finally reduced 
to the lunar condition of a precise accord of its diurnal and annual 
periods. On any hypothesis whatever, it is certain that the rotations 
of the planets are very much slower (notwithstanding too the 
acceleration due to contraction) than they originally were. This 
fact certainly offers no objection to the nebular hypothesis. 
“ Mr. Durron questioned the validity of Ennis’ hypothesis, that 
the rotation of a nebular mass could be initiated by purely internal 
movements. 
Other remarks were made by Mr. FrisBy. 
Mr. S. M. Burnett then made a communication on 
THE CHARACTER OF THE FOCAL LINES IN ASTIGMATISM, 
showing that the two lines which limit the focal interval of Sturm 
have been erroneously assumed to be straight. There is only one 
