290 On the Physical Geology of the United States, §c. 
and if it has diminished in volume, it must have increased in its 
velocity of rotation, and produced greater velocities in the great 
equilibrating currents of the ocean. 
M. Pontecoulant, after going into an analytical investigation of 
the disturbing action of the sun, moon and planets upon the earth, 
deduces the conclusion that the action of those bodies upon the 
terrestrial spheroid will never produce any appreciable displace- 
ment in the position of its poles on its surface, nor any sensible 
variation in the quickness and uniformity of its motion of diurnal 
rotation, which, he remarks, are important results and insure for- 
ever the stability of terrestrial latitudes, and invariability in the 
length of the day.* 
The equation of the mean dayt+ reduced to time, estimating the 
circumference as equal to one day, amounts to a period of only a 
few minutes in several millions of years, and it is unnecessary 
for astronomers, says La Place, to notice it. 
M. Poisson in his Mechanics, speaking of the diminution of the 
volume of the earth and of the shortening of the day, says, “A 
diminution due to this cause of one ten millionth part of a day, 
would suppose a decrease of one twenty millionth part of the length 
of the radius; and as we are certain that the day has not experi- 
enced this diminution for twenty-five hundred years, it follows that 
the mean radius of the earth has not varied three metres during 
this long interval of time by the effect of cooling, if the mean tem- 
perature of the earth has not yet arrived at a permanent state.”’$ 
So far as I have ascertained, philosophers have not considered 
the effect of centrifugal force, by an increased velocity of rotation 
of the earth. In an article in the American Journal of Science, 
Vol. xtvi, pp. 344-346, on the possible variation in the length of 
the day, I suggested that there might be compensating forces 
that would tend to maintain the time of rotation uniform, and 
the day unchanged in length, even if the earth be undergoing a 
slight change in its dimensions, either secularly or paroxysmally. 
* Pontecoulant, Théorie Analytique du Systéme du Monde, T. II, p. 224. 
+ The formula for calculating this is given by La Place, and the value above 
mentioned, when calculated approximatively by a method indicated in the Mecan- 
ique Celeste, (Bowditch’s translation, Vol. II, pp. 855 and 867, 3152 6 to f,) gives 
a variation of about one centesimal second in a thousand years. 
+ Mecanique Celeste, translated by Bowditch, Vol. II, p. 867. 
§ Poisson’s Mecanique, T. IT, 460. 
