192 ANNUAL OF SCIENTIFIC DISCOVERY. 



would alternately accelerate and retard the movements of one more distant ; 

 and physical astronomy shows, that, in our planetary systems a like period- 

 icity results from the inequality of the times in which the several planets 

 perform their revolutions. But, as the tide-Avave rolls around the earth with 

 the same mean angular velocity as the moon, their mutual action will not 

 exhibit the periodicity which characterizes planetary disturbances. In the 

 analytical solution of this problem, the equation depending on the differ- 

 ence of motion of the moon and the tide-wave would acquire by integration 

 a divisor infinitely small ; and this proves its secular character. If Laplace 

 finds no such divisors, it is because all the modifications in the action of the 

 moon on the waters of the ocean arc not embrace;! in his investigations on 

 the subject. Leaving the supposed case, we shall now pass to the actual 

 condition of the agencies concerned in tidal phenomena on our globe. At 

 her present distance the revolution of the moon occupies more time than the 

 earth's period of rotation ; and the tidal wave which has the greatest disturb- 

 ing influence being always east of our satellite, must add to its velocity, 

 while it retards that of the earth. We may remark, however, that the ad- 

 ditional velocity imparted to the moon would give her a larger orbit, and in- 

 crease the period of her revolution. Hence the orbital motion of the moon, 

 as well as the rotary motion of the earth, sustain a loss depending on the 

 difference of the tidal force on opposite sides of our globe, and so very 

 insignificant, that some millions of years would be required to cause a re- 

 duction of one per cent, in the momenta of these vast bodies. I must, how- 

 ever, question the results of Laplace, who finds that the change in the 

 length of the day has not ^amounted to the one hundredth part of a second 

 during the last 2,000 years. This conclusion is based on a comparison of 

 ancient and modern eclipses ; and the time of the earth's rotation is thus as- 

 certained from the revolutions of the moon, making corrections for the dis- 

 turbances operating on the latter body. But all the disturbing influences 

 have not been yet taken into consideration ; and as the one noticed in the 

 present article operates on the earth and moon, we cannot regard either of 

 these bodies as an infallible chronometer for measuring the vast ages of 

 eternity. 



OX THE DIRECTION OF GRAVITY OX THE EARTH'S SURFACE. 



Professor Hcnnessy, in a paper before the British Association, Dublin, 

 stated that for all practical purposes the direction of gravity was considered 

 perpendicular to the earth's surface, and a similar assumption was often 

 made in writings claiming a high degree of scientific accuracy. This arose 

 from defining the earth's surface as the surface of equilibrium of the waters. 

 If the earth were stripped of its fluid covering, the irregular surface so laid 

 bare would present considerable inequalities. From what is now known re- 

 garding the depth of the ocean, the continents would appear as plateaus 

 elevated above the oceanic depressions to an amount which, although small 

 compared to the earth's radius, would be considerable when compared to its 

 outswelling at the equator, and its flattening towards the poles. The sur- 

 face thus presented would be the true surface of the earth, and would not be 



