OF ARTS AND SCIENCES. - 295 



at a scieulific soiree in the house of Lord Northtimpton. Three 

 voUimes of Perigal's kinematic curves are preserved in the archives of 

 the Royal Society of London, of the Royal Astronomical Society, 

 and of the Royal Society. 



But all these anticipations of the Lissajous curves, theoretical and 

 experimental, are antedated by two publications whicli appeared at 

 Boston in 1815.* Li this year Professor Dean, of Burlington, Ver- 

 mont, published a curious memoir on the " Motions of the Earth as 

 seen from the Moon." It is well known that the time of the moon's 

 rotation on its axis is equal to the time of its revolution in its orbit. 

 The result of this equality (whether regarded as a mere coincidence 

 or the effect of gravitation) is seen in the fact that the same side of 

 the moon is always turned towards the earth. This statement would 

 be literally true if the moon's motions of rotation and revolution were 

 in parallel planes, and the momentary velocities as well as the average 

 velocities were always equal. But the plane of the moon's equator 

 is inclined to the plane of the moon's orbit at an angle of 6° 39' ; so 

 that an observer on the earth, at one time, overlooks the north pole of 

 the moon to the extent of 6° 39', and about a fortnight later the south 

 pole. Moreover, the velocity of rotation is uniform, but the velocity 

 of revolution is unequal in different parts of the elliptical orbit. 

 Therefore, although the whole periods are the same for botli motions, 

 the moon at perigee revolves faster than it rotates, and at apogee it 

 rotates faster than it I'evolves. Hence, in the course of one revolu- 

 tion, an observer on the earth overlooks the eastern or the western 

 edge of the moon to the extent of 6° 18' each way. or the greatest 

 equation of the centre of the moon's orbit. These effects are familiar 

 to astronomers under the name of the moon's libratious, which en- 

 able them to see every month four sevenths of the moon's surface, 

 though the remaining three sevenths are forever hidden from view. 



Professor Dean investigates the influence of these peculiarities in 

 the moon's motion on the position of the earth as seen by a lunar 

 observer. If the two motions of the moon were equal and parallel, 

 without any qualification, the earth would always occupy the same 

 place in the lunar firmament. If the observer were happily situated 

 at the centre of the moon's visible disk, the earth would always be in 

 his zenith. But the inclination of the planes of the moon's equator 

 and orbit will make the earth appear to oscillate over a north and 



* Memoirs of Amer. Acad, of Arts and Sciences, 1st series, vol. iii. p. 241 

 (1816). 



