REPORT OF THE SECRETARY. 9 



azimuthal motion of the apsides of the quasi-elliptical orbit. Inasmuch 

 as in all actual experiments with the freely suspended pendulum the vi- 

 brations soon assume the "spherical" character, these latter expressions 

 are really important as corrections to the aziinuthal motion properly clue 

 to the earth's rotation, and may explain the small variations from the 

 latter which the experiments generally exhibit. It is believed that these 

 corrections have never before been applied, or indeed actually put into 

 simple analytical shape. It is further shown that if a freely suspended 

 pendulum is made to swing through a great circle with very high velocity, 

 the plane of its orbit remains invariable in direction, in space, and that 

 in this phase the phenomenon is identical with that shown by a gyro- 

 scopic disk, as it was arranged by Foucault to exhibit the rotation of 

 the earth. 



A third paper by the same author is '' on the Phenomena of Preces- 

 sion and Nutation as affected by the internal structure of the earth," 

 and is an attempt to corroborate the dictum of Sir William Thompson, 

 that the phenomena of the precession and nutation do authorize some con- 

 clusions — very limited, indeed — concerning the internal structure of the 

 earth, inasmuch as it is proved that the very commonly received geo- 

 logic hypothesis of a thin crust enveloping a molten fluid is inconsist- 

 ent with the actual phenomena as observed. 



As the basis of the argument, the theorem is analytically demonstrated 

 that an entirely fluid earth (i. e., entirely destitute of solid crust and 

 without internal viscidity) would exhibit neither precession nor nuta- 

 tion. In other words, that the tilting effects of the solar and lunar 

 attractions would be exactly neutralized by the centrifugal forces due 

 to the tidal protuberances they develop. Pari ratione, if the figure of 

 the earth yields at all to the attractions, the precession and nutation 

 will be neutralized in exact proportion to the extent (as compared with 

 a perfect fluid globe) to which that yielding obtains. 



Sir W. Thompson has proved that even an earth entirely solid must 

 yield, unless its rigidity to the depth of two or three thousand miles 

 greatly exceeds that of steel ; a thin crust, say thirty or forty miles 

 thick, such as geological hypothesis attributes to the earth, if envelop- 

 ing a fluid nucleus, would yield nearly as much as if the earth were 

 entirely fluid. But the observed rates of precession and nutation con- 

 form almost exactly to the hypothesis of perfect rigidity. Hence, the 

 hypothesis of a thin crust is untenable. Incidentally the fallacy of the 

 experiment (with rotating spherical glass shells, containing water) and 

 argument of M. Delaunay to invalidate the conclusions of Professor 

 Hopkins and Professor Thompson is exhibited, and the opinions of 

 Poisson concerning the internal structure of the earth are, according to 

 the author, shown to coincide better with observed facts than those of 

 any other physicist. 



Another paper has been examined and accepted for publication 

 entitled " The Secular Variations of the Orbits of the Planets," by John 



