ON THE SPECIAL PROBLEMS OF DYNAMICS. 203 
Motion as affected by the Rotation of the Earth, and Relative Motion in general. 
Article Nos. 74 to 85. 
74, Laplace (Méc. Céleste, Book X.c. 5) investigates the equations for the 
motion of a terrestrial body, taking account of the rotation of the Earth (and 
also of the resistance of the air), and he applies them to the determination 
of the deviations of falling bodies, &c. He does not, however, apply them to 
the case of the pendulum. 
75. We have also the memoir of Gauss, ‘‘ Fundamental-gleichungen, cc.” 
(1804): the equations ultimately obtained are similar to those of Poisson. I 
have not had the opportnnity of consulting this memoir. 
76. Poisson, in the “‘Mémoire sur le mouvement des Projectiles &c.’’ (1838), 
also obtains the general equations of motion, viz. (omitting terms involving 
n*), these may be taken to be : 
x dy . dz 
> Fa X+2n op sin-+ 5,05 3) 
ay dw . 
GPa bs Ee 
(see p. 20), where the axes of w, y,z are fixed on the Earth and moveable with 
it: viz., z is in the direction of gravity; x,y in the directions perpendicular 
to gravity, viz., y in the plane of the meridian northwards, w westwards; g 
is the actual force of gravity as affected by the resolved part of the centrifugal 
force ; 3 is the latitude. There are some niceties of definition which are 
carefully given by Poisson, but which need not be noticed here. 
77. Poisson applies his formule incidentally to the motion of a pendulum, 
which he considers as vibrating in a plane; and after showing that the time 
of oscillation is not sensibly affected, he remarks that upon calculating the 
force perpendicular to the plane of oscillation, arising from the rotation of the 
Earth, it is found to be too small sensibly to displace the plane of oscillation 
or to have any appreciable influence on the motion—a conclusion which, as is 
well known, is erroneous. He considers also the motion of falling bodies, but 
the memoir relates principally to the theory of projectiles. 
78. That the motion of the spherical pendulum is sensibly affected by the 
rotation of the Earth is the well-known discovery of Foucault ; it appears by 
his paper, ‘‘ Démonstration Physique &c.,”” Comptes Rendus, t. xxxii. 1851, 
that he was led to it by considering the case of a pendulum oscillating at the 
pole ; the plane of oscillation, if actually fixed in space, will by the rotation 
of the Earth appear to rotate with the same velocity in the contrary direction ; 
and he remarks that although the case of a different latitude is more compli- 
cated, yet the result of an apparent rotation of the plane of oscillation, dimi- 
nishing to zero at the equator, may be obtained either from analytical or from 
mechanical and geometrical considerations. Some other Notes by Foucault 
on the subject are given, ‘Comptes Rendus,’ t. xxxy. (1853). 
79. An analytical demonstration of the theorem was given by Binct, 
‘Comptes Rendus,’ t. xxii. (1851), and by Baehr (1853). Various short 
papers on the subject will be found in the ‘ Philosophical Magazine,’ and 
elsewhere. 
80. In regard to the above-mentioned problem of falling bodies, we have a 
Note by W. 8., Camb. and Dub. M. Journ. t, iii. (1848), containing some errors 
