7176 
normal to that plane, with a constant angular velocity 
wsindA, where w is the angular velocity of the earth 
about its polar axis, and / is the latitude of the nor- 
mal axis, the path of the body, in space, will evi- 
dently be a spiral curve; and from the properties of 
that spiral, the centrifugal force at its origin, which 
is the deflecting force resulting from the earth’s 
motion on its axis, is readily found to be 2ovsina 
(see Science, iii. No. 57 ). 
The same result that is here found from the prop- 
erties of the spiral which the body describes in space 
was found by Mr. Ferrel from the equations of motion 
on a spherical surface (see eq. 58, Professional papers 
of the signal-service, No. viii., 1882, p. 30); but, by 
assuming that the motion of the body in space is in 
the circumference of a circle, he finds for the time, 
T, of a revolution in that circumference, — 
‘r= secd X 4 day;’ 
and he says, ‘‘ The gradual gyration of a vibrating 
pendulum is caused by this same deflecting force, 
and hence the time of gyration is the same as that 
of 7 in the preceding equation.”’ 
But it is well known that the time of gyration of 
a vibrating pendulum is sec@ X 1 day. 
This discrepancy may be explained as follows: — 
Let P represent the position of the normal axis or 
centre of the tangent plane ABCD, which therefore 
SCIENCE. 
| KrakatoaLafitode....__.6°09' 30” South 
| a L ongitude... 105° 27 00° East 
H Saucelitos Latitude.....37°5} North == 
peoveroweee--ee Longitude..122°29' West = 
H Kadiak Latitude 
rotates about P with the velocity wsindA, or wcos 6, 
if we adopt Mr. Ferrel’s notation; and because the 
radius of curvature at P is the same for the spiral 
PA’A as for the circle s, the centrifugal force at P 
will be the same, whether the body move in the spiral, 
or in the circumference of the circle s: but if we 
suppose the body to describe the circumference of 
the circle s by moving along the radius vector PA’, 
while the radius vector rotates about P, the circum- 
ference of s will obviously be described while the 
A 
radius vector makes a half-revolution about P ; that 
is, in the time t= sec@ X 4 day. The time 7 of 
gyration of a vibrating pendulum, however, does not 
correspond with the time Tin which the circle s would 
2982 
andviach Ids. 
be described, but is the time in which the spiral 
PA’A is described, and hence — 
= sec X 1 day, 
as has been abunaeaan proved by experiment. 
J. E. HENDRICKS. 
Des Moines, Io., May 29. 
[Vox. IIL, No. 73, 
