1851.] OF THE ROYAL INSTITUTION. 73 
Thus in general in any illustrative or analogous case, so long as 
the avis of vibration continues parallel to itself, the arc of vibration 
will continue parallel to itself; but if the avis do not continue 
parallel, the direction of the are of vibration will deviate. This dis- 
tinction has been laid down and illustrated experimentally, by Mr. 
Wheatstone. 
The investigation as pursued by M. Binet (Comptes Rendus, 1851, 
No. 6-7,) as well as by other mathematicians, is primarily founded on 
the method long since proposed by Euler, of resolving the rotatory 
motion of one point on the earth’s surface into two, one about the 
vertical of that point, the other about an axis at right angles to it: 
of which the latter is the part effective in determining the direction 
of gravity on the pendulum, and is proportional to the sine of the 
latitude of the point. 
M. Binet makes this general theorem the foundation of an analy- 
tical investigation, in which the conditions of the motion of the pen- 
dulum generally are expressed by certain differential equations, the 
integration of which conducts him to certain expressions, which when 
simplified by the consideration of limiting the vibration to small ares, 
gives the azimuthal velocity uniform in the direction from E. to W. 
and in a simple proportion to the sine of the latitude: giving there- 
fore the deviation for one hour in the latitude of Paris about 114° and 
the time of a complete revolution 32" 8". An investigation has also 
been made independently by the Astronomer Royal, leading to very 
nearly the same result. 
Other mathematical solutions have also been proposed by Dr. 
Day of Bristol, and by Mr. J. R. Young (late Professor of Mathe- 
matics at Belfast). The latter gentleman has obtained as a conse- 
quence of his investigations one remarkable result, which he states 
thus: 
‘“‘ The arc of the circular rim of the table subtended by the angle 
of deviation at its centre, is always (in one revolution of the earth) 
exactly equal to the difference in /ength of the two parallels of latitude 
described by the centre and extremity of the meridional diameter of 
the table.” [See Mechanic’s Mag. May 3rd & 10th, 1851.] 
The lucid and able illustrations of the subject given by Professor 
Sylvester have thrown much light on the explanation. 
, Modifications of the principle have been suggested by M. Chasles, 
on the idea of the difference of rotatory velocity between any two 
points on the same meridian, which difference, insensible as it might 
seem to be for the minute length of a vibration, he shows, will in 
successive vibrations become sensible. This idea is nearly the same as 
that announced by Laplace (Mécanique Céleste, vol. iv. c. 5.), who in- 
fers a deviation in the plane of a projectile fired in the direction of the 
meridian. The same idea has been discussed also by other mathe- 
maticians : and has been further carried out by M. Poinsot who 
has suggested, that if two balls suspended by separate strings, 
hanging together in contact, and consequently both partaking in 
