Royal Institution. 563 



places do not seem to be more discrepant than would accord gene- 

 rally with the differences of latitude. The experiment at Paris gave 

 about 11° 30', at Bristol 11° 42', at Dublin rather more than 12°, at 

 York about 13°. 



To apprehend the theoretical principle, it is necessary to take 

 into account, — 1st, the simple inclination of two successive positions 

 of the meridian of a place to each other after any interval of time ; 

 2ndly, the independence of the motion of the ball of the pendulum, 

 of the rotation of the point of support; and 3rdiy, that the ball, 

 though free in this sense, is not however wholly free, being continually 

 drawn down by gravity in a direction continually changing (rela- 

 tively to the original direction of vibration) as the earth revolves. 

 Hence, though from the second cause the ball would have a ten- 

 dency always to preserve a motion parallel to its original motion, 

 and thus to deviate regularly from the meridian, it will (from the 

 third cause) not preserve this exact parallelism, but will take an in- 

 termediate direction. The exact determination of this direction 

 cannot be made on any general considerations, but must be the 

 result of detailed mathematical investigation. 



Thus in general in any illustrative or analogous case, so long as 

 the axis of vibration continues parallel to itself, the arc of vibration 

 will continue parallel to itself; but if the axis do not continue 

 parallel, the direction of the arc of vibration will deviate. This 

 distinction has been laid down and illustrated experimentally by 

 Mr. Wheatstone. 



The investigation, as pursued by M. Binet (Comptes Rendus, 1851, 

 Nos. 6, 7), as well as by other mathematicians, is primarily founded 

 on the method long since proposed by Euler, of resolving the rota- 

 tory 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 direc- 

 tion 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 arcs, 

 gives the aziumtlial velocity uniform in the direction from E. toW., 

 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 11^°, 

 and the time of a complete revolution 32'' S"". 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. 11. Young (late Professor of Mathematics 

 at Belfast). The latter gentleman has obtained as a consequence of 

 his investigations one remarkable! result, wliicli lie 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 tlie earth) 

 exactly equal to the difference in length of the two parallels of lati- 



