•V 



410 Rev. C. S. Lyman on the Pendaltnn Experiment. 



* 



sions, whichj when simplified by^^he consideration of limiting 

 the vibration to small arcs, gives the azimiuhal velocity uniform 

 in the direction from left to right, and in the simple proportion of 

 the sine of the latitude. 



Prof O'Brien of Kings College, London, in an article on Sym- 

 bolical Mechanics, in the August number of the Philosophical 

 Magazine, investigates the same problem, and concludes, "that 

 the effect produced by the earth's rotation on the pendulum is 

 proportioned in every respect to the sine of the latitude." 



Perhaps the simplest and most satisfactory method of illustra- 

 ting the subject to minds not specially trained to mathematical 

 investigations, is that adopted by Prof. J. D. Dana, in a comma-, 

 nication made to the Scientific Association at Albany, and pnb- 

 lished on page 200 in this volume ; viz., by drawing lines paral- 

 lel to each other along any circle of latitude on an artificial globe 

 in the manner fully described in the article referred to.* These 

 lines, it is true, taken as representing the successive positions and 

 directions of the plane of vibration, are not strictly parallel, nor is 

 it necessary to regard them as such, except when considered as f 



placed at indefinitely small distances apart. The continually 



changing direction of the axis of suspension causes a corresponding 



change in the absolute position of these lines, and hence, consid- 

 ered as in space, they do not lie in the same plane, and of course 

 are not in all respects parallel. But as precisely the same change 

 takes place in the position of the horizontal plane over which 

 the pendulum vibrates, and in the direction of the force of grav- 

 ity, causing that direction to remain relatively constant, the rela- 

 tive effect, as has been remarked already, is exactly the same as 

 if no such change of position occurred, or as if the successive 

 positions of the line of vibration were in one continued plane, 

 the line maintaining a constant parallelism to itself. But if these 

 lines are parallel, why is not the last in the series, when we have 

 gone round a circle of latitude, parallel to the first? This is not 

 the case, because the lines, though relatively parallel, are not, for 

 the reasons before mentioned, to be treated as absolutely so. 

 They are to be regarded as lines drawn on the surface of a cone 

 at its base — the cone being that formed by the successive merid- 

 ional tangents to a given circle of latitude, and having its apex 

 at the point where all these tangents meet the axis of the earth 

 produced. Such lines, if not parallel, strictly speaking, when 

 regarded as on the curved surface of the cone, will become truly 

 so, when that cone, considered as made of paper, is cut open from 

 its center outward and spread out on a flat surface. 



has 



article was in type, that the same method of iHus-. 



.^ 





