.-* 



411 



I 



4 



Rev. C. S. Lyman on the Pendulum E 



111 the accompanying figure 

 the cone formed by the tangents 

 has for the periphery of its' 

 base the circle of latitude B 0, 

 and the incUnation of any two 

 meridians to each other at this 

 parallel of latitudej is represent- 

 ed by the angle formed at the 

 apex of the cone by the corres- 

 ponding tangents. Let the ar- 

 rows a^ bj Cj represent successive 

 positions of the pendulum plane; 

 now, as the earth revolves on its 

 axis, the angle formed by this 

 plane with the meridian, or rath- 

 er with its tangent, is continual- 

 ly increasing, but evidently in- 

 creasing not by an amount as 

 great in a given time as the an- 

 gular motion of the earth on its 

 axis in the same time ; for the motion of a place B going round 

 with the earth at the rate of 15^ an hour, takes place in a circle 

 having for its radius the line B bj while the same motion of B 

 considered as around A, (or in other words, the relative angular 

 change in the direction of the meridian), takes place in a circle 

 of which the radius is B A, a radius as much greater than the 

 other as the hypothenuse of a right angled triangle is greater than 

 one of its sides; consequently, the circumferences of circles be- 

 ing proportioned to their radii, the angular change in a given time 

 must be less in the larger circle than in the smaller, and as much 

 less as the line B 6 is less than B A, or as the sine of an angle is 

 less than radius, (B b being the sine of the angle B A b, when 

 B A is made radius.) But the angle B A i, in the right angled 

 triangle A B D, is the complement of the angle at D, which lat- 

 ter is the cotnplement of the latitude; consequently B A b=the 

 latitude ; B i is the sine of the latitude ; and therefore the angu- 

 lar change in the direction of the meridian, and consequently the 

 apparent motion of the pendulum plane; is proportioned to the 

 sine of the latitude. 



Now when the pendulum has made one complete revokuion 

 around the earth in the circle BC, it has evidently made but a 

 part of a revolution in the circle of which A B is radujs ; and the 

 total change of inclination of the parallel arrows drawn on a 

 globe to the successive meridians in going once round the globe, 

 nsust in like manner equal only a corresponding part of 360^. 

 The last line in the series of quasi parallels, therefore, can only 

 he parallel to the first, when the circuit has been made at the 



** 



m. 



