Rev. C. S. Lyman on the Pendulum Experimeut. 407 



rather than the other, is somewhat doubtful. Many of the pub- 

 lished observations, especially those with long pendulums, seem 

 to indicate such a result. At Providence the motion in three- 

 fourths of the trials was towards the left. With shorter pendu- 

 lums the ellipticity in each direction seems to have been about 

 equal — though in Mr. Bunt's long series the preponderance was 

 also towards the left. 



But the most marked ellipticity, and the one constantly observ- 

 ed in these experiments, is that which may be considered as ac- 

 cidental, and which varies both in amount and direction in differ- 

 ent trials. In the experiments at New Haven, the minor axis of 

 the ellipse rarely exceeded a tenth of an inch. Mr. Bunt in some 

 of his trials, and several others, have found it equally small ; 

 while others, owing doubtless to a faulty apparatus, or to aerial 

 currents, or unskillful managemennt, have found it amount some- 

 times to two, three or more inches. 



This motion in an elliptic orbit, from whatever source it may 

 originate, necessarily gives rise to a progressive motion of the 

 apses of the ellipse in the same direction in which the orbital 

 niotion takes place, 



Mr. Airy the Astronomer Royal, Mr. Galbraith of Dublin, and 

 Mr. Thacker of Cambridge, have investigated the nature of this 

 n^otion, and have given as the result of their inquiries, essentially 

 the same formula for computing the progressive angular motion 

 of the apses of the ellipse. These formulas, together with the 

 extended analysis of Messrs. Galbraith and Haughton, are pub- 

 hshed in the August number of the Philosophical Magazine. 



The Astronorner Royal concludes from his investigation that, 

 " If the length of the pendulum be a, the semi-major axis of the 

 ellipse described by the pendulum be h, and the semi-minor axis 

 De c, then the line of the apses of the ellipse will perform a com- 

 plete revolution in the time of a complete double vibration (' 



1. e. 



the time of describing the ellipse) multiplied by — -. " 



To reduce this to a convenient form for computing the pro- 

 gressive motion of the apses of the ellipse per hour, let m repre- 

 sent that hourly motion, T the time of a complete revolution of 

 the apses, and t the time in seconds of a double vibration of the 



Penduluni. then, as above, T-/-^. Bat; (Tbeing in seconds) 

 *^ =-v?r- X 3600. SubstitutinjT the above value of T, 



T 



m 



360^x36 0x3^ ^ 4ggooo— 



■If a ^71 feet =852 inches, ^- 9,333 seconds, J = 24 inches, 

 and e=z0-2 inches, (b and c being the arithmetical mean of the 







