125 



6 being a small arc, the powers of which above the third may 

 be neglected, and vanishing twice during each oscillation. 



"From equation (8) it is easy to see, that the plane of os- 

 cillation undergoes a periodic variation in azimuth ; in conse- 

 quence of which the projection of the centre of oscillation of 

 the pendulum on the horizon will describe a curve resembling 

 a figure of eight, in which, if the pendulum be in the meri- 

 dian, the motion in the northern loop is retrograde ; and in 

 the southern loop progressive. 



" The variation in azimuth produced by the second term 

 of equation (7) will be insensible, unless 6 become nearly 

 equal to ir, in which case the change in azimuth will become 

 indefinitely great; for, integrating (7), we find, the initial 

 motion being in the meridian, 



d<t> 7 > . . 6 - sin 6 cos 6 ... 



-^- = k sin A - k cos A r-z-r. . (9) 



at sin 2 



If in this equation 6 be equal to tt, the second term will be infi- 

 nite and negative, denoting that the plane of vibration swings 

 round suddenly to the west. This result is evident without ana- 

 lysis ; for if the pendulum be started in the meridian, so as to 

 pass the lowest point with a velocity due to twice its length, 

 it will reach the top of the circle without velocity, and fall 

 suddenly to the west, in the prime vertical. 



" If the pendulum were to perform a complete revolution 

 with a high velocity, the time of revolution in azimuth of the 

 plane of its motion would tend to the limit 23 ft 56 m ; but 

 when the motion is oscillatory, the theoretical time of revolu- 

 tion in azimuth will 23'' 56 m x cosec A, as has been proved for 

 small arcs of vibration by M. Binet. Comptes Rendus de 

 V Acad, des Sciences, Feb. 17, 1851)."] 



Professor Allman read a notice of the emission of light by 

 Anurophorus jimetareus Nicholi (Leptura fimetarea, Linn.) 

 During a walk over the Hill of Howth, near Dublin, on a 



