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) itis 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 Joop progressive. 
‘‘ The variation in azimuth produced by the second term 
of equation (7) will be insensible, unless become nearly 
equal to 7, in which case the change in azimuth will become 
indefinitely great; for, integrating (7), we find, the initial 
motion being in the meridian, 
& _ kein d — eos 9S 088 (9) 
Ifin this equation @ be equal to 7, 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" 56"; but 
when the motion is oscillatory, the theoretical time of revolu- 
tion in azimuth will 23" 56” x cosec A, as has been proved for 
small arcs of vibration by M. Binet. Comptes Rendus de 
l Acad. des Sciences, Feb. 17, 1851).”’ 
Professor Allman read a notice of the emission of light by 
Anurophorus fimetareus Nicholi (Leptura jfimetarea, Linn.) 
During a walk over the Hill of Howth, near Dublin, on a 
