Amplitude of Vibrations qf Double Frequency. 503 



they touch one pair of: opposite magnetic poles in the 

 turning part which represents the Weber element, with the 

 result that one of its axes becomes fixed and rotation can 

 consequently occur only about that axis. The magnetic 

 properties o£ the model system then resemble those of 

 pyrrhotite, a crystal of which, as Weiss * showed^ will take 

 up magnetic induction readily in one plane, but not in the 

 direction perpendicular to that plane. The model may also 

 be adjusted to exhibit differences o£ magnetic quality along 

 different axes in the plane of magnetization. Such differences 

 were in fact observed in pyrrhotite by Weiss. He found 

 that when a crystal was turned about its non-magnetic axis in 

 a fixed field there were abrupt magnetic changes at intervals 

 of 60°. This is just what a study of the model would lead one 

 to expect, for the projecting magnets in the turning element 

 lie in planes 60° apart round any one of its magnets taken as 

 axis. Periodic variations along axes inclined at 120° to one 

 another in the plane of easy magnetization are consistent 

 with cubic symmetry on the part of the iron atom : they 

 follow 7 directly from the assumed grouping of magnet poles 

 at the corners of a cube. And they will occur at intervals 

 of 60° if we ascribe the hexagonal structure of the crystal 

 to twinning in successive layers. 



If Hull's view of the structure of the iron atom be correct, 

 it seems not improbable that the Weber element includes not 

 only the duplet of electrons which he places near the nucleus, 

 but also the innermost octet, the members of which are 

 somewhat further away from the nucleus, leaving the other 

 and more distant octets to constitute what I have called the 

 fixed elements. 



LVII. On the Amplitude of Vibrations maintained by Forces 

 of Double Frequency. By N. G. Krishnaiyar, M.A., 

 Lecturer in Physics, University College, Rangoon f . 



LORD RAYLEIGH % was the first to discuss the theory 

 of the vibration maintained by an influence whose 

 frequency was double that of the vibration maintained. 

 A well-known example of such maintenance is the longi- 

 tudinal form of Melde's experiment. His differential 

 equation took the form 



y + ky-\- (n 2 — 2u sin 2pt)y = 0, 

 k and a being small quantities. 



* Weiss, Jour, de Pkys. iv. p. 469 (1905). 



t Communicated by the Author. 



\ c Theory of Sound. 1 vol. i, pp. 81-85. 



