276 Mr. A. Schuster on the Influence of the 



Maxwell had some private information from Joule, in which 

 unpublished experiments on the bending of magnetic needles 

 were referred to. 



At any rate the question seems worthy of consideration, 

 because for a number of years the Greenwich Observator} r has 

 published observations made with needles 9, 6, and 3 inches 

 long, which show a systematic difference in the observed dip 

 amounting to more than a minute of arc between the longest 

 and shortest needles. 



It is clear that the mere displacement of the ends of the 

 needle by the bending is eliminated by the method of observa- 

 tion which is uniformly adopted, but in addition there is 

 the effect alluded to by Maxwell, which is not so easily dis- 

 posed of. The bending of the needle causes a displacement 

 of the centre of gravity, and a little reflection will show that 

 this displacement must cause a diminution in the apparent 

 dip. Let h be the distance of the centre of gravity from the 

 axis of rotation, (j> the dip, and 8 the small angle through 

 which the needle is turned by the displacement of the centre of 

 gravity. Equating the moments of the forces which balance 

 in the position of equilibrium, we find 



mgh sin cj> = TM8 (1) 



M represents the magnetic moment of the needle, and T the 

 earth's magnetic force. In order to form an estimate of the 

 angle 8, we must take account therefore of the displacement h 

 and the magnetic moment of the needle. It is assumed that the 

 needle when it is straight has its centre of gravity in the axis 

 of rotation. Errors due to non-fulfilment of that condition 

 are eliminated by the method of observation. 



The needles used at Greenwich have the form shown in 

 fig. 1, It would not repay the trouble to determine the 



Fie. 1. 



bending for such a shape. It will be sufficient to carry out 

 the calculations for the shapes indicated by the dotted lines ; 

 that is to say, to imagine needles having cross sections which 

 are either uniform or diminish uniformly. 



The effect of pointed needles will be found to be smaller 

 than that of rectangular magnets ; and we shall be justified 

 in assuming that needles having the actual shape in use will 

 give an intermediate result. 



The amount of bending of rectangular bars is well known, 



