Till. REMAKES ON THE THEORY OF THE COMPOUND 

 MAGNETIC NEEDLE. 



Proceedings of the Royal Irish Academy, 1848. 



WHEN two magnetic needles are united by a fixed vertical axis 

 passing through their centres, and perpendicular to both, the 

 moment of the force exerted by the earth upon them is the sum 

 of the moments which it exerts upon each needle separately, and 

 is, therefore, 



X (M sin u + M' sin M') ; 



in which M and M' denote the magnetic moments of the two 

 needles, u and u the angles which their magnetic axes make with 

 the magnetic meridian, and X the horizontal component of the 

 earth's magnetic force. In the state of equilibrium this moment 

 is nothing ; so that if u and U Q ' denote the corresponding values 

 of u and u' t there is 



M sintfo + -3/'sinw'o = 0. (1) 



Consequently, if two lines be taken from any point of the vertical 

 axis, parallel to the magnetic axes of the two needles, and pro- 

 portional to their magnetic moments, M and M', the diagonal of 

 the parallelogram constructed upon them must lie in the magnetic 

 meridian, when the compound needle is at rest. 



Again, if we substitute u = t( + *', ' = '< + ''> i Q * ue general 

 expression of the statical moment, it becomes, in virtue of (1), 



X(M cos + JT cos ') sin /. 

 Hence the compound needle is acted upon as a single needle, 



