270 Dr. Tyndall on the Laws of Magnetism. 



it will take up a position oblique to the magnetic meridian. Let 

 the angle which the needle makes with the latter be a. 



The effective portion of H which now tends to turn the needle is 



H sin a. 

 The portion of h which tends to turn the needle in the oppo- 

 site direction is 



h cos a. 



These forces are now in equilibrium^ and hence 

 H sin « = A cos a, 

 or 



/i = H tana. 



Supposing the power of the magnet to be changed, that it has 

 become stronger or weaker, without however having its position 

 changed. Let // be the force corresponding to h in the former 

 case, and «' the angle corresponding to «, then we have 



A' = H tan «', 

 and hence 



h _ tana* 



h' ~ tan a' 



The quantities h and A' express the relative streng-ths of the 

 magnet, these strengths being proportional to the tangent of the 

 angle which the needle makes with the magnetic meridian. 



8. If the magnet be an electro-magnet, we have the means of 

 measuring the intensity of the current which circulates in the 

 sui'rounding helix. We know that this intensity is proportional 

 to the tangent of the angle {jS) which the needle of the tangent 

 galvanometer, under the influence of the current, makes with the 

 magnetic meridian. 



9. Lenz and Jacobi have proved, that for a double intensity 

 tangent « is doubled, for a treble intensity it is trebled; in 

 general, that the strength of the magnet is directly proportional 

 to the intensity of the exciting current f. But the latter, as we 

 have said, is proportional to tangent /3 ; and hence, in the follow- 

 ing investigation, tan /8 is assumed to express " the strength of 

 the magnet." 



M. Miiller of Freiburg, as will be seen from a " report " con- 

 tained in the pi-eceding Number of this Magazine, denies the 

 universality of this law, Eut a reference to the dimensions of 



* The same demonstration holds good for the tangent galvanometer, 

 if instead of the magnet in its different states we substitute currents of 

 different powers. Tlie tendeney of the latter being to set the needle at 

 right angles to the magnetic meridian, their action is precisely similar to 

 that of the magnet. 



t PoggendorfF's Annalen, vol. xlvii. p. 244. 



