122 HENRY A. KOWLAND 



strongly magnetized than the steel, because the magnetism was more 

 diffused; and as the magnetism was not distributed so nearly at the end 

 as in the steel, its magnetic moment and time of vibration were less. 



It is for these reasons that many makers of surveyors' compasses find 

 it unnecessary to harden the needles, seeing these are long and thin. 



We might deduce all these facts from the formulae on the assumption 

 that r is greater the harder the iron or steel. 



Having now considered briefly the distribution on electromagnets 

 and steel magnets, and found that the formulae represent it in a general 

 way, we may now use them for solving a few questions that we desire 

 to solve, though only in an approximate manner. 



VI. 



M. Jamin, in his recent experiments on magnetic distribution, has 

 obtained some very interesting results, although I have shown his 

 method to be very defective. In his experiments on iron bars mag- 

 netized at one end, he finds the formula s rl to apply to long ones as I 

 have done. Now it might be argued that as the two methods apparently 

 give the same result, they must be equally correct. But let us assume 

 that the attraction of his piece of soft iron F varied as some unknown 

 power n of the surface-density d. Then we find 



F=Ce nrL , 



which shows that the attractive force or any power of that force can 

 be represented by a logarithmic curve, though not by the same one. 

 Hence the error introduced by M. Jamin's method is insidious and not 

 easily detected, though it is none the less hurtful and misleading, but 

 rather the more so. 



However, his results with respect to what he calls the normal mag- 

 net 10 are to some extent independent of these errors ; and we may now 

 consider .them. 



Thus, in explaining the effect of placing hardened steel plates on 

 one another, he says, " Quand on superpose deux lames aimante'es 

 pareilles, les courbes qui represontent les valeurs de F [the attractive 

 force on the piece of soft iron] s'e!6vent, parce que le magnetisme quitte 

 les faces que 1'on met en contact pour se refugier sur les parties ex- 

 te"rieures. En meme temps, les deux courbes se rapprochent 1'une dc 

 1'autre et du milieu de 1'aimant. Get effet augmente avec une troisieme 



10 <On the Theory of the Normal Magnets,' Comptes Rendus, March 31, 1873; 

 translated in Phil. Mag., June, 1873. 



