STUDIES ON MAGNETIC DISTRIBUTION 127 



is not much affected, but R is increased. Where the magnet is used 

 merely to affect a compass-needle, we should then see that the hole 

 through the centre has little effect where the magnet is short and thick ; 

 but where it is long, the attraction on the compass-needle is much dimin- 

 ished. Where the magnet is of the U-form, and is to be used for 

 sustaining weights, the practice is detrimental, and the sustaining-power 

 is diminished in the same proportion as the sectional area of the magnet. 

 The only case that I know of where the hole through the centre is an 

 advantage, is that of the deflecting magnets for determining the inten- 

 sity of the earth's magnetism, which may be thus made lighter without 

 much diminishing their magnetic moment. 



In conclusion, let me express my regret at the imperfection of the 

 theory given in this paper; for although the equations are more general 

 than any yet given, yet still they rest upon two quite incorrect hypoth- 

 eses; and so, although we have found these formula? of great use in 

 pursuing our studies on magnetic distribution, yet much remains to be 

 done. A nearer approximation to the true distribution could readily 

 be obtained; but the result would, without doubt, be very complicated, 

 and would not repay us for the trouble. 



In this paper, as well as in all others which I have published on the 

 subject of magnetism, my object has not only been to bring forth new 

 'results, but also to illustrate Faraday's method of lines of magnetic 

 force, and to show how readily calculations can be made on this system. 

 For this reason many points have been developed at greater length than 

 would otherwise be desirable. 



