the Means of augmenting indefinitely the Power of Magnets. 433 



bably complicated) which I have not yet studied ; it does not 

 vary sensibly with the breadth. All my experiments have been 

 made upon steel springs of 1 millim. thickness. The laws which 

 I shall state will probably apply to other thicknesses, with dif- 

 ferent values of the coefficients. 



I. When two similar magnetized plates are superposed, the 

 curves representing the values of F rise, from the magnetism 

 leaving the faces which are placed in contact to take refuge at 

 the exterior parts. At the same time the curves approach each 

 other and the middle of the magnet. This effect is increased on 

 the addition of a third and a fourth plate. Finally the two 

 curves unite in the middle. 



From this moment the combination of force is at its maximum. 

 A greater number of plates makes no change in its intensity at 

 any point ; and if we dismount the pile in order to study sepa- 

 rately each of the layers which compose it, we find that they have 

 lost a portion of their first magnetization as much greater as 

 there were more of them. In short, all addition to the limit- 

 number of the plates is to no purpose and a useless expenditure 

 of steel. This final magnet, the only one susceptible of precise 

 definition, is the only one to be employed, since it gives the 

 maximum of effect : I shall call it the normal or boundary magnet. 

 It will be seen that then all magnetic questions become unex- 

 pectedly simple. 



II. The curve representing the force F in the normal magnet 

 is a parabola represented by the equation F = A<£ 2 , x being the 

 distance to the centre of the plate, and A a coefficient which 

 varies with the length. This law is proved by the following 

 numbers. It will be observed that the values of F rise rapidly 

 at first with the number of layers, arriving very slowly at their 

 maximum, which they do not afterwards exceed. (/ denotes the 

 half-length.) 



Values of the force F. 

 2/=480. 



Distance to 

 the centre. 



3 plates. 



7 plates. 



9 plates. 



15 plates. 



Calculated. 



millims. 



grms. 



grms. 



grms. 



grms. 



grms. 



240 



41 



42 



482 



54-3 



57-6 



220 



25-4 



36 



40-2 



45 



48-4 



191) 



13-9 



25-6 



32- (> 



272 



3(51 



140 



9-5 



170 



16-5 



20- 1 



190 



90 





7-8 



85 



8-(5 



8-1 



40 





1-2 



1-5 



15 



1-8 



Phil. Mag. S. 4. Vol. 45. No. 302. June 1873. 2 F 



