the Means of augmenting indefinitely the Power of Magnets. 435 



nine to fourteen for 300. We may say it is approximately pro- 

 portional to the length. 



IV. The preceding Tables show that the separating-force at 

 the extremity of the normal pile augments with the length 2L 

 It is 54 grammes for 480 millims., 38 for 310, 25 for 200, and 

 12 for 100. If we make the quotients of these forces by the 

 half-lengths /, we find : — 



Length 21. 480. 400. 310. 250. 200. 100. 



F 54-0 44-1 37-8 31'5 25-0 12-5 



y = F 0-225 0-220 0-244 0-252 0-250 0-250 



The first two quotients are a little too low^ because the num- 

 bers of the plates were not sufficient to give the exact limit of F ; 

 all the others are equal. We shall thence conclude that the se- 

 parating-force F, at the extremity of a normal pile is exactly 

 proportional to its length — which is expressed by the formula 

 F, = /c 2 /. 



If I vary, kH will be represented by a right line Ac, making 

 with the #-axis an angle of which the tangent is k 2 , — /c 2 varying 

 doubtless with the thickness of the plates, but remaining con- 

 stant when that thickness is invariable. 



V. We have previously found that, for a given plate of length 

 2/, F varies with the distance to the centre according to the law 

 F=A# 2 . If sc=I 3 we have F;=AZ 2 , from which we deduce 



7,2 



F,=A/ 2 =& 2 /, A=y; 

 and consequently the general equation becomes 



f=j* 2 (i) 



When the pile terminates in B, the parabolic curve of the 

 values of F is A M C ; if it is limited to D, it is A N E. All 

 these parabolas are tangents at A to Ax } and pass through the 

 points of the straight line AE C which correspond to the differ- 

 ent lengths of the normal piles. In fine, the law of the separa- 

 ting-forces is expressed by means of a single coefficient k, which 

 depends solely on the thickness of the elementary plate and on 

 the kind of steel employed, the mean of /c 2 being equal to 0*240. 

 The values of F corresponding to the various plates, inserted in 

 the preceding Tables, were calculated according to the above 

 formula; sufficient accordance will be found between the ob- 

 served and the calculated numbers. 



VI. We shall assume, with Coulomb, that the separating-force 



2F2 



