Lifting Power of the Electro-Magnet. 



529 



by a factor decreasing as L or -f increases. Admitting a limit o^ L = A, the 

 most obvious form of this factor is J. — i, which would give — 



dL _d^ 



L X {A - L) ~ 'bir'' 

 integrating which — 



A-L 



= Kx^\ 



A 



Trying this by the numbers of Table xii., I found for -j- 0-9918, so near 



unity that b may be taken = A, and the equation becomes finally — 



Ay.^ 



L = 



£ + ir- 



(18) 



B being the t^ which will give half yl, a quantity which, as I formerly re- 

 marked, seems to have some marked properties, among which are that A is 

 constant for every -^ which is greater than it, and that for all below it the L 

 is not the same for direct and reverse currents if there be any permanent mag- 

 netism. The formula supposes L to vanish with i^; and, therefore, only ap- 

 plies to the higher portion of the series. Perhaps it may be a residual portion 

 of the true formula ; but at all events it represents so much, that its constants 

 appear to have a real physical significance, and I therefore give them in — 



Table XXXV. 



Of these the first represents the first 10 of Table xxx., No. 155 being 

 omitted, because in it the excitement appears to have been too weak to bring 



