log/, 



507 



&c. 



Lifting Power of the Electro- Magnet. 



sufficiently exact, and easier for computation than their true values, 



In practice I found it best to take a; = — 4 and + 5. 



Having obtained the sum of any number of the terms Q, the sums of the 

 preceding terras are successively obtained by the factors already given, and the 

 multiplication must be continued till the products are certainly of an order that 

 may be neglected. 



If the sum of all these integrals = S\ 



M= f^ xS'.z = uFA X beS', 

 tan e 



and as = 27r X number of spires in helix (=s), 



M = f,FAx27rbS'. (10) 



The computation of iS' is much facilitated by the terms Q containing only 

 the inverse first power of m as a factor, so that when their sum is once got for 

 any values of z, it is known for any other with a given b. The terms derived 

 from Q are similarly computed in sum. 



I have tabulated a few values of it, which will suffice to make an approxi- 

 mate comparison of this theory with observation. 



Table II. 



For any point within or without the helix, 



S'z'±S"z" 



S = ' 



z' + z" ■ 



It is useless to pursue the analytic part of the inquiry further at present, 

 because the distribution of the magnetism excited by the spires in a closed cir- 

 cuit (which is quite a different problem from that of a magnetic bar) depends 



VOL. XXII. 3 u 



