Lifting Poioer of the Electro-Magnet. 523 



K in this we consider d and z as variables, /i a function oi z, and differentiate 

 for the maximum, we obtain the equations, 



= (P (d + c) — az, 

 zdfi(^ az } (16) 



Substituting, in the second, for az its value in (16), 



zdfx ( , d } ' , , „ 



When z is determined by any particular condition, (16) gives the most 

 advantageous diameter of wire, and vice versa. 



If it be not, and if the relation between it and /u be known, the two equa- 

 tions give the d and z for the absolute maximum. In the case of my magnet 

 (when 6' =3, J = 1-13) Nos. 55, 58, 60, 61, 65, and 28, give the means of ex- 

 pressing that relation by an interpolation formula, A — Bz+Cz^ — Dz^. Sup- 

 posing the battery to consist often Groves' such as I use, ii=47, with these 

 I obtain 



ir = 8-39, 



(/= 0'14725, or nearly No. 9 of the wire gauge, 

 5 = 999, 

 ^f =2780-29. 



A much higher power, however, would be obtained if the ten cells were 

 grouped as five double cells, and the helices made to suit this condition. In 

 this case i? = 11-75 ; and we find for the best an-angement, 



2 = 8-33, 



f/= 0-2106, a little more than No. 6, 

 s = 538-18, 

 juT^= 3549-60. 



5. I suppose the current to traverse the helices consecutively ; but they are 

 frequently used collaterally with the notion of obtaining a more powerful cur- 

 rent. This is not to be recommended in ordinary cases. If the numbers of 

 the spires be s' and s", and their resistances p and />", 



VOL. XXII. 3 Y 



