TO THE THEORY OF ELECTRICITY. 81 



which, in order that our solution may be applicable, must not 

 be less than ft, and consequently the angle </> OT O must be 

 between and TT : when this is the case, OT is immediately de- 

 termined from < by what has preceded. In fact, by finding the 

 value of II from the initial values -ST O and < , and making 

 ?= i?r + iy + i*r 10, we obtain 



?-. 



n ^- e ( 



f being the initial value of f. 



We have, in the latter part of this article, considered the 

 body A at rest, and the line X', parallel to the direction of 5, 

 as revolving round it : but if, as in the former, we now suppose 

 this line immovable and the body to turn the contrary way, so that 

 the relative motion of X' to X may remain unaltered, the electric 

 state of the body referred to the axes X, F, Z, evidently de- 

 pending on this relative motion only, will consequently remain 

 the same as before. In order to determine it on the supposition 

 just made, let X' be the axis of x, one of the co-ordinates of p, 

 referred to the rectangular axes JT', F', Z, also y, z, the other 

 two ; the direction X' F', being that in which A revolves. 

 Then, if w' be the angle the system of lines L, L\ &c. forms 

 with the plane (x\ z), we shall have 



</>, as before stated, being the angle included by the axes X, X'. 

 Moreover the general values of V and will be 



V= ft (x cos m' -I- y' sin ') and ?= J7r + iy - Jr', 



and the initial condition, in order that our solution may be ap- 

 plicable, will evidently become c OT O = r' = a quantity be- 

 twixt and TT. 



As an example, let tan 7 = , since we know by experiment 



that y is generally very small ; then taking the most unfavour- 

 able case, viz. where VT^ = 0, and supposing the body to make 

 one revolution only, the value of determined from its initial 

 one, 5J> = JTT + Jy JOT'^ will be found extremely small and only 



6 



