290 



KEPORT — 1879. 



In this way the following results were obtained for condenser B (corrected for 

 absorption) :■ — 



Omitting the first value, as 5 seconds is too small a period to be measured 

 accurately by ear, the mean capacity of condenser B becomes 0-3211. 



Without assistance I was unable to repeat with the same accuracy the experi- 

 ments with condenser A. There was much less absorption with this condenser, 

 but greater leakage, owing, I believe, to the surface of the ebonite a good deal. 

 The mean of all values gave for A the capacity 0-332 mfds. 



If, therefore, the capacity of A is defined as the apparent capacity, deter- 

 mined by the throw of a galvanometer with a period of between 3 and, say, 15 

 seconds, I think the value 0-331 mfds. will be correct to the last figure. 



10. On an Electrical Gyrostat. By Professor G. Forbes, F.R.S.E. 



11. On the Condition ivhich must be fulfilled by any number of Forces 

 directed toivards Fixed, or Movable, Centres, in order that any given 

 curve should be described freely by a particle acted on by these Forces 

 simultaneously ; and an analogous Problem. By Arthur Hill Curtis, 

 LL.D. 



I. When a particle describes a curve freely under the action of any number 

 of forces the equations of motion can be reduced to the two foollowing : — 



zr^Fj ^ + F 2 -^ + &c. . 

 vdv = - (Fj dr x + F 2 dr 2 + &c.) 



orj) ! = jFs,*=-2F dr, 



(1) 

 (2) 



F 1( F 2 , &c, being forces acting along 



r,, n, 



&c, and tending to diminish them, 



while c v c 2 , &c, are the chords of curvature coinciding in direction with these 

 lines respectively, and dr v dr v &c, are the projections on them of the element of 

 the curvilinear path of the particle. 



From the above equations the following equation results : — 



;^F(dc + 4:d}-)+cdF^ =o, 



(3) 



but, if <f) v <f> 2 , &c, denote the forces respectively codirectional with F 1( F 2 , under 

 which singly the given curve would be described, we must have, as particular 

 cases of (3), <p x {d^ + 4 dj\) + c d<p 1 = o ) cp 2 (dc 2 + 4dr 2 ) + c 3 dcj) 2 = o ) &c, &c. 



