339 



insensible or almost infinitely small interval of time separating them ; for 

 otherwise they would neutralize each other at the moments of break of 

 contact of the original helix connecting the electrodes of the battery. 



To Dr. Callan we must all feel deeply indebted for the amount of 

 labour, care, and intelligence he has devoted to chemical electricity, and 

 its extension to the induced electric helix. We must congratulate him, 

 also, on the great success which has attended his improvements and mo- 

 difications of galvano-electric instruments ; which have, by economizing 

 their production, brought them within the means of many experimenta- 

 lists who, otherwise, could not expect to use or get access to such instru- 

 ments ; and, finally, we may hope that he will continue his exertions, 

 and his liberality in allowing scientific and curious people to see his 

 great instruments in action — a favour which has led me to make this 

 communication, in the hope that it may call more attention to the sub- 

 ject of induced electric action, on the great scale realized by Dr. Callan' s 

 iron helixes and galvanic batteries. 



Mr. John Ptjeseh, Jun., M. A., read the following paper : — 

 Oi^ THE Application^ of Corioli's Equations of Eelative Movement 



TO THE P£,0BLEM: OP THE GyEOSCOPE. 



In treating the problem of determining the apparent^' motion of Fou- 

 cault's gyroscope, difi'erent methods have been adopted. f Probably the 

 most satisfactory is that of deducing the equations from the consideration 

 of Corioli' s ' ^ forces fictives' ' in relative motion. Corioli has shown that if 

 the co-ordinate axes to which the movement of a system is referred are 

 not fixed, but have a motion of their own in space, we may treat the 

 question in all respects precisely as if these axes were fixed, provided we 

 suppose superadded to the force (P) which acts upon any molecule 

 two others, the first a force (P^ equal and opposite to that which would 

 impress on the molecule accelerations equal to those of a point coincid- 

 ing at the instant with the molecule, but invariably connected with the 

 moving axes — the second force {P") perpendicular to the relative path of 

 the molecule. Into the value or direction of this last it is unnecessary 

 for the present purpose to enter more particularly. J 



* By apparent motion, here and afterwards, is meant the motion that would be ap- 

 parent to a spectator on the earth's surface — that is, the motion with respect to co-ordi- 

 nate axes invariably connected with the earth ; by absolute motion, the motion with 

 respect to axes whose direction is fixed in space. 



t This is the course taken by M. Quet, in a memoir that appeared on the subject of 

 relative motion, in Liouville's Journal. My apology for reopening the question is, that 

 in that paper the author seems to me to have needlessly complicated the problem by an 

 assumption which, at first sight, appears calculated to simplify it. This will be explained 

 in the sequel. 



X For the deduction of the expressions for these forces in magnitude and direction, 

 see " Duhamel, Cours de Mecanique," or Corioli's original papers in the "Journal de 

 I'Ecole Poly technique." 



