Spteeial Epochs in Vibrating Systems. 511 



instance, if a coil is given of small inductance, its ohmic 

 resistance is first measured. It is then joined in series with 

 the coil o£ considerably larger inductance, and the inductance 

 of the two coils together measured as above described. The 

 larger inductance is then determined separately, and the 

 small inductance becomes known by the difference. In this 

 manner it is possible to determine with very fair accuracy 

 the inductance of quite small coils of wire. 



In conclusion we have pleasure in mentioning the assistance 

 rendered to us in portions of this work by Dr. G. A. Hemsa- 

 lech, who devoted a considerable amount of time to the 

 experimental work at one stage of the investigation. 



LII. Note on the Special Epochs in Vibrating Systems. By 

 James W. Peck, M.A., Lecturer in Physics in the Uni- 

 versity of Glasgow*. 



I~N a vibrating system there are two special states which 

 may occur, viz. : — '(1) The system may be at rest in all 

 its parts at the same instant ; (2) The system may be in its 

 undisturbed configuration at the same instant in all its parts. 

 If these states occur at all, they will recur periodically. In 

 what follows the conditions under which such special states 

 will occur are found. 



Call the time at which the system comes to rest simulta- 

 neously in all its parts the rest epoch ; and the time at which 

 the system, is passing through its undisturbed position in all 

 its parts the undisturbed epoch, both to be reckoned from the 

 initial time at which the system starts off with arbitrarily 

 given displacements and velocities. It will be shown that in 

 the general case when both the initial displacements and 

 velocities are completely arbitrary (consistent with the con- 

 ditions of the system) the two special epochs will not occur ; 

 but that by relating the system of initial displacements to the 

 system of initial velocities in a certain way the rest epochs 

 may be made to occur ; by relating them in another way the 

 undisturbed epochs may be made to occur ; and that the con- 

 dition which makes the one set of epochs possible makes the 

 other impossible, and vice versa. 



Take any continuous elastic system finite in one dimension 

 (length /) and fixed at both ends. The general equation of 

 its one-dimensional vibrations is 



d* 2 V x* ' U) 



where y is the displacement coordinate at the time / of the 

 * Communicated by Prof. A. Gray. 

 2 M 2 



