370 Prof. A. L. Clark on a Method of 



clamped at one end, and carrying a small mirror on the other 

 end, which is free to vibrate. This loop is suspended between 

 the poles of a magnet (electro or permanent), so that with 

 every change of direction of the current through this loop, it 

 will tend to rotate one way or the other according to Max- 

 well's rule, i. e. y " Every portion of the circuit is acted upon 

 by a force urging it in such a direction as to make it enclose 

 within its embrace the greatest possible number of lines of 

 force." 



Now if a beam of light falls on the mirror, the reflexion 

 will be drawn out into a line by the vibration of the mirror. 

 This beam of light coming from this mirror falls on a second 

 mirror, arranged as the first but actuated by another current 

 and with its plane of vibration perpendicular to that of the 

 first. In the resultant reflexion we find our means of mea- 

 suring the amount by which one mirror leads the other, or, in 

 other words, by how much the phase of the current in the first 

 leads that in the second. 



We will call the direction of vibration of the beam of 

 light as given by each mirror alone the axes of X and Y 

 respectively. That is, the axis of X is the figure from the 

 first mirror while the second is stationary, and the axis of Y 

 that from the second while the first is stationary. 



The equation of a simple harmonic motion of amplitude a 

 along the axis of X may be expressed 



x — a sin 0, 



where 6 is a linear function of the time. 



Also the equation of another harmonic motion of amplitude 

 b, along the axis of Y, whose time differs from 6 by an 

 amount </>, is 



?/ = 6sin (0 — <p>. 



Combining by eliminating 6 since 



sin 0= — , cos 6=. ~ \/a 2 —w* 

 a a 



the resulting equation is 



y — ~ {x cos (j) — s/d^—x 2 sin <j>) , 



an equation in x and y, independent of the periodic time. 

 This equation is the equation of an ellipse. The resultant 

 reflexion, then, is an ellipse whose shape depends upon a, b, 

 and ({>. 



