384 



Transactions of the Society. 



theless only imperfectly attuned. The effect which they will produce 

 may be determined by considering them as equal concurrent forces 

 coinciding at a point in space and inclined at angles proportionate to 

 their differences of phase. This method of solution leads to the 

 construction of a polygon of forces ; and if we consider the total impulse 

 from each eighth as a single force, we shall evidently obtain the figure 

 88 in which the three equal sides represent the three equal impulses, 

 and the common angle of inclination of these sides to one another is 



2tt 



equal to ^~, the proportion which their common difference of phase 

 bears to a complete wave oscillation. The fourth side will, on this 



Fig. 88. 



Fig. Sf>. 



hypothesis, represent in length the amplitude of the resulting wave 

 at the point p 2 and in direction its relative phase. This would give 

 us an approximation to the true result ; but as the impulses actually 

 received are not sharply distinguished by marked differences of phase, 

 but pass into one another by imperceptible gradations, the true result 

 itself must be reached by substituting for the three sides of fig. 88 

 the corresponding arc of a circle of fig. 89, having the angular value 

 £ 2 ir. The chord of that arc will then represent in magnitude and 

 direction the amount of light received by the point in question, and 

 its phase relatively to the contemporaneous phase of the wave-front 

 from which the illumination is derived. From this it is easy to 

 calculate that the total effect of the impulses transmitted through 



