164 PROFESSOR KELLAND, ON THE 



The common assumption, that the intensity is measured by the square 

 of the excursion of a vibrating particle, although bearing a great air of 

 probability, is still not so obvious as to derive no benefit from a confir- 

 mation such as our conclusions tend to give it. 



The hypothesis respecting the intensity of vibrations in different di- 

 rections, and at different distances, as stated by Mr Airy, is this: that 

 a vibrating particle transmits vibrations equally in all directions, but with 

 an intensity varying inversely as the distance. This hypothesis is not alto- 

 gether conformable to our conclusion, which appears to require that vibra- 

 tions transmit forces equally in all directions, and to all distances. Fortu- 

 nately, none of the approximate results deduced from either hypothesis 

 are vitiated by it, since the variation of distance is not taken into consi- 

 deration in the solution. Of course, these observations are based on the 

 supposition, that the division of a complete wave into elementary portions, 

 in the manner always employed to effect the exhibition of results dedu- 

 cible from a change of circumstances in the mode of transmission, is 

 allowable. My object, at present, being rather the demonstration of a pro- 

 perty of undulations, than an application to the theory either of light or 

 heat, I have contented myself with alluding to the bearings of the result 

 to which we have arrived. What has been said will be confirmed by the 

 following problem, with which the preceding is intimately connected. 



" The whole intensity of light reflected at the surfaces of two plane 

 mirrors, inclined to each other at any angle, is not altered by the interference 

 of the light from the one mirror with that reflected from the other." 



■»■ 



To this problem we shall annex the same limitations, and apply the 

 same processes as to that already solved. That is to say, we shall conceive a 

 lens placed before the mirrors, so as to bring the reflected light to two foci 

 lying in a line perpendicular to that which bisects the angle between the 

 mirrors. 



Let C be the projection of the line of intersection of the mirrors ; O, P, 

 the foci to which the rays from the mirrors respectively converge. Then 

 each wave on leaving the lens will be a portion of a sphere, of which the 

 centre is the point of convergence. 



