REPORT ON PHYSICAL OPTICS. 303 



spire, or be opposed ; so that in the case of two such disturb- 

 ances, for example, the second may have the effect either of aug- 

 menting or diminishing the first, and the absolute velocity of the 

 ethereal molecules may be increased, or lessened, or even wholly 

 destroyed by the union. In fact, if the form of the function 

 which expresses the wave-disturbance, be assumed to be that 

 by which the law of vibration of the cycloidal pendulum is re- 

 presented, the sum of two coexisting disturbances will be a sin- 

 gle disturbance of the same form, provided the component un- 

 dulations have the same length ; and the effect of two such co- 

 existing undulations will be a single undulation of the same 

 length, but differing in the position and magnitude of the space 

 of greatest vibration from either of the components. The mag- 

 nitude of the resulting vibration may be the sum, or difference 

 of those of the component vibrations, or it may have any value 

 intermediate to these limits. When the component vibrations 

 are equal, the resultant may even vanish altogether ; and two 

 lights of equal intensity when added together will produce 

 darkness, provided that the interval of retardation of one wave 

 on the other is an odd multiple of the length of half a wave. 



This important con sequence of the theory of waves — the princi- 

 ple of interference of the rays of light — was first distinctly stated 

 and established by Dr. Thomas Young, although some of the 

 facts bj'^ which its truth is experimentally confirmed were known 

 to Gi'imaldi*. The genei-al calculation of the intensity of the 

 resulting light, for any relative position of the interfering waves, 

 is due to Fresnel ; and has been followed out and developed by 

 Sir John Herschel in his valuable Essay on Light. When a 

 beam of homogeneous light is transmitted through two small 

 apertures in a card, or plate of metal, the light will diverge from 

 each as from a new centre. If the two apertures are close toge- 

 ther, and the diverging pencils received on a reflecting surface, 

 a series of parallel straight bands is observed, perpendicular to 

 the line connecting the apertures, and separated by intervals 

 absolutely dark. That these alternations of light and darkness 

 are produced by the mutual action of the two pencils. Young 

 proved by the fact, that when one of the beams is intercepted, 

 the whole system of fringes instantly disappears, and the dark 

 intervals recover their former brightness. 



The experiment of Fresnel is still more satisfactory. In this 

 important and instructive experiment, the fact of interference is 

 placed beyond all question. The two pencils proceed from one 



• This ingenious philosopher even stated explicitly that an illuminated body 

 may be rendered darker by the addition of light, and adduced a simple experi- 

 ment in proof of it. Physico-Mathesis de Liimine. Bologna, 1663. 



