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XX. On the Theoretical Investigation of the Absolute Intensity of Interfering 

 Light. By The Rev. P. KELLAND, A.M., F.R.SS., Lond. and Edin., F.C.P.S., 

 Professor of Mathematics in the University of Edinburgh, late Fellow and 

 Tutor of Queen's College, Cambridge. 



(Read 4th April 1842.) 



THE subject of the following Memoir has been already touched on in a com- 

 munication which I made to the Cambridge Philosophical Society, and which ap- 

 pears in the seventh volume of their Transactions, Art. IX. For the better un- 

 derstanding of what follows, it is desirable to state briefly the contents of that 

 paper. Its object is to estimate the quantity of light which is received on a screen 

 of unlimited dimensions, after passing through a certain aperture, or suffering 

 reflection at two mirrors, as in the case of the interference experiment, so as to 

 exhibit the appearance of bands. The question to be answered is this : Does in- 

 terference restore light or increase it, as it seems to do in the case of a grating 

 placed before a lens, whereby, instead of one, a number of luminous images are 

 produced ? Or does it destroy light, as it seems to do in the case of interference 

 by the reflection of two portions of a ray at different surfaces inclined to one an- 

 other, where, instead of an uniformly bright field, at least near its centre, the eye 

 is presented with a series of dark bands ? The subject is treated by taking the 

 ordinary expression for the intensity of light at any point of a screen placed in 

 the focus of a lens on which the light falls, and, by integration, determining the 

 whole intensity, or the total quantity of light which falls on the screen. The con- 

 clusions deduced from this process are, 1. That when an aperture is placed be- 

 fore the lens, the total intensity of the light which passes to the screen varies as 

 the magnitude of the aperture. 2. That when a grating is placed before it, the 

 total intensity of the light received on the screen is to the quantity which falls on 

 the grating, as the space left open by the wires to the whole space on which the 

 light falls. 3. That when light falls on two mirrors, inclined by a small angle to 

 each other, the whole quantity of light received on the screen is equal to the 

 quantities which would be received from each of the mirrors separately. These 

 results all concur in the establishing of the following answer to our question. 

 The effect of interference, whether produced by diffraction or admixture, is to dis- 

 place, but neither to destroy nor to produce light. The total quantity of light which 



VOL. XV. PAET II. 4 Q 



