338 The Astronomer Royal on the Bands formed by the 



on the one hand) and the extent of the spectrum and the thick- 

 ness of the retarding -plate on the other hand, dominates over 

 all the succeeding deductions. The expression in page 9, line 



2 X e 

 16, "the interval between the bands is —7—," is subject to 



this limitation. In a word, I have stated what is the law of 

 variation of the breadth of the bands lichen the aperture of the 

 eye is varied, and when the extent of spectrum, $c. receives a 

 corresponding variation, so as to preserve the condition of page 

 8 line 20 : but I have not stated what is the law of variation 

 of the breadth of the bands when the aperture of the eye is 

 varied without varying other parts of the experimental arrange- 

 ment. This latter limited variation was the variation made in 

 Prof. Powell's experiments, and therefore my expression does 

 not apply to these experiments. 



i will now proceed to investigate expressions which will 

 apply to Prof. Powell's experiments. 



For this purpose I beg to refer to the diagram in page 10 

 (remarking that the numerical values of the ordinates are to 

 be found in the table of page 4), which represents the differ- 

 ent degrees of intensity of light in the successive slightly dif- 

 fused images formed by the light coming from successive por- 

 tions of the spectrum, when viewed under the conditions of 

 this experiment. And I must request the reader to remember 

 that the effect of viewing a spectrum (as distinguished from a 

 collection of all the various qualities of light in one point) is, 

 that supposing the first curve to remain in its place, the second 

 curve will be drawn back by a certain quantity C, the third 

 by 2 C, the fourth by 3 C, and so on ; and that in order to 

 obtain the expression for the intensity of the light received by 

 the eye, the ordinates which are then in the same vertical line 

 must be added together. This quantity C is absolutely con- 

 stant while the extent of spectrum and thickness of retarding 

 plate are constant, and does not in any degree depend on the 

 aperture of the eye. 



Then it must be remarked that the effect of enlarging the 

 aperture of the eye is to diminish the horizontal extent of 

 each of the curves in the same proportion, leaving the centre 

 of each in the place defined by the movement which I have 

 just mentioned ; and that the effect of diminishing the aperture 

 of the eye is to enlarge the horizontal extent of each of the 

 curves in the same proportion, leaving the centre of each in 

 the place as above defined. 



Suppose, then, that the quantity C is equal to three inter- 

 vals of ordinates, as at present marked in the diagram of page 

 10. Then if, in a change of experiment, the aperture of the 



