332 Mr. H. F. Talbot's Experiments on Light 



light from passing. Whence it is plain that intermediate posi- 

 tions may be found which give any precise degree of obscura- 

 tion that may be desired. 



The next step I took in pursuing this inquiry was to re- 

 verse the first experiment, of a luminous body in motion, by 

 viewing its image reflected from a revolving mirror. For in- 

 stance, the image of the sun was made to describe a portion 

 of a great circle of the heavens by causing the mirror to re- 

 volve round an axis properly situated. The moving image 

 thus produced a band of light half a degree broad, and if the 

 preceding reasoning is true, the intensity of light in the cen- 

 tral part of this band is diminished in the proportion of the 

 sun's diameter to 360°, that is, of 1 to 720. The band is 

 therefore, in its central part, 720 times fainter than the sun's 

 image at rest, (reflected from the same mirror,) and towards its 

 borders it is gradually fainter. But as the light will still be 

 too bright for comparison with terrestrial flames, it must be 

 diminished further by a second operation of the same kind. 

 And this may be done in various ways. The most simple 

 seems to be to employ a screen having an aperture through 

 which a small portion of the band only can be seen, for in- 

 stance, half a degree of its length, and then treating this se- 

 parated portion as a new luminary. By help of a second re- 

 volving mirror it may be again weakened 720 times, so that 

 the effect on the eye is then diminished a number of times ex- 

 pressed by the square of 720, or about half a million, great 

 care being, however, necessary in this second experiment as 

 to the position of the observer's eye*. For a photometrical 

 comparison of objects which are exceedingly unequal in 



* As this seems liable to error, except when the second mirror is so 

 distant from the screen that all its parts may be considered equidistant 

 from it, the following method may be preferable, though it involves some 

 mathematical calculation. It has been already remarked, that the sides of 

 the luminous band or zone are fainter than its central part ; because the 

 image of the sun's disk takes a shorter time to traverse any point in that 

 zone the more distant it is from the central line. This want of uniformity 

 requires that we should determine what is the average brightness of the 

 zone ; and this resolves itself into the mathematical problem, " What is 

 the average value of all the chords of a circle, supposing an infinite num- 

 ber of them to be drawn infinitely near to each other (but equidistant)? 

 And the answer given to this question by the integral calculus is, that the 

 average line is equal in length to the quadrantal arc of the circle. This 

 arc bears to the diameter the ratio of 785 to 1000 nearly, therefore the 



78 5 



average brightness of the zone is only of the brightness of its central 



part. 



Now, if by help of a second revolving mirror, we cause the image of this 

 zone to move in a direction perpendicular to its length, it will be expanded 



