248 Mr. Brougham's Experiments and Observations on 
and small hole in it ; the rays passing through this, fell on a 
small pin, so placed that the images formed might be at right 
angles to the shadow; one of these I measured, together with 
its distance from the shadow, the distance of the shadow from 
the hole, the breadth of the shadow, and the diameter of the 
pin ; these measures were as follows. In fig. 7. C is the 
centre, and B en the circumference of the pin, GM the chart, 
and GD a line in it, being the axis of all the images, at right 
angles to CD, the distance of C from D the centre of the 
shadow, and also to the shadow itself ; GE is the parallel side 
of the image, G being red, E violet, and F the confine of the 
green and blue ; Ce is a radius parallel to ED, and CA ano- 
ther drawn through B, the point where OB is incident, at the 
angle OB A, to which (by what was before shown) ABF is 
equal. By measurement GE is ^th of an inch, CB g^th, 
CD 4^; now the shadow being lessened by a penumbra, this 
added to half the shadow, and their sum to the distance be- 
tween the penumbra and the violet, gave ED ^£th of an 
inch. From whence it is easy to calculate, that the angle of 
incidence being 77 0 20', the angle of the red’s reflection ABG 
is 75 0 50', and that of the violet's 78° 51'. Now the natural 
sines of 77 0 20', 75 0 50', and 78° 51', are as 9756, 9695, and 
9811 ; or as 250, 248, and 251 ; which are very nearly as 
77 2’ 77’ an d 78 ; and making an allowance for the omissions 
made in the reductions, the errors in the operations and mea- 
surements, they may be accounted as accurately in the above 
proportion. Now these extremes, 77 and 78, are the very 
proportions of the red's refrangibility to the violet's* So that 
the reflexibility of the red is to that of the violet as the re- 
* Optics, Book I. Parti. Prop. 7. 
