/*36 PHILOSOPHICAL TRANSACTIONS. [aNNO I/QQ, 



the rays by reflection ? Tliis is what has always hindered us from even suspect- 

 ing such a thing as different reflexibility. I shall however take an opportunity 

 of removing this obstacle, in the 2d part of the plan, when I come to explain 

 the reason of the colours made by the reflecting body, and the manner of their 

 formation. At present I shall only caution those who may wish to repeat the 

 above experiments, that the hole in the window-shut must be small, the room 

 quite dark, the pin well polished, and the desk, chart, &c. placed at a distance 

 from the pin not greater than 3 feet, otherwise the images will be dilute and dim; 

 nor, on the other hand, less than 6 inches, otherwise they will be too short, and 

 the colours not far enough separated from each other. 



My next object of inquiry was the different degrees of reflexibility belonging 

 to each ray. It appears, not only from mathematical considerations sufficiently 

 obvious, but also from the experiments I have related, that though the different 

 rays have at the same or equal incidences different angles of reflection, yet each 

 ray is constant to itself in degree of reflexibility, and that its sine of reflection 

 bears always the same ratio to its sine of incidence. The question then is, what 

 are the sines of reflection of the different rays, the sine of incidence being the 

 same to all ? 



Obs. Q. In summer, at noon, when the sun's light was exceedingly strong, and 

 there was not the vestige of a cloud in the sky, I produced an uncommonly 

 fine set of images, by fixing at an inch from the small hole, ^i- of an inch dia- 

 meter, a pin -^ of an inch diameter. One of the brightest of these I let pass 

 through the desk to the chart below at 2-1- feet from the pin, and the image was 

 3 inches from the shadow in a straight line. I delineated it carefully, by draw- 

 ing two parallel lines for the sides, and marking the semi-circular ends. Then 

 with the point of a small needle I marked the confines of the contiguous colours 

 on one of the parallel sides, and afterwards drew across the image parallel lines; 

 this operation I repeated wiih the same and different images, at many distances 

 from the pin, and on different days, with various kinds of pins, and sizes of 

 holes, &c. &c. and all these repetitions were made before I once examined the 

 result of any one measurement, that I might be unprejudiced in trying the 

 thing over again. I then compared the sketches of divided images, which I 

 thus obtained, and found sufficient reason to conclude, that the differences be- 

 tween the sines of reflexion in the different rays were in the harmonical order. 

 For the divisions were nearly as -^ ; -^ ; -V ". tV ; -rV ; ttV* tV 5 which, when 

 compounded with the scale, give 1, ii, -f«y, i, h -?-, +i, 4- ; and these are exactly 

 the change of the notes in an octave, obtained by taking the sums of the octave, 

 and a 2d major, a 3d major, a 4th, a 5th, a 6th major, a 7th major, and an 8th, 

 instead of the difference between a double octave, and a 2(1 major, a 3d major, 

 and so on. Thus the spectrum by reflection is divided exactly as the spectrum 



