VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 325 



The only new analogy, and doubtless a very important one, discovered by Mr. 

 B., among these 3 classes of phenomena, is that which results from the harmonic 

 relations among the distinct parts of the coloured spectrums, produced by refrac- 

 tion, reflexion, and flexion. Can the spectrum by reflexion be calculated exactly, 

 on the principles above laid down, in order to compare the result of this calculation 

 with experiment ? Its harmonic division is a relation detected between this pheno- 

 menon and that of refraction, which strengthens the opinion, already so probable, 

 on the identity of the principle on which these 2 phenomena depend. I dare not 

 go farther. 



In weighing these considerations, we shall recollect the proposition advanced by 

 Mr. B. viz. that " the reflexibility of the rays is inversely as their refrangibility." 

 But we must observe the sense of this assertion. Newton made a ray to pass 

 out of glass into air, by the plane face of a prism, under a known angle of inci- 

 dence; and having observed the angle of refraction of the red and the violet rays, 

 he found these angles and their sines as below: 



Common angle of incidence 31° 15' 0" sine 50 



Angle of refraction of the red 53 4 58 77 



Angle of refraction of the violet 54 5 2 78 



Mr. B. made a ray to fall on the convexity of a metallic fibre, in an unknown 

 angle of incidence; and having observed the reflexion, he concluded the following 

 angles and sines: 



Angle of common incidence 77" 20' sine 77 \ 



Angle of reflexion of the red 75 50 77 



Angle of reflexion of the violet 78 51 78 



Here we indeed see, that the numbers 77 and 78 expressed in both places, are the 

 limits, in the one case of refraction, in the other of reflexion; but we cannot 

 conclude the inverse ratio of the quantities measured in the observation of these 2 

 phenomena: the disparity of circumstances in these 2 experiments opposing it. 

 Mr. B. himself remarks the difference of incidence. But this is not the only one; 

 and it is sufficient to recollect that, by the same incidence, the dispersion of the 

 coloured rays varies according to the nature of the mediums, to destroy all idea of 

 regular proportion, expressed in a precise and general manner, without regard to 

 the diversity of mediums. The prop, asserted by Mr. B. then only means, that those 

 rays which occupy the most space on the refracted spectrum, occupy less on the re- 

 flected one; and that both show the harmonic division. This is sufficient indeed to in- 

 dicate some analogy, but not to found, without some other proof, the unity of principle. 

 It is in the same sense the prop, must be understood which establishes that " the 

 flexibilities are as the reflexibilities directly, and as the refrangibilities inversely." 

 And there is still much more disparity in the circumstances and in the results, as 

 Mr. B. has taken care to remark. Thus, the harmonic division of the coloured 

 spectrum furnishes an analogy still much weaker, in favour of the identity of a 

 common principle, to which these 3 phenomena must be related. And yet it must 



