50 



A POPULAR ACCOUNT 



plate of air, having previously passed 

 through a plate of glass. We are re- 

 quired to find the interval of the fits^when 

 the same ray enters the air obliquely to 

 its surface, as in the direction A P. 



With P as a centre, and P D as a 

 radius, let a semicircle CDC' be de- 

 scribed, and let C C' be considered as 

 the surface of the plate of air. Let P F 

 be the direction which the ray AP would 

 take, if it were refracted by passing from 

 air into glass. From F, draw F n per- 

 pendicular to C P. Continue the line 

 A P to the circle at E, and from E draw 

 E m perpendicular to C P. Divide the 

 interval mninio 107 equal parts, and 

 let o be the point of division nearest to 

 m. From o draw o p perpendicular to 

 C P, and meeting the circle in p. From 

 D draw D G, touching the circle at D, 

 and from P draw Pp, and continue it to 

 meet D G at T. Continue PD below 

 D, and take P H equal to P T. Through 

 H draw H K perpendicular to H P, and 

 continue P E until it meet it at I. Then 

 P I will be the interval of the fits of the 

 oblique ray, and P H will be the thick- 

 ness of a plate of air through which 

 the ray passes between two successive 

 fits. 



It appears from hence that the inter- 

 val of the fits of an oblique ray depends 

 on three things ; first, the angle of obli- 

 quity ; second, the refrangibility of the 

 light ; and third, on the refracting power 

 of the media which bound the thin trans- 

 parent plate through which the light 

 passes. The relation by which the in- 

 terval depends on these elements, ap- 

 pears complex in the preceding explana- 

 tion. This complexity is, however, only 

 apparent, and arises from the necessity 

 of throwing our account of it into a 

 popular form. Expressed in the lan- 

 guage of Trigonometry and Algebra, it 

 is sufficiently simple.* 



(67.) The manner in which Newton de- 

 duced this relation from observation of 

 the rings may easily be conceived, by 

 recurring to the method by which he 



* It is very doubtful, as Newton does not give the 

 details of his observations at great obliquities, and 

 as the making the observations with accuracy at 

 obliquities beyond 75 must be a matter of great 

 difficulty, whether the construction is to be depended 

 on; particularly as the observations, as far as from 

 to 75, agree sensibly with the simple formula, secant 

 < obliquity (or, if we use the figure in the text, P H, 

 instead of being equal to PT, will be equal to the 

 distance from P to the intersection of P E produced 

 with D T), This formula is consistent with the 

 theory of undulations. Biot does not say that he has 

 repeated these observations at great obliquities, and 

 found them to be correct. He Is evidently at a loss 

 to know how they were made. 



discovered the interval of the fits, when 

 the incident light was perpendicular. 

 In that case, the thickness of the plate 

 of air, which reflected the colour in each 

 ring, was found by measuring the dia- 

 meter of the ring. When he viewed 

 the rings obliquely, he found them en- 

 larged, and, consequently, the thickness 

 of the air at which the light was reflected 

 was increased. Its increased thickness 

 was computed in the same manner as 

 before, by measuring the diameter of 

 the ring. By a careful comparison of 

 the thickness thus deduced with the 

 thickness which reflected the same 

 colour perpendicularly, he discovered 

 the method already explained of finding 

 the magnitude PH by knowing PD and 

 the obliquity. The thickness at which 

 a given tint will be reflected at a given 

 obliquity being found, the interval of 

 the fits was easily discovered. In the 

 case where the ray penetrated the me- 

 dium perpendicularly, twice the thick- 

 ness of the air was equal to the length 

 of the course of the ray in passing 

 through it and returning, and this, there- 

 fore, was the interval of the fits. But 

 when the ray, as in the present case, 

 penetrates the air obliquely, the course 

 of the ray in passing through it and re- 

 turning is more than twice the thickness 

 of the air. Let PH (Jig. 48) be the 



Fig. 48. 

 P 



A. 



rr. 



thickness of the air, and let A H be the 

 ray entering, and H B emerging. The 

 lines AH and H B taken together, 

 form the course of the ray within the 

 plate of air. These lines, therefore, 

 taken together, or twice A H, is the in- 

 terval of the fits. 



In explaining the laws which govern 

 these phenomena, we have referred con- 

 stantly to a thin plate of air inclosed 

 between two surfaces of glass. The 

 presence of air, or any other material 

 agent, is not necessary for the produc- 

 tion of the effects. The lenses which 

 we have described (54) would exhibit 

 the same rings of colour if placed under 

 an exhausted receiver. All that is ne- 

 cessary to produce the phenomena is, 

 that two refracting surfaces should be 

 placed close together, so as to include 

 between a thin transparent space. In 

 passing the first surface the rays will be 



