13^ PHYSICAL OPTICS, 



Comparifon of fringes nearcft it, to be fo contracted that the Tnotion of the 

 mc4urcs, light bounding the fliadow might be redlilinear, we fliould thus 



n^ake a fufficient compenfation for this deviation ; but it is dif- 

 ficult to point out what precife trad of the light would caufe 

 it to require this correftion. 



The mean of the three experiments which appear to have 

 been leaft affefled by this unknown deviation, gives ,0000127 

 for the interval appropriate to the difappearance of the brighteft 

 light ; and it may be inferred, that if they had been wholly 

 exempted from its e|Fe6ls, the meafure would have been fome- 

 vvhat fmaJler. Now the analogous interval, deduced from thes 

 experiments of Newton on thin plates, is .00001 12, which is 

 about one-eighth lefs than the former refult ; and this appears 

 to be a coincidence fully fufficient to authorife us to attribute 

 thefe two clafles of phenomena to the fame caufe. It is very 

 eafily (hown, with refpe€l to the colours of thin plates, that 

 each kind of light difappearsand reappears, where the dlffer- 

 , cnces of the routes of two of its portions are in arithmetical 



progreflion ; and we have feen, that the lame law may be in 

 general inferred from the phenomena of diffra^led light, even 

 independently of the analogy. 



The diflribution of the colours is alfo fo iimilar in both cafes, 

 as to point immediately to a firailarity in the caufes. In the 

 thirteenth obfervation of the fecond part of the firft book, 

 Newton relates, that the interval of the glaffes where the rings 

 appeared in red light, was to the interval where they appeared 

 in violet light, as 14 to 9 ; and, in the eleventh obfervation of 

 the third book, that the diflances between the fringes, under the 

 fame circumftances, were the22d and 27th of an inch. Hence, 

 dedu6ling the breadth of the hair, and taking the fquares, in 

 order to find the relation of the difference of the routes, we have 

 the proportion of 14 to 9^, which fcarcely differs from the pro- 

 portion obferved in die colours of the thin plate. 



We may readily determine, from this general principle, the 

 form of the crefted fringes of Grimaldi, already defcribed ; for 

 it will appear that, under the circumftances of the experiment 

 related, the points in which the diiferences of the lengths of the 

 paths defcribed by the two portions of light are equal toacon- 

 ilant quantity, and in which, therefore, the fame kinds of light 

 ought to appear or difappear, are always found in equilateral 

 hyperbolas, of which the axes coincide with the outlines of the 



ihadow. 



