7 
relative to physical Optics. 
for the interval appropriate to the disappearance of the brightest 
light; and it may be inferred, that if they had been wholly 
exempted from its effects, the measure would have been some- 
what smaller. Now the analogous interval, deduced from the 
experiments of Newton on thin plates, is .0000112, which is 
about one-eighth less than the former result ; and this appears 
to be a coincidence fully sufficient to authorise us to attribute 
these two classes of phenomena to the same cause. It is very 
easily shown, with respect to the colours of thin plates, that 
each kind of light disappears and reappears, where the diffe- 
rences of the routes of two of its portions are in arithmetical 
progression ; and we have seen, that the same law may be in 
general inferred from the phenomena of diffracted light, even 
independently of the analogy. 
The distribution of the colours is also so similar in both cases, 
as to point immediately to a similarity in the causes. In the 
thirteenth observation of the second part of the first book, 
Newton relates, that the interval of the glasses 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 observation of 
the third book, that the distances between the fringes, under the 
same circumstances, were the 22d and 27th of an inch. Hence, 
deducting the breadth of the hair, and taking the squares, in 
order to find the relation of the difference of the routes, we have 
the proportion of 14 to 9^, which scarcely differs from the pro- 
portion observed in the colours of the thin plate. 
We may readily determine, from this general principle, the 
form of the crested fringes of Grimaldi, already described ; for 
it will appear that, under the circumstances of the experiment 
related, the points in which the differences of the lengths of the 
