Elements of natural philosophy (Volume 2-3) . milar series of partial reflections at eachsurface. Thus it will appear evident that the differentportions into which the waves have been separated mustgo through a length of route differing by the length ofthe interval between the glasses and the thickness ofthe glasses, or the different multiples of those whichthey have respectively traversed. They will, therefore,in general^ emerge after traversing routes which differby considerable quantities. Among these portions, however, there are two which,(if we abstract the very small difference in the in
Elements of natural philosophy (Volume 2-3) . milar series of partial reflections at eachsurface. Thus it will appear evident that the differentportions into which the waves have been separated mustgo through a length of route differing by the length ofthe interval between the glasses and the thickness ofthe glasses, or the different multiples of those whichthey have respectively traversed. They will, therefore,in general^ emerge after traversing routes which differby considerable quantities. Among these portions, however, there are two which,(if we abstract the very small difference in the in-terval between the glasses at the points where they re-spectively pass,) will have gone through different routesof precisely equal length. These two waves will be, 1st. One which passes di-rectly through the firstplate A i?, equal to £, andthrough the interval B C,equal to % between theplates, is then reflectedat C, in the first surfaceof the second plate, re-turns along CD, equal to?, and a thickness D E,equal to the first, or t\ Fig. ELEMENTS OF OPTICS. 291 at the first surface it is reflected again and passes the whole system EF + F G + GII, equal to 2 t + i\ 0r Explanation; upon the whole, it has travelled over 4 t + 2 i. 2d. Another portion proceeds directly through thewhole A B + B O + Cd, equal to 2 t + i, is reflected atd, in the last surface, retraces the distance de + ef,equal to t + i, is reflected at the second surface of the firstglass and pursuing the course f g + g h, equal to i + t,emerges after having, on the whole, passed through4 t + 2 /, or a route exactly equal in length to that ofthe former, neglecting, as before, the difference in i. It will be seen that out of all the possible combina-No other wavestions of different successive reflexions, these two are the™ ones which will give routes precisely equal; all theothers will differ by quantities amounting to some mul-tiple of t or i. If we now recur to the small differencein the interval
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