To explain then the reasons of these phenomena according to our principles, let ab be the straight line which represents a plane surface bounding the transparent substances which lie towards C and towards N. When I say plane, that does not signify a perfect evenness, but such as has been understood in treating of reflexion, and for the same reason.  Let the line AC represent a portion of a wave of light, the centre of which is supposed so distant that this portion may be considered as a straight line.  The piece C, then, of the wave AC, will in a certain space of time have advanced as far as the plane ab following the straight line CB, which may be imagined as coming from the luminous centre, and which consequently will cut AC at right angles.  Now in the same time the piece A would have come to G along the straight line AG, equal and parallel to CB; and all the portion of wave AC would be at GB if the matter of the transparent body transmitted the movement of the wave as quickly as the matter of the Ether.  But let us suppose that it transmits this movement less quickly, by one-third, for instance.  Movement will then be spread from the point A, in the matter of the transparent body through a distance equal to two-thirds of CB, making its own particular spherical wave according to what has been said before.  This wave is then represented by the circumference SNR, the centre of which is A, and its semi-diameter equal to two-thirds of CB.  Then if one considers in order the other pieces H of the wave AC, it appears that in the same time that the piece C reaches B they will not only have arrived at the surface ab along the straight lines HK parallel to CB, but that, in addition, they will have generated in the diaphanous substance from the centres K, partial waves, represented here by circumferences the semi-diameters of which are equal to two-thirds of the lines km, that is to say, to two-thirds of the prolongations of HK down to the straight line BG; for these semi-diameters would have been equal to entire lengths of km if the two transparent substances had been of the same penetrability.

Now all these circumferences have for a common tangent the straight line BN; namely the same line which is drawn as a tangent from the point B to the circumference SNR which we considered first.  For it is easy to see that all the other circumferences will touch the same BN, from B up to the point of contact N, which is the same point where an falls perpendicularly on BN.

It is then BN, which is formed by small arcs of these circumferences, which terminates the movement that the wave AC has communicated within the transparent body, and where this movement occurs in much greater amount than anywhere else.  And for that reason this line, in accordance with what has been said more than once, is the propagation of the wave AC at the moment when its piece C has reached B. For there is no other line below the plane ab which is, like