Less with the view of dwelling upon the phenomenon itself than of introducing it in a form which will render subsequently intelligible to you the play of theoretic thought in Newton’s mind, the fact of refraction may be here demonstrated.  I will not do this by drawing the course of the beam with chalk on a black board, but by causing it to mark its own white track before you.  A shallow circular vessel (RIG, fig. 4), half filled with water, rendered slightly turbid by the admixture of a little milk, or the precipitation of a little mastic, is placed with its glass front vertical.  By means of a small plane reflector (M), and through a slit (I) in the hoop surrounding the vessel, a beam of light is admitted in any required direction.  It impinges upon the water (at O), enters it, and tracks itself through the liquid in a sharp bright band (O G).  Meanwhile the beam passes unseen through the air above the water, for the air is not competent to scatter the light.  A puff of smoke into this space at once reveals the track of the incident-beam.  If the incidence be vertical, the beam is unrefracted.  If oblique, its refraction at the common surface of air and water (at O) is rendered clearly visible.  It is also seen that reflection (along O R) accompanies refraction, the beam dividing itself at the point of incidence into a refracted and a reflected portion.[4]

[Illustration:  Fig. 4.]

The law by which Snell connected together all the measurements executed up to his time, is this:  Let A B C D (fig. 5) represent the outline of our circular vessel, A C being the water-line.  When the beam is incident along B E, which is perpendicular to A C, there is no refraction.  When it is incident along m E, there is refraction:  it is bent at E and strikes the circle at n.  When it is incident along m’ E there is also refraction at E, the beam striking the point n’.  From the ends of the two incident beams, let the perpendiculars m o, m’ o’ be drawn upon B D, and from the ends of the refracted beams let the perpendiculars p n, p’ n’ be also drawn.  Measure the lengths of o m and of p n, and divide the one by the other.  You obtain a certain quotient.  In like manner divide m’ o’ by the corresponding perpendicular p’ n’; you obtain precisely the same quotient.  Snell, in fact, found this quotient to be a constant quantity for each particular substance, though it varied in amount from one substance to another.  He called the quotient the index of refraction.

[Illustration Fig. 5]