Polish of the Glass, and therefore I did not include it in these
Measures. Now the different Magnitude of the hole in the Window-shut,
and different thickness of the Prism where the Rays passed through it,
and different inclinations of the Prism to the Horizon, made no sensible
changes in the length of the Image. Neither did the different matter of
the Prisms make any: for in a Vessel made of polished Plates of Glass
cemented together in the shape of a Prism and filled with Water, there
is the like Success of the Experiment according to the quantity of the
Refraction. It is farther to be observed, that the Rays went on in right
Lines from the Prism to the Image, and therefore at their very going out
of the Prism had all that Inclination to one another from which the
length of the Image proceeded, that is, the Inclination of more than two
degrees and an half. And yet according to the Laws of Opticks vulgarly
received, they could not possibly be so much inclined to one another.[D]
For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
made therein through which a beam of the Sun's Light was transmitted
into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
the Prism is feigned to be cut transversely through the middle of the
Light. Or if you please, let ABC represent the Prism it self, looking
directly towards the Spectator's Eye with its nearer end: And let XY be
the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
two Rays, the first of which comes from the lower part of the Sun to the
higher part of the Image, and is refracted in the Prism at K and H, and
the latter comes from the higher part of the Sun to the lower part of
the Image, and is refracted at L and J. Since the Refractions on both
sides the Prism are equal to one another, that is, the Refraction at K
equal to the Refraction at J, and the Refraction at L equal to the
Refraction at H, so that the Refractions of the incident Rays at K and L
taken together, are equal to the Refractions of the emergent Rays at H
and J taken together: it follows by adding equal things to equal things,
that the Refractions at K and H taken together, are equal to the
Refractions at J and L taken together, and therefore the two Rays being
equally refracted, have the same Inclination to one another after
Refraction which they had before; that is, the Inclination of half a
Degree answering to the Sun's Diameter. For so great was the inclination
of the Rays to one another before Refraction. So then, the length of the
Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
Degree at the Prism, and by Consequence be equal to the breadth _vw_;
20