_Exper._ 15. The Sun shining into a dark Chamber through a little round
Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
Image painted on the opposite Wall by his direct Light, PT his oblong
coloured Image made by refracting that Light with a Prism placed at the
Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
refracting again the same Light sideways with a second Prism placed
immediately after the first in a cross Position to it, as was explained
in the fifth Experiment; that is to say, _pt_ when the Refraction of the
second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
3t_ when it is greatest. For such will be the diversity of the
Refractions, if the refracting Angle of the second Prism be of various
Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
of thirty or forty to make the Image _2p 2t_, and of sixty to make the
Image _3p 3t_. But for want of solid Glass Prisms with Angles of
convenient Bignesses, there may be Vessels made of polished Plates of
Glass cemented together in the form of Prisms and filled with Water.
These things being thus ordered, I observed that all the solar Images or
coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
to the place S on which the direct Light of the Sun fell and painted his
white round Image when the Prisms were taken away. The Axis of the
Spectrum PT, that is the Line drawn through the middle of it parallel to
its rectilinear Sides, did when produced pass exactly through the middle
of that white round Image S. And when the Refraction of the second Prism
was equal to the Refraction of the first, the refracting Angles of them
both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
that Refraction, did when produced pass also through the middle of the
same white round Image S. But when the Refraction of the second Prism
was less than that of the first, the produced Axes of the Spectrums _tp_
or _2t 2p_ made by that Refraction did cut the produced Axis of the
Spectrum TP in the points _m_ and _n_, a little beyond the Center of
that white round Image S. Whence the proportion of the Line 3_t_T to the
Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
and this Proportion a little greater than that of _t_T to _p_P. Now when
the Light of the Spectrum PT falls perpendicularly upon the Wall, those
Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
Tangents of the Refractions, and therefore by this Experiment the
Proportions of the Tangents of the Refractions are obtained, from whence
the Proportions of the Sines being derived, they come out equal, so far
as by viewing the Spectrums, and using some mathematical Reasoning I
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