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with the incident ray, and that inside the liquid prism, although the relative positions of the eye and object will not be the same, as if there were no refraction but that of this latter prism.
We may sometimes save the trouble of grinding a solid substance into a prismatic form, by placing it in a fluid of the same refracting power as itself, which, in fact, amounts to using instead of the substance, another of the same refracting power, and appears to involve a petition of the point in question, namely, the refracting power of the substance; but it is not so in practice, because by placing a bit of any transparent substance in a dense fluid nearly of the same colour, and diluting this with a rarer fluid, we shall soon see when the fluid is reduced to the same density as the solid, by there being no irregular refraction caused in light passing through the liquid and the solid, which, in fact, will become in many cases quite invisible in the liquid. It is evident, that it is quite indifferent in making the optical experiment afterwards, whether the light pass through the bit of the solid substance or not.
Canada balsam, diluted with spirit, is a convenient liquid to use for solid substances of small densities.
For further particulars, I beg leave to refer the reader to Biot's Physique, vol. III. Dioptrique, Chap. I, or to Dr. Brewster's Treatise on new Philosophical Instruments.
CHAP VIII.
REFRACTION AT SPHERICAL SURFACES.
75.Prop. A RAY of light is refracted at a spherical surface, bounding two different media; given the point where it meets the axis; required the point where the refracted ray meets the axis.
Figs. 66, 67, 68, 69, represent four different cases.
