It is possible to make the hyperchromatic and achromatic experiments objectively as well as subjectively. After what has been already stated, a short description of the method will suffice, especially as we take it for granted that the compound prism before mentioned is in the hands of the observer.
Let the sun's image pass through an acute-angled prism of few degrees, prepared from crown-glass, so that the spectrum be refracted upwards on an opposite surface; the edges will appear coloured, according to the constant law, namely, the violet and blue above and outside, the yellow and yellow-red below and within the image. As the refracting angle of this prism is undermost, let another proportionate prism of flint-glass be placed against it, with its refracting angle uppermost. The sun's image will by this means be again moved to its place, where, owing to the excess of the colouring power of the prism of flint-glass, it will still appear a little coloured, and, in consequence of the direction in which it has been moved, the blue and violet will now appear underneath and outside, the yellow and yellow-red above and inside.
If the whole image be now moved a little upwards by a proportionate prism of crown-glass, the hyperchromatism will disappear, the sun's image will be moved from its place, and yet will appear colourless.
With an achromatic object-glass composed of three glasses, this experiment may be made step by step, if we do not mind taking out the glasses from their setting. The two convex glasses of crown-glass in contracting the sun's image towards the focus, the concave glass of flint-glass in dilating the image beyond it, exhibit at the edges the usual colours. A convex glass united with a concave one exhibits the colours according to the law of the latter. If all three glasses are placed together, whether we contract the sun's image towards the focus, or suffer it to dilate beyond the focus, coloured edges never appear, and the achromatic effect intended by the optician is, in this case, again attained.
But as the crown-glass has always a greenish tint, and as a tendency to this hue may be more decided in large and strong object-glasses, and under certain circumstances produce the compensatory red, (which, however, in repeated experiments with several instruments of this kind did not occur to us,) philosophers have resorted to the most extraordinary modes of explaining such a result; and having been compelled, in support of their system, theoretically to prove the impossibility of achromatic telescopes, have felt a kind of satisfaction in having some apparent ground for denying so great an improvement. Of this, however, we can only treat circumstantially in our historical account of these discoveries.