The author observes that, “in combining the surfaces of an achromatic eye-piece, a very limited question is resolved. The condition is, that pencils of light falling upon the first surface in directions parallel [approximately] to the axis of the instrument, emerge from the last surface in such a way, that the different rays into which each is decomposed may be parallel among themselves. On account of this restriction, achromatism can be obtained by the use of only one medium, and it is unnecessary to combine substances acting differently on the light of various colours.”

The author then proceeds to show that, since the only required conditions are that two refractions shall take place of a certain amount and at certain distances, these conditions may be fulfilled by two refracting surfaces, or by a single lens of a certain thickness.