On the color correction of achromatic telescopes

ALTHOUGH much has been written on the theory of the achromatic telescope, I am not aware that any attempt has hitherto been made to treat the color correction rigorously as a function of the wave length of the light; and, on that account, much obscurity, and some positive error, has crept into the text books on the subject. The theory given in the following pages is based upon fundamental equations which neglect the thickness of the lenses, as has always been done heretofore, and which suffice to give the refractive indexes to scarcely more than four places of decimals. All the subsequent operations upon these equations are rigorously accurate; and it would have been useless to attempt greater precision in the refractive indexes, while the thickness of the lenses is neglected. .As achromatic telescopic objectives are usually composed of two lenses, rarely of three, and hardly ever of a greater number; it has been thought sufficient to write the equations in the form applicable to triple objectives, but no difficulty will be experienced in extending them to a greater number of lenses, when necessary. Our fundamental equations are