Just as the past progress of astronomy has, in a great measure, been due to the improved construction of our instruments, so its future progress must depend much on the accurate confection of our telescopes, and most of all on the excellence of the object-glasses.

In the actual formation of a compound lens, after the thicknesses and curvatures have been fixed, we have to make the tools to the proper shapes and with those to grind and polish the glass. It is impossible, even with the greatest care, to bring the workmanship so close to the computations as that appreciable differences may not be found, and hence the finished lens hardly ever comes so near to our expectations as that it may not be necessary to test it by actual trial. One important matter to be so settled is the exact position of the principal focus, since that is needed for determining the length of the tube.