The optical quality and properties of over 200 telescopes residing in museums and private collections have been measured and tested with the goal of obtaining new information about the early development of the achromatic lens (1757-1770). Quantitative measurements of the chromatic and spherical aberration of telescope objective lenses were made and are discussed within the context of John and Peter Dollond's description of their efforts to overcome these two optical defects inherent in any single lens. Their work was chronicled in the Philosophical Transactions of 1758 and 1765. An important finding of this investigation is that a particular form of the achromatic lens that has been suggested as being a rare and early form by some investigators, and presumably introduced by Chester Moor Hall, was in fact found to be numerous and present in most museums and many private collections. It is shown that the colour correction of an early eighteenth-century doublet telescope objective is very sensitive to the ratio of the flint to crown glass focal lengths, as well as the variations of the indices of refraction with colour. This sensitivity would preclude any simple recipe for constructing an achromatic lens. The third order theory of spherical aberration of Nevil Maskelyne is reexamined, in which he pointed out that John Dollond developed a theoretical formula equivalent to what today is called geometric third order spherical aberration theory. (Contains 24 figures and 55 footnotes.)