[T]he instrumental conceptions derived from the use of a common globe are sufficient, in almost every case, for the understanding of the instruments … - George Biddell Airy

The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good telescope, when a diaphragm bounded by a rectilinear contour is placed upon the object-glass, though sometimes tedious is never difficult. The expressions which it is necessary to integrate are always sines and cosines of multiples of the independent variable, and the only trouble consists in taking properly the limits of integration. Several cases of this problem have been completely worked out, and the result, in every instance, has been entirely in accordance with observation. These experiments... have seldom been made except by those whose immediate object was to illustrate the undulatory theory of light. There is however a case of a somewhat different kind; which in practice recurs perpetually, and which in theory requires for its complete investigation the value of a more difficult integral; I mean the usual case of an object-glass with a circular . The desire of submitting to mathematical investigation every optical phænomenon of frequent occurrence has induced me to procure the computation of the numerical values of the integral that presents itself in this inquiry: and I now beg leave to lay before the Society the calculated table, with a few remarks upon its application.

[T]his Fifth Edition is required to meet the demand of a somewhat wider class of students than those for whom the Lectures were originally intended. ...Mr. Stirling has been at liberty to prepare the modifications and additions ...

Complete knowledge of every theoretical and instrumental detail can only be obtained by those who will devote... a large portion of their lives; but sound knowledge of the principles... can be obtained by the reasonable efforts of persons possessing common opportunities for general knowledge.