It is not simply that a clear understanding is acquired of the movements of the great bodies which we regard as the system of the world, but it is that we are introduced to a perception of laws governing the motion of all matter, from the finest particle of dust to the largest planet or sun, with a degree of uniformity and constancy, which otherwise we could hardly have conceived. Astronomy is pre-eminently the science of order.

I had long wished for some opportunity of endeavouring to explain... the principles on which the instruments of an Observatory are constructed, (omitting all details, so far as they are merely subsidiary,) and the principles on which the observations made with these instruments are treated...
Such an opportunity appeared to present itself in the course of Lectures which I engaged to give to the Members of the and their friends.

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[P]erhaps one of the most valuable results to be derived from a truly intellectual study of Astronomy is, the habit of keeping up a sustained attention to all the successive steps of a long series of reasonings. Power, and with it dignity, are gained to the mind by this noble exercise.

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The elucidation of the theory of centripetal and disturbing forces is necessarily less complete. Still... a general conception of the nature of the action of those forces... sufficient to preserve the student from the gross errors... may be obtained from explanations like those here offered. The methods of ascertaining the weight of the Earth and other bodies are... more difficult of explanation; yet... something may be done even in these.

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[H]ow much of the fundamentals of Astronomy may be obtained with the coarsest observation with the unaided eye. ...the science which is thus obtained by personal observations is vastly superior (as far as it goes) to that which is obtained by any other method. ...The knowledge ...inferred from actual personal observation carries with it a degree of reality and certainty, as the veritable science of external objects, which nothing else can give.

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.

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.

In conversing with persons who are not officially attached to Observatories or in other ways professionally cognizant of the technicalities of practical Astronomy but who nevertheless display great interest... these persons appear to regard the determination of measures like those of the distance of the Sun and Moon as mysteries beyond ordinary comprehension... [and] when persons well acquainted with the general facts of Astronomy are introduced into an Observatory, they are for the most part utterly unable to understand anything which they see...
The measure of the Moon's distance involves no principle more abstruse than the measure of the distance of a tree on the opposite bank of a river. The principles of construction of the best Astronomical instruments are as simple and as closely referred to matters of common school-education and familiar experience, as are those of the common globes, the steam engine, or the turning-lathe; the details are usually less complicated.

In the application of the ordinary principles of geometry and trigonometry to such Astronomical measures... it may sometimes be expedient to resolve the process into several successive steps, and these steps may perhaps require different kinds of treatment. But... all are simple and within ordinary comprehension, and the only complexity arises from the circumstance that the student may find it necessary to have a clear view of several such steps at once...