curves which represent horizontal sections of hill and valley at successive elevations above the level of the sea—that is, by lines of equal height—and it is the same in its principle. It is obvious that, if lines be imagined in the field of view, winding around through all those portions of a nebula which have exactly equal brightness, these lines, transferred to our chart of stars, will give a faithful representation of the nebula and of its minutiæ, and of the suddenness as well as of the amount of transition from one degree of shade to another.
"By far the greatest obstacles to the successful comparison of modern observations on nebulæ with those which own, at least, a brief antiquity, exist in the want of precision with which the labors of former observers have been conducted, and hence all attempts to trace the slow progress of their changes end in uncertain conjectures and conflicting probabilities. I shall not, therefore, incur the charge of unnecessary minuteness in endeavoring to render, by every means, our knowledge of the present form and state of at least these few nebulæ, as far as possible, standard; and, although laden with the necessary imperfections of original observations, yet free from adventitious and unnecessary vagueness in the communication of them. In order to supply, to any future observer, those slight particulars which a chart cannot easily urge upon the notice of any but the original compiler, and further, to indicate the degree of certainty with which different features of the nebulæ were recognized, it is thought proper to bring under this head the enumeration of various facts not expressed in the journal of observations. These are divided into 'things certain,' 'nearly certain,' 'strongly suspected,' and 'slightly suspected.' Thus much for observation—for rendering the idea of the object as perfect as may be in the mind of the observer. For the most unimpaired communication of this idea or perception, the theory of the process adopted is briefly—1. To form an accurate chart of all stars capable of micrometrical measurement in and around the nebula. 2. From these, as the greater landmarks, to fill in with all the lesser stars, down to the minimum visible by estimation, which, with care, need not fall far short of ordinary measurement. 3. On this, as a foundation, to lay down the nebula.
"The first intention was to intrust entirely to careful estimation the copying of the stars which were to form the groundwork of the nebula, since no means of measurement were then at hand. The following is a sketch of the course of procedure adopted in pursuance of this plan: The limits of the nebula were traced as far as long and close examination could discern them, and a rough chart was made of the principal stars within it. This preparation was indispensable, because, in the consequent mapping down of all the visible stars in the nebula, it was necessary to use a light out-of-doors, and the object, of course, became invisible. The distance between any two conspicuous stars favorably situated in the nebula was then chosen as a standard of reference; and, from this as a base, a kind of triangulation was carried out by the eye to all the stars in the neighborhood, and these were successively marked on a sheet of paper at the time; their magnitudes were also affixed to each according to a fictitious scale, for which a few stars, conveniently situated, furnished standards of reference as to size. A lamp was close at hand, whose light could be cut off at pleasure; and almost direct comparison was thus instituted between the stars in the field of view and those on the paper, and corrections made where any distortions in the latter were observable. As the work advanced from night to night, the reference to the lamp was necessarily less and less direct, since a longer exclusion of light was necessary to see the fainter stars. Finally, the nebula itself was drawn upon the map by the guidance of the stars already
