ing as many separate bands of equal breadth; in each of these bands, the lines are ruled at a certain known distance; and the distances are so adjusted in the successive bands, as to form a regularly diminishing series, and thus to present a succession of tests of progressively increasing difficulty. The distances of the lines differ on different plates; all the bands in some series being resolvable under a good objective of 1-4th inch focus, whilst the closest bands in others defy the resolving power of a 1-12th inch objective of large aperture. Thus a "test-plate" whose widest lines are at a distance from each other of 1-1000th of a Paris line, or of 1-11,200th of an English inch, and whose closest lines are at 1-5000th of a line, or 1-56,000th of an inch, from each other, will serve as a very fair test for the angular aperture and defining power of object-glasses below 1-4th inch focus; the superiority of each in these particulars, being judged of by the number of bands which it will resolve into well-defined lines, and by the sharpness and clearness of these lines; while the performance of a 1-4th inch objective may be accounted very satisfactory, if it will enable them all to be clearly distinguished. But if the first of the bands should have an interval of only 1-4000th of a Paris line, or 1-45,000th of an English inch, between its lines, and the last should have its lines approximated to 1-10,000th of a Paris line, or 1-112,000th of an English inch, then only a few of the easier bands will be resolved by the 1-4th inch, a few more by the 1-8th inch, and even the 1-12th inch will probably not enable any band to be distinctly resolved, whose lines are closer than 1-7000th of a Paris line, or 1-79,000th of an English inch. At present, therefore, the existence of separate lines of a narrower interval than this, is a matter of faith rather than of sight; but there can be no reasonable doubt that the lines do exist; and the resolution of them would evince the extraordinary superiority of any objective, or of any system of illumination, which should enable them to be distinguished. The mathematical certainty with which the degree of approximation of these lines may be ascertained, and the gradation of the series which they present, gives to M. Nobert's test-plate a very high value for the determination of the relative merits of different objectives, of that class, at least, in which angular aperture and definition are of the first importance; whilst it also serves to test the degree in which these capabilities are possessed by object-glasses of medium power, in which other attributes also have to be considered. The value of the minuter Diatomacea, as furnishing, in their surface-markings, admirable test-objects for the highest powers of the Microscope, was first made known by Messrs. Harrison and Sollitt, of Hull, in 1841; and it cannot be questioned that this discovery has largely contributed to the success of the endeavors which have since been so effectually made, to perfect this class of objectives, and to find out new methods of using them to the best advantage. The nature of these markings will be described

hereafter; and it will be sufficient in this place to give a table of the average distances of the lineation of different species,' which will serve to indicate their respective degrees of difficulty as "tests." The greater part of those which are now in use for this purpose, are comprehended in the genus Pleurosigma of Prof. W. Smith, which includes those Navicule whose "frustules" are distinguished by their sigmoid (S-like) curvature (§ 184).

The first seven of the foregoing may be resolved, with judicious management, by good 1-4th or 1-5th in. objectives; the remainder require the 1-8th or 1-12th in., for the satisfactory exhibition of their markings. Several very difficult tests of this description have been furnished by Prof. Bailey of West Point (U. S.), among them the very beautiful Grammatophora subtilissima and the Hyalodiscus subtilis; the latter, being of discoid form, and having markings which radiate in all directions, very much like those of an engine-turned watch, is a useful test for observers who have not facilities for obtaining oblique light in any direction; since, whatever may be the azimuth from which the oblique pencil may proceed, some portion of the disk will always

This table is taken from Prof. W. Smith's admirable Monograph on the Diatomacea; and it includes most of the species usually employed as tests. These should always be mounted between two pieces of thin glass, according to the method hereafter to be described (§ 122), in order to avoid, as much as possible, the production of aberrations in the illuminating pencil. The number of lineations must be considered as an average, the extremes sometimes varying to a considerable amount on either side. A much higher estimate is given by Messrs. Harrison and Sollitt in the "Quart. Journ. of Microsc. Science," vol. ii, p. 62 ; the Pleurosigma fasciola being reckoned by them to contain 90 lines in 1-1000th of an inch, the Nitzschia sigmoidea 100 lines, and a species cited as Navicula arcus (which can scarcely be the one so named by Ehrenberg, and termed by Prof. W. Smith Eunotia arcus) no less than 130. The last they speak of as "so extremely difficult, that, in order even to catch a glimpse of its delicate markings, the observer must be in possession of glasses of a very large angle of aperture and the finest definition, have the most careful management of oblique light, and in addition be possessed of a large share of patience." The Author cannot but believe that there is some error in these measurements; since, as the well-defined lines upon Nobert's test-plate have not yet been resolved, when they have approximated more closely than the highest numbers mentioned in Prof. W. Smith's table, it can scarcely be imagined possible that the delicate markings of a Navicula should even be "glimpsed," if they be as much closer than those of the species previously accounted most difficult, as those of the latter are than those of the easiest.

be in the best possible position in regard to the light, whereas, in the case of other finely-lined tests, it is only when the most favorable position has been attained, perhaps after tedious and troublesome trials, that the markings are displayed.'

103. Determination of Magnifying Power. The last subject to be here adverted to, is the mode of estimating the magnifying power of Microscopes, or, in other words, the number of times that any object is magnified. This will of course depend upon a comparison of the real size of the object, with the apparent size of the image; but our estimate of the latter will depend upon the distance at which we assume it to be seen, since, if it be projected at different distances from the eye, it will present very different dimensions. Opticians generally, however, have agreed to consider ten inches as the standard of comparison; and when, therefore, an object is said to be magnified 100 diameters, it is meant that its visual image, projected at 10 inches from the eye (as when thrown down by the Camera Lucida, § 49) upon a surface at that distance beneath, has 100 times the actual dimensions of the object. The measurement of the magnifying power of Simple or Compound Microscopes by this standard is attended with no difficulty. All that is required is a stage-micrometer accurately divided to a small fraction of an inch (the 1-100th will answer very well for low powers, the 1-1000th for high), and a common foot-rule divided to tenths of an inch. The micrometer being adjusted to the focus of the objective, the rule is held parallel with it, at the distance of ten inches from the eye. If the second eye be then opened, whilst the other is looking at the object, the circle of light included within the field of view, and the object itself, will be seen faintly projected upon the rule; and it will be very easy to mark upon the latter the apparent distances of the divisions on the micrometer, and thence to ascertain the magnifying power. Thus, supposing each of the divisions of 1-100th of an inch to correspond with 13 inch upon the rule, the linear magnifying power is 150 diameters; if it correspond with half an inch, the magnifying power would be 50 diameters. If, again, each of the divisions of the 1-1000th inch micrometer correspond to 6-10ths of an inch upon the rule, the magnifying power is 600 diameters; and if it correspond to 1,2% inch, the magnifying power is 1200 diameters. In this mode of measurement, the estimate of parts of tenths on the rule can only be made by guess; but greater accuracy may be obtained by projecting the micrometer-scale with the Camera Lucida at the distance of ten inches from the eye, marking the intervals on paper, taking an average of these, and repeating this with the compasses ten times along the inch-scale. Thus, if the space given by one of the divisions of the 1-1000th-inch micrometer,

1 See Prof. Bailey's interesting memoirs in Vols. II and VII of the "Smithsonian Contributions to Knowledge."

repeated ten times along the rule, gave 6 inches and 2 tenths, the value of each division would be 625 of an inch, and the magnifying power 625. The superficial magnifying power is of course estimated by squaring the linear; but this is a mode of statement never adopted by scientific observers, although often employed to excite popular admiration, or to attract customers, by those whose interest is concerned in doing so.'

An ingenious method has been devised by Prof. Harting, of Utrecht, for determining "the utmost limits of penetrating and separating power possessed by a Microscope," by using as test-objects the very reduced images of various bodies formed by air-bubbles in gum-mucilage. The mode of obtaining and employing these images for the above purpose, will be found in the “Quarterly Journal of Microscopical Science,” vol. i, p. 292.

CHAPTER V.

PREPARATION, MOUNTING, AND COLLECTION OF OBJECTS.

UNDER this head it is intended to give such general directions respecting the preparation, mounting, and collection of Objects, as will supersede the necessity of frequent repetition when each particular class is described; and also to enumerate the materials and appliances, which will be required or found advantageous.

SECTION 1. PREPARATION OF OBJECTS.

104. Microscopic Dissection.-The separation of the different parts of an Animal or Vegetable structure by dissection, so as to prepare any portion for being minutely examined under the Microscope should be accomplished, so far as may be found practicable, with the naked eye; but the best mode of doing this, will depend in great degree upon the size and character of the object. Generally speaking, it will be found advantageous to carry on the dissection under water, with which alcohol should be mingled where the substance has been long immersed in spirit. The size and depth of the vessel should be proportioned to the dimensions of the object to be dissected; since, for the ready access of the hands and dissecting instruments, it is convenient that the object should neither be far from its walls, nor lie under any great depth of water. Where there is no occasion that the bottom of the vessel should be transparent, no kind of dissecting-trough is more convenient, than that which every one may readily make for himself, of any dimensions he may desire, by taking a piece of sheet gutta percha of adequate size and stoutness, warming it sufficiently to render it flexible, and then turning up its four sides, drawing out each corner into a sort of spout, which serves to pour away its contents when it needs emptying. The dark color of this substance enables it to furnish a background, which assists the observer in distinguishing delicate membranes, fibres, &c., especially when magnifying lenses are employed; and it is hard enough, without being too hard, to allow of pins being fixed into it, both for securing the object, and for keeping apart such portions as it is useful to put on the stretch. When glass or earthenware troughs are employed, a piece of sheet-cork, loaded with lead, must be provided, to an