MICROSCOPE 277 attached to the limb (the axis of which passes through the point at which the object-plane is intersected by the optic axis of the body) is hung the swinging tail-piece invented by Mr Zentmayer of Philadelphia, which, carrying the whole illuminating apparatus, may be so set as to give to the axis of the illuminating pencil any required degree of obliquity. To the upper part of it is attached a rack-and-pinion movement carrying the "substage," which is provided with two milled-headed screws for centring it pre cisely with the microscope-body. Into this may be fitted the achromatic condenser, parabolic illuminator, polarizing prism, or any other kind of illuminating apparatus ; whilst at its lower end it carries the mirror, the position of which may be varied by sliding its fitting up or down the "tail-piece," or by turning the arm which carries it to one side or the other ; while, if direct illumina tion from a lamp should be preferred, it may be turned altogether aside. By swinging the tail-piece round above the stage, oblique light may be reflected from the mirror, through the condenser, upon the upper surfaces of objects. The condenser usually fitted to this instrument is of about T * T inch focus, with a large back lens ; behind which are placed an iris-diaphragm for reducing the light to the central rays, and a diaphragm-plate with apertures of the various forms most suited for the resolution of lined objects by oblique rays. No instrument, in the writer s judgment, is better adapted than this for the highest purposes of microscopical research. It works [ admirably with every power from the lowest to the highest, and is I capable of receiving any one of the numerous pieces of apparatus which have been devised for special researches of various kinds. ! The detailed description of these not being here admissible, it will be sufficient to indicate the polariscope and the spectroscope as the most important of these accessories. MICROMETRY. The microscopist has constant need of some means of taking exact measurements of the dimensions of the minute objects, or parts of objects, on the study of which he is engaged ; and the accuracy of the operation will of course be proportioned to the correctness of the standard used, and the care with which it is applied. The instruments employed in microscopic micrometry are of two kinds, the measurement being taken in one by the rotation of a fine screw with a divided milled head, whilst in the other a slip of glass ruled with lines at fixed distances gives a scale which forms a basis of computation. Each of these has its advantages and its disadvantages. The stage-micrometer constructed by Frauenhofer was formerly much used by Continental microscopists, and has the advantage of indicating the actual dimensions of the objects to be measured ; but it has the two special disadvantages that a sufficiently small value cannot be conveniently given to its divisions, and that any error in its construction and working is augmented by the whole magnifying power employed. This instrument has now, however, almost entirely given place to one of those to be next described. The screw-micrometer ordinarily used in astronomical measure ments (see MICROMETER) can be adapted to the eye-piece of the microscope in a manner essentially the same as that in which it is applied to the telescope, its two parallel threads of which one is fixed and the other made to approach towards or recede from this by the turning of the screw being placed in the focus of the eye glass, and being therefore seen as lines crossing its field of view. The object is so focussed that its image is formed in the same plane ; and, the latter being brought into such a position that one of its ends or margins lies in optical contact with the fixed line, the screw is turned so as to bring the movable line into the like coincidence with the other. But the distance between the lines, as given by the number of divisions of the micrometer, will here be the measure ment, not of the object itself, but of its magnified image ; and the value of these divisions, therefore, will depend upon the amplifica tion given by the particular objective used. Thus, suppose each division of the micrometer to have an actual value of TTJFinrth of an inch, and the visual image to have one hundred times the linear dimensions of the object, the theoretical micrometric value of each division would be routh of TvvTsvtti, or one-millionth, of an inch, a degree of minuteness, however, not practically attainable. It is necessary, moreover, to determine the micrometric value of the divisions of the micrometer, not only for every objective, but for variations in the conditions under which that objective may be employed, as regards the length of the tube or "body" of the microscope, which is varied not only by the draw-tube, but also, in many cases, in the working of the fine adjustment or slow motion, and also, in the case of the large-angled powers furnished with adjustment for thickness of the covering-glass, for the degree of separation of the front- from the back-glasses of the objective, which makes a very sensible difference in its magnifying power. I This determination is made by means of a divided glass stage- micrometer put in the place of the object, so that the lines ruled upon it at fixed intervals shall be projected upon the field of view. The ! stage-micrometer is usually ruled either to lOOOths of an inch or lOOths of a millimetre ; and it is convenient that one of the divisions of its image should be made to coincide exactly with a certain number of divisions of the screw-micrometer. This may be done by lengthen ing the draw-tube, so as to increase the amplification of the scale until coincidence has been reached ; and the exact amount of this lengthening should be noted, as should also the precise position of the milled head of the slow motion (if it acts on the objective, instead of on the body as a whole), and of the adjusting screw-collar of the objective itself. Thus, if two lines of the stage-micrometer separated by 1000th of an inch be brought into coincidence with the two threads of the eye-piece micrometer, separated by forty divisions of the screw milled head, the value of each of those divi sions is Tiroinrth of an inch. If the above conditions bo precisely recorded for each objective used in micrometry, the micrometric value of the divisions remains the same for that objective, whenever it is employed under the same conditions. The errors to which micrometers are subject arise (1) from in equalities in the ruling of the stage-micrometer, (2) from irregulari ties in the screw of the eye-piece micrometer, (3) from " lost time " in its working, and (4) from the thickness of its threads. In order to eliminate the first and second, it is well to determine the rela tion of the divisions of the two micrometers by the comparison of a considerable number of both ; the third proceeds from an imper fection of workmanship which, if it shows itself sensibly, entirely destroys the value of the instrument, while the fourth can be rectified by the exercise of skill and judgment on the part of the observer. For, if the micrometer is so constructed as to read zero when one thread lies exactly upon the other, its divisions indicate the distance between the axes of these threads when separated ; and the dimensions of any object (such as a blood-corpuscle) lying between their borders will obviously be too great by half the thick ness of the two threads, that is, by the entire thickness of one thread. When, on the other hand, the measurement is being made (as of the distances of the stria; on diatoms) by the coincidence between certain lines on the object and the axes of the threads of the micrometer, the dimensions indicated by the divisions of the screw milled-head will be correct. The costliness of a well-constructed screw-micrometer being a formidable obstacle to its general use, a simpler method (devised by Mr George Jackson) is more commonly adopted, which consists in the insertion of a ruled-glass scale into the focus of an ordinary Huygenian eye-piece, so that its lines are projected on the field of view. This scale (ruled, like an ordinary measure, with every fifth line long, and every tenth line double the length of the fifth) is fixed in a brass inner frame, that has a slight motion in the direc tion of its length within an outer frame; and this last, being intro duced through a pair of slits into the eye-piece just above the diaphragm, and being made to occupy the centre of the field, is brought exactly into focus by unscrewing the eye-glass as far as may be requisite. When the image of the object to be measured is brought by the focal adjustment of the object-glass into the same plane, a small pushing-screw at the end of the micrometer (whoso action is antagonized by a spring at the other end) is turned until one of the long divisions of the scale is brought into optical contact with one edge of the image of the object to be measured, and the number of divisions is then counted to its other edge, the operation being exactly that of laying a rule across the real object if enlarged to the size of its image. The micrometric value of each division of this eye-piece scale must be carefully ascertained for each objective, as in the case of the screw-micrometer, the error arising from in equality of its divisions being eliminated as far as possible by taking an average of several. The principal point of inferiority in this form of micrometer is that, as its divisions cannot be made of nearly so small a value as those of the screw-micrometer, an estimate of fractional parts of them often becomes necessary, which is objectionable as involving an additional source of error. To meet this objection, Hartnack has introduced the diagonal scale used in mathematical instruments before the invention of the vernier. Another mode of making micrometric measurements, which for some purposes has considerable advantages, is to employ a stage- micrometer in combination with some form of camera lucida attached to the eye-piece of the microscope, so that the image of its divisions may be projected upon the same surface as that on which the image of the object is thrown. By first using the ruled stage-micrometer, and marking on the paper the average distance of its lines as seen in the central part of the field, and then ruling the paper accordingly, the micrometric value of the divisions so projected may be exactly determined for the objective employed and the distance of the drawing-plane from the eye-piece, so that, when the image of any object is projected under the same conditions, the dimensions of that image or of any parts of it can be exactly measured upon the divided scale previously projected, and the true dimen sions of the object thus easily ascertained. If, for example, the lines of a stage-micrometer ruled to the thousandth of an inch should, when thus projected, fall at a distance of an inch apart, then the application of an ordinary scale of inches (divided into
tenths) to the image of an object projected by the same objective