The last item obtained with a stop of an inch in diameter, indicates an aperture of 50° by the usual methods, whereas the true angle is only 30, an error being shown in excess of more than fourteen times. The annexed diagram demonstrates the cause of this error. The central angle shown is the true aperture assigned 03 .002 50 by the small stop at the base. The oblique angles represent the pencils, including the field of view, and showing light or an image at the eye-piece, up to an angular range of 50°. It is these outside rays which are superadded to angle of aperture taken by the usual method, and which are the cause of erroneous indications greatly in excess of the true angle. The foregoing is a mere illustration of excessive angles, indicated from oblique pencils, or angle of view alone, irrespective of true angle of aperture, for, of course, limiting stops of known diameter placed on the front lens serve no purpose for measuring full central angles. The difficulty of estimating the degrees of these angles accurately, by such minute measurements as the focal distance, and working diameter of the front lens, may be avoided by halving this as an unknown quantity, and obtaining the value of the central angle by the differential results, shown between a half-obscured front surface and an entire one. That which is understood (and, in fact, always has been) as a definition of angle of aperture, in a micro object-glass, is a triangle having a base equal to the available diameter of the front lens, and a height equal to the focal length measured therefrom. Now it is clear that if half the front lens is stopped off diametrically close to the surface, only half the base of the triangle must remain, and consequently but half the existing angle or cone of rays in the axial direction. By the sector measurement such is not shown to be the case. The apparent degrees from a half diameter of incident front surface are much in excess of a half quantity, because the rays that form the oblique pencils extend behind and under the half stop, nearly to the margin of the field of view beneath. These are beyond the true axial angle of aperture, and are the cause of the false quantity always measured in excess of the proper angle, the rays including the angle of field must therefore be deducted up to the centre. This the half stop enables us to accomplish. Using the sector measurement the rule is this. Subtract the degrees shown by half the lens from the degrees of the entire lens, and twice the difference is the aperture. By this simple rule we eliminate the angle of field, which has hitherto been erroneously added to angle of aperture. In order to obscure the half of the front lens, take a small piece of tinfoil with a clean-cut edge, lay this on a glass slip, and smear its upper surface with a bit of dry soap (anything moist will bedew the glass), place this on the microscope stage, and bring the edge in focus under the object-glass, until it exactly bisects the field vertically. Then lower the object-glass on to the foil, which will adhere to the front lens. The microscope body may then be laid horizontally, and the apparent aperture of the open half of the lens measured by the sector, which invariably indicates considerably more than half of the full aperture, taken by the same method. In objectives of large angle, twice this half measurement will amount to absurd and impossible angles. The application of the above rule will require to be thoroughly investigated before it can be finally adopted. In every case it brings out a reduction on the degrees of aperture indicated by all the modes of measurement in present use. I give its test, on what I have repeatedly stated to be fabulous apertures, viz. 180. I have one of these objectives-a-yet in ridiculous disproof of such an aperture (which would bring the focal plane on to the surface of the front lens), it is remarkable for its working distance, and will penetrate through the cover of any object in my cabinet, and used with thick covers, either as immersion or dry, its performance is very fine. Taken by the sector, the open aperture, or what I will term angle of field, is 180°. The aperture of half this lens is 115°, twice the difference is 130'; this represents the degrees of the central pencil, which is the true aperture. I take another example of an immersion lens, in which the maker actually claims "plus 180°." On trying this by the sector, the light image vanished at a range of 178°, beyond which it was totally obscured. The aperture of half the lens was 114°, twice the difference is 128°. IV.-Improvements in the Micro-spectroscope. By F. H. WARD, M.R.C.S., F.R.M.S. (Read before the ROYAL MICROSCOPICAL SOCIETY, December 13, 1878.) PLATE XVII. EARLY in this year we were reminded by Mr. Crisp* that one of the objects of this Society was the promotion and diffusion of improvements in the optical and mechanical construction of the microscope, and as during the last twelve months I have been making some experiments with a view to modifications of the micro-spectroscope, and have just received from the maker an instrument which differs in several particulars from the usual form, I have ventured to bring it before the Society, and after pointing out the features in it which I believe to be new, shall leave it in your hands to decide whether it is an improvement or not. One of the first things which struck me as being an imperfection in the ordinary instrument was the slit, and the facility with which its jaws collect dust, thus causing those objectionable black lines across the spectrum, and though when the spectroscope is to be used in conjunction with the microscope the slit is much more protected from dust than in a table spectroscope, yet, nevertheless, from its internal position it is more difficult to get at, and sometimes little particles remain after several attempts to remove them. I cannot claim to have done much work myself in this branch, but I am told that with an instrument in constant use, the slit is liable to get out of order, and requires adjustment to maintain the perfect parallelism of the jaws and the integrity of their opposed edges. As soon as I began to make inquiries on the matter, I found I was by no means the first who had recognized these difficulties, and that during the last twelve years others had been considering what could be employed as a substitute for the slit. Returning one night from one of our meetings, it suddenly occurred to me that if a rectangular glass prism was taken and the apex of the right angle carefully ground off and the resulting face polished, it would transmit a narrow pencil of light, which would work admirably in spectroscopic examinations, any light falling upon the sides of the DESCRIPTION OF PLATE. FIG. 1.-New micro-spectroscope. 2.-Plan of internal platform, showing prism fitting, with three prisms in situ, comparison prism with slot, &c. 3.-Tube carrier for comparison stage. * Journal of the Royal Microscopical Society,' vol. i. p. 121. prism being at the same time totally reflected. I thought the matter over for several days, and then conferred with Mr. Hilger, than whom I suppose no more competent authority exists on the construction of instruments for all the branches of spectrum analysis, and the result was a visit to his workshop with some prisms to put the matter to the test. A few minutes sufficed to remove the right angle from the prisms, and a few touches on the polisher gave a brilliant but narrow surface, quite sufficient to indicate as a rough experiment whether the method were likely to answer if more carefully carried out. Not having a microscope at hand to which it could be easily adapted, and wishing to submit the plan to as severe a test as possible, we opened widely the slit of a table spectroscope and secured the prism in the centre of the opening. The battery of this instrument consisted of four large prisms, each with an angle of 64°, the faces of which had a width of three inches, and as it was so arranged that the ray should traverse them four times, the length of the path in the centre of the prisms was about 25 inches. Placing some sodium salt in a Bunsen flame, we tested the result, and found the D lines well separated and beautifully distinct and sharp. We also tried lithium, calcium, and carbon, and the results were equally good. I was so pleased with what I considered the success of the attempt, that I directed Mr. Hilger to construct me an instrument for my microscope in which three prisms should be substituted for the usual slit, and supplied him with a plan by which either one of the three could be slipped into position for use. Subsequently, when I had it in my possession and tested it by examining the continuous spectrum of various solutions, I found the result, however, by no means satisfactory: I do not think there is any other word by which to describe it than failure. The bands across the spectrum were far worse than those from the dirtiest slit ever seen. Trying it again for the sodium line, I found it sharp and bright, though only single on account of the much diminished magnifying power, and I was reluctantly compelled to acknowledge that, good as it might be for bright line spectra, it had failed for continuous spectra. The next question to decide was, whether the failure was due to an optical or mechanical cause, whether the theory was right, but the practical working out of it imperfect: I was disposed to believe it was the latter, and not being deeply versed in optics, I could only satisfy my own mind by further experiments. I examined with a lens the edges of the linear surfaces, if I may use such an expression, of the prisms, and found that they were not perfect, that there were minute depressions, tiny splinters of glass gone, which, though invisible to the naked eye, were, I believed, the cause of the mischief. I had them reground and repolished several times with varying results, which I need not describe. I had meditated from the first employing quartz as being harder and consequently more durable, but I wished to make use of glass if it were practicable. The next step was to grind three quartz prisms with great care and attention, and the result proved, I think, fairly satisfactory, and are now submitted for your verdict. It will, I think, be evident to everyone that if such a prism as I have described can without disadvantage be substituted for the usual slit, the narrow face of the prism may be very readily cleaned from any dust which may settle on it, by withdrawing the fitting and gently wiping it with a handkerchief or other suitably soft material. For want of a more expressive term, I have called this arrangement a "solid slit." It would perhaps be hazardous to state that it is quite a new feature in glass grinding to produce a surface of almost no width with nevertheless sharp edges, but at any rate I believe it is new, and there can be no doubt that with more practice the workmen would become more proficient in the production of such surfaces; upon these, of course, the whole value of the arrangement rests. It is very pleasant to believe our own designs perfect, our ideas right, and our geese swans; but if you do not accept this which is the main feature of my instrument, some of the minor alterations, which 1 will lay before you as briefly as possible, may meet with some approval. Presuming that this prism arrangement is condemned, you will see that I have here a slit arrangement, which slides in the same dovetail as the prism fitting. This is opened and closed by a micrometer screw from the outside, the head of which is divided for registration if necessary, the edge of the fitting carries an index, which slides past a silvered scale divided into 100ths of an inch. A better arrangement would have been to have a vernier instead of an index, and the readings then would have given thousandths, and the position of absorption bands or lines obtained by means of the bright spot above the direct vision prisms. There could be no more easy method, I think, for cleaning the jaws of a slit than by this method of making the fitting removable from the side. It is manifest that the distance between bands at the opposite extremes of the spectrum may be more rapidly measured by this sliding movement than by numerous turns of a micrometer screw; such screw, I think, should only be used as a fine adjustment, and if it has such work thrown upon it as I have suggested, it would, I believe, be found to rapidly deteriorate. It may perhaps be argued that this sliding movement does not give such facility as a screw for accurately placing any line in exact juxtaposition with the point of the bright spot, but I feel sure that anyone would find |