Dr. Koch has never seen the flagella in B. termo, but he has made no effort to do so, because, as he tells us, he used low-angled glasses which are incompetent to the demonstration; and has made no special provision for illumination, without which it is utterly impossible to see this fine organic fibre. Dr. Koch too, by using a method in which drying, staining, and mounting are involved, is, I am inclined to think, making the demonstration more difficult. He, however, without having made any effort to discover it, has no doubt that the discovery of it is a demonstration in the proper sense, although extremely difficult to make; and he believes that the entire group of motile Bacteria are endowed with flagella.

There is not the slightest doubt that this inference is correct. In all extremely delicate work with high-power lenses, the first difficulty is the greatest. If once an object has been seen, however difficult, it is immensely easier to see it again. On the other hand, I have learned from experience that there is as great a diversity in different individuals in the sensitiveness of the retina, as there is in sensitiveness of the olfactory or auditory nerves. It is impossible to enable some persons to see objects beyond a certain limit of minuteness; as it is to enable others to detect certain scents, or hear notes pitched higher or lower than a given point. This is illustrated by the telescope as well as by the microscope, and has application to the practised as well as the casual observer. It is therefore fortunate that the constantly accumulating refinements of photography will ultimately provide us with a film equal toperhaps finer than the most sensitive human retina in its powers to fix the minutiae of detail, in form and structure, revealed by our highest powers and best lenses. But even then the efficiency of the results will be influenced by the delicacy of the retina, and the perfection of the eye of the manipulator.

In the matter of the delicate flagella of B. termo the great difficulty had been overcome; and for some time subsequently there was considerable fascination, in spite of the great difficulty, in repeating again and again the observation. At first we could only get the result with the "supplementary stage" illumination referred to in our joint paper. Since, however, I have succeeded with Powell and Lealand's sub-stage condenser, and with Wenham's reflex illuminator, using with this last apparatus, glycerine, Letween the prism and the under side of the glass slip.

The secret of success, skilful manipulation and the right kind of lens being assumed, is the manner in which the Bacteria are prepared. They should be taken from an old and thick maceration; not a recent infusion with a thin fluid; and then should be very gradually accustomed to thinner and thinner fluid, until, by two or three days' habituation in Cohn's fluid, for a few hours they will live in water. And it is in this that they should be examined;

for the comparative opacity of the natural fluid makes it impossible to see the flagella, and in the water there is obviously a greater contrast between it and the sarcode of the flagella, than there is in the thick decomposing fluid. And I have repeatedly observed that if the Bacteria are taken from a recent infusion which is little more in substance than water,-probably from some difference in the density of the sarcode,-the flagella cannot be discovered.

After repeatedly, and in different ways, having demonstrated the flagella, it struck me that much would be gained if it were possible to measure its diameter. To do this by a direct method was impossible with any instrument with which I am acquainted; but it might, it appeared to me, be done with very approximate accuracy by an indirect method. To this end I made a series of investigations with Powell and Lealand's "new formula" objective, and with what appeared to me extremely interesting results. But subsequently they furnished me their and inch lenses on the same formula. And as immersion lenses their performance is remarkably beautiful. I also had a very fine immersion by the same makers; and at my request they made me a 3, the first they had ever made. This lens was made with a view to the special class of observations in which I have been engaged, and it is an extremely beautiful one. The angle is moderate, and the lens with the same front is both immersion and dry. Its definition when properly used is very crisp and clear, and its "penetration," considering its magnifying power, is very considerable.

My purpose was, having been furnished with these lenses, to make a series of indirect measurements with each of these lenses separately, and then compare the results and obtain an average.

My method was as follows, viz. :

1. It was necessary, and comparatively easy, to measure accurately the absolute diameter of the Bacterium body, as, for example, in Fig. 10, Plate IX., to find the actual distance from a to y.

2. Next it was needful to make a very careful camera lucida drawing of the body and a part of one of the flagella. The microscope being in an upright position the ordinary camera lucida cannot conveniently be used; but an extremely useful instrument, made by M. Nachet, of Paris, to meet this emergency, answers admirably. It is, indeed, much easier to draw with than the ordinary camera lucida; and in using it with high powers all that is required is, that the right hand employed in drawing be illuminated a little more intensely than the " field," when it will appear extremely "ghostly," but very sharp and clear, and the pencil point is admirably defined.

A fine white surface is needed which will receive a mark without such rough edges as are made, with even very hard pencils, on the finest London or Bristol cardboard. That which I find to

answer best, is the "enamelled cards" which are used by the printers for visiting cards. I also use a HHHH, Windsor and Newton or Faber pencil (with the wood cut considerably away in the former, the latter being obtainable in solid cylinders, which are slid into holders), which is brought to its final point by gentle rubbing on the surface of the finest ground glass, or, better still, a very fine hone. With these appliances a drawing was made, first, of the lower half of the body of the B. termo, and then, which was the really critical matter, a pencil mark was made over a half or twothirds of the flagellum, not over the whole; for in this way the flagellum image and the pencil mark could be carefully compared, as shown at Fig. 11, where the dotted part a represents the image of the flagellum as seen beyond the pencil line c; and a very close approximation may thus be made between them.

Having determined that the pencil mark, as at c, Fig. 11, accurately corresponded to the image of the flagellum, this drawing was taken and magnified from five to ten diameters, the amount of magnification being accurately determined beforehand. By this means it was easy to determine the ratio existing between the now measurable diameter of the pencil line representing the flagellum and the diameter of the body. But this latter was a known quantity; and therefore it was easy to determine the actual diameter of the flagellum. Thus at b, Fig. 11, there is an outline camera drawing of the lower half of a B. termo magnified 2000 diameters. c is the pencil line corresponding to a part of the flagellum, the dotted line a representing the remainder, with which the pencil line could be compared. At Fig. 12 we have the same drawing magnified five diameters; and in this condition it is quite easy by means of the "screw micrometer" to find the ratio existing between the magnified image of the drawing of the body and that of the flagellum. In other words, it is soon seen how many flagellum spaces are needed to cover the diameter of the body. In the case before us, the bacterium drawn at Fig. 11 had a diameter of 400th of an inch. The ratio of the flagellum to the body, as seen in Fig. 12, is as 10 to 1; and 2040010201000th of an inch, the actual size of the flagellum.

Now I made fifty separate drawings and measurements with each of the four lenses; the same conditions being observed in each case. The results expressed in decimal fractions are as follow, viz.:

(1) The mean value of fifty measurements made with the 1th inch objective, gives for the diameter of the flagellum 0.00000489208.

(2) The mean value of fifty measurements made with the eth inch objective gives 0·00000488673.

(3) The mean value of fifty measurements made with the th inch objective gives 0·00000488024.

(4) The mean value of fifty measurements made with the 3th inch objective gives 0·00000488200.

We thus obtain a mean from the whole four sets of measurements, which gives for the value of the diameter of the flagellum of B. termo 0-00000488526, which expressed in vulgar fractions is equivalent to 2000th of an inch nearly; that is to say, within a wholly inappreciable quantity.

Now if we suppose that as the method is only an approximate one, and the errors are entirely on one side, which I know no reason for doing, and therefore in round numbers reduce this fraction to the 00000th of an inch, it nevertheless provides us with a fact of much interest; and indicates, as I believe, that an atom of semi-transparent structure the goooooth of an inch may become visible under proper conditions of illumination and general manipulation. How far this is the actual limit with transparent or nearly transparent objects, I will not venture to affirm. But I am inclined to believe that it comes very near to it. But why, whether from the limitations involved in the nature of the luminiferous æther, and the conditions of light vibrations, it is not my province to pronounce.

The calculations of which this paper gives the results have been carefully revised by my friend Mr. C. H. Stearn, of Liverpool.

II.-The Mastax-Framework in Melicerta ringens and Conochilus, described by F. A. BEDWELL; with further Notes on these Rotifers.

(Read before the ROYAL MICROSCOPICAL SOCIETY, June 5, 1878.)
PLATES X. AND XI.

LORD Sydney Godolphin Osborne, in January last, entrusted to me the agreeable duty of describing the mastax of M. ringens from a series of slides of that organ as dissected by him from the rotifer itself, and mounted. I must premise that it is quite impossible for me to hope to do justice to the great beauty of the contents of these slides, either by pen or pencil, they must be seen to be enjoyed; the accompanying drawings simply express diagrammati

DESCRIPTION OF PLATES.

PLATE X.

FIG. 1.-Details of framework of mastax of M. ringens diagrammatically treated. a, b, c, form the ramus: a, frontal blade; b, central blade; c, alula. dd, manubria. ee are rigid attachments, which in life are connected with the angles cc of each alula, and by lifting the alule they force up the free edge bb of the central blade of the ramus, and bring down the turreted edge of the frontal blade of the ramus. f is the fulcrum, the hinge, confused by flattening, see Fig. 6. pp are the teeth, fifteen in number, removed from their supports; in nature they lie with their points fixed in the turreted serrations of the frontal blade of the ramus, roots being attached to the manubria, along the lines g h.

their

FIG. 2.-The letters repeated. This figure represents the free edge of the ramus, lifting up to the under side of the teeth, and bending them towards the rectangular position which they are seen to possess in life when masticating food. (Five of the teeth have been removed.)

FIG. 3.-Explained in text.

FIG. 4.-A mechanical illustration of the ramus, to be cut out in cardboard, and explained in the text.

FIG. 5.-One of the large teeth.

PLATE XI.

FIG. 6. This diagram represents the hinge fulcrum and the two rami of Conochilus volvox. The letters refer to the same parts as in M. ringens; the points cand e are united in life, as also are those parts at K and H which have been separated in the diagram.

FIG. 7.-This figure is explained in the text, and represents the hinges H and K when the organ is at work, and shows how the arms of the ramus springing from K meet together, and how the arms that drive the alulæ rise upwards at H, and so lift up the alulæ.

FIGS. 8, 9, 10, are transverse imaginary sections of the mastax, and show how, as the end of the alula c is lifted upwards, the points of the teeth tend to come downwards.

FIG. 11 is a transverse section showing an abnormal position, explained in the text and seen by the writer, and arising from the manubria d, giving their forward blow along the teeth at a moment when the alulæ c were not lifting the points b upwards, so that the teeth bent the wrong way at the points p.

FIG. 12.-The eye of Conochilus.

FIG. 13.-Corrected diagrammatic representation of wheel of Conochilus, showing its relation to the sinus into which the food flows on its way to the

mastax.