given by Professor Stokes the object is supposed to be self-luminous, emitting a pencil of rays of 180° in glass, which pencil was shown to pass by a single refraction, without aberration, from the front lens, and to present to the second lens a pencil in air of only just beyond 81°. Professor Stokes did not say the whole of this pencil can be made available in a practical construction, but he stated that a very considerable portion of it-largely in excess of what is available in a dry lens-could be so used. After this demonstration the question of the possibility of immersion lenses having apertures exceeding the maximum possible in dry lenses would be settled from the theoretical point of view. His opinion on the validity of Professor Keith's computation of the aperture of Tolles' -Mr. Crisp's lens-must also be conclusive. It remained to endeavour to support the computation by actually measuring the aperture of the lens before the meeting-which he proposed doing, not of course expecting any general agreement at this stage of the discussion as to the least objectionable way of measuring apertures, especially with this individual lens. He would be content to show the measurement by Professor Abbe's apertometer, the results obtained with which he had found to correspond with those obtained by a modification of Professor Robinson's method which was submitted to Professor Stokes, and for the accuracy of which he had his authority. A method was specially commended by Mr. Charles Brooke in one of his Presidential addresses, viz.: to measure the working diameter of the front lens, which is taken as the base line of an isosceles triangle; taking the exact focal distance as the perpendicular, the triangle would represent the angle of aperture. The objection to this method in practice, was that when it was tried with the lens, the data furnished were so various and contradictory that no reliance could be placed on the results: in one case the focal distance being given as 0.13, then 018; in another 025,-the working diameter being given first as 043, then as ⚫033. Professor Stokes said that of course it would be understood that, as stated by Mr. Mayall, he confined himself to the consideration of a point as if it were self-luminous, and contemplated that the object was illuminated by immersion; if they let in light to the plane surface in air they would be limited to twice the critical angle.

The President announced that they had received a letter from Professor Abbe, thanking the Society for the honour done to him by his election as an Honorary Fellow of the Society.

Mr. Charles Stewart (Secretary) read a paper by the Rev. W. H. Dallinger, "On the Measurement of the Diameter of the Flagella of Bacterium termo, a contribution to the question of the ultimate limits of vision with our present lenses."

The President said that what must have struck everyone who had listened to this paper was the extreme smallness of the objects measured, for if Mr. Dallinger was correct (and there was no reason for doubting his correctness), then it was clear that objects of very much greater minuteness could be rendered visible than had usually been considered possible. These objects were about the smallest which the microscope would show, and yet it appeared that they

probably stood higher in the scale of organisms than some other objects which were generally considered to be higher. He thought that these investigations of Mr. Dallinger would tend to raise such objects to a much higher rank than that previously assigned to them.

The President said they had two other papers before them; one of these was from Mr. F. A. Bedwell, "On the Framework of the Mastax of Melicerta ringens and Conochilus," and the other was a translation by Mr. Kitton of a paper by M. Paul Petit, "On some New Genera and Species of Diatomacea." The latter paper was, of course, unsuitable for reading in extenso, and would be taken as read. The paper by Mr. Bedwell was of considerable interest, and went into the minute structure of the organ at some length; but in his opinion, apart from the illustrations (which would be handed round), it would scarcely be possible to do full justice to the author or his subject in the time left at their disposal, and it would therefore now be taken as read, and would appear in the Journal together with the illustrations in September. He would also call attention to the extremely good slides of the mastax of Melicerta and Conochilus made by Lord S. G. Osborne, which had been sent up by Mr. Bedwell for examination by the meeting.

Mr. J. W. Stephenson (Treasurer) read a "Note on the effect produced on P. angulatum and other Tests by excluding the central dioptric beam of light," which he explained was accomplished by placing a central stop at the back of the objective, so that the diffraction spectra alone formed the image.

Mr. Frank Crisp (Secretary) said that, in view of the four months' vacation now commencing, he should like to call the attention of the Fellows to the experiments on diatoms immersed in a solution of indigo or other coloured liquid, a note of which had appeared in the last number of the Journal (vol. i. p. 79), and the important conclusions that those experiments pointed to, particularly in regard to the motions of diatoms. The experiments were well worthy of being repeated and confirmed, and if any Fellow during the vacation would be kind enough to do so, he would, no doubt, be able to make a very interesting communication to the Society when they met again.

up

the

The President suggested that Professor Stokes should take question of the limits of visibility, which in his hands would doubtless receive some important advancement towards a conclusion. He also mentioned that some specimens of drawings reproduced by the autographic process (which was exhibited at their recent scientific evening, by Mr. Pumphrey, of Birmingham) had been sent to the Society for distribution.

At the conclusion of the meeting Mr. Stephenson exhibited P. angulatum under the conditions described in his "Note," and with the new oil-immersion lens, using a deep astronomical piece by Dollond, The diatom appeared of a brilliant blue on a perfectly black ground, and the definition left nothing to be desired.

sen.

Mr. Mayall, jun., also demonstrated the aperture of Tolles' immersion lens by Professor Abbe's apertometer. He first exhibited the apertometer with Zeiss's new oil-immersion lens, recording

a balsam angle greater than 106°; then he showed the aperture of a high-angled dry lens to be within double the critical angle, i. e. less than 82° in glass; then he showed the aperture of Tolles' immersion to be in excess of the limit for dry lenses, i. e. greater than 82° in glass. The demonstration was conducted in the presence of Professor Stokes, Mr. W. G. Lettsom, Mr. J. H. Dallmeyer, Mr. F. Crisp, and others interested in the subject.

The meeting was then adjourned to the 9th October, and the President reminded the Fellows that the library and reading room would as usual be closed during the month of August.

Donations to the Library, &c., since April 3, 1878:

Ditto.

Ditto.

Ditto.

Club.

Society.

S. S. Wigg, Esq.

Papers and Proceedings of the Royal Society of Tasmania, 1876
Transactions of the Watford Natural History Society. Part 9
Journal of the Linnean Society: Zoology. No. 74

Report and Abstract of Proceedings of the Croydon Microscopical
Club, 1877..

The following gentlemen were elected Fellows of the Society :

Dr. James Edmunds; Major Richard O'Hara.

WALTER W. REEVES,

Assist.-Secretary.

OF THE

ROYAL MICROSCOPICAL SOCIETY.

SEPTEMBER, 1878.

I.-On the Measurement of the Diameter of the Flagella of Bacterium termo: a Contribution to the Question of the "Ultimate Limit of Vision" with our present Lenses. By Rev. W. H. DALLINGER.

(Read before the ROYAL MICROSCOPICAL SOCIETY, June 5, 1878.)

PLATES VIII. AND IX.

It will be remembered by this Society that two years ago, having in conjunction with Dr. J. J. Drysdale completed as far as we then purposed a series of observations on the life-histories of a group of monads, we determined to use the experience thus gained, and if possible to study in a similar way the Bacteria. We commenced on B. termo; and our first object was to make out clearly its normal form, and to discover if possible the agency by which movement was effected.

In the case of the large form known as Spirillum volutans,

7.-Photograph of Bacillus subtilis, showing flagella. By Dr. Koch x 500. 8.-Ditto, ditto (or as Dr. Koch thinks a variety, B. amylobacter), also photographed, and faintly showing flagella × 700 diam.

FIG. 9.-Bacillus subtilis x 4000 diam.

10.-B. termo.

11.-A camera lucida outline of the lower part of B. termo, magnified 2000 diam. c is the pencil line intended to cover the image of a part of the flagellum; and a represents by dots the part of the image with which the line can be compared.

FIG. 12 is the above drawing placed on the stage of the microscope, and magnified 5 diam. In this way the ratio between the diameter of the body of the Bacterium and the diameter of the flagellum can be compared by means of the wires of a screw micrometer. The ratio here shown being as 10 to 1.

VOL. I.

Cohn had demonstrated, what Ehrenberg had suspected, and we had readily confirmed, that its movements were produced and controlled by a pair of fine flagella, one at each end of its spiral body. This was extremely suggestive: while we had further the analogy of the minuter monads, many of them being only four or five times larger than the larger forms of B. termo-these also being endowed with one or more flagella, suggesting the probability that all these forms depended for movement on similar motile filaments.

We therefore determined to endeavour to discover whether, by care and delicate manipulation, flagella could be demonstrated on B. termo itself.

Fortunately at this time we were furnished with a "new formula" lens, which possessed precisely the qualities needed. Carrying out our method of admitting nothing, in our conjoint work, which both had not seen, I commenced the search; and after many hours' effort, and the use of a great variety of delicate appliances, I succeeded in clearly demonstrating a pair of flagella, one at each end of the body of B. termo, without the shadow of a question. Dr. Drysdale now, independently, commenced the search, simply employing the same methods, and ultimately demonstrated it as completely as could be desired. We were then able to study it together, seeing the delicate fibre as distinctly as the body of the B. termo itself, and I made careful drawings from this, which Dr. Drysdale accepted and confirmed.*

Most of the forms at present grouped as Bacteria vary, very considerably, in size. Some, for example, that may be designated B. termo will be as large again as others; and this is the case throughout, only that the variation will be still greater in those forms which, instead of dividing into two parts, divide into several. There is for instance very great variety in the length of S. volutans. But the average length of B. termo, resulting from a hundred measurements made from this form as taken from six different infusions, was the Tooth of an inch. The average of one hundred measurements of S. volutans (taken only from one infusion) was the Tooth of an inch, but these were large. In Fig. 2, Plate VIII., I give a drawing of a recent specimen of S. volutans magnified 2000 diameters; and at Fig. 1`a B. termo is placed beside it, as it was seen by Dr. Drysdale and myself, magnified 4000 diameters.

Since this account of the discovery of flagella on B. termo was published, several valuable monographs have appeared on the subject of Bacteria. From the point of view I am now specially considering one of the most interesting and valuable is by Dr. Eug. Warming. In it he points out that the flagella are common to the *Monthly Microscopical Journal,' vol. xiv. p. 105.

† Om nogle ved Danmarks Kyster levende Bakterier.' Kjöbenhavn, 1876.