be thankful," but let us prosecute the search for higher achievements still.

Reasons for the Construction of the Tables.

It often happens that even opticians, as well as amateurs, are at a loss to draw accurately on a large scale (necessary for useful inquiry) the path of a ray of light traversing successively media in contact, possessing different refractive properties and densities, and at different angles of incidence measured from the normal to the surface at the points of penetration or emergence. Frequently the possession of such tables would have greatly assisted the writer in original research; and he therefore supposes others would find them equally useful. They require to be calculated for refractions from one substance into another, and not merely for a ray passing from air into a more refracting medium.

Thus though the indices of refraction are for

the path of the ray of light cannot be shown on paper very readily, except as passing from air into the substance whose refractive index is known, and then only by taking the sines of the angles of incidence and refraction, as : 1. But the practical difficulty is greatly increased when the ray is passing from one medium into another of considerable deflecting power, as from glass into water; for the mutual or intermediate index of refraction is then considerably modified. Having carefully calculated these quantities, I may state that the actual index of refraction for a ray of light passing

The deviations of the ray entirely depend upon these quantities peculiar to the refraction between the contiguous media. For example

Suppose a brilliant particle be immersed in Canada balsam, and that a ray of light emanating from it traverses successively, the balsam, the glass cover, a layer of water, and then one of glass (the front lens of the objective), are there any optical advantages gained

The

by the use of this immersion lens? Mr. Ross confidently advertises his immersion lenses as giving most brilliant definition, and with perfect good faith. And their superior action in many cases testifies most strongly to the inferiority of the dry objectives. superb definition of Messrs. Powell and Lealand's newly-contrived immersion lenses leaves little to be desired. But those eminent makers acknowledge that their best dry objectives are inferior to their immersion glasses. There must therefore be a cause of this inferiority. A study of deviation, especially when a minimum, may possibly account for some of the causes of this fact, now well accredited with advanced microscopists, and proved by the enumeration (not merely by, the resolution) of Nobert's XIXth band by Powell's immersion alone. The dry lens would not do it in Dr. Woodward's hands.

The method of obtaining the ratio of the lines of refraction and incidence between two media whose refractions are known out of air, can be obtained by dividing the one index by the other.

Thus suppose it be required to find the refractive index between plate glass and water, i.e. between " and "

G

1.500 1.336

Suppose, again, a ray of light emanating from a brilliant bead immersed in Canada balsam penetrates it at an obliquity of 43°; if now there is air on the other side of the cover, the ray will be entirely turned back by internal total reflexion, and it cannot reach the objective or the observer's eye at all. But now insert a drop of water, and it will then only deviate just about seven degrees, and attain an obliquity of 50° in the film of water. Again, every ray of greater obliquity, up to 62° 57', will be able to reach the facet lens of the objective via water, whilst only those less oblique than an angle of 41° 48′ can possibly reach the objective via air.

One advantage, then, of water versus air is that it enables the objective to gather oblique rays, striking it via water which could not reach it viâ air.

Another advantage will be seen directly, that up to 100° objective aperture the deviation caused by the water is three times less than that caused by air; and therefore eccentrical aberration is correspondingly diminished. The immersion lens, therefore, prevents the escape of more than half of the rays diverging from a podura bead if mounted in Canada balsam, so that the quantity of rays transmitted by the water is two and one-fourth greater than that by the dry lens, as will be shown.

Journal,

But it will be seen hereafter that the water itself introduces a new compensation for spherical aberration. To avoid the analytic calculations the fact will be geometrically displayed in the drawing accompanying the second part of this paper, where every refracted line has been laid down by calculation, and the angles assiduously protracted by scale.

The course of each ray is given by the following table for refraction from plate glass into air, and the mode of calculating the tables is indicated by two examples in the appendix.

The practical importance of " Tables of Deviation" for compound refractions will be acknowledged at once by persons accustomed to original research in optical science. Their calculation, as will be seen in the appendix, involves considerable expenditure of time; but if these tables should in any way advance microscopical perfection, and enable us to clear away the errors still easily detected in most of the objectives now in use, the writer will be amply rewarded for his pains.

Apparently deviations for every degree up to 52, and then for increments of 5° and 10° are sufficiently close for practical use. The refractions are in each case actually taken to the nearest minute.

By these tables the ingenious amateur and optician will at once be able to delineate the course of a pencil of rays through a variety of compound refracting media with precision and confidence.

In the first table comparative deviations and refractions, and the angles of total internal reflexion beyond which obliquity no ray can pass, corresponding to given angles of obliquity of a ray just about to enter the front lens of the objective, have been carefully

calculated and verified.

The semi-aperture of an objective being given, the middle column representing that aperture at once gives on inspection, in the left and right columns, the deviations which the ray had suffered in entering air or water, and the diverging of the pencil radiating within the slide (mounted with Canada balsam) from the observed microscopical particle supposed to be brilliant with illumination. If the action of the Canada balsam be required in addition, which is neglected in this table, the deviation will require a minus correction exactly given in Table III., which is one minute for each degree of incidence or obliquity up to 10° nearly, and so on.

The table requires but little explanation. It will be at once seen on inspection that a ray of light up to 50° obliquity in water, just entering the objective, suffers only one-third the deviation that a ray of the same obliquity would have undergone through air.

Again, a pencil of 35° 16′ emanating or diverging from an observed particle in Canada balsam will enter the objective through a film of air at an obliquity of 60°, and therefore cannot be transmitted, unless the objective possess an aperture of 2 × 60°, or 128°; whilst the same aperture of objective will, with the optical advantage of water immersion, transmit an oblique pencil radiating from the brilliant particle of 50° 29′ instead of 35° 16′ as with the dry lens.

This example at once demonstrates that the addition of a water film is equivalent to largely increasing the aperture. So that via water a given objective will admit with a small aperture as large a radiant pencil diverging from the observed particle as a much greater aperture-objective will admit with the dry lens.

In other words, when we use an immersion system we can immediately reduce the aperture, i. e. reduce eccentrical aberration, and secure less deviation (one-third nearly), and the mystery of the superiority of the water lens is at once laid bare by a study of this table. The relative semi-apertures of dry and immersion objectives to admit identical divergent pencils from this particle are therefore found in the extreme left and right hand columns marked ' in each case; being the angle of incidence on the objective. So that in each case

Sin. = μ sin. p'. (μ, o and p', being general.)

Thus by the table the apertures of dry and immersion lenses transmitting the same pencil from the object mounted in balsam are, doubling the semi-apertures (for water films),

Considering, therefore, the enormous difficulties encountered in absolutely correcting the oblique and eccentrical pencils of an objective, and how much their defects are diminished by reducing the aperture, the extraordinary difference between the immersion and dry objective as regards the aperture required to transmit the same actual divergent pencil radiating from the particle in the balsam, we need not be astonished at the comparative ease and cheapness with which foreign opticians construct really good immersion waterlenses.

(To be continued.)

V.-On Synchata Mordax. By C. T. HUDSON, LL.D.

PLATE LVI.

THREE years ago I found S. mordax swarming at Christmas time in a pond near Exmouth on the road to Budleigh Salterton, and though I have frequently since met with specimens I have never till lately found it in sufficient numbers to make it worth while to renew my attempt to make out its structure. However, in the beginning of this March I captured some in a clear pond at Portbury, and by April they had so multiplied in the pond that every dip of a twoounce bottle would bring up a score of them. They were not to be found everywhere in the pond, but kept mainly to one spot which I noticed was sheltered by hillocks from the prevalent west wind, and in which the water crowfoot was growing. Throughout April they swarmed, but since then their number has been steadily decreasing; and now it requires an hour's search to catch a dozen, the pond all the while remaining apparently unaltered. I had hoped, both here and at Exmouth, to have found the males under such favourable circumstances; but I was disappointed. If I had caught one I think I should have noticed it, as I know the male of S. tremula.

Synchæta has had but scant justice done it. All the drawings I have seen (except Gosse's of the mastax) give only the vaguest hints of its internal structure, and represent it from only one (and that invariably the same) point of view; whereas it should be drawn from at least three points of view to convey an accurate idea of its shape. The difficulty of obtaining under the microscope any view of Synchata except that usually given is very great. It is the swiftest swimmer for its size among the Hydatinea, as well as the