14. The preceding investigation will apply, with a very trifling modification, to Sir DAVID BREWSTER's experiment, in which the retarding plate, instead of being placed in front of the object-glass of a telescope, is held close to the eye. In this case the eye itself takes the place of the telescope; and if we suppose the whole refraction to take place at the surface of the cornea, which will not be far from the truth, we must replace ƒ by the diameter of the eye, and by the angular extent of the portion of the spectrum considered, diminished in the ratio of m to 1, m being the refractive index of the cornea. When a telescope is used in this experiment, the retarding plate being still held close to the eye, it is still the naked eye, and not the telescope, which must be assimilated to the telescope considered in the investigation; the only difference is that must be taken to refer to the magnified, and not the unmagnified spectrum.

Let the axis of x be always reckoned positive in the direction in which the blue end of the spectrum is seen, so that in the image formed at the focus of the objectglass or on the retina, according as the retarding plate is placed in front of the object-glass or in front of the eye, the blue is to the negative side of the red. Although the plate has been supposed at the positive side, there will thus be no loss of generality, for should the plate be at the negative side it will only be requisite to change the sign of g.

First, suppose g to decrease algebraically in passing from the red to the blue. This will be the case in Sir DAVID BREWSTER's experiment when the retarding plate is held at the side on which the red is seen. It will be the case in Professor PowELL's experiment when the first of the arrangements mentioned in art. 2 is employed, and the value of N in the table of differences mentioned in art. 5 is positive, or when the second arrangement is employed and N is negative. In this case is negative, and therefore g<-(h+k), and therefore (15.) is the expression for the intensity. This expression indicates a uniform intensity, so that there are no bands at all.

Secondly, suppose g to increase algebraically in passing from the red to the blue. This will be the case in Sir DAVID BREWSTER's experiment when the retarding plate is held at the side on which the blue is seen. It will be the case in Professor POWELL'S experiment when the first arrangement is employed and N is negative, or when the second arrangement is employed and N is positive. In this case is positive; and since varies as the thickness of the plate, g' may be made to assume any value from -(4g+h+k) to + by altering the thickness of the plate. Hence, provided the thickness lie within certain limits, the expression for the intensity will be (16.) or (17.). Since these expressions have the same form as (1.), the magnitude only of the coefficient of cos g', as compared with the constant term, being different, it is evident that the number of bands and the places of the minima are given correctly by the imperfect theory considered in Section I.

15. The plate being placed as in the preceding paragraph, suppose first that the breadths h, k of the interfering streams are equal, and that the streams are contiguous,

so that g=0. Then the expression (17.) may be dispensed with, since it only holds good when g'=0, in which case it agrees with (16.). Let To be the value of the thickness T for which g=0. Then T=0 corresponds to g'=—(h+k), T=T, to g'=0, and T=2T to g'=h+k; and for values of T equidistant from To, the values of g' are equal in magnitude but of opposite signs. Hence, provided T be less than 2T, there are dark and bright bands formed, the vividness of the bands being so much the greater as T is more nearly equal to To, for which particular value the minima are absolutely black.

2,

Secondly, suppose the breadths h, k of the two streams to be equal as before, but suppose the streams separated by an interval 2g; then the only difference is that g'=-(h+k) corresponds to a positive value, T2 suppose, of T. If T be less than T, or greater than 2T-T2, there are no bands; but if T lie between T, and 2T-T2 bands are formed, which are most vivid when T-To, in which case the minima are perfectly black.

Thirdly, suppose the breadths h, k of the interfering streams unequal, and suppose, as before, that the streams are separated by an interval 2g; then g'(h+k) corresponds to a positive value, T2 suppose, of T: g'=-(hk) corresponds to another positive value, T1 suppose, of T, T1 lying between T2 and To, To being, as before, the value of T which gives g'=0. As T increases from To, g' becomes positive and increases from 0, and becomes equal to h✩k when T=2T-T1, and to h+k when T=2T - T2. When T<T, there are no bands. As T increases to T1 bands become visible, and increase in vividness till T=T1, when the ratio of the minimum intensity to the maximum becomes that of h-k to h+3k, or of k-h to k+3h, according as h or k is the greater of the two, h, k. As T increases to 2T-T1, the vividness of the bands remains unchanged; and as T increases from 2T-T1 to 2T-T2, the vividness decreases by the same steps as it before increased. When T=2T-T2, the bands cease to exist, and no bands are formed for a greater value of T.

Although in discussing the intensity of the bands the aperture has been supposed to remain fixed, and the thickness of the plate to alter, it is evident that we might have supposed the thickness of the plate to remain the same and the aperture to alter. Since ∞o T, the vividness of the bands, as measured by the ratio of the maximum to the minimum intensity, will remain the same when T varies as the aperture. This consideration, combined with the previous discussion, renders unnecessary the discussion of the effect of altering the aperture. It will be observed, that, as a general rule, fine bands require a comparatively broad aperture in order that they may be well-formed, while broad bands require a narrow aperture.

16. The particular thickness To may be conveniently called the best thickness.' This term is to a certain extent conventional, since when h and k are unequal the thickness may range from T1 to 2T-T, without any change being produced in the vividness of the bands. The best thickness is determined by the equation

242 MR. STOKES ON THE THEORY OF CERTAIN BANDS SEEN IN THE SPECTRUM.

Now in passing from one band to its consecutive, g changes by 27, and by e, if e be the linear breadth of a band; and for this small change of we may suppose the de 2π Hence the best aperture for a

changes of g and proportional, or but

given thickness is that for which

=dr e

4g+h+k=21ƒ.

እf

If g=0 and k=h, this equation becomes h= e

The difference of distances of a point in the plane xy whose coordinates are §, 0 from the centres of the portions of the object-glass which are covered by the interfering streams, is nearly

and if ò be the change of when this difference changes by λ,

Hence, when the thickness of the plate is equal to the best thickness, e=d, or the interval between the bands seen in the spectrum is equal to the interval between the bands formed by the interference of two streams of light, of the colour considered, coming from a luminous line seen in focus, and entering the object-glass through two very narrow slits parallel to the axis of y, and situated in the middle of the two interfering streams respectively. This affords a ready mode of remembering and calculating the best thickness of plate for a given aperture, or the best aperture for a given thickness of plate.

17. According to the preceding explanation, no bands would be formed in Sir DAVID BREWSTER'S experiment when the plate was held on the side of the spectrum on which the red was seen. Mr. AIRY has endeavoured to explain the existence of bands under such circumstances. Mr. AIRY appears to speak doubtfully of his explanation, and in fact to offer it as little more than a conjecture to account for an observed phenomenon. In the experiments of Mr. TALBOT and Mr. AIRY, bands appear to have been seen when the retarding plate was held at the red side of the spectrum; whereas Sir DAVID BREWSTER has stated that he has repeatedly looked for the bands under these circumstances and has never been able to find the least trace of them; and he considers the bands seen by Mr. TALBOT and Mr. AIRY in this case to be of the nature of NEWTON's rings. While so much uncertainty exists as to the experimental circumstances under which the bands are seen when the retarding plate is held at the red side of the spectrum, if indeed they are seen at all, it does not seem to be desirable to enter into speculations as to the cause of their existence.

* Philosophical Transactions for 1841, Part I. p. 6.

XVII. An Experimental Inquiry undertaken with the view of ascertaining whether any, and what signs of current Electricity are manifested during the organic process of Secretion in living animals, being an attempt to apply some of the discoveries of FARADAY to Physiology*. By H. F. BAXTER, Esq.

Communicated by Sir BENJAMIN BRODIE, Bart., F.R.S.

Received May 6,-Read May 25, 1848.

THE conjecture and experiment of WOLLASTON†, the cautious opinion of PROUT‡, the experiments of DONNE § and of MATTEUCCI, are so well known that a mere allusion to them may be deemed sufficient. BECQUEREL¶, in speaking of MATTEUCCI's experiment, adds, "Si de nouvelles expériences confirment les résultats, il faudrait en conclure réellement que les organes qui sécrètent un liquide acide ou alcalin, ont des facultés électriques analogues à celles de la pile.”

POUILLET** inserted one of the platinum extremities of a galvanometer into the jugular vein of a rabbit, the other into the carotid artery, without any effect being produced on the needle. MÜLLER says, "With the galvanometer no electric current can be discovered in the blood. I perceived no variation of the magnetic. needle of the multiplier, even when I inserted one wire into an artery of a living animal, the other into a vein."

The galvanometer that was used in these experiments is one of the common and ordinary construction, astatic, consisting of but few coils; the needles suspended by silk-worm silk, and the electrodes attached by screws. As the object was to ascer

* It would be unjust to BECQUEREL not to state, that great and important assistance was obtained during the progress of the inquiry from his valuable work, entitled "Traité de l'Électricité," respecting one class of phenomena especially, viz. the action of an acid and an alkali upon each other when separated by a membrane or any other porous diaphragm. But, at the very commencement of the inquiry, it soon became apparent that no real progress could be reasonably expected until clearer ideas had been obtained as to the origin of the power in the voltaic circle. This led to the study of those admirable memoirs of FARADAY. The inquiry and the study of those memoirs went hand-in-hand. The opinions supposed were those from FARADAY; the experiments, tests of those opinions. The endeavour to master the meaning of that important, comprehensive, and expressive phrase, "an axis of power having contrary forces, exactly equal in amount, in contrary directions," was the mental difficulty; in that consists the requisite mental labour. It is not too much to add, that without those memoirs the inquiry would not have been continued. + Philosophical Magazine, vol. xxxiii. p. 488.

On Stomach and Urinary Diseases, 3rd edit. p. xxv.
Ibid. tom. iv. p. 300.
¶ Ibid. p. 301.

§ BECQUEREL, Traité de l'Électricité, tom. i. p. 327. ** Journal de Physiologie, tom. v. p. 5. †† MÜLLER's Physiology, translated by BALY, vol. i. p. 148, 2nd edit. Made by NEWMAN of Regent Street. There is one advantage attending the use of a galvanometer that is not very delicate in its construction in these experiments; the vibrations of the needle soon subside, and consequently more information can be obtained from a single experiment.

tain, if possible, the existence of the current, an accurate description of its delicacy will not be necessary. It is sufficiently so to indicate the existence of a current during the combination of an acid with an alkali, such as very dilute solutions of nitric acid and of potash, when separated by a membrane.

In several unsuccessful experiments, the following electrodes were used:-Two platinum wires, 4th of an inch in thickness and eleven inches in length, were pointed at one extremity, to be easily inserted into a blood-vessel or an organ, and coated with sealing-wax for about two inches, leaving the extreme point bare to the extent of one-fourth of an inch, the other extremities being attached to the galvanometer. But during the inquiry, in consequence of the stiffness of the wires forming the electrodes occasioning a motion of the whole instrument, when making and breaking contact, the following alteration was made in the arrangement. Thick copper wires ten inches in length were connected with the galvanometer by the screws, and each of the free extremities so bent as to rest in a separate wooden cup containing mercury. A platinum plate, an inch square, was attached to one extremity of each of the platinum electrodes to increase the extent of surface, and being placed in the wooden cups, a communication was formed with the galvanometer by means of the mercury, the pointed extremities serving, as before, to be inserted into the different parts of the animal. Great care was taken to ascertain that the different contacts were perfect, and no result upon the needle occurred from the whole arrangement, when a circuit was formed with a weak solution of salt, or water, previous to each experiment.

It will be unnecessary to relate the experiments, thirteen in number, upon cats, kittens, a guinea-pig and rabbits, in which an endeavour was made to ascertain whether the effect of a diverted current might not be obtained by inserting the electrodes into the portal vein alone, supposing that the stomach and liver formed poles similar to those of a galvanic circle; or whether a current might not be obtained by inserting them into the portal and hepatic veins. These failures, combined with theoretical reasoning, led to the supposition that the effect sought for existed in a different quarter. The inquiry will therefore commence with relating the last of the unsuccessful experiments.

Experiment 1.-Rabbit, six weeks old. (a). One electrode inserted into the vena porta, the other into the vena cava, at the entrance of the hepatic veins; no effect. (b). Caput coli, and a vein coming from the same part; a slight effect appeared: the electrodes were cleaned and reinserted, but the same effect did not occur. (c). Stomach and liver. (d). Stomach and vena porta. (e). Stomach and gall-bladder; no effect.

In these and the following experiments the electrodes were cleaned after the formation of a previous circuit, whenever the substances adhering to them might influence the result. Repeating the experiments of MATTEUCCI and of DONNÉ, only once did the effect occur, and that but slight, in the guinea-pig. The following fact may perhaps account for it.

Instead of the plates dipping into the mercury, the points were used for this purpose, and the surface of the plates served to form the free extremities of the electrodes.