neutral, becomes alkaline and broken up into several organic groups. 4th, That if the mucus of the gall-bladder be carefully removed by alcohol or acetic acid, and the perfectly fresh bile be then evaporated, these changes do not take place.

From these facts it follows that the mucus of the gall-bladder is a highly catalytic body, and that the analysis of bile which has been left in contact with it, under the conditions above stated, must lead to varying and unsatisfactory results.

From these considerations it naturally occurred to try the effect of placing the mucus of the gall-bladder in contact with hepatic bile; but the experiment was not performed, as it was found impracticable to obtain the mucus of the gall-bladder free from cystic bile without precipitation by reagents. Desiring, however, to ascertain whether the mucus is principally retained in contact with the inner surface of the gall-bladder or diffused through its contents, the author subjected the gall-bladder and its contained fluid, taken from an ox just slaughtered, to a freezing mixture of snow and salt, until all but the central part of the fluid was frozen, and on pouring out the latter found it to contain mucus; thus showing that this secretion is not merely confined to the inner surface of the gall-bladder for the purpose of protection and lubrication of the subjacent membrane, but is diffused throughout the bile contained in that reservoir.

Leaving now the mucous secretion, the object was first to ascertain whether the mucous membrane itself possesses the property of changing the molecular structure of the bile; then to observe whether it possesses any analogy to other mucous membranes, such as the epithelial membrane of the calf's stomach, &c., in acting upon animal fluids and solutions of bodies which readily break up into binary forms; to examine, in the next place, its action upon albumen, the white of an egg being the substance selected; and, finally, to determine its effects on the biliary secretion, as produced in the liver before its admission into the gall-bladder.

Action of the Mucous Membrane of the Gall-bladder upon Bile. December 11, 1855.-The mucous membrane of the gall-bladder was dissected, or rather stripped from the other portion of the viscus, and washed in several waters, until the mucous secretion and bile disappeared; a small portion was now placed in an evaporating dish

and covered with fresh ox-bile, from which the mucus had been carefully removed; the bile also was tested with diluted acetic acid, giving no precipitate or appearance of turbidity. The whole was, at 1 P.M., placed in a warm situation. At 3 P.M. the solution was tested with acetic acid, when it became densely turbid. Temperature, 43° 5 C. The peculiar odour of musk was very distinct in this solution, though not perceptible in the remainder of the fresh bile. A small quantity of water was added, to replace that lost by evaporation, and the solution returned to its warm situation. 6 P.M. again tested, with similar results; the musky odour very strong. 7.30 P.M. again tested, when not only was the solution rendered turbid, but a white precipitate was thrown down; the fluid was also distinctly alkaline.

The mucous lining of the gall-bladder is therefore a catalytic body capable of producing molecular changes in the bile.

Action of the Mucous Membrane of the Gall-bladder upon certain Bodies which readily break up into Organic Groups.

Milk. December 18.-A portion of mucous membrane was scraped and washed with scrupulous care, in order that the whole of the mucus might be removed; it was then covered with fresh milk and exposed to a temperature of 32° C. In one hour the fluid was separated into serum, turbid with caseine, and an over-stratum of a creamy substance greatly resembling butter, thus exhibiting a catalytic influence very analogous to the action of rennet. The whole contents of the evaporating dish were then set aside, as having effected the object of the experiment; on the 21st, however, the author was induced to taste the fluid, and, to his astonishment, found it intensely bitter, and, what is more remarkable, on applying Pettenkofer's well-known test of sugar and sulphuric acid, with increase of temperature, the characteristic rose-tint was developed. The musky smell was not observable.

Honey. December 26.-A portion of mucous membrane, carefully washed, was covered with a solution of honey (one measure of honey to three of water). After six hours' exposure at 38° C., it was found bitter, and gave a precipitate with diluted acetic acid; this was not the case with the original solution. The fluid, being slightly acid, was carefully neutralized with carbonate of soda. The taste,

after another period of six hours, was very bitter. On the 28th the fluid had evaporated down to a thick honey consistence.

The next remark on this subject, in the author's rough notes taken at the time, is the following:

January 27.-"The honey solution is now nearly evaporated. A mass of crystals (grape-sugar) with a small quantity of syrup, intensely bitter." The syrup could be readily poured off from the crystals. The mucous membrane was not in the slightest degree decomposed; swelled and elastic, not splitting into layers.

It is well known that, after long keeping, granules of grape-sugar are found in honey; therefore, on the 22nd of April, the honey from which the experiments were made was re-examined, and found to be nearly homogeneous and not separated into crystals and syrup; indeed the whole physical appearances are so different from the honey after being operated upon, that the author cannot doubt the influence of the membrane in effecting the changes registered.

At this stage of the inquiry an important doubt suggested itself. In the above experiments no small importance has been attached to the circumstance of bitterness becoming developed in the various solutions when kept in contact with the membrane. In every case indeed the membrane was washed with jealous care, but the fact is palpable, that it is almost impossible to divest the membrane of every trace of bitterness; when this is effected as far as practicable, in a very few minutes the damp membrane increases perceptibly in bitterness. When washed, submitted to pressure between folds of blotting-paper, stretched out on a board and dried as rapidly as possible in a current of warm air, it is still bitter. May not the bitterness alluded to in the above cases be attributed to disintegration of the mucous membrane itself? The following experiments seemed sufficiently simple in their conditions and adapted to answer the query. A body was selected in which well-known molecular disturbances are easily established-cane-sugar.

Sugar. December 28.-A portion of membrane was covered with a solution of white sugar; another portion, of the same size, was covered with lukewarm water, and both were exposed to a temperature of 32° C. One hour having elapsed, the watery solution was just perceptibly bitter, the saccharine solution decidedly so.

December 29.-The watery solution was rendered very slightly

turbid on the addition of diluted acetic acid; this reagent, however, threw down a distinct precipitate from the saccharine solution.

January 5, 1856 (from note-book).—"The mucous membrane infused in simple water is today looking disintegrated, in layers, the solution opake and slimy; slightly alkaline, just bitter. The mucous membrane in sugar very bitter, perfectly transparent. I believe that the difference of the mucous membrane, as infused in water and in syrup, appears to be well established."

January 9." The sugar solution is perfectly transparent, very bitter, very slightly alkaline; the membrane is much swelled out and thickened; fresh. The watery solution is becoming decomposed, alkaline, has lost its bitter taste, very turbid; the membrane is shrivelled and separating into layers. Microscopic examination referred the turbidness to broken-down epithelium."

The report of the above series of experiments has been thus minutely transcribed, because it seems to place the active agency of the mucous membrane beyond reasonable doubt, so far as the class of bodies alluded to is concerned; but principally because, as will be seen in the sequel, Pettenkofer's method alone appears to fail in some cases as a discriminating test of the bile.

Action of the Mucous Membrane of the Gall-bladder upon Albumen. January 27.—“ At 3 P.M. took a portion of dry mucous membrane and carefully washed it in several waters; it was then plunged into the white of an egg. 8 P.M. the glairy fluid is bitter."

January 31.-"The solution apparently increasing in bitterness; a little water added to supply the loss by evaporation."

February 18.-"The albumen solution has from time to time been diluted with water. Today I can barely detect bitterness, nor is the colour changed. On applying Pettenkofer's test, the play of colour, supposed to be characteristic of bile, was very distinct in the fluid portion; the albumen coagulated by the heat, retaining its white colour."

This result was perplexing; on the 19th, therefore, an experiment was made on the white of an egg, per se, to ascertain whether the effect was due to the albumen. The white of an egg was first boiled in water, to coagulate the albumen, and the filtered fluid, containing soluble albumen and probably other organic matters, was examined

Hence, by the general theorem, we conclude [V]=[V1], and so demonstrate the affirmative answer to the question stated above.

I think it unnecessary to enter on details suited to the particular case of lateral electrostatic influence between neighbouring parts of a number of wires insulated from one another under a common conducting sheath, when uniform or varying electric currents are sent through by them; for which a particular demonstration in geometry of two dimensions, analogous to the demonstration of Green's theorem to which I have referred as involving the consideration of a triple integral for space of three dimensions, may be readily given; but, as a particular case of the general theorem I have now demonstrated, it is obviously true that the potential in one wire due to a certain quantity of electricity per unit of length in the neighbouring parts of another under the same sheath, is equal to the potential in this other, due to an equal electrification of the first.

Hence the following relations must necessarily subsist among the coefficients of mutual peristaltic induction in the general equations given above,

On the Solution of the Equations of Peristaltic Induction in symmetrical systems of Submarine Telegraph Wires.

The general method which has just been indicated for resolving the equations of electrical motion in any number of linear conductors subject to mutual peristaltic influence, fails when these conductors are symmetrically arranged within a symmetrical conducting sheath (and therefore actually in the case of any ordinary multiple wire telegraph cable), from the determinantal equation having sets of equal roots. Regular analytical methods are well known by which the solutions for such particular cases may be derived from the failing general solutions; but it is nevertheless interesting to investigate each particular case specially, so as to obtain its proper solution by a synthetical process, the simplest possible for the one case considered alone. In the present communication, the problem of peristaltic induction is thus treated for some of the most common cases of actual submarine telegraph cables, in which two or more wires of equal dimen