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and we find from the equations of conduction,
do

đo
d9

dr9
kc =(1+2f+9) kom=(1-2f+9)
dt

dt

dw

M"w.
kc =(1-9)
dt

dura

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+

ke dgi _ da

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d294

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CASE IV.-Cable of six wires symmetrically arranged.
Equations of mutual influence,

cv,=.+f92 +98)+9(93+9) + hq.
&c.
&c.

&c. Equations of conduction,

d'96

d`q
+
dt dx? dxa dix dx2 dr

dx2 Then assuming

91 +92 +93 +94 +95 +96=0 4.-14+93-96+95-9=9 3(%. +9.)--=w, ; 39+9)--=w, ; 3(95+92)--=wg; 3(9.-91)-9=pii 3(93-96)-9=Pz; 3(93-92)-9=ps;

33Pa which require that

Wi+wa+wn=0, and pi+P2+P;=0;
we have
do
do d9

.de
kc : [(fh) kc
dt

dt

dạw
kc
=[1—(f+9)+h]

=(1+(1-9)-h]d

[9—9dt

dt These equations, integrated by the usual process to fulfil the prescribed conditions, determine o, J, W., W.,, W3, Pi, P2, P3 ; and we then have, for the solution of the problem,

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dw

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; kode

dx?'

=

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;

9=1 (0+9+w, +pi); 95=2(a+9+w.+pa); 9;= (0+9+w, +p); 9.=(r=8+w.–P.): 9=(-8+w-a): 9:=(-9+,-0.)

; 0.Pa o w.

1

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V. "

Experimental Researches on the Functions of the Mucous Membrane of the Gall-bladder, principally with reference to the Conversion of Hepatic into Cystic Bile.” By GEORGE KEMP, M.D. Cantab. Communicated by the Rev. W. CLARK, M.D., F.R.S., Professor of Anatomy in the University of Cambridge. Received May 1, 1856.

(Abstract.) Referring to the well-known difference in taste and other physical properties between the bile as it immediately proceeds from the liver and the same fluid after it has been retained for a time in the gallbladder, the author observes, that the nature of this difference and the agency by which it is effected, are questions which have not yet met with the attention they deserve, and that he had accordingly been led to make them the subject of experimental inquiry. As, however, it is only on rare occasions that the hepatic bile can be procured in quantity sufficient for chemical experiment, and then only at the risk of its being altered by pathological conditions of the secreting organ, the author considers that, however clearly individual facts on the subject may be demonstrated, any deductions made therefrom must be referred to the lower department of probable evidence; and it is with this reservation that he lays his conclusions before the Royal Society, whilst, at the same time, he believes that, so far as the nature of the case admits, he has been able to elicit a new fact respecting the mucous membrane of the gallbladder, which may lead to the better comprehension of the functions of mucous membranes generally.

Assuming, in the first place, that the change in properties which the bile undergoes in the gall-bladder is brought about either by the mucous secretion of that reservoir, or by some operation exerted by its internal membrane, it is observed, with respect to the action of the mucus, 1st, that when left in the gall-bladder in contact with the cystic bile, it is capable of subverting the composition of that fluid. 2nd, That this change is much accelerated by even a moderately elevated temperature. 3rd, That when the contents of the gall-bladder are evaporated to a syrupy consistence, the bile, at first

VOL. VIII.

N

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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 ers, until the mucous secretion and bile disappeared ; a small portion was now placed in an evaporating dish

V. “Experimental Researches on the Functions of the Mucous

Membrane of the Gall-bladder, principally with reference to the Conversion of Hepatic into Cystic Bile.” By GEORGE KEMP, M.D. Cantab. Communicated by the Rev. W. CLARK, M.D., F.R.S., Professor of Anatomy in the University of Cambridge. Received May 1, 1856.

(Abstract.) Referring to the well-known difference in taste and other physical properties between the bile as it immediately proceeds from the liver and the same fluid after it has been retained for a time in the gallbladder, the author observes, that the nature of this difference and the agency by which it is effected, are questions which have not yet met with the attention they deserve, and that he had accordingly been led to make them the subject of experimental inquiry. As, however, it is only on rare occasions that the hepatic bile can be procured in quantity sufficient for chemical experiment, and then only at the risk of its being altered by pathological conditions of the secreting organ, the author considers that, however clearly individual facts on the subject may be demonstrated, any deductions made therefrom must be referred to the lower department of probable evidence; and it is with this reservation that he lays his conclusions before the Royal Society, whilst, at the same time, he believes that, so far as the nature of the case admits, he has been able to elicit a new fact respecting the mucous membrane of the gallbladder, which may lead to the better comprehension of the functions of mucous membranes generally.

Assuming, in the first place, that the change in properties which the bile undergoes in the gall-bladder is brought about either by the mucous secretion of that reservoir, or by some operation exerted by its internal membrane, it is observed, with respect to the action of the mucus, Ist, that when left in the gall-bladder in contact with the cystic bile, it is capable of subverting the composition of that fluid. 2nd, That this change is much accelerated by even a moderately elevated temperature. 3rd, That when the contents of the gall-bladder are evaporated to a syrupy consistence, the bile, at first

VOL. VIII.

N

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

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