and those by which it descends, are in distinct organs. He first made an experiment, in which, by preventing the forma tion of the tubers, the upper part of the plant was rendered much more luxuriant and prolific; in this manner shewing that the sap was carried from the leaves and stems down to the tubers. He afterward, in a second experiment, carefully removed the whole of the bark from several of the stems, and yet he found that the tubers were produced, although they were of smaller than ordinary bulk. Hence he concluded that his position respecting the inverted action of the alburnous vessels is proved; since, in the latter experiment, no other passage appears by which the sap could be conveyed from the upper to the lower parts of the plant.-We admit that the reasoning is plausible; yet we must be permitted to add that the hypothesis will require the aid of more experiments, before it can be considered as absolutely established.

Description of the Mineral Basin in the Counties of Monmouth, Glamorgan, Brecon, Carmarthen, and Pembroke. By Mr. Edw. Martin. The large cavity described in this paper is said to be composed of limestone, and to be the reservoir in which all the coal and iron ore of South Wales is deposited. Mr. Martin gives an apparently accurate account of its extent, and of the number and thickness of the different strata which it contains.

Observations on the Camel's Stomach, respecting the Water it contains, and the Reservoirs in which that Fluid is inclosed; with an Account of some Peculiarities in the Urine. By E. Home, Esq. F.R.S.-The peculiar property in the camel's stomach, by which it is enabled to take in a large stock of water before it commences its journies across the deserts, has been long known: but the exact structure and mechanism of the part have never yet been fully ascertained. Mr. Home's paper, however, has now furnished us with a clear and interesting account of this curious piece of comparative anatomy. In order to illustrate the subject, he begins by describing the digestive organs of the ox; which, in many respects, agree with those of the camel in their disposition and uses. In the ox, the first and second stomachs are included in one general cavity; the drink passes immediately into the second stomach; and it is from this cavity that the food is projected into the mouth, in order to undergo the second mastication. When the food is again swallowed, it is immediately carried to the third stomach; and after having been detained there for some time, it passes into the fourth, which is the immediate organ of digestion. The camel has the same number of cavities with the ox, and their general REV. FEB. 1807. disposition,

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disposition is considerably similar. The food, however, does not seem to pass into the second stomach before it is returned into the mouth, but is ejected from a particular part of the first; and after having been chewed, it is directly returned into the third. The drink passes into the second stomach, and, when this is filled, runs over into that part of the first in which the food is lodged; and it would appear that the animal has a voluntary power of discharging the water from the second stomach, so as to moisten the food in the first. When the cud has been chewed, it descends directly to the second stomach, and/ passes immediately into the fourth.-The apparatus by which these actions are performed is well explained, and illustrated by some good engravings.

The experiments on the urine, as here communicated by Mr. Hatchett, were performed by Mr. Brande. He was not able to detect any benzoic acid, but he found a little of the uric; and he discovered in it the phosphat of lime. This was likewise found in the urine of the cow; and these fluids agreed, moreover, in not containing any salts composed of soda. Yet these latter salts exist in the urine of the horse and the ass, which again differs from that of the other animals in not exhibiting any traces of the ammoniacal salts.

In mentioning the mode of killing the camel which was the subject of these experiments, by pithing, Mr. Home points out the erroneous manner in which this operation is often executed, and which has led to the discouragement of the practice:

The operation was performed with a narrow double-edged poniard passed in between the skull and first vertebra of the neck; in this way the medulla oblongata was divided, and the animal instantaneously deprived of sensibility. In the common mode of pithing cattle, the medulla spinalis only is cut through, and the head remains alive, which renders it the most cruel mode of killing animals that could be invented.'

MATHEMATICS, ASTRONOMY, &C.

Observations upon the Marine Barometer, made during the Examination of the Coasts of New Holland and South Wales, in the Years 1801, 1802, and 1803. By Matthew Flinders, Esq. Commander of his Majesty's Ship Investigator.-If there be any connection between the wind and weather and the variations of the barometer, it is certainly most desirable that seamen should be acquainted with the laws of that connection: but it is evident that they can only be ascertained by long, patient, and careful observation.

In the paper before us, Capt. Flinders furnishes some valuable remarks, which, as far as they go, will be useful to the mariner;

and

and if other navigators make observations, and cause them like the present to be registered, we shall gradually accumulate sufficient conditions and data for a theory and a system :-some future philosopher may arise who will arrange, compare, and combine the facts which he finds recorded.

On the necessity for every ofheer being provided with a barometer, Capt. F. says:

The barometer seems capable of affording so much assistance to the commander of a ship, in warning him of the approach and termination of bad weather, and of changes in the direction of the wind, even in the present state of meteorological knowledge, that no officer in a long voyage should be without one. Some experience is required to understand its language, and it will always be necessary to compare the state of the mercury with the appearance of the weather, before its prognostications will commonly be understood; for a rise may foretel an abatement of wind,-a change in its direction, or the return of fine weather, or if the wind is light and varia ble, it may foretel its increase to a steady breeze, especially if there is any casting in it; and a fall may prognosticate a strong breeze or gale, a change of wind, the approach of rain, or the dying away of a steady breeze. Most seamen are tolerably good judges of the appearance of the weather; and this judgment assisted by observation upon the quick or slower rising or falling of the mercury, and upon its relative height, will in most cases enable them to fix upon which of these changes are about to take place, and to what extent, where there is only one; but a combination of changes will be found more difficult, especially where the effect of one upon the barometer is counteracted by the other; as for instance, the alteration of a moderate breeze from the westward with dull, or rainy weather, to a fresh breeze from the eastward with fine weather, may not cause any alteration in the height of the mercury; though I think there would usually be some rise in this case. Many combinations of changes might be mentioned, in which no alteration in the barometer would be expected, as a little consideration, or experience in the use of this instrument, will make sufficiently evident; the barometer alone, therefore, is not sufficient; but in assisting the judgment of the seaman, is capable of rendering very important services to navigation.'

A new Demonstration of the Binomial Theorem, when the Exponent is a positive or negative Fraction. By the Rev. Abram Robertson, A. M. F.R.S., Savilian Professor of Geometry at Oxford. Since the invention of the law of the binomial theorem, frequent attempts have been made to demonstrate it on clear and exact principles; and the author of the present demonstration has already inserted one somewhat similar, in a preceding volume of the Transactions (viz. that for 1794-) We shall briefly state the principle on which the proof before us is founded.

If m, m', be integer numbers, then it is easily proved that

If these series be multiplied together, there results a series 1 + Av + A ́ v2 + A ̋ v2 + &c.

in which

A = m + m2

A'=

A"=

m2 + m2—m+m2 + 2mm2 (m+m) (m+m—1)

2

(m+m') (m+m—1) (m+m' — ›)

1.2. 3

&c.

Now although the formulas for (1+v)m (1+v) have been deduced on the supposition of m, m' being whole numbers, yet if such series as t+mv+ &c. and 1+m'v &c. be multiplied together, values of A, A, A", will be precisely the same with regard to form, whatever m, m' are, and consequently will be the same if m, m be fractions. The actual multiplication,' says Mr. R. will end in the same powers of m and m', the same combinations of them, and the same numerals, whether we consider m and m' as whole numbers or as fractions. By virtue of this property, if 1+1+111— i v2 + &c. be assumed the 4th root of 1+v; then, if we multiply this series into itself, the result will be 1+v+1·1 (−1) v2 + &c.; and if this series be multiplied into itself, the result will

and consequently, the 4th root of was rightly assumed. A similar method may be used for the root. Now, if this demonstration of the binomial has any claim to originality, it must be in the remark relative to the property of the coefficients A, A', A", &c. remaining the same in regard to form, whatever be the indices.-In the 19th volume of the Novi Commentarii Petropol. we have a demonstration of the binomial by Euler; and in the summary which always precedes the memoirs themselves, the reporter thus speaks of Euler's solution :

"1+nx+&c. de quá quidem serie constat, eam casu n numeri integri, æqualem esse (1 + x), generatim, vero hujus seriei valorem indicandum,

indicat

indicat Illust. Auctor signo [n]. Quodsi nunc duo talia signa [m] [n] in se invicem ducantur, et productum exprimi supponatur per seriem

1 + Ax + Bx2+ &c.

coefficientes A, B, C, per litteras met n determinari evidens est, patet que modum quo hæc determinatio sit, ab indole m et n non pendere, ideoq. eundem esse sive m, n, supponantur integri, sin fracti. At si m, n, numeri integri, est omnino

[m] [n] = (1+x) m+n = [m+n]

inde generatim quoque

[m] [n] = [m+n]" &c. &c.

If we consult the memoir itself, we shall find that the method of demonstration essentially rests on this principle: "hic autem imprimis observari convenit, hanc compositiones rationem non ab indole literarum m et n pendere, sed perinde se esse habituram, sive ha litera met n denotent numeros integros, sive alios numeros quoscunque. Hoc ratiocinium non vulgare probe notetur, quonium ei tota vis nostræ demonstrationis innititur."-We think that these extracts prove, beyond the possibility of a doubt, that the principle of Mr. Robertson's demonstration is precisely the same with that which was adopted by Euler thirty years ago. It is not our wish, on the sameness of the principle and the simplicity of the two demonstrations, to found a charge of plagiarism against Mr. R.: but he must abandon all claim to originality or priority of invention; which must be awarded to Euler.

The honor of the invention, however, does not deserve to be violently contested. Euler's demonstration, when reduced to plainness from his uncouth symbols, is not a direct demonstration he assumes a series for the case in which the index is a fraction, and then proves that this series was rightly assumed this is very different from assuming

(I+x)" = I + ax + bx2+ &c,

and then deducing b=a. x c = b. "=2, &c.

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New Method of computing Logarithms. By Thomas Manning, Esq.

'If there already existed (says the author) as full and extensive logarithmic tables as will ever be wanted, and of whose accuracy we were absolutely certain, and if the evidence for that accuracy could remain unimpaired throughout all ages, then any new method of computing logarithms would be totally superfluous so far as concerns the formation of tables, and could only be valuable indirectly, inasmuch as it might shew some curious and new views of mathematical truth. But this kind of evidence is not in the nature of human affairs. Whatever is recorded is no otherwise believed than on the evidence of testimony;

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