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occasion, was one combining in a high degree simplicity with accuracy; and the quantities of gas. operated on, together with the great care to discover and avoid every possible source of error, have produced a most satisfactory coincidence in the general results of the numerous experiments here described.

In each of the ten first experiments, between three thousand and four thousand cubic inches of common air were respired in the space of from ten to eleven minutes each; and in all of them it was observed that the quantity of expired was less than that of inspired air, although, if the chemical effect of respiration is merely the acidification of carbon in the lungs, there ought to be no difference between the two quantities, as a cubic inch of oxygen gas produces precisely the same bulk of carbonic acid. From experiments in which a similar deficiency has appeared, it has been supposed by former enquirers that a portion of the oxygen or azot of the inspired air was actually absorbed : but in the ten experiments here alluded to the deficiency is upon the whole so small, and yet so variable, from to of the whole, that it is probably entirely accidental: and is in our. opinion well accounted for, by the following remark.

"The deficiency, in our opinion, principally arises from the difficulty in bringing the lungs precisely to the same state after, as before the experiment; and it must be recollected that the operator commenced by a forcible expiration into the open air, but finished by a forcible expiration into the mercurial gasometer. Now, although this gasometer was counterpoised by weights in the scale attached to it, yet we can easily conceive that more resistance might be afforded to the complete evacuation in the latter case than in the former, and consequently the lungs might contain a few inches more after the experiment than before it."

In the 11th experiment, 3460 cu

bic inches of air were respired in 11 minutes, and a deficiency of 23 inches was thereby incurred. The air previously to being breathed, consisted of 21 oxygen, and 79 azot, in 100 parts; but after respiration it consisted of 8. 5 carbonic acid, 12. 5 oxygen, and 79 azot.

In the 12th experiment an assistant was made to respire 3300 cubic inches of air, which, after passing through the lungs, were found to have encreased to 3311 inches: the time employed was only 5 minutes, but notwithstanding that in this case the respiration was twice as rapid as in the former one, the expired air contained as before, s. 5 per cent of carbonic acid,

In the 13th experiment, the same operator, who performed all the others except the 12th, respired 9890 inches in 24 min. 37 sec. The deficiency after the process amounted only to 18 inches; and the expired air was found to consist of 8 carbonic acid, 13 oxygen, and 79 azot.

In the 15th, experiment, 300 cubic inches of common air were breathed repeatedly till the operator nearly fainted; the residual gas on analysis was found to consist of 10 carbonic acid, 4 oxygen, and 86 azot, but its absolute quantity was not ascertained.

In the 16th experiment respiration was performed on gas obtained from oxymuriat of potash consisting of 97. 5 oxygen, and 2.5 azct. 3260 inches were respired in 9min. 20 sec. and there appeared a deficiency of 67 inches. The gas feriespiration consisted of 11 carbonic acid, 83 oxygen, and 6 azot.

Here it is plain that a greater quantity of carbonic acid was form ed from oxygen, than from commoa air, and the experimenters infer that one use of azot is to regulate the quantity of oxygen consumed in respiration. The additional quan tity of azot, which made its ap pearance in this, and the preceding

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experiment is supposed to arise "From that portion still retained in the lungs, notwithstanding the forced expiration at the beginning of the experiment, and considering that in the 14th and 15th experiment, where the same air was repeatedly breathed, the proportion of azote was in the one case 85, and in the other 86 per cent. it seems fair to presume, that the residual air contained in the lungs after a forced expiration may amount in 100 parts, to not more than 16 oxygen, and 84 azote : any one who reflects upon the structure of the lungs, and the minute ramifications of the extremities of the bronchial vessels; and when he also considers that those parts of the lungs with which the air comes in contact, if spread out would present a surface equal to that of the superficies of the whole body; and lastly, that this viscus is so exceedingly spongy and porous, That when once inflated, it is ever after impossible by ordinary mechanical means to expel the air completely, he will easily perceive, not only that a large portion of air must remain for a considerable time in contact with the internal surface of the lungs, where it is liable to lose a portion of its oxygen, but also that the residual quantity of air in the lungs, after the most violent attempts at expiration, may be very considerable."

In order to prove the truth of this explanation, 3420 inches of gas of the same purity as that used in the former experiment, were respired and received successively into 13 different gazometers. The first portion was found to contain 25 per cent of azot, the second and third portions contained 10 per cent, and the last portion 5.5 per cent. The general average of the whole amount of azot was 6.5 per cent.

From the above facts the following conclusions may be drawn: Atmospheric air when subjected to a single inspiration, returns charged with from 8 to 8.5 per cent. of carbonic acid, nor by any number of subsequent inspirations does the a mount exceed 10 per cent.

When respiration is attended with distressing circumstances a portion of oxygen is probably absorbed.

There is no evolution of hydrogen or any other gas except carbonic acid during respiration; and from the quantity of carbonic acid generated exactly corresponding with that of the oxygen consumed, there does not appear to be any of this latter expended in the formation of water.

absorption of azot. There does not appear to be any

18, Description of an Apparatus for the Analysis of the compound inflẩmmable Gasses by their Combustion; with Experiments on the Gas from Coal, explaining its Application. By Wm. Henry, M. D.

The object of the apparatus here described is to enable the chemist to analyse the compound inflammable gasses by combustion with oxygen, instead of detonation; the former method being both more accurate in itself, and allowing a greater quantity of gas to be submitted to experiment. For the results of the experiments here related, we must refer to the original.

By

19. An Account of some Peculiarities in the anatomical Structure of the Wombat; with Observations on the female Organs of Generation. Everard Home, Esq. F. R. S. 21. Eclipses of the Satellites of Jupiter, observed by John Goldingham, Esq. &c. at Madras.

The discovery of the difference of longitude between two places by means of the satellites of Jupiter is supposed to be an easy process: but the remarks in this paper will point out many circumstances to be taken into consideration, which materially affect the attempt. For the circumstances at both places should be similar, and favourable: the telescopes should have equal powers, and both immersions and emersions should be observed. If the circumstances are favourable at one place, and not in another, very different results will be obtained. Tables are given of the eclipses of each satellite observed, with the circumstances at◄

tending them. The expression planet high, continually occurs. We wish that the height had been more accurately ascertained. It may indeed be discovered with sufficient ease by a person with a globe and

the nautical almanac before him, but a column assigned to the height would have been more satisfactory. This paper should be read by all young observers on the eclipses of Jupiter's moons.

ART. IX. Organic Remains of a former World. An Examination of the mineralized Remains of the Vegetables and Animals of the Antediluvian World generally called Extraneous Fossils. By JAMES PARKINSON. 4to. Vol. 2.

IN his former volume Mr. Parkinson treated of thedifferent vegetable remains that have been discovered in a fossil state in the volume now before us he enters on the description of animal fossils, but proceeds no further than the Zoophytes, reserving the rest of his subject for a future volume. The genera here treated of are the Tubiporites, Madreporites, Alcyonia, Encrinites, and Pentacrinites, very few of which can be referred with any probability to those living species of Zoophytes with which we are hitherto acquainted.

The descriptions are full and well compacted, and display throughout that minute accuracy which can only be attained by a long and intimate acquaintance with the general subject and the individual specimens, and are accompanied by figures from original drawings so admirably executed as to leave all former graphical representations of these subjects far behind. But besides the reputation of an accurate describer, Mr. Parkinson merits the higher praise of an original discoverer, and he has satisfactorily solved one of the two great difficulties attending all theories with regard to the formation of fossils. That which he has not solved is the remarkable fact that though the hard parts of these Zoophytes in their live state are

for the most part composed of carbonat of lime and are fre quently also when fossil composed of this substance, yet there are numerous instances of fossil zoophytes compleatly penetrated by Aint, and what adds to the difficulty is that these silicified remains are generally found imbedded in limestone in which hardly an atom of silex is to be discovered. The second difficulty is to explain how the exquisitely minute organization of these animal fossils can be retained, at the same time that the process of petrification is compleat and the whole is apparently become a mere mineral body. This entire removal of animal matter however Mr. Parkinson has demonstrated in several instances to have been gratuitously assumed without proper examination; for on immersing specimens of calcareous fossil Zoophytes in very dilute muriatic acid, the earth was by degrees taken up, and there remained behind a fine membrane of animal matter which exhibited in some instances even the form and colour of the recent animal. With the silicified fossils the same method of analysis could not be resorted to, but there is a high analogical probability that in these, as in the others, there exists a cellular tissue of animal matter in the interstices of which only the silex is deposited.

ART. X. Mathematicks simplified and practically illustrated by the Adaptation of the principal Problems to the ordinary Purposes of Life, and by a progressive Arrange ment applied to the most familiar Objects in the plainest Terms, together with a complete Essay on the Art of surveying Lands, and by such simple Inventions as may for ever banish the Necessity of costly and complex Instruments. By Capt. THOMAS WILLIAMSON. 1808.

THIS title promises much, and is not drawn up according to the rules in Horace's art of poetry. To banish costly and complex instruments, you must previously determine, that you will do nothing but coarse work but if the writer had read the account of the measusement at the base on Hounslow heath, he would have learned that apparently so simple a thing as the measurement of a straight line of five miles cannot be performed but by very costly and complex instruments, and at a very great expense of labour and time. Nil sine magno vita labore dedit is true in mathematics as in other things. What an immense distance there is between the measurement of a piece of open field land, and the survey of a kingdom. A chain and a cross bar in the hands of a country schoolmaster may serve very well the purpose of a farmer and a a country squire: but how far

would these talents be of use in the measurement of a degree on the earth's surface. We must not deceive ourselves. Mathematics is not any more than any other science thus to be simplified. Very few propositions in Euclid will do for the ordinary workman, and in fact he will do without any, as he learns the art in his apprenticeship, and knowing nothing of principles, is competent only for that routine of work which he has seen practised by his master: and perhaps for ordinary purposes this is the best education. Such persons however cannot read this work, and to others it will not be useful as an explanation of the science on which the art is founded. If however the work does not answer completely to the title, many useful hints are interspersed, which will be of service to the practical mathematician.

ART. XI. Problems in some of the higher Branches of Algebra. VIETA was the first person who discovered the property of certain equations, that, if they contained so many roots, that the number of them was denoted by the index of the highest power of the unknown term,then the coefficients of the unknown terms were equal to certain functions of the roots, and the known term was equal to the product of all the roots. This discovery of Vieta has been considerably extended, and it is now found to be the property of all equations, where the number of the unknown terms is equal to the number of the highest index of theunknown terms,

and the unknown terms being arranged according to their indices, have alternate signs. There is a singular beauty in this property of equations, which leads to many curious results; and if it had been made use of with prudence,and according to the strict laws of mathematical reasoning, which can never be overstepped without great injury to the science, Algebra would not present a rugged mysterious face to its students, but might have been pursued as a noble improvement of the mind. Unfortunately the spirit of generalising took possession of the schools, and the great skill of the

scholars was displayed in throwing about x's and y's from one side of the equation to the other, without any regard whatsoever to their value, or to any absurdity that might result from the process. Hence what is true only in particular cases was affirmed to be true universally, and mystery and nonsense went hand in hand together, in producing new chimeras to terrify the astonished student.

On the truth of Vieta's original proposition, extended to legitimate cases, is founded the theorem on the sums of the powers of the roots in any equation, and in the investigation of this theorem appear the sum of the roots, the sum of the products of the roots taken in pairs, by threes, by fours, and so on, and the product of all the roots. Of course, if a problem is given to us, in which the sum of certain powers of numbers, and the sum of the products of these numbers in various ways are given; by comparing this case with the general theoremi, many ingenious solutions may be discovered. This is the art in several of the problems before us, and the work would have been rendered much more valuable and useful, if the writer had given the general theorem, by which the reason would have been easily seen of his future assumptions.

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+A-B√ and this fatal and
useless error pervades a great part
of the work. The ingenuity dis-
played by the writer, in the ma-
nagement of erroneous terms, con-
vinces us that he is able to discover
more elegant solutions, by adhering
strictly to mathematical principles.
We recommend to him in particu
lar to examine again his sixteenth
problem by these principles, be.
cause, as it stands at present, the
conclusion is evidently absurd.
What is -s-√g?
sğ?

The seventeenth problem requires a great deal of examination. The first thing to be done by the author is to write down his equation intelligibly, for how can the sum of various unknown numbers be equal to 0. The names of Bombellis, Des Cartes, and Euler, are no vindication of such an assumption. This advantage will attend also the process of writing intelligibly, and using only mathematical reasoning, that the causes of the failure of the rules given by very celebrated mathematicians will be easily detected, and the student, when he comes to the conclusion of his work, will be perfectly satisfied with every part of it.

We were stopped in many parts of the application of his theorems, where unintelligible terms are used; as for example, in p, 3, where one number is said to be equal to the ART. XII. The Means of finding the Longitude at Sea, developed in Four Astronomical, Geographical, Nautical, Historical, Mathematical, and Mechanical Dissertations. By Major-General GRANT, OF late years the number of those who appear before the public with matters which require much previous learning and study, with out having the necessary qualifications, seems to have increased rapidly; formerly the opinion of inspiration was confined to religion

l'iscount DE VAUX. 4to. pp. 163,
alone, now it pervades every sci-
ence and art under heaven, and we
have on all sides inspirati, arrived
at perfect knowledge, without hav
ing gone through the tedious paths
of previous instruction. If Horace
were revived he would find we can
now mock at his ancient adage,

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