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nearly the plan pursued by Mr. Atwood in his sixth section ; and it is sufficiently plain in those cases in which the parts of a system revolve round a fixed Axis. If, however, the velocities of the parts of the system do not vary as their distances from the centre of motion, (which case happens when the parts of the system are connected with flexible strings,) although the accelerating force may be found, yet the determination of the velocity will frequently depend on a difficult Integral. A confirmation of the truth of this remark may be obtained from the problem given by Mr. A. towards the end of his sixth section; which problem, in consequence of its erroneous solurion, has been several times discussed in a valuable work intitled Leybourn's Mathematical Repository. Here we may remark that this problem was solved (and exactly solved) seventy years ago by Bernoulli. If we recollect rightly, for we cannot immediately refer to the proper documents, neither Thomas Simpson nor Atwood, nor yet the subsequent demonstrators of the problem, have noticed this circumstance. The determination of the accelerating force, then, is one method of solving this class of problems. Foreign mathematicians employ the theorem of the Conservatio Virium Vivarum. In Mr. Leybourn's publication, just mentioned, a partial demonstration of this thcorem has been given by Mr. Dawson ; and the employment of it undoubtedly leads to the solution of problems with greater facility and conciseness than the former method.

This theorem was employed by Bernoulli as a principle for the solution of various problems in Dynamics; and it is indeed most fruitful in the consequences to which it leads. The merit of this mathematician, and of Leibnitz, is not always in this country fairly and sufficiently appreciated. They were emulous, perhaps envious, of Newton; and therefore Englishmen, zealous in opposing their claims to mathematical distinction and pre-eminence, depressed their real merit beyond its just level. We still in some measure retain, and our books communicate to us, this prejudice: but it would be corrected if we now examined their writings; and we should then probably confess that, although Newton was the greatest mathematician and philosopher, Bernoulli and Leibnitz were certainly very great mathematicians and philosophers.

At p. 265. cor. 5. a wrong inference is made concerning the convertibility (if we may so term it) of the centres of suspension and oscillation. If S, 0, G, be the centres of suspension, ose cillation, and gravity, respectively, it does not followimmediately, because SO. SG= id' + m'd+ &c. that, if S be transferred to O, O will be transferred to S: the thing is true, but a process or proposition is omitted; it ought to be shewn that

SG

SG=

mg + m'g'"* + &c.

m+m+ &c. GO Bi gi g", &c. being the respective distances of the particles m, m', m", &c. from the centre of gravity.

In the first volume of this work are contained, besides Mechanics properly so called, Hydrostatics, Hydrodynamics, Pneumatics, &c. We approve the latter part of the volume less than the first. The subjects, indeed, are in their nature rather vague, and bear not easily the strictness and precision of mathematical discussion : but the author has not laboured with felicity; his article on Hydrostatics is rather meagre, and to our taste much too wordy.-—Over the second volume, which contains the account of Machines, we have whiled away many an hour, and have gained some instruction. The drawings are well executed, and, which is scldom the case, adequately present to the eye the construction of the machines. Mr. Gregory, however, sometimes writes too much or not enough: for instance, in Archimedes' screw, the mathematical processes, which do not go one-tenth of the way to explain its theory, should have been omitted, and a plain description of the uses and mode of action of the machine alone retained :-while to aid the explanation of the machine next described, (the shoe-maker's implement to enable him to work in an upright posture,) a diagram ought to have been added.

To the second volume, and the accompanying volume of plates, this publication is principally indebted for its claim to distinction and patronage. It is our duty and our wish to state and enforce that claim ; for although, in the nicety or fastidiousness of criticism, we should reject some parts and alter others, yet the performance on the whole is useful and valuable, creditable equally to the talents and the industry of its author.

Art. III. New Olservaticus on the Natural History of Bees, by

Francis Huber. Translated from the Original. 12 mo. PP. 310.

55. 6d. Boards. Longman and Co 1806. SINCE

NCE the experimenis reported in these pages appear to

have been conducted with great accuracy, and especially since they lead in several instances to curious and very unexpected results, we cannot refrain from expressing our surprize that, during a term of fifteen years, they should have remained inaccessible to the more English reader. This singular fact may, perhaps, be partly ascribed to the general diffusion of the French language among our men of science, and partly to a defect of zeal in the prosecution of entomological studies.

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At all events, the British public are indehted to the present translator ; who has executed his task with care and fidelity, and who appears to be no mean proficient in that department of Natural History to which we have just alluded.

It is well known to cootinental naturalists, that M.Huber de voted a very considerable portion of his life to the observation of the manners and habits of those interesting little creatures which supply us with the sweets of their labours, and astonish us by the wonders of their social economy. The patience and ingenuity which characterize his investigations, and the intimate corres pondence which he cultivated with Bonnet, impart additional authenticity and value to his communications.

• It is a remarkable circumstance (says the translator) that he laboured under a defect in the organs of vision, which obliged him to employ an assistant in his experiments. Thus these discoveries may be said to acquire doable authority. But independent of this the experiments are so judiciously adapted to the purposes in view, and the conclusions so strictly logical, that there is evidently very little room for error. The talents of Freis Burnens, this philosophic as. sistant, had long been devoted to the service of the author, who, after being many successive years in this manner aided in his re searches, was at last deprived of him by some unfortunate accident.'

Our object, then, is not to criticize M. Huber's statements, since all the circumstances with which they are accompanied sufficiently remove every thing like doubt, at least from our own minds : but we apprehend that we shall render an acceprable service to many of our readers, if we present them with a summary of some of the principal results.

M. Huber's observations are contained in thirteen letters addressed to the cekbrated Bonnet of Geneva: but they manifest little of the liveliness or digressive reflections which are so much adapted to the spirit of epistolary compositions. They are rather to be considered as a series of propositions related with gravity and undeviating connection with the subject, and deriving their interest from the striking and satisfactory information which they convey. It may be proper to premise that the experiments were all made with what the author calls leaf or book lives. Aware of the inconveniences attending those of glass, constructed on Réaumur's principles, he took several small fir boxes, a foot square, and fifteen lines wide, and joined them by hinges, so that they could be opened and shut like the leaves of a book.

• When using a hive of this description, (he says) we took care to fix a comb in each frame, and then introduced all the bees neces. sary for each particular experiment. By opening the different divisions successively, we daily inspected both surfaces of every comb. There was not a single cell where we could not distinctly see what

passed

passed at all times ; nor a single bee, I may almost say, with which we were not particularly acquainted. Indeed, this construction is nothing more than the union of several very flat bives which may be separated. Bees, in such habitations, must not be visited before their comba are securely fixed in the frames, otherwise, by falling out they may kill or hurt them, as also irritate them to that degree that the observer cannot escape stinging, which is always painful, and sometimes dangerous : but they soon become accustomed to their situation, and in some measure tamed by it ; and, in three days, we may begin to operate on the hive, to open it, remove part of the combs, and substitute others, without the bees exhibiting too formidable symptoms of displeasure. You will remember, Sir, that on visiting my retreat, I shewed you a hive of this kind that had been a long time in experiment, and how much you were surprized that the bees so quietly allowed us to open it.'

The first three letters relate to the impregnation of the queen-bee. On this part of his subject, the author first refutes the opinions of Swammerdam, Debraw, and the Lusatian observers, and then establishes, in the most convincing manner, two very important facts; namely, that the queen is impregnated by union with the male, and that this union is accomplished in the air.- Some physical and anatomical details occur on this point, which we refrain from particularizing.- Various experiments, which seem to be perfectly conclusive, are also adduced to prove that, when the sexual union is retarded beyond the twentieth day, only an imperfect impregnation takes place; and the queen, instead of laying the eggs of workers and males equally, will lay none but those of males. M. Huber candidly avows his inability to explain his own discovery. He concludes, however, that, as no fact in nature is unique, it is most probable that the same peculiarity will also be found in other aninals. An extremely curious object of research would be to consider insects in this new point of view. I say insects,' continues he, for I do not conceive that any thing analogous will be found in other species of animals. The experiments now suggested would necessarily begin with insects the most analogous to bees; as wasps, humble bees, mason bees, all species of flies, and the like. Some experiments might also be made on butterflies; and, perhaps, an animal might be found whose retarded fecundation would be attended with the same effects as that of queen bees.'

M. Huber's researches likewise completely corroborate M. Schirach's beautiful experiments on the conversion of common worms into royal worms. It appears, however, from the details, that the German observer mistook when he affirmed that the subjects of this conversion should be three days old, since the experiment succeeds equally well with those of two days R4

old, old, or even with those which have been only a few hours in existence. M. Schirach bad, moreover, too rashly maintained that the females were incapable of laying royal eggs.

The following sentences, though apparently hypothetical, are ultimately reduced to truisms by the test of various experiments, and afford a satisfactory confirmation of the discovery of fertile workers made by M. Rienis.

From M. Schirach's elegant discoveries, it is beyond all doubt that common bees are originally of the feinale sex. They have recrived from nature the germs of an ovary, but she lius allowed its expansion only in the particular case of their recciving a certain aliment while a worm. Thus it must be tlie peculiar object of inquiry whether the feruile workers get that aliment u bile worms.

• All iny experiments convince me that becs, capable of laying, are produca in bives that have lost the queen. A great quantity of royal joily is the prepared for feeding the larvæ destined to replace ler. Therefore, if fertile workers are produced in this situation alane, it is evident their origin is only in those hives where bees prepare the royal jelly. Towards this circumstance, I bent all my attention. It indued me to suspect that when becs give the rugal irruinient to certain worms, they cither by accident or a particular instinct, the principle of which is unknown to me, drop some particles of royal jelly illo cello contig nous to those containing the worms destined for queens. "The laive vf workers, that have accidentally received portions of su active an aliinuit, must be more or less affccied by it; and their ovaries should acquire a degree of expansion. But this expansion will be imperfect; why? because the royal food has been administered only in small portions, and, besides, the larvæ having lived in cells of the emailest dinensions, their parts cannot extend beyond the ordinary proportious. Thus, the beis producid by them will resemble common workers in size and all the external characteristicn. Added to that, they wil have the faculiy of laying some eggs, solely from the cist of the wining portion of royal jelly mixed with their alimcat.'

Indeed, it appears from the sequel that the author succeeded in produciog fertile workers in the five, at pleasure.

With regard to the combats of the queens, the massacre of the males, and the reception of a stronge queen, M. lluber confirms gosi of the ons vions of lcsumur, and bears easti mony to their superior accuracy, when compared with those vi the German and Lusarian writers. Having distinctiy 18certained that the queen is oviparous, a circumstance which the French naturalishid loft undecided, this ingenious observer jext informis us that 110 extraordinary aid or attention is required for thieir exclusion; and that the periods of existence, assigned to the three sorts of bees before they assume their ultiplate form, have now been exactly determined.

The

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