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ftill higher ratio of the velocities, by the conftant increment of velocity (or rather indeed decreasing increment in the medium) and increafing increment of refiftance, it would at length. happen that the falling body would have acquired fuch a velocity as would meet with a refiftance equal to the conftant force of gravity to generate the velocity; after which it would continue to fall with this conftant velocity without increafing or decreafing. And the quantity of this greateft velocity is calculated by fir Ifaac Newton in his Principia. This velocity in fuch a body as the mufket bullet is about 400 feet per fecond of time. But as Mr. Robins had, from an excellent mode of experiment, determined the initial velocity of fuch a bullet, discharged by the force of fired gunpowder, to be above 1600 feet per fecond, Mr. Muller triumphs on the feeming impoffibility of the existence of fuch a velocity, and quotes fir Ifaac's propofition as the teftimony. Not perceiving that bis theorem refpects only velocities gradually generated by gravity, and was never intended to countenance an opinion that velocities greater than that could not poffibly be generated by other powers.

The difcourfe, near the end of the hiftory, concerning opinions about the cause of gravity, and the existence of a fubtle etherial medium, might have been spared, as being but little connected with his fubje&t. Nor has Mr. Glenie combated his fubject with the best artillery in the world.

The latter part of the book contains the new method of deriving the theory of projectiles in vacuo, from the properties of the fquare and rhombus, that is the parabolic theory of gunnery, for fuch to all fenfe is the curve that would be described by a body projected in vacuo. This invention confifts in demonftrating certain properties belonging to the lines and angles formed by the various intersections of the fides and diagonals of a fquare and two rhombufes having a common fide, and then fhewing that the interfections of certain lines in them are found in the projectile cuive or parabola, he transfers all the aforefaid properties to the folution of the cafes of projectiles or gunnery. But no advantage to the artillerift is hereby derived, as we are not from hence furnished with any new rules or methods, nor is the mode of obtaining the ufual rules by this means near so easy or natural as the common direct way from the known properties of the parabola. So that all the purpose answered by this method of obtaining the rules, is to fhew the author's ingenuity in geometrical subjects. Not that it was neceffary in this cafe however to be of the deepest or moft acute kind; for having remarked the properties of fuch figures as abovementioned, when confidered as connected with

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a parabola, and as those properties must always attend fuch figures whether fo connected with the parabola or apart from it, it required no great exertion of genius to think of first pointing out fuch properties in those figures, and then applying them to the parabola, as if they had been thus originally obtained without previoufly knowing that they had before belonged to it.

A Syftem of Military Mathematics. By Lewis Lochée, Master of the Military Academy, Little Chelsea. 2 vols. 8vo. 125. ferved. Printed for the Author, and fold by T. Cadell.


T is the common fault of school mafters to be troubled with an infatiable defire of exhibiting in print their performances, and method of teaching, to the public. This generally arifes from a fuperficial knowledge of the fubje&s of which they treat, and in which they are employed; fo that being little acquainted with the beft authors, and having ftumbled on a method of their own at the commencement of their profeffion of teaching, which their conftant habit of delivering to their pupils has rendered clear to themselves, while other modes are obfcure to them, they imagine that it must be the same to others if it were published, and that the publication will ferve as an advertisement and recommendation to their school. Though fuch publications may fully evince, to the really learned, the ignorance and pedantry of such authors, yet there is no doubt but that, like the fpecious advertisements of quack medicines, they but too often have their effect on the aefy belief of many parents, &c. who hence conceive a good opinion of the abilities of thefe quacks in fcience.-We have been induced to throw out thefe obfervations on the perusal of this performance, although it is not the worst of its kind that we have seen. We agree with the author in thinking several practical branches of mathematics, very ufeful in forming a diftinguished military character and conduct; but think he carries the opinion too far when he says, mathematical knowledge has been found as neceffary to the foldier, as it ever was to the aftronomer; and has contributed to form a Turenne and a Vauban, no less than an Archimedes and a Newton;' as we are of opinion that there are certain other qualities and qualifications that have a greater fhare in forming the diftinguished foldier, than a deep or critical knowledge of mathematics. But perhaps Mr. Lochée's notions of what is meant by a great knowledge of mathematics may differ from our own; nay, this feems rather likely, when we confider the following pa

paragraph, which he has inferted, a little to foften the rigour with which he had infifted on the indifpenfable knowledge of a great degree of mathematical fcience for every military officer. As military ftudents, however, are defigned, not for a contemplative, but for an active and bufy life, it is expedient that they should generally decline fach inveftigations as ferve only for amulement, and confine themfelves chiefly to thofe that are immediately applicable to their common duties and employments. On this principle, the following work, begun and finished folely for their improvement, has been formed: and if, in fome inftances, the more intricate parts of algebra and geometry are opened, it is only for the fake of thole fuperior minds, who may be capable of purfuing them, and who, by enlarging their ideas in the investigation of the higher and more speculative parts, will acquire greater ftrength and facility both in the comprehenfion and application of the lower and more practical: it is, furely, always right, to give free fcope to the exercifes of the intellectual faculty, till it is found that mere fpeculation is purfued to the neglect of practice.' For we have not found in this work any fuch things as we have been accustomed to confider as the intricate parts of . algebra and geometry,' &c. and we are inclined to fufpect that ftudents who are taught no more of the fciences of arithmetic, algebra, and geometry than are laid down in this work, will never make any diftinguished figure, either in a military. or any other capacity, from the advantage alone of that degree of it. Befides the matter of this performance, we think the manner of it is not calculated for initiating youth into the knowledge of thefe fubjects, it being generally very tedious and trifling.

The fubje&s of this performance, as we have already hinted, are arithmetic, algebra, and practical geometry; all of which are treated in a fuperficial and unfcientific manner, the definitions, demonftrations, &c. being often imperfect and unmathematical.

As there are many better treatifes on thefe fubjects already extant, we can difcover no occafion for the publication of this, it containing no new difcoveries nor improvements, so that its publication may probably be attributed to other motives Nor is this probability leffened by the opinion which the reader may form of an author's modefty who could follicit leave to dedicate fuch a performance to the king.

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Obfervations on Chronic Weakness. By Thomas Withers, M. D. 800. zs. 6d. ferved. Cadell.

TH HOUGH chronic weakness is confeffedly the origin of a great variety of diforders, it has hitherto never been treated by medical writers with that degree of attention and accuracy which the importance of the fubject requires. An attempt, therefore, to inveftigate the nature of this indifpofition, fo prolific of numerous and ftubborn complaints, cannot fail of being highly acceptable to thofe who wifh the advancement of phyfical knowledge, especially when it is executed by one who has had great experience in the hiftory and cure of the disease...

This fpecies of weaknefs termed chronic, is diftinguished from that which accompanies acute diforders by the flow and gradual progrefs of its invafion. According to Dr. Withers,

• Chronic weakness ufually begins with morbid affections of the ftomach and bowels. The fun&ions of the alimentary canal are of the first importance; but its structure is delicate and tender. Flatulence, acidity, heart-burn, coftiveness, or colic pains frequently afford the firft figns of the approaching difeafe. A, diminution of appetite and a flight dejection of fpirits foon occur. The mufcular ftrength is impaired, and the patient feels a languor and an averfion to motion. This difpofition to indolence continually grows ftronger, and a fenfer of weariness is eafily induced.

By degrees thofe fymptoms increafe, and the whole conftitution is more and more depreffed. The fimple folids are relaxed, and the nervous power is diminished. The uneasiness of the mind, arifing from a debilitated ftate of the body, be comes more confiderable, and contributes much to accelerate the progrefs of the difeafe. The aliment is often taken without appetite, and is very imperfectly digefted. The ftomach and bowels are diftended with air, and, in confequence of that distenfion, they are thrown into convulfive contractions, attended with pain and anxiety. A confiderable quantity of limpid water, or of the acid and putrid matters contained in the ftomach, regurgitates frequently into the mouth. In this state of the patient there is fometimes a fense of palpitation in the breaft, with a fhortnefs and difficulty of breathing. The head, from the great connection which fubfifts between that part and the ftomach, is affected with pain and dizziness. The pain of the head in fome cafes is extremely constant and fevere. The dizziness arifes fometimes to fuch a height that the patient staggers like a drunken man. The food, according to its nature, is apt to run too far into the ácid or putrid fer

fermentation, and to load the alimentary canal with acrid and offenfive matters. In this fituation of the patient, a diarrhæa fometimes takes place, which is a natural and falutary effort of nature. At other times obftinate coftiveness and colic pains fupervene.'

In the minute and accurate description which our author has given of this disease, he mentions, as a concomitant symptom, a relaxation of the organa virilia, attended with a discharge of vifcid mucus from the urethra and veficulæ feminales. When this symptom occurs, however, we should be inclined to confider it rather as a cafual than a characteristic attendant of the disease; and to fufpect, that, inftead of being produced by the general weakness of the body, the latter was the effect of a partial imbecility previously exifting in the feminal veffels, from which a copious or long continued difcharge had reduced the vigour of the conftitution.

Dr. Withers juftly fuppofes that the proximate cause of chronic weakness confifts chiefly in a defect of nervous energy, in an increased mobility of the nervous fyftem, and in a diminished cohesion of the fibres; and he likewife acquiefces in the common doctrine respecting the predisposing and occafional caufes, the operation of which he explains upon the principles of phyfiology. After offering a few obfervations on the diftinction of the difeafe, and the circumftances which ought to guide the prognoftics, he proceeds to the method of cure, which is comprized under three indications: namely, to avoid the occafional causes, to obviate particular symptoms that aggravate the complaint, and to restore the tone and vigour of the system.

Several writers have recommended an animal diet as the most suitable in a weak state of the stomach and bowels; but Dr. Withers is of opinion that a mixture of animal and vegetable food is the most conducive to health. For the prefervation of health in a found conftitution, fuch a regimen is undoubtedly the moft proper; but it is certain that in those habits where the alimentary canal is difpofed to generate acidity, a very small quantity even of the mildeft vegetable food will produce many troublesome symptoms. Nor feems there to be any juft ground for apprehending an alcalefcent difpofition of the fluids in a conftitution of this kind, fo long as the tendency of the animal food to putrefaction can be counteracted by a moderate portion of bread; for it is almost inconceivable how small a quantity of this fubftance will com. municate an acefency to the chyle, when fermentation is carried too far in the digestive process.


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