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still higher ratio of the velocities, by the confiant increment of velocity (or rather indeed decreasing increment in the medium) and increasing increment of resistance, it would at length happen that the falling body would have acquired such a ve. locity as would meet with a resistance equal to the constant force of gravity to generate the velocity; after which it would continue to fall with this constant velocity without increasing or decreasing. And the quantity of this greatest velocity is calculated by fir Ifaac Newson in his Principia. This velocity in such a body as the musket bullet is about
feet cond of time. But as Mr. Robins had, from an excellent mode of experiment, determined the initial velocity of such a bullet, discharged by the force of fired gunpowder, to be above 1600 feet per second, Mr. Muller' triumphs on the seem. ing impossibility of the existence of such a velocity, and quotes fir Isaac's proposition as the testimony. Not perceiving that bis theorem respects only velocities gradually generated by gravity, and was never intended to countenance an opinion that velocities greater than that could not pollibly be generated by other powers.
The discourse, near the end of the history, concerning opinions about the cause of gravity, and the existence of a subtle etherial medium, might have been spared, as being but little connected with his subject. Nor has Mr. Glenie combated his subject with the best artillery in the world.
The latter part of the book contains the new method of deriving the theory of proje&iles in vacuo, from the properties of the square and rhombus, that is the parabolic theory of gunnery, for such to all sense is the curve that would be described by a body projected in vacuo. This invention consists in de. monftrating certain properties belonging to the lines and angles formed by the various intersections of the Gides and diagonals of a square and two rhombuses having a common side, and then Thewing that the intersections of certain lines in them are found in the projectile cuive or parabola, he transfers all the aforesaid properties to the solution of the cases of projectiles or gunnery. But no advantage to the artillerist is hereby derived, as we are not from hence furnished with any new rules or methods, nor is the mode of obtaining the usual rules by this imeans 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 Thew the author's ingenuity in geometrical subjects. Not that it was necessary in this case however to be of the deepest or most acute kind; for having remarked the properties of such figures as abovementioned, when considered as connected with
a parabola, and as those properties must always attend such figures whether fo connected with the parabola or apart from it, it required no great exertion of genius to think of first pointing out such properties in those figures, and then apply. ing them to the parabola, as if they had been thus originally obtained without previoufly knowing that they had before belonged to it,
A System of Military Mathematics. By Lewis Lochée, Master of
tbe Military Academy, Little Chelsea, 2 vols. 8vo. 125. fewed.
Printed for the Author, and fold by T. Cadell. T is the common fault of schoolmasters to be troubled with
an insatiable defire of exhibiting in print their performances, and method of teaching, to the public. This generally arises from a superficial knowledge of the subjeas of which they treat, and in which they are employed.; so that being little acquainted with the best authors, and having stumbled on a method of their own at the commencement of their profession of teaching, which their constant habit of delivering to their pupils has rendered clear to themselves, while other modes are obscure to them, they imagine that it must be the same to others if it were published, and that the publication will serve as an advertisement and recominendation to their school. Though such publications may fully evince, to the really learned, the ignorance and pedantry of such authors, yet there is no doubt but that, like the specious 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 these quacks in science. We have been induced to throw out these observations 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 useful in forming a distinguished military character and conduct; but think he carries the opinion too far when he says, ' mathematical knowledge has been found as necessary to the soldier, as it ever was to the astronomer ; and has contributed to form 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 share in forming the diftinguished soldier, 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 seems rather likely, when we consider the following
paragraph, which he has inserted, a little to soften the rigour with which he had infifted on the indispensable knowledge of a great degree of mathematical science for every military officer.
• As military students, however, are deligned, not for a contemplative, but for an active and busy life, it is expedient that they should generally decline fach investigations as serve only for amusement, and confine themselves chiefly to those that are iminediately applicable to their common duties and employments. On this principle, the following work, begun and finished folely for their improvement, has been formed i and if, in some instances, the more intricate parts of algebra and geometry are opened, it is only for the fake of those superior minds, who may be capable of pursuing them, and who, by enlarging their ideas in the investigation of the higher and more speculative parts, will acquire greater strength and facility both in the comprehenfion and applicacion of the lower and more pradical : it is, surely, always right, to give free scope to the exercises of the intellectual faculty, till it is found that mere fpeculation is pursued to the neglect of practice.' For we have not found in this work any such things as we have been accustomed to consider as the intricate paris of . aigebra and geometry,' &c. and we are inclined to fufpect that students who are taught no more of the sciences 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. Besides the matter of this performance, we think the manner of it is not calculated for initiating youth into the knowledge of these subjects, it being generally very tedious and trifling
The fubjects of this performance, as we have already hinted, are arithmetic, algebra, and practical geometry; all of which are treated in a superficial and unscientific manner, the definitions, demonftrations, &c. being often imperfect and uumathematical.
As there are many better treatises on these subjects already extant, we can discover no occafion for the publication of this, it containing no new discoveries nor improvements, so that its publication may probably be attributed to other mo. tives Nor is this probability leflened by the opinion which the reader may form of an author's modesty who could lola licit leave to dedicate such a performance to the king.
Observations on Chronic Weakness. By Thomas Withers, M. D.
8vo. zs. 6d. Jered. Cadell. THOUGH chronic weakness is confessedly the origin of a
great variety of diforders, it has hitherto never been treated by medical wri'ers with that degree of attention and accuracy which the importance of the subject requires. An attempt, therefore, to investigate the nature of this indisposition, fo prolific of numerous and stubborn complaints, cannot fail of being highly acceptable to those who wish the advancement of physical knowledge, especially when it is executed by one who has had great experience in the history and cure of the disease.
This fpecies of weakness termed chronic, is distinguished from that which accompanies acute disorders by the flow and gradual progress of its invasion. According to Dr. Withers,
• Chronic weakness usually begins with morbid affections of the stomach and bowels. The funcions of the alimentary canal are of the first importance; but its structure is delicate and tender. Flatulence, . acidity, heart-burn, costiveness, or colic pains frequently afford the first signs of the approaching disease. A diminution of appetite and a flight dejection of spirits soon occur. The muscular strength is impaired, and Ihe patient feels a languor aod an aversion to motien. This disposition to indolence continually grows stronger, and a sense of weariness is easily induced.
By degrees those symptoms increase, and the whole conftitution is more and more depressed. The fimple folids are relaxed, and the nervous power is diminished. The uneasiness of the mind, arising from a debilitated state of the body, becomes more considerable, and contributes much to accelerate the progress of the disease. The aliment is often taken withe out appetite, and is very imperfectly digested. The stomach and bowels are disteuded with air, and, in consequence of that diftension, they are thrown into convulsive contractions, attended with pain and anxiety. A considerable quantity of limpid water, or of the acid and putrid matters contained in the ltomach, regurgitates frequently into the mouth. In this state of the patient there is sometimes a sense of palpitation in the breaft, with a shortness and difficulty of breathing. The head, from the great connection which subsists between that part and the stomach, is affected with pain and dizziness. The pain of the head in some cases is extremely constant and severe. The dizziness arises sometimes 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.
fermentation, and to load the alimentary canal with acrid and offensive matters. In this situation of the patient, a diarrhæa fometimes takes place, which is a natural and falutary effort of nature. At other times obstinate costiveness 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 viscid mucus from the urethra and vesiculæ seminales. When this symptom occurs, however, we should be inclined to consider it rather as a casual than a characteristic attendant of the disease ; and to suspect, that, instead of being produced by the general weakness of the body, the latter was the effect of a partial imbecility previously existing in the seminal vessels, from which a copious or long continued discharge had reduced the vigour of the constitution.
Dr. Withers justly supposes that the proximate cause of chronic weakness consists chiefly in a defe&t of nervous energy, in an increased mobility of the nervous system, and in a diminished cohesion of the fibres; and he likewise acquiesces in the common do&rine respecting the predisposing and occasional caufes, the operation of which he explains upon the principles of physiology. After offering a few observations on the dirtinction of the disease, and the circumstances which ought to guide the prognostics, he proceeds to the method of cure, which is comprized under three indications: namely, to avoid the occasional causes, to obviate particular symptoms that aggravate the complaint, and to restore the tone and vigour of the system.
Several writers have recommunded 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 ve. getable food is the most conducive to health. For the preservation of health in a sound constitution, such a regimen is undoubtedly the moft proper ; but it is certain that in those habits where the alimentary canal is disposed to generate acidity, a very small quantity even of the mildest vegetable food will produce many troublesome symptoms. Nor seems there to be any just ground for apprehending an alcalescent disposition of the fluids in a constitution of this kind, so long as the tendency of the animal food to putrefaction can be counteracted by a moderate portion of bread; for it is almoft inconceivable how small a quantity of this subftance will com. municate an acesency to the chyle, when fermentation is carried too far in the digestive process.