S

N

P

B

Let S be the sum of the sides, and the square of N equal to the given rectangle contained by the sides, and BAC the given vertical angle.

Analysis. About the triangle ABC describe a circle. Bisect the angle BAC by the straight line AD, meeting the circumference in D. Join AD and draw DE DF perpendicular to AB and AC, join DB DC, then is one of the angles ABD acute, the other ACD will be obtuse, that is, if the point E fall within the circle, the point F will fall without. Comparing the triangles AED and ADF, also BED and DCF, we find AE=AF, DE DF, and BE CF, hence AE+ AF AB+AC=S, but AF + AE

=

S 2,

=

hence A E is given.

=

2AE.. AE Again, AB-AC is evidently 2BE, also ABAC+ BE2 AE2 (5th and 2nd Elem.) But AB AC N2 .. N2 + BEAE2, or BE? AE2-N2; therefore, BE2, and consequently BE, is given, hence AB and AC are each of them given.. in the triangle ABC the two sides and the included angle is given to construct it.

The composition from the above analysis is so evident, that it will be unnecessary to give it.

2nd. When P difference of the sides. Then, as in the first case, 2BE AB-ACP, hence BE is given; also, since AB AC + BE2, or N2 + BE2 AE2, and N2 and BE2, are each of them given.. AE2 or AE is given, therefore we have the same data given to construct the triangle as in the first case.

Cor. 1. From the figure it is manifest, that EDA is half the sum, if the an

Cor. 2. Also from what has beer. shown, the following useful theorem in trigonometry is at once deduced:Since DE is perpendicular to AB, AE:EB, or 2AE: 2EB:: tan. ADE: tan. EDB, that is, AB+ AC: AB-AC :: tan. (ACB + ABC) : tan. § (ACB— ABC.)

Yours, &c. A WOOLWICH CADET.

HYDRAULIC EXPERIMENTS. REMARKS BY THE ED. VOCIS RATIONIS ON THE REPLY OF TREBOR VALENTINE. P. 186. Sir,-Your correspondent, Mr. Trebor Valentine, in his reply to "Ed. Vocis Rationis," No. 406, page 186, has been pleased to pronounce the latter to be "seemingly ignorant of even the first principles of every branch of mechanical science." There is one thing I submit to be a great deal more certain, and that is, that a person capable of so expressing himself respecting any fellow searcher after truth, must necessarily be ignorant of (one of) the first principles of literary and scientific controversy-namely, courtesy. What proofs has Mr. Trebor Valentine given that he is himself so versant with every branch, or indeed with any branch of science, as to be capable of judging of the acquirements of others? Are we to look for his qualifications in the clumsy, bungling, absurd, calculation of the overshot water-wheel, with which he favoured the readers of the Mechanics' Magazine, in No. 399, p. 72 ? Or, in his unfortunate letter to Mr. Baddeley, No. 388, p. 352, respecting the experiment with the goose-quill and bottle? I trust that, humble as my attainments may be, I have, at least, so far effectually handled these matters as, even in "the present advanced state of general knowledge" to have converted no less an advanced personage than Mr. Trebor Valentine, from the error of his way" of using the "goose-quill,” and of thinking on and publishing his pneumatic" absurdities" and over-shot calculations, in the valuable pages of the Mechanics' Magazine. If Mr. Valentine will not allow me to take the lead, I hope he will permit me, at least, to use my humble endeavour to keep pace with "the present advanced state of general knowledge." C'est une grande folie de vouloir être sage tout seul.

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But to the point:-On looking into Mr. Valentine's grand "show of the fallacy'' of my proofs, I observe, 1st. That in the proof respecting the experiments with the bottle and quill, he has been able to detect nothing but what was perfectly correct.

And 2nd. That as to my proof res pecting the syphon, he has disproved nothing, nor shown any "fallacy;" but, on the contrary, confirmed all I have advanced.

Mr. Valentine has, however, made

some

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from drawing into the syphon. It is a "first principle" with air to be uppermost; hence small bubbles of air, on the stroke of the air-pump, would draw in by his finger, and pass in that form through the water, as far as the bend of the syphon (it being a principle" of air not to descend through water into a vacuum) where it would remain at the top of the syphon, in the form of a large bubble, the effect of which, in conjunction with the stroke of the air-pump would bring "the water in the leg connected with the ""whilst the water remain

perfectly safe in making such propositions, because of their general inapplicability for the purposes of "general knowledge.' I question whether he himself ever made the experiment in the way he proposes. It was my plan to propose such experiments as might suit the pockets of the "general" readers of the Mechanics' Magazine, that they might be enabled to satisfy themselves respecting them. I accordingly proposed a small syphon, and for this farther reason, that if propositions are found to be true in the small-in all cases similar, and with corresponding proportions, they would be found true in the great. The Ed. Voc. Rat. will be perfectly "satisfied" if Mr. V. will have the goodness to send him the Brobdignag syphon with which Mr. V. himself made the experiment.

Mr. Valentine has another proposition, which though not quite so monstrous, is not much better suited to "general" pockets, viz., that of bending five or six feet of half-inch lead pipe into the form of a syphon." But this has nothing to do with showing "the fallacy" of my proof with a different syphon. If Mr. V.'s experiment with the syphon did not succeed, the reason may have been as follows:-In case the stroke of the airpump did bring the water out of the long leg, it was because the other end was not well closed, or air-tight, i. e. Mr. V.'s finger placed over the orifice was not sufficient against the stroke of the air-pump, so as to prevent the air

The difficulty of keeping the air out against a vacuum or the powerful stroke of an air-pump by such means, may be ascertained by the following experi ment:--Take a glass bottle half filled with water, insert through the cork, made air-tight, a long tube, so that when the bottle is inverted the end of the tube may extend above the surface of the water; then on exhausting the air by means of the tube, (however careful you may have been in making the cork air-tight), you will perceive numerous small bubbles of air pass upwards through the water as you continue to exhaust. Therefore, the admission of air must have been the cause of failure in Mr. V.'s syphon experiment. Hence I repeat, that you cannot by means of suction or the air-pump, draw any water from a perfectly air-tight vessel or syphon. Thus much for Mr. Valentine's show of fallacy"biu ziy second proof.

In his third paragraph, Mr. V. revives the old story respecting my stating to Mr. Whirlygig, "that the water rose of itself in the vacuum." Respecting which, he will find my meaning explained by what was said in reply to Mr. Baddeley, No. 401, p. 102, "That it did not rise simply by the mechanical power of the lever. Water would rise in a vacuum without the aid of any mechanical power. You may produce a vacuum by means of heat, and the water will rise into it by means of atmospheric pressure alone, and move upwards to the height of 32 feet." Therefore, it was perfectly a waste of paper and print for Mr. V. to revive this question, merely for the purpose of displaying his skill in" showing a fallacy" where no fallacy was meant or intended. It were, therefore, waste of time and "space" to go through this paragraph, the result of

which is, that it upsets his own argument in the preceding paragraph respecting the syphon, and tends to confirm his opponent's statement on that head, namely, respecting the difficulty of drawing water by means of suction without the assistance of the pressure of the atmosphere.

Mr. V. also contradicts his own statement respecting the means by which the 32-feet upright column of water is confined in the tube. In one part he says,

• It is the upward pressure which confines the water in the tube;" and in another, "Here again he (Ed. V. R.) is perfectly right, the contents will not quit the pipe, the whole column remaining as though the bottom of the pipe were plugged, which is sufficient proof that it was not either balanced or supported in any way by the water below."

Really, Sir, after these precious samples of Mr. V.'s ability in using the "goose-quill," it were beneath criticism to follow such a reasoner further. I will at present only notice, that his next object is an attempt to fix an error on the "sober calculation," which he does by squeezing in for the odd decimal parts, and by rejecting 10lbs. the weight of the gallon of water which stands above the moveable sucker of the common liftpump; "the weight of this water," he says, we have nothing to do with," in depressing a puinp-handle. Now, Sir, it is evident, that it would be impossible to get out any water with the common lift-pump without lifting this water, ergo, we have nothing to do with the weight of the water absolutely lifted. Quod est absurdum. Therefore, we have to do with it. Yours, &c.

ED. Vocis Rationis.

June 28, 1831. P. S. Since Mr. Valentine (in which, I grant, he is backed by the Old School) appears so strenuously opposed to my theory respecting the lifting of the whole 32-feet upright column of water by means of the moveable sucker; and since I have hitherto reserved my proofs in case the matter should be "disputed" (see note, No. 401, p. 102); and since it has been so learnedly disputed; it may not be amiss in this place to furnish one of the learned disputers with a small dose (as he appears not much to relish such things) by way of one of my proofs or reasons for rejecting the old theory. Sup

13

pose a cylinder, 32 feet in length, and 4 inches bore, furnished with a solid moveble piston, air-tight; depress the piston nearly to the bottom of the cylinder, and then plug the bottom of the cylinder so that the surfaces of both piston and plug may be in close contact. In this posi tion there is nothing between the plug and piston. Now, draw the piston up, you will find that it will require great force to do it; and if you lose hold of the piston-rod when drawn up, it will fly back as if discharged from a musket (this a person may often experience in cleansing a gun-barrel when the touch-hole has been accidentally stopped, and some water lies above the cleansing-piston, which has the effect of making it airtight). Now, it is evident in the above case, that the solid piston has only the pressure (beside friction) of the external air to lift, in which experience proves that the greater force is required. Again, suppose the piston in its original position at the bottom of the cylinder; take out the plug, and admit the air; in this case experience proves that the piston may be drawn up with great ease, and will not fly back, Now, it is not very material in this respect, whether we admit air or water in lieu of it to the bottom of the cylinder, for both are fluid; and in the latter case experience proves that we can raise a piston with much greater ease when air or water (which comes in lieu of air) is freely admitted by the bottom of the cylinder, than we can if neither water nor air is admitted. But according to the old. theory, the labour ought to be greater in the latter case than in the former; for, in the first case there would be only the. pressure of the air to be lifted-and in the other case (according to the old theory) there would be the additional increasing weight of the 32-feet upright column of water, i. e. in the first case there would be only the weight of atmospheric pressure, viz. 1884lbs. and in the latter case 358 lbs. (allowing 170lbs. for the weight of the 32-feet water in cylinder), and yet experience proves that it requires less force to raise the supposed greater than it does the less weight, which is absurd. The above is also confirmed by the labour being increased in case of accidental stoppage of the holes at the bottom of the suction-pipe; or, as Mr. Valentine says, by too small a suction-pipe.'

ED. V. R.

SAFE REMEDY FOR RATS.

Sir, I have no doubt but that you must, as well as myself, have long since remarked with mingled feelings of astonishment, disgust, and regret, the facility with which any individual man, woman, or child, can obtain poison (generally arsenic or oxalic acid) at the chemists and apothecaries, by merely saying that it is to kill rats, or clean boot-tops!! It is sufficient that the parties do not candidly avow that they want "the two penn'orth of arsenic" to poison either themselves or some body else, for it to be served out to them as a matter of course!!! I could show you a list of 38 cases of murder, suicide, or accidental poisoning, which have lately occurred in this country, which had they taken place in any other country in Europe (not to mention France), would have subjected the vendor of the poison to very heavy inflictions of fine and imprisonment. Here, all that these real aiders and accomplices in crime have to fear, is a slight censure of a coroner's jury, who, forsooth, cannot help expressing their regret that such deadly poison should have been sold (perhaps to a child!) with so little caution."

The apothecary, however, has sworn that he did not know to what purpose the arsenic was intended, and that he wrote "poison" on the packet. Innocent, simple soul! how could he suppose that it was bought for any other purpose, when the little girl positively told him, it was to kill rats!" Besides, he wrote "poison" on the paper-quite a sufficient check and spell upon those who wanted poison! And after all these

66

precautions," why should he, good man, be expected to forego the profit of his trade upon two penny worth of poison! To the hulks, to the hulks, say I!But I must proceed to the purpose of this letter, which is, to acquaint such of your readers as may be troubled with rats, that they may poison them with a substance which is not poisonous, and with which there is no danger of their dogs, poultry, pigs, children, or neighbours, being any of them poisoned.

Let those who wish to poison rats without applying to the chemist, intimately mix a pound of plaister of Paris (in its unslacked state) with an equal quantity of oatmeal. Let him place this within the reach of the rats-they will eat of it

eagerly and without being deterred by, any bad taste. By the humidity contained in their stomachs, the plaister of Paris will "set" and form an indigestible, hard mass, which will in fact present upon dissection a good cast of the rat's stomach, and speedily produce a kind of Aldermanic death, i. e. by irremediable indigestion.

Neither dogs, poultry, children, nor neighbours, will lap or pick up a dry, pulverulent mixture like this. I cannot quite answer for pigs; but I am pretty sure that neither a quadruped nor a biped hog, whatever might be his appetite, would be inclined or capable of swallowing enough of such an inconve nient" exhibition" to occasion the fatal indigestion which I know it will infallibly cause in rats and mice. Any how, it must be evident to most men, that no such danger can attend the employment of plaster of Paris, as of arsenic, nux vomica, or corrosive sublimate, for the purchase of which, moreover, there would no longer be any pretence.

Rats are very intelligent animals; so the better to beguile them, it is well to begin by giving them pure oatmeal. Those who first discover and partake of it, will speedily communicate the glad tidings to their relatives and neighbours, who may then be swept off all at once; as we shall soon have the pleasure of seeing occur to the far more rapacious, mischievous, and detestable biped boroughing (burrowing) fraternity.

I have not had an opportunity of try ing the mixture of oatmeal and plaster of Paris upon the beetles which infest kitchens, but I think it will be found efficacious.

Yours, &c. FRANCIS MACERONĘ. London, Sept. 1.

FALSE ALARM OF FIRE, OCCASIONED BY A SINGULAR ATMOSPHERIC PHENOMENON.

Sir,-About half-past four o'clock on Sunday morning, the 25th instant, I was called up, with information that a

It was on an analogous principle that the ancients, especially the Greeks, used bull's blood as a poison, which being drank fresh drawn, formed an indigestible coagulum in the stomach. In this manner, we are told, that Midas, Dioscorides, Hannibal, and a multitude of others, terminated their existence; a rather round-about method this, compared to the modern Prussic acid operation.

large fire had broken out, in the direction of Whitechapel.

On looking through my chamberwindow, which faces the West, I saw the moon shining most beautifully, and my room filled with her silvery beams; but on the buildings opposite, I could plainly perceive the reflection of a strong red light, which I naturally concluded to be occasioned by the fire. Having hastily dressed myself, I proceeded along Fenchurch-street, from whence, the horizon in the direction of Whitechapelchurch, appeared illuminated by a dense red light, covering about the same space, and bearing an exact resemblance, to that occasioned by an extensive conflagration.

On reaching the end of Fenchurchstreet, and endeavouring to ascertain, as near as possible, the situation of the fire, I found myself completely baffled; the reflection having spread considerably, and instead of being confined, as at first, to one spot, it began to be more generally diffused over the horizon. It then occurred to me, that the appearance I witnessed was the effect of atmospheric phenomena; and, on reaching Aldgatechurch, my suspicions were confirmed, by there finding collected, the firemen who had been drawn to the spot by the same cause as myself.

After I had watched the sky for some time, from Aldgate, the redness appeared to separate in the form of streaky clouds, showing the grey sky between, presenting, for some time, a magnificient spectacle.

The appearance, at the commencement, was so completely similar to that of a large confiagration, that numbers of the firemen, hastened with their engines at full speed towards the eastern part of the metropolis, as also did a great number of spectators, who naturally enough concluded the fire to be of unusual magnitude.

What rendered the phenomenon somewhat more extraordinary and unexpected, was, that the sun did not rise till six o'clock that morning, while this singular appearance was presented so early as half-past four.

As I find the phenomenon was seen, by a great number of persons residing in, and near the metropolis, I hope some of your readers will be able to give a more particular account of its appear

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EXPEDITIOUS

SHORTENING A RIVER
MODE OF EXCAVATION.

We extract the following interesting account of a recent shortening of the great River Mississipi, between New Orleans and Louisville, from a New York paper:

"The navigation has been shortened about 42 miles by cutting off two bends in. the river. The first bend is that where the Red River empties itself. The distance round the bend was 18 miles. Captain Shreve, the superintendant for improving the navigation of the Mississipi and Ohio, commenced making an excavation across the peak of land at the narrowest point. The object was effected by cutting a canal 17 feet wide by 22 feet deep. The water was let through the canal about the 28th of January, fourteen days after the commencement of the work. In two days the water had excavated a channel to such an extent, that the steamer Belvidere passed up through it. On the same day the United States steamer Heliopolis passed up the same channel. Since that time the steam-boats have all passed through the cut up and down. In five days it was the main channel of the river, about half a mile in width, and of equal depth with other parts of the river. The excavation was made by the steam-boat Heliopolis in an unexampled and expeditious manner. By laying the boat's head on shore two scrapers of large size, were worked by lines from four windlasses on the main-shaft of the boat; two lines to each scraper, one a sixinch line to haul the scraper into the bow of the boat; the other, a three-and-ahalf inch line passed through the leading block on shore as far out as was necessary, and fastened to the back-end of the scraper to draw it out. In this manner the scrapers were kept in continual operation, loaded and unloaded by their own motion attended by two men each, moving the earth out, and throwing it into the river, where it was washed away at the rate of at least a ton weight per minute. The other bend 200 miles above Natchez, which has been cut off, is not so perfect a navigation. The distance ronnd it is 24 miles. That channel has been formed by cutting a small ditch through, two years ago. Last fall the timber was cut off the