52 AEROSTATICS. She shroudeth vice in vertues vaile, A honey fhower raines from her lips, Shee makes thee feeke, yet feare to find; She letteth fall fome luring baites Soft foules the binds in tender twist, With foothing words, inthralled foules Her little fweet hath many fowres, Like winter rofe, and fommer ife, Moodes, paffions, fancies, jealous fits, Her houfe is Sloth, her doore Deceite, Her dyet is of fuch delight, As please till they be paft; Her fleepe in finne doth end in wrath, Plow not the feas, fowe not the fands, July = AEROSTATIC S. TRANSLATION OF A MEMOIRE READ BEFORE THE ROYAL ACADEMY OF SCIENCES AT PARIS, ON SATURDAY_THE_24TH OF JANUARY, 1784. BY M THOMAS DODORET; CONTAINING THE EXPLICATION OF A SIMPLE METHOD OF DIRECTING THE NEW AEROSTATIC MACHINES, IN PATHS WHICH ARE OBLIQUE TO THE MOTION OF THE WIND. WHEN the equilibrium of the air the fame direction that the air moves ceafes in any region of the in. atmosphere, it neceffarily caufes a becaufe, when they are not used, they We may, therefore, employ oars ; current in that fluid, If the whole will have no effect in retarding the mafs moves on with an equal pace, the motion of the balloon, but will be fituation of the particles of the air will carried themselves along with the comnot be altered with refpect to one another; and it is evident that in this they are made ufe of, they will only mon mass of the atmosphere: and when cafe, a body which is fufpended in it give the balloon a kind of compound will be carried on by the motion of the direction, making an angle more or whole mafs of air, and the particles lefs acute with the direction of the of the fluid which immediately touch wind, according as the velocity imit will be in a state of inactivity with preffed on the balloon by them, in refpect to this body, and its appendages an oblique direction to that of the will be carried on, without leaving any wind, bears a greater or lefs proportion vacuum, in the fame pofition, and in to the velocity of the wind." But But it is almost impoffible that the atmosphere (which as all bodies in motion have a tendency to move in a traight line) should move fo equally and uniformly, in every part, round fach a circular body as the terreftrial globe; becaufe the progreffive motion of the wind, when it blows ftrong, is only an effect of fucceffive and repeated percuffions. It appears, therefore, that bodies which float in the atmosphere ought to be fubject to the ordinary laws of impulfion: that is to fay, the velocity which each current of wind communicates to the different parts of a body floating in the air, will be in the inverfe ratio of the mafs of each of thefe parts, which are collected together into one volume. It is from the effect of this principle, that certain clouds overtake thofe which before preceded them, in the fame region, and at the fame elevation; for if this was not the cafe, clouds which confift of the greateft volume, or mafs, would be able, during the fhort intermiffions of the feveral gufts of wind, to overtake again those which confift of a lefs volume; whereas thofe which confist of the greatest volume ought to move floweft. This remark is important, as it inconteftibly proves that the wind does not communicate the fame degrees of fwiftness to every body which floats in it. It is this differencein the fwiftnefs, or pace, which occafions thofe ftrange and uncommon appearances that we obferve in the fituation of the clouds, which are continually changing with refpect to each other. Thofe which are thickest, or denfeft, advancing flower; and we often fee the extremities of thefe clouds which are tranfparent, and of courfe lefs folid, detach themfelves from the main body of the cloud. From thefe obfervations I have constructed my project, which is very fimple, and as follows: more I place at the upper end of the globe a kind of rods or beams, fo as to crofs each other at right angles; and correfponding with other rods or beams of the like kind, fixed at its lower part. They may be called the upper and lower beans or rods; and which will then form two frames, the beams of which crofs at right angles, in the middle of which is the globe. Thefe beams or rods ought to exceed in length, on each fide, the horizontal diameter of the globe. I place fails between the upper and lower beams, which will fhut as a curtain against the globe, or extend, at pleasure, by means of cords paffed through pullies at the extremity of the beams, and near the globe. Acrofs each of these beams Iadd another, to fuftain a counterpoife, to keep it in equilibrio with the fail on the other fide: any of the goods which you mean to tranfport will ferve for this purpofe. Things being thus difpofed, the fails and the counterpoife being fhut close to the globe, I let it take its flight till it comes to the height defired, or where I wish it to continue. If by a wind at eaft, for example, I wish it to go north-east from the spot I am in, I draw, at the fame time, two cords; the one to the left, which extends the fail fixed to the beam oppofite the fouth, and the other to the right, which draws the counterpoife oppofite on the north beam, to keep the extended fail in equilibrio. The effect of this manoeuvre does not appear even doubtfull in theory. The fail, when extended, prefents a large furface to the flux of air, and ought, therefore, to receive a ftrong impulfe, whilft the counterpoise oppofite,not having the furface augmented, as the fail has, will not receive any augmentation to force it on; and the two hemifpheres, the fouth and north of the machine, with all their apparatus, will be equally balanced, but the one being more violently pufhed than the other, ought to be confidered as at reft, relative to the excefs of velocity in the other, in the fame manner as will happen when one extremity of a body is in motion whilft the other is at reft; the hemifphere which is pushed moft violently turning round to the other hemifphere, which refifting, by reafon of its lefs velocity, will drive the force to the centre. Hence the counterpoife placed on the north beam becomes neceffarily the center of a circular motion; but such a rotation cannot take place, unk fs I to the north eat, or by fetting the fails on the north fide you may go towards the fouth-eaft; and fo, according as you extend the fail, and remove the counterpoife to or from the globe, fo will the wind act on the fail, and make it go fafter or flower. If the machine should acquire in the long run a rotatory motion, fufficiently rapid to elude one part of the action of the wind on the fails (which is hardly credible) it will be an eafy matter to stop it by furling the fail which is towards the fouth, as in the cafe of the firft example above defcribed; and at the fame inftant unfurling that towards the north. In cafe the gentlemen of the Academy fhould find any merit in the above plan of direction, I truft they will do me the favour to acquaint me therewith, and to certify the date. the centre of the globe gets out of the direct line of the wind which it was in before, and paffes to another line, parallel to that direction on the north fide; the globe will then turn to the north until the fail has very near defcribed a quarter of a circle towards the caft, and prefents no more of its furface to the wind*. Then I fhut the fail up against the globe, and alfo the correfpondent weight which holds it in equilibrio; and at the fame time, by pulling another cord, I extend the fail fixed to the other beam, and alfo its oppofite counterpoife; which will caufe the globe to turn towards the fouth: the effect defcribed above will again take place; that is, the center of the globe will again go out of the line of the wind in which it was, and pafs to another line parallel to it, but more northerly. Incontinuing the fame manœuvres, you may, by an eaft wind, go By increafing the number of the beams or rods, it is obvious that the wind may be made to act, with greater conftancy, nearly at right angles to the furface of the fails. 1 LITERARY (Signed) THOMAS DODERET. Paris, 24th Jan. 1784. ARTICLE REVIE W.. LXXI. THE Philofophical Tranfactims of the Royal Society of London, Vol. LXXIII. for the Year 1783. 4to. Lockyer Davis. As thefe experiments are directed to a very ufeful purpofe, and relate to a fubject at present but little underflood, we fhall give an account of them in the author's own words: He begins by obferving that the calculations of the late Sir Charles Knowles, and many more of a fimilar nature, that are to be met with in Belidor's Architecture Hydraulique, and other books, are founded upon a fuppofition that the effect of the wind is directly as the furiace ucon which it acts. If, for instance, its force be estimated as one upon one fquare yard, its force upon two fquare yards thould be estimated as twe, upon three fquare yards as, three, &c. but in this proportion is not to be depended upon, nor muit the refittance of furfaces be estimated merely by their extent; but feveral other circumstances mat be taken into confattration. "No figures can refemble each other more than a parallelogram and a fquare, having the fame fuperficial contents, as they are both bounded by four straight lines meeting at right angles, yet they oppofe different degrees of refiftance to the air. "If two fimilar cards, for instance, are placed oppofite the wind, one upon its end, and the other on its fide, and both inclined to the fame argie, the wind will have the greater effect upon the card that is placed end-ways. To determine the difference of resistance between these two furfaces, and to ascertain the effect of other figures moving through the air, I tried the following experiments. The two first are to be found in Mr. Robins's Treatife upon Gunnery, but I thought it proper to repeat them, that they might be more readily compared with others made with the fame apparatus, efpecially as Mr. Robins made ufe of a machine 'conftructed upon a fmaller fcale than mine, ard turning upon friction wheels, which are not proper for machines of this nature, nor indeed for any purpofe, where an uniform motion is required. Having faffenel a ftrong joift of wood from one fide of a large room to the other, fo as to form a kind of bridge at fome diflance from the floor, I erected a perpendicular thaft or roller, which turned freely in brafs fockets fixed into the floor and bridge, upon pivots of hardened fteel, one-fixteenth of an inch in diameter. On each fide of this roller was extended an arm of deal, feather-edged, and fupported by stays of the fame material, feathered in the fame manner, to oppofe as little furface as poffible to the air when in motion. "Round the upper part of this roller was wound a ftring of catgut, which, paling over pullies properly difpofed, was faftened to a fcale that defcended into the well of an adjoining ftair-cale. "The extremity of thefe arms defcribed a fpace of more than forty feet in every revolution, the weight delcending in the fame time only fix inches. The time in all the following experiments was the fame; and, as each revolution was performed in four feconds, the velocity of the end of the arm on which the furface was fixed was at the rate or about feven miles an hour. "The first figure that I tried was a parallelogram of tin, nine inches long, and four inches wide. Its longett fide was placed parallel to the floor, at the extremity of one of the arms. Its shortelt tides were inclined to an angle of fortyfive degrees from the perpendicular, and in this fituation it was carried round with its furface against the air. I now Atter fuffering it to revolve until I was fatisfied that its motion was become uniform, I put as much weight into the feale as moved it with a velocity of five turns in twenty feconds. I then changed the fituation of the parallelogram, placing its thortelt fides parallel to the floor, and inclined to the fame angle as before. found, that more weight was required to produce the lame velocity, though the quantity of surface was the fame as in the preceding experiment. The weight necellary to put the machine alone in motion, with the velocity above mentioned, was two pounds and an half. When it carried the parallelogram with one of its thouit fides downwards, it required four pounds and an halt aaditional weight; and when the parallelogram was reyerfed, another half pound was barely fufficient to give it the fame velocity. 64 The difference, therefore, occafioned by placing the tame parallelogram with its longer or thorter fides inclined from the direction of its motion, was equal to one-tenth of the greatest refiitance. "It has been obferved, that in these two experiments the mean velocity of the plane was not the fame, as its extremity extended farther from the centre of the machine in one than in the other. This is ftrictly true; but the use of the parallelogram bore fo fmall a proportion to the length of the radius to which it was faltened, that the error arifing from this circumitance is fcarcely perceptible, and the advantage being in favour of that which required the leat weight, I did not think it necellary to bring it into accounts inches long, and four broad, in the place of the parallelogram, the difference was increafed from one-tenth to one-feventh of the weight employed to give them the required velocity. Purfuing the fame reafoning that led me to the laft experiment, it occurred to me, that even againit figures of exactly the fame thape, the refiitance of the air, when the dimensions of the figures were enlarged, would not be increafed in the fame proportion as the fize of the planes, but in a much higher ratio; and that, by bending the planes as a fail, the rellitance would be itill further increafed, though the fection of air that would be intercepted by the planes mult by thete means be confiderably leffened. "The refult far furpaffed my expectations. A fquare of tin, containing fixteen fquare inches, placed perpendicularly, was retiited as two and a half. Aiquare, containing fixty-four inches, or tour times the former quantity, instead of meeting with a refiitance as ten or our times the former refiftance, required no lefs than fourteen pounds to give it the fame velocity. "Four-tenths (or nearly half as much again) was an increase of rentance, that made me fufpect fome error in the experiment; but having repeated it feveral times with great care, and having examined all the parts of the machine, I was latished that I had made no mistake. "I now placed the parallelogram of nine inches long upon the arms of the machine, with its fhorteft fides parallel to the horizon, bending it to tuch an arch that its chord meatured eight inches, and inclining it to an angle of forty-nve degrees. And though the tection of air that it intercepted was by thefe means diminished oneninth, yet the relitance was increafed from five to five and a half. And when the parallelogram was bent yet farther, and its chord contracted almost to even inches,, the refiitance was increated to five and three-quarters. "I mention thete numbers in grofs, to avoid confufion; but in the fubjoined table the mea fures and weights are fet down exactly."" He further obferves, that " Dr. Hook, Monf. Parent, and other mathematicians realoned upon a fuppofition" that the air in motion followed the tame laws as light; and that it was reflected from furfaces with the angle of reflection equal to the angle of incidence, which is not the cafe, as it never makes an angle with the plain, but is always reflected in curves. He concludes with remarking," that the general caufe of the different reliitance of the air upon furfaces of different ihapes, is the itagna tion of that fluid near the middle of the plane upon which it fizikes. The thape and fize of the portion thus itagnated differs from the shape and angle of the plane. The elasticity of the air permits the parts in motion to comprefs thote which are hirit itopped or retarded by the plane, and forms, as it were, a new furtace of a different fhape, for the reception of thote particles which fucceed. With the alittance of a good folar microfcope the curves et the air ftriking againit different Turfaces may be delineated, and when the general facts are once clearly afcertained, mathematicians will have an ample field for curious and useful fpeculation. TABLE. TABLE. Turns. Time. Weight. Turas. Time. Weight. Machine alone Ditto, with one of its shortest With a lozenge nine inches long, and four broad, with its longeft fide parallel to the horizon four inches by four inches 5 Ditto, eight inches by eight inches ART. LXXII. Les Ami des Enfans. The Children's Friend. Tranflated from the French of M. Berquin. Fol. III. 12mo. Is. Cadell and Elmfley. CLAYTON, Lord Ormfby's man. The fcene is in the chamber of Auguftus. SCENE 1. AUGUSTUS. AUG. What, is it for me O, do let me have it, dear papa! and I will always be fo dutitui, and ftudy to hard LORD O. If I could depend upon that!— But perhaps you do not know that a word requires the carriage and manners of a gentleman; and that, if you wear one, you must no longer confider yourself as a boy; that you must behave with attention and decorum, and always remember, that it is not the part of the fword to adorn the man, but the man the fword. Auc. O, that will be no difficulty. I fhall understand very easily how to adorn mine; and then I thall have nothing more to do with thofe lower fort of people. LORD O. Whom do you mean by those lower fort of people? AUG. Why, thofe that have no right to wear a fword, or a bag, and that are not people of fafhion, like you and me. LORD O. Auguftus, there are none, who, in my opinion, thould be called the lower fort of people, but thole whofe notions are mean, and whole actions are yet worfe, who are difobedient to their parents, and rude and ill-bred to all others. I often, therefore, fee many of the lower fort of people among the first nobility, and many whom I think noble among those who ap pear to you the lower fort of people. Auc. This is juft what I think too. AUG. So, this is my birth-day! I am glad they told me of it, for elfe I thould have palled it by, and now it gives me a fair title to expect LORD O. Why, then, did you talk just fome new prefent from papa. I wonder what it now of the right of wearing a fword and a bag? will be! Let me think, what can he give me ? Can you fuppofe the real dignity of people of I faw Clayton had something hid under his coat, He rank confifts in fuch paltry ornaments? They when he went to papa's rocn just now. would not let me go in with him, to fee what it may ferve, indeed, to diftinguish different fta tions of life, because it is proper that different was. However, only for being obliged to behave a little well to-day, I would have made itations fhould be diftinguished in the world. him fhew it me whether he would or not. But, But a rank the most exalted will only make a man appear yet meaner, if he is unworthy of mum! I fhall know now; for I am fure that's filling it. papa's step. SCENE 11. Lord OR MSBY (with a frord and fword-belt in his hand) and AUGUSTUS. LORD O. O, here you are, Auguftus. I have already wished you joy of your birth-day; but fancy you don't think that quite enough, do you? AUG. O yes, papa- -but what is that you have in LORD O. Something that would not very well fuit you yet; a iword, you fee. AUG. So I think too, papa: but it won't make me appear meaner to have a fword, and to wear it? |