354 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[September, 



(|iiaiitity to aero. Now all llic jjaititles iu the same level surface have no 

 tomlency to move ujioii that surface, because the jiressure is the saTuc in all 

 (Urectious: wherefore if we add the couditiou tli.it every level surface shall 

 have a dtterminale ligure when one of ils points is given, it is evident, both 

 that the fignre of the mass will be ascertained, and that the immobility of the 

 particles will be established. Maclaurin's demonstration of the equilibrium 

 of the elliptical spheroid will always be admired, and must be instructive 

 from the accuracy and elegance of the investigation. That geometer was the 

 first who discovered the law of the forces in action at exery point of the 

 spheroid ; and it only rtniaiucrl to deduce from the known forces the pro- 

 perties oil \\hich the equilibrium depends. These properties he states as 

 three in number : and of these the two, which relate to the action of the 

 forces at the surface and the centre of the spheroid, afe the same with the 

 principles of Huyghens and Newton, and coincide with two of the conditions 

 laid down above. The third jnoijerty of equililirinm, according to ilaclaurin, 

 consists in this, that eveiy particle is impelled equally by all the rectilineal 

 cauals standing upon it and extending to the surface of the spheroid. Now 

 it does not follow from this ]iroi)erty that a ](article is reduced to a state of 

 rest within the spheroid, by the equal pressures u]ion it of the surrounding 

 fluid; because these pressures may not be the effect of all the forces that 

 urge the mass of the spheroid, but may be caused by the action of a part only 

 of the mass. Maclanrin demonstrates that the pressure impelling a particle 

 in any direction is equivalent to the effort of the fluid in a canal, the length 

 of which is the ditt'erence of the polar semi-axis of the surface of the spheroid 

 and a similar and concentric surface drawn through the particle, whieb evi- 

 dently implies both that the jn-cssures upon the ]iarticlc are caused by the 

 action of the fluid befwccn the two siu'faces, and likewise that the pressures 

 are invariably the same upon all the particles in any interior surface, similar 

 and concentric to the surface of the spheroid. Such surfaces are therefore 

 the level surfaces of the spheroid ; and e\ en- ])articlc of the fluid is at rest, 

 not because it is pressed equally in all directions, but because it is jjlaced on 

 a deterniiiKite curve surface, and has no tendency to move on that surface on 

 account of the equal pressures of all the particles in contact with it on the 

 same surface, ilaclanrin seems ultimately to lia\e taken the s.ime view of 

 the matter, when he says that " the surfaces similar and concentric to the 

 surface of the spheroid, are the level surfaces at all depths. (Fl. §. CtO.) It 

 thus appears that the conditions laid down above as necessary and sufhcient 

 for au equilibrium, agree exactly with the demonstration of Maclanrin, when 

 the true im])ort of what is jn'oved by that geometer is correctly understood. 

 The general coiulitions for the equiHbriuni of a fluid at liberty being explained, 

 the attention is next directed to another jiropcrty, which is important, as it 

 furnishes an equation that must be verified by every level surface. If we take 

 any two points in a fluid at rest, and open a commiinicafion between them by 

 a narrow canal, it is obvious that, whatever be the ligure of the canal, the 

 cftbrtofthc fluid contained in it will be invariably the same, and equal to 

 the dift'erence of the pressures at the two orifices. As the pressure in a fluid 

 in equilibrium by the action of accelerating forces, varies from one point to 

 anotlier, it can be represented mathematically only by a function of three co- 

 ordinates, that determine the position of a point: but this function must be 

 such as is consistent with the iirojierty that obtains in every fluid at rest. If 

 rt, li, c, and a', h\ c', denote the co-ordinates of the two orifices of a canal ; 

 and ip (n, h, c) and <fi («', V , c') reju-esent the pressures at the s.ame points; 

 the function <p («, //, c) must have such a form as will be changed into </> (a', 

 I)', c'), through whatever variations the figure of a canal requires that a, h, c 

 nmst |iass to be finally equal to a', b<, c'. From this it is easy to prove that 

 the co-ordinates in the expression of theln-essure must be unrelated and in- 

 dependent quantities. The forces in action are deducible from the jircssure ; 

 . for the forces produce the variations of the pressure. As the function that 

 stands for the pressure is restricted, so the expressions of the forces must be 

 functions that fulfil the conditions of integraliility, without which limitation 

 an equilibrium of the fluid is impossible. Tluit,, when the forces are given, 

 the ju'cssurc may be found by au integration, which is always possiljle when 

 an equilibrium is possible : and as the pressure is constant at all the points 

 of the same level surface, au equation is hence obtained that must be verified 

 by every level surface, the upper surface of the mass being included. But 

 although one equation ajqilicahle to all the level surfaces may be found in 

 eveiy case in which an equilibrium is jiossible, yet that equation alone is not 

 suflicient to give a determinate form to these surfaces, except in one very 

 simple su])position respecting the forces in action. "NVhen the forces that urge 

 the particles of the fluid, are derived from iudepcndent sources, the figure of 

 the level surfaces requires for its determination as many independent equations 

 as there are different forces. In the latter jiai't of the i)aiier the principles 

 that have been laid down are illustrated by some ]H'ol»lems. In the first 

 problem, which is the simplest case that can be jiroposed, the forces arc sup- 

 posed to be such functions as are indepemlent of the figure of the fluid, and 

 are completely ascertained when three co-ordinates of a jioint are given. On 

 these suppositions all the level surfaces arc determined, and the luoblem is 

 solved, by the equation which expresses the equality of ju'cssure at all the 

 points of the same level surface. .Vs a particular example of the first problem, 

 the figure of equilibrium of a homogeneous fluid is determined on the supjjosi- 

 tion that it revolves about an axis, and that its particles attract one another pro- 

 portionally to their distance. This exanijde is deserving of .attention on its 

 own account; but it is chiefly remarkal;lc because it would seem at first, 

 fiom the mutual attiaction of the particles, that peculiar artifices of investi- 

 gation were required to sol\e it. Hut in the proposed law of afh'action, the 



mutual action of the particles niion one another is reducible to an attractive 

 force tending to the centre of gravity of the mass of fluid, and proportional 

 to the distance from that centre ; which brings the forces under the condi- 

 tions of the first problem. The second problem investigates the equilibrium 

 of a homogeneous jjlanet in a fluid state, the mass revolving about au axis, 

 and the particles attracting in the inverse proportion of the square of the 

 distance. The equations for the figure of equilibrium are two ; one deduced 

 from the equal pressure at all the points of the same level surface ; and the 

 other expressing that the stratum of matter between a level surface and the 

 up]ier surface of the mass, attracts every paitiele in the level surface in a 

 direction perpendicular to that surface. No point can be proved in a more 

 satisfactory manner than that the second equation is contained in the hypo- 

 thesis of the problem, and that it is an indispensable condition of the equili- 

 brium. Yet, in all the analytical investigations of this problem, the second 

 equation is neglected, or disappears in the processes used for sim])lifying the 

 calculation, and making it more manageable ; which is a remarkable instance 

 of attempting to solve a problem, one of the necessary conditions being 

 omitted. The equations found in the second problem, are solved in the third 

 problem, proving that the figure of equilibrium is an ellipsoid. 



The Society adjourned over the long vacation, to meet again on the 2Ist 

 of November. 



COLLEGE FOR CIVIL ENGINEERS. 

 We direct the attention of our readers to the prospectus of the 

 above institution, which is appended to our Journal ; we have not 

 time or space to devote to it so largely as we should wish tliis month, 

 but we shall not omit to make our remarks in the next. We shall 

 merely mention now, that before the promoters can expect to have 

 tlie support of the profession, there must be some alteration made 

 in the mode of instruction, and an addition to tlie council; besides, 

 we do not like the wholesale way of manufacturing engineers from 

 the cradle, as it would appear by the tables in the prospectus is the 

 intention of the promoters. 



llir Roi/al Jmili'my of Sciniccs of Berlin api~reciating the ntility of the 

 works published by the t'ouut De Pambour, and particulary of his theory of 

 the steam-engine which hasjust appeared in this countev, has, in its sitting of 

 the 6th of June, elecied him, by unanimity of vofes, member of the academy. 



STEAJM NAVIGATION. 



T!ic British Queen. — In the notice of this splendid vessel in our .luly num- 

 ber. A\e omitted to state that the decorations of the salotm and passengers 

 a'jiartincnls were entrnslcd to Mr. Simpson, of the West .Sliund, Lon- 

 don, who has displayed considcralile taste in the finishing;,' M'e «ill here 

 give a short description of the aparlnients. Immediately leading from the 

 principal staircase and the state-room are two saloons, the one adapted for 

 a dining, and the other as a draii ing or ladies' room, either of which are espe- 

 ( iallv' spacious and agreeable. The dining-room. 6(1 feet long and about .^0 

 feet wide, is most elaborately fitted up and decorated in the l'",lizabellian style, 

 Willi devices and historical subjects painted in a very superior manner on a 

 new material wlilcli gives to the painting the apjearance of being worked in 

 fapi'sfry or w orslcd work : it is further enriched by additional carvings of 

 flowers, ornaments, gilding. Sec., and is.™ mnssr. exceedingly chaste and uni- 

 que. The staircase is of a novel description in a ship, having a double thght 

 of stairs descending on cilber side, and is very rich')' carved in Knglish oak. 

 The drawing or ladies' rcJom is much smaller than tlie preceding, init deco- 

 rated very neatly in white with gold mouldings and arabesque li-ngings in 

 corresponding colours, .so that for extent, as they form a vista or nearly 100 

 Jeet in length, for variety and e'egancc. it can be safely said that this suite 

 of rooms has nc\ er yet been surpassed. 



Gnrcrnmeiii Steamers. — It is not gencrall)' known that a sfeamci* of very 

 large tonnage is about to be lannebcdfrom C'hath m Dockyard. It will have 

 1 ciMi I oi^wu and finished in the iiicre.libly short sjiace of eight weeks. M'e are 

 informcfl that this extreme cxpeditinn Is an experiment uiifler direciion of the 

 GM\crninent. in orcler lo ascertain the shortest pnssib'e limi" in which such a 

 vessel can l,e completed. The numtcr of hands has Keen utilimi'.ed ; In tart, 

 the men are working on her at the present moment as thick as bees in a hive, 

 and they are allowed to make as many working hours per day as they can. 

 The sum apportioned 'or the labour, we understand. Is 4.000/. ; and .should it 

 not cost that, the overplus is to be divided among the men. The experiment 

 has excited the greatest possible Interest in the neighbourhood. — Greeiiwieh 

 Gazette. 



The Ci/rln/is Steam Friffate. — 'fills magnifiecnt vessel, the largest steam man- 

 of-war in the world, was lately launched from Penibr(>ke Dockyard. Her 

 dimensions are as follows ;— Leng:h. 22.') feet, beam letween paddles 38 feet, 

 depth of bold 21 feet. Her tonnage is about 1.300. belngSOO tons larger than 

 the Gorgon, launched from the sarne slip about eighteen nionlhs since. Her 

 ec|uipmenf, as a man-of-war, will be the same in all respects as a frigate, 

 liaxing a complete gnu or main deck as well as an upper or quarterdeck. On 

 the main deck she will carry eighteen long 3(J-pouiidcr3, and on I he upper 

 deck f( iir '18-ponndeis and two Oti-pouuders on swivels, carrying a ball often 

 inches di.inicter, and sw ee]iing riiuud the horizon 'i'lO degrees. — I'hc Cyclops, 

 hie file \essel already referred to, will le commanded by a post captain, 

 these two being the only steamers taking a frigate's rank. Her crew will 

 consist of 210 men, 20 engineers and stokers, and a lieutenapfs party of 



