I8i8.] 



THE CIVIL ENGINKER AND ARCHITECT'S JOURNAL. 



359 



Then, on the supposition that the angle of deflection is very- 

 small, as it must be in all practical cases, the momentum of the 

 force tendintr to restore the equilibrium of flotation is, by the 

 principles of mechanics, — 



m =^ ( d] w sin m. 



This equation is general, whatever may be the form of the 

 floating body ; but the subsidiary calculations are more intricate in 

 some cases than in others, and in consequence, the formula in 

 those cases vvill be more difficult in its application, and the labour 

 will be much more tedious and irksome. 



By attentively examining the constitution of the above equation, 

 there are certain inferences tliat olfer themselves, which it may be 

 useful to specify. They are as under : — 



P 



1. If the first term of the parenthetical expression be 



greater than the second, (/, th« leverage is affirmative, and the 

 force tends to restore the body to its original state. 



2. When the two parenthetical terms are equal, there is no force 

 tending either to restore or destroy the equilibrium ; for, in that 

 case, the momeijtum is nothing. 



3. Mlien the first of the parenthetical terms is less than the 

 second, the leverage is negative, and the force tends to destroy 

 the etiuilibrium and overset the body. 



4. M'heu tlie weight of the body remains constant, the stability 



d) sin (p. 



6. When the centre of gravity of the whole floating mass is 

 lower than the centre of buoyancy, or that of the part immersed, 

 the term d, or the distance between the centres of gravity, is nega- 

 tive, and the whole parenthetical quantity I — d\ becomes 



affirmative; a circumstance which greatly increases the stability 

 of flotation, as we have already intimated. 



If, in the vertical line passing through the centre of gravity of 

 the whole body and that of the immersed portion, there be taken 

 a point distant from the centre of buoyancy, by a quantity equal 



P 

 to , that point is called the melacentre by naval architects, 



because it must always be situated above the centre of gravity of 

 the mass, in order that the body may float with stability. These 

 things being premised, we shall now give an example of the method 

 of calRllating the momentum of stability, according to the above 

 formula ; and if the process be well considered in this particular 

 case, there can be little difficulty in applying the same principles 

 to similar cases, even when the section of the body is of a very 

 different form. 



Example. — In the prismatic body of fir formerly mentioned, and 

 of which we have given a transverse section, the length of the 

 water-line C D is 25'8 inches ; the vertical distance G </, 8'5 inches, 

 and the whole weight of the floating body 5,200 lb. ; what is the 

 momentum of stability, or with what force does the body endea- 

 vour to restore itself, when deflected from the equilibrium through 

 an angle of 5 degrees. 



By a previous calculation, we have found the area of the im- 

 mersed triangular section to be 439 square inches, omitting the 

 fraction ; hence, by the formula, we have — 



/ 25-83 \ 



Momentum = I -— -—- — 8-5 1 x 5200 X sm 5°. 



\12 X 439 / 



,12 X 439 

 The length of the water-lineis 25-8 in. 



log. 



1-4116197 

 3 



25-8^= 17173-502 log. 4-2348591 



Area of the immersed section = 439 sq. in. ar. co. log. 7-3575355 



Constant number, 12 ar. co. log. 8-9208188 



Natural number, 3-2599 



Consequently, we have — 



'■ •' 12 X a 



P 



25 8^ 



log. 0-5132134 

 = 3-2599 ; which, 



12 X 439 



being less than the term d = 8-5 inches, the third inference shows 

 that the leverage at which the weight of the body acts is negative, 

 and the force tends to overset it, the momentum of instability 

 being ( — 8-5 -|- 3-2599) X 5200 X 0-08716 = — 2374-981 pounds. 



FIRE-PROOF BUILDINGS. 



The advantages of building our dwellings fire-proof is so gene- 

 rally acknowledged, that it is needless to say a word in its favour; 

 but the great difficulty in the way has been the expense in con- 

 structing the floors and ceilings. To Dr. Fox, of Bristol, are we 

 indebted for the erection of buildings that are fire-proof, and at 

 the same time quite as economical as the ordinary timber-built 

 floors. About 15 years since. Dr. Fo.x built a private asylum at 

 Northwoods, near Bristol, on a large scale, containing no less than 

 120 rooms. Externally, it is built in tlie ordinary way with brick- 

 work, but the floors are constructed as shown in the annexed en- 

 graving ; and in order to make our description practical, we shall 

 describe tlie weight and size of the bearers as adapted to one of 

 the rooms at Nortliwoods. The floor is 18 feet by 13 feet ; the 

 joists, which are placed lengthwise, are of cast-iron, of the j,- 

 shape, and are 3 inches deep at the bearings, and 5^ inches deep 

 in the middle ; fths of an inch thick at the bottom, and § inch 

 at the top. The depth includes the flange at the bottom, which is 

 2^ inches wide, and |ths of an inch thick, on the underside. Each 

 joist weighs 15g lb. per foot, and they are placed 18 inches apart. 





-J 



4miimm: 





Upon the flanges are laid stout fillets of wood, about 1 inch square, 

 clove out of short ends of deals, with a space of about half an inch 

 between each slip. Upon these fillets is laid a thickness of coarse 

 mortar, portions of .which pass through the spaces, and form a key 

 for the ceiling. Uyon the coarse mortar is placed a layer of 

 pugging or concrete, and finally a composition composed of lime, 

 ashes, and sand, well beaten down, and trowelled on the face. 

 After the whole has become tolerably dry, linseed oil is rubbed 

 over the surface, which renders the floor perfectly non-absorbent 

 of moisture. The ceiling is then put on below — lirst a coating of 

 lime and hair, tlien a floating coat, and at the conclusion the set- 

 ting coat. AVhen the whole has stood for a few days, the floor 

 forms a solid mass, and is very stiff" and strong. 



Models, showing the form of construction, may be seen at 

 Messrs. Fox and Barrett's offices, 46, Leicester-square. 



References to Engraving. 



a, Plaster Ceiling, formed in the orilinary way. — d, b, &, Cast-iron Joists. 

 c. Strips of Wood, Slate, or otlier material, with narrow spaces between 

 each. — d, a coat of coarse Mortar, forming a bed for the concrete above, 

 and a key for the ceiling below. — e. Layer of concrete or pugging. — f a 

 facing layer of composition, forming a floor of great hardness, toughness, 

 and Uurabiliiy, and perfectly fiee from absorption. 



Blasl-Furnaccs. — Remarkahle Accident. — At one of our blast-furnaces, 

 blown with heated air, while the blast was shut off for a few minutes, as is 

 usual after casting, an explosion took place inside the pipes, which, from its 

 effects, we consider extraordinary. In the pipes immediately outside one of 

 the stoves for heating the blast, and at the end next the furnace, is a stop, 

 valve — a circular disc of cast-iron, IJ inch thick, and \'2 inches diameter, 

 cutting off the connection between a line of cold-blast pipes and the hot-air 

 pipes. This valve, by the force of the explosion, was literally shattered. 

 Several of the joints in the line of cold-blast pipes, with which the breaking 

 of this valve opened a connection, were blown out, and another stop-valve, 

 in the large main, at a distance of 20 yards, v\'as also broken in pieces ; 

 there the explosive mixture escaped in flame at the waste. The furnace, at 

 the same time, belched out a great quantity of the materials in front. Will 

 any of your scientific correspondents have the kindness to explain the nature 

 of the explosive compound likely to be formed in the hot-air pipes ? It ap. 

 pears to have generated in the furnace, and tired by the pipes of the stove 

 being red-hot, which they very soon become (if the fireman is at all care- 

 less) when the blast is not passing through them. — An Old Scbscribkb : 

 Merihyr Tgduil, Oct. 31. — iJechanics' Magazine. 



