...Next, let us consider the integral JJzs cos This integral is equivalent to ¡$xdV; consequently, if ~x, y, z, be the co-ordinates of the centre of gravity of the enclosed volume F, we get J/ xz cos vdS = \\xd V = xV; in like manner JJ xs cos \dS = zV. Again,...

...coining to rest. Ans. -, where r is the radius of the cylinder. 131. Vis 1 iva of any System.—If x, y, z be the coordinates of the centre of gravity of any moving system of masses at any instant, x, y, z the coordinates of the element dm at the same instant;...

...be .(1.) « being a constant. Let x,, y,, 2, be the co-ordinates of the centre of gravity of a fiat plate having its middle plane coincident with the...following results for the whole body:— volume weight Jx t £ co-ordinates of centre of gravity x, = dz jf. .d* jf. dz t dz f dz .(4.) When the centres of...

...find their motion. The mode of using D'Alembert's principle for the solution may be stated thus. Let x, y, z be the co-ordinates of the centre of gravity of any one of these bodies referred to three rectangular axes fixed in space. Let three other co-ordinates...

...against fixed points, curves, or surfaces and are acted on by given forces; find their motion. Let x, y, z be the co-ordinates of the centre of gravity of any one of these bodies referred to three rectangular axes fixed in space. Let three other co-ordinates...

...dimension of a cross-section whose distance from the plane xy is z, so that its area shall be af., a being a constant. Let x,, y,, z, be the co-ordinates...following results for the whole body:— volume weight V= aft. dz; tf dz; ,.(2.) co-ordinates of centre of gravity / «, fdZ fs"- dz J Vi f* dz ~- J" dz I .(4.)...

...have followed, to determine the relation between the pressure, volume and temperature of a gas*. Let x, y, z, be the coordinates of the centre of gravity of a molecule of mass ?u, and X, Y, Z, the components of force acting upon it. Then its motion is governed...

...are at the corners of a regular tetrahedron while the fifth is at the centre of the tetrahedron. Let x, y, z be the coordinates of the centre of gravity of the five corpuscles, &, 77,, £„ £„ 77.,, £,, £„ 77,, f,, £, 77,, £ the coordinates of the...

...V be the volume of the space bounded by any varying closed surface S. As yet we need not suppose V constant. Let x, y, ~z be the co-ordinates of the centre of gravity. We have ........................ (5), where [ ] indicates that the expression within it is to be taken...

...V be the volume of the space bounded by any varying closed surface S. As yet we need not suppose V constant. Let x, y, z be the co-ordinates of the centre of gravity. We have Vx = ±ff[a?dydz] (5), where [ ] indicates that the expression within it is to be taken between...