Wig and for unit of length mo. Hence if 7=mv the theorem is true. If we suppose a portion of the tube to be straight, and the whole to be moving with velocity v parallel to this line, and against the motion of the cord, we shall have the straight part of the cord reduced to 'rest, and an undulation, of any, but unvarying, form and dimensions, T running along it with the linear velocity Suppose the cord stretched by an appended mass of W pounds, and suppose its length I feet and its own mass w pounds. Then I = Wg, Im=w, and the velocity of the undulation is ✓ feet per second. (0) When an incompressible liquid escapes from an orifice, the velocity is the same as would be acquired by falling from the free surface to the level of the orifice. For, as we may neglect (provided the vessel is large compared with the orifice) the kinetic energy of the bulk of the liquid; the kinetic energy of the escaping liquid is due to the loss of potential energy of the whole by the depression of the free surface. Thus the proposition at once. (k) The small oscillations of a liquid in a U tube follow the harmonic law. The tube being of uniform section S, a depression of level, 4, from the mean, on one side, leads to a rise, x, on the other; and if the whole column of fuid be of length på, we have the mass 2a Sp disturbed through a space x, and acted on by a force 2 Sxgp tending to bring it back. The time of oscillation is therefore ($ (a)) 21 and is the same for all liquids whatever be their densities. INDEX. 494 (6) Aberration gives hodograph of Earth's orbit 53 motion 63 variable 33; average 33; angular 57; in a fixed direction 44 angular velocity about the pole 295 in straight line, uniform 43 352 Maximum 317 Varying 282 hill, or cavity 496; by a crevasse 497 336 subtended at a point 485 position of 107, 108.. questions 391 Homogeneous Attraction not modified by interposition is normal to equipotential surfaces direct analytical calculation of 494 of a circular arc for a particle at its of a right cone for a particle at its ticle in its axis 494 (a) of two equal uniform discs, one posi- of an Ellipsoid 535, 537; of homo of a uniform limited straight line on particle infinitely near its surface 488 441 note an 439 tion 541 of a 384 Attraction of an uninsulated sphere under the influence of an electrified particle 493 internal point 479; converse proposi. external point 488 both within or both without 492 equilibrium of a non-rigid body 584 - requisites for a good 383 statical principles of 592 bar 625; supported at ends or middle 625; at ends and middle 627 body 679 401 689 question relative to 598; inverse pro- blem 600 195, 542, 582; centrobaric bodies Centre of pressure 688, 703 motion of centre of inertia of a rigid through centre of inertia 551 by Green 543, properties of 545; tum 177 gravity at a place 187 - polygon 443 iron, wool 265 37; of a force, effective 193 tions 34; Simple Harmonic Motions in 568 408; a material point 470; of parallel of any number of couples 567 et seq. very small 486; solid angle of 481; surface by a small cone 487 293, 683 rem $41 soids 535 Confocalellipsoids, corresponding points plane 91, examples 36; of a rigid solid 100 Dissipation of Energy, instances 347, Dissipative systems' 292 Distortion, places of maximum, in a cylinder 678 167; one degree of constraint of the points supporting it 636 Double-weighing 384 Dubamel's application of Ivory's theo. inch to grammes per sq. centimetre 661; other units 362-366 Edge of regression 139, Elastic body, a perfectly 643 centre of a section of a wire 608; of a wire about 628 tion, of a line, equal to unity 460 619, properties of 620; Kirchoff's ki. and elastic curve 620 and a force, composition of 568 et seq: Electric images 528; definition 530; 14; average 14; of a surface 120 of vectors 531; electric image of a 121; principal, Euler's Theorem 132 sphere, a plane 531; application to the matter on a spherical shell Hected 533; uniform solid sphere Elements of a force 184 Ellipsoid, central 337 Ellipsoid, attraction of a, 533; corre. sponding points on two 535.; Ellips. oidal shell defined 535; attraction of of a point 165. of a body 167; one ternal point 536; Potential constant cerning 537: equipotential surfaces of 477 ; mean density of the earth ex Ivory's 540; comparison of the po tentials of two 537 struction of a, from its edge 133 Empirical formulae, use of 350 Energy, kinetic 179; kinetic energy of & system 334; energy in abstract of, equal to unity 460; of the common the theory of energy 244; potential energy of a conservative system 145; of 147 of energy of visible motion 347; po- strained isotropic substance 666 motion in 105 differential 163 408, 470, on smooth and rough curves et seq., of a revolving mass of fluid 710 505, 526, of ellipsoidal shell 537 in grammes per square centimetre 661; other units 362-366. for the conduct of experiment 325; use results of experiment 347 Impact 276 matics of a 16; flexible and inexten. face 125, of a wire 60;; laws of Aesure and torsion 607; axes of pure flexure lemma 704; stability of 705 et seq.; axes 719 with glacier motion 683 199, source of the idea of 173, de. |