This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 Excerpt: ...If a be the length of the simple equivalent pendulum of the rigid body, and also the mean proportional between the radius of curvature at P and distance of P from the line of force; then if P move with velocity J(ga), instead of unit velocity, the tangent at P if initially will always be perpendicular to OT (fig. 78). ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 Excerpt: ...If a be the length of the simple equivalent pendulum of the rigid body, and also the mean proportional between the radius of curvature at P and distance of P from the line of force; then if P move with velocity J(ga), instead of unit velocity, the tangent at P if initially will always be perpendicular to OT (fig. 78). At the time t, measured from the instant when P is at A and OT in the vertical position OA let the angle A'OT = 0, and the arc AP= s; then s = lga) t. The equation of motion of the pendulum is 10. Define an electric image, and find the surface density on an uninsulated spherical conductor (radius a) under the influence of a quantity e of electricity at an external point at a distance /from the centre of the sphere. When the sphere is insulated and the whole charge on the sphere is--e, find the position of the line of no electrification on the surface of the sphere, and the quantities of electricity on each side of this line. (Maxwell, Electricity, 157). When uninsulated the charge induced on the sphere is eJi ana" tne 8urface density at any point is ejp i where r is the distance from the influencing point. Hence if the sphere be insulated'and have a charge--eyrs, we must superpose on the preceding system a charge e--jJ, uniformly distributed with surface density; and therefore the density at any point will be Aira f At the line of no electrification on the surface of the sphere r=f; hence if A be the influencing point (fig. 79), B the image, 0 the centre of the sphere, and EE' the line of no electrification; then AE=AC, and therefore BE=EC. The quantity of electricity on EDE' and r! = a--2af cos 5 +/, a/sin 0d0 = rdr. Therefore the quantity of electricity on EDE' and therefore the quantity on EdE' a3. d' / a / a xi. What is ...
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