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«·’›Õ… 241 - The Efficiency of a machine is a fraction expressing the ratio of the useful work to the whole work performed, which is equal to the energy expended. The limit to the efficiency of a machine is unity, denoting the efficiency of a perfect machine in which no work is lost. The object of improvements in machines is to bring their efficiency as near to unity as possible.˛
«·’›Õ… 119 - The tendency of a couple is to turn the body to which it is applied in the plane of the couple ó that is, the plane which contains the lines of action of the two forces. (The...˛
«·’›Õ… 129 - Then each force will be proportional to the distance between the lines of action of the other two. The direction of the middle force, C, is contrary to that of the other two forces, A and B.˛
«·’›Õ… 251 - ... mechanism, and the resistance of the air pump and other parts of the engine. For example, the useful work of a marine steam engine in a given time is the product of the resistance opposed by the water to the motion of the ship, into the distance through which she moves : the lost work is that performed in overcoming the resistance of the water to the motion of the propeller through it, the friction of the mechanism, and the other resistances of the engine, and in raising the temperature of the...˛
«·’›Õ… 16 - To find the area of a trapezoid. RULE. Multiply half the sum of the two parallel sides "by the perpendicular distance between them : the product will be the area.˛
«·’›Õ… 120 - ... the ratio of the mass of a given volume of the substance to the mass of an equal volume of water, in which case it is equal to the specific gravity. In its application to gases, the term ˛
«·’›Õ… 4 - Suppose a* =n, then x is called the logarithm of n to the böge a ; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The- logarithm of n to the base a is written Iog0 n ; thus logÑii = a; expresses the same relation, as a* = n.˛
«·’›Õ… 146 - P= f fpdxdy=lv^T (4.) The centre of stress is the point on the surface AA perpendicularly opposite the centre of gravity of the ideal solid. The simplest, and at the same time the commonest case of this kind is where the stress is uniformly-varying; that is, where its intensity at a given point is simply proportional to the perpendicular distance of that point from a given straight line in the plaue of tho surface A A.˛
«·’›Õ… 4 - ... between 1 and 10 is obtained by moving the decimal point of the number (actual or implied) the required number of digits. The power of 10, for a number greater than 1, is positive and is one less than the number of digits before the decimal point in the original number. The power of 10, for a number less than 1, is negative and is one more than the number of zeros immediately following the decimal point in the original number. Hence...˛
«·’›Õ… 223 - The Radius of Gyration of a body about a given axis is that length whose square is the mean of all the squares of the distances of the indefinitely small equal particles of the body from the axis, and is found by dividing the moment of inertia by the mass...˛