Professional Papers Volume 3 (Paperback)

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. 1853 Excerpt: ...with two cylindrical weights of equal dimensions, whose moment of inertia is known, suspended at opposite ends of the magnet; if, K = the moment of the suspended magnet and stirrup, (the value required, ) K' = the moment of inertia of the weights, T' and T = the times of vibration with and without the weights, T' K= K' the moment of inertia of the weights is calculated by the formula, where: I = interval of the points of suspension, or length of the magnet diminished by the depth of the grooves in which the threads rest, r = the radius of the cylinders, and 2 p their mass, expressed respectively in feet and grains. The value of K must be ascertained with very great accuracy from the mean of several series of observations with and without the weights; once satisfactorily determined, it may be employed as a constant quantity, and the observations with weights need not be repeated in after determinations of the intensity. A small correction must be applied for the changes in the dimensions or form of the suspended mass, produced by changes of temperature; the correction consists in multiplying the value of K by 1-f-2 e (l1--t), where i1 denotes the actual temperature of the magnet, t the temperature corresponding to the time of the original observations, and e the coefficient of dilatation of steel for 1 Fahrenheit = 0.0000063. Calculation.--The product of the horizontal intensity into the magnetic moment of the suspended magnet is obtained by the formula. mX---Tjrr where x = circumference of circle to diameter 1. K = the moment of inertia of suspended magnet and stirrup. T = the time of vibration, corrected. The observed times of vibration must be corrected for the force of torsion of the suspension thread, the rate of chronometer, the arc of vibration, the c...