A treatise on analytical statics, with examples

by Isaac Todhunter

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. 1866 ...originally occupied and the weight to that which the substance originally occupied. 150. In the construction of a balance the following requisites should be attended to. (1) When loaded with equal weights the beam should be perfectly horizontal. (2) When the weights differ, even by a slight quantity, the sensibility should be such as to detect this difference. (3) When the balance is disturbed it should readily retu to its state of rest, or it should have stability. We shall now consider how these requisites may be satisfies To find how the requisites of a good balance may be sattsfia Let P and Q be the weights in the scales; let AB = 2a Let Che, the fulcrum, h its distance from the straight lia which joins A and B. Let W be the weight of the beai k the distance of the centre of gravity of the beam from this centre of gravity being supposed to lie on the perpe dicular from C on the straight line which joins A and Let S be the weight of each scale; so that P and S vertically through A, and Q and 8 vertically through jBl Let 6 be the angle which the beam makes with the horizon when there is equilibrium. The sum of the moments of the weights round C will ba zero when there is equilibrium, by Art. 57. Now the length of the perpendicular from C on the line of action of P and S is acos0--h sin 6; the length of the perpendicular from (& on the line of action of Q and 8 is a cos 6 + h sin 0; and thJ length of the perpendicular from G on the line of action of H is k sin 6. Therefore (Q+ S) (acos0+Asin 0)-P+S) (acos 6-hsm6) + Wk sin 6 = 0; This determines the position of equilibrium. The first requisite--the horizontally when P and Q are equal--is satisfied by making the arms equal. For the second we observe that for a given difference of P and Q the sensibility ...

82 pages, Paperback

First published August 20, 2015

About the author

English mathematician known for his writings on the history of mathematics.