. The Encyclopaedia Britannica; ... A dictionary of arts, sciences and general literature. asy to devise very exact means for ascertaining whetheror not it was horizontal, and, if not, whether it slanteddown the one way or the other; and thus the instrumentmight serve to determine whether P was equal to, or greateror less than, Q; and this obviously is all that is required toconvert the contrivance into an exact balance. 3. Lever Balances.—This class of balances, being moreextensively used than any other, forms the most impor-tant division of our subject There is a great variety oflever balanc
. The Encyclopaedia Britannica; ... A dictionary of arts, sciences and general literature. asy to devise very exact means for ascertaining whetheror not it was horizontal, and, if not, whether it slanteddown the one way or the other; and thus the instrumentmight serve to determine whether P was equal to, or greateror less than, Q; and this obviously is all that is required toconvert the contrivance into an exact balance. 3. Lever Balances.—This class of balances, being moreextensively used than any other, forms the most impor-tant division of our subject There is a great variety oflever balances ; but they are all founded upon the sameprinciples, and it is consequently expedient to b^n byBumming up these into one general theory. 262 BALANCE Theory of llu Lever Balance (fig. 2). — In developingthe theory of a machine, the first step always is andmust be that we substitute for the machine as it is afictitioui machine, which, while it closely corresponds in itsworking to the actual thing, is free from its defects. Inthis sense what now follows has to be understood. Imagine. Fio. 2.—Diagram jllustrating the theory of the Lever Balance. an inflexible beam suspended from a stand in such a mannerthat, whUe it can rotate freely about a certain horizontalaxis fixed in its position with respect to both the stand andthe beam, and passing through the latter somewhere aboveits centre of gravity, it cannot perform any other the beam at each end to be provided with avertical slit, and each slit to be traversed by a rigid linefixed in tho beam in such a situation that both lines areparallel to, and in one and the same plane with, the axis ofrotation; and suppose the mass of the beam to be sodistributed that the line connecting the centre of gravityS with its projection O on the axis of rotation stands perpen-dicular on that plane. Suppose now two weights, P andP, to be suspended by means of absolutely flexible strings,the former from a point A on the rigid line
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