80. Suppose, for example, that the two arms be 10 inches and 11 inches long, then, if 1 lb. weight be placed in the pan of the 10-inch end, its moment is 10; and if ¹⁰/₁₁ of 1 lb. be placed in the pan belonging to the 11-inch end, its moment is also 10: hence 1 lb. at the short end balances ¹⁰/₁₁ of 1 lb. at the long end; and therefore, if the shopkeeper placed his weight in the short arm, his customers would lose ¹/₁₁ part of each pound for which they paid; on the other hand, if the shopkeeper placed his 1 lb. weight on the long arm, then not less than ¹¹/₁₀ lb. would be required in the pan belonging to the short arm. Hence in this case the customer would get ¹/₁₀ lb. too much. It follows, that if a shopman placed his weights and his goods alternately in the one scale and in the other he would be a loser on the whole; for, though every second customer gets ¹/₁₁ lb. less than he ought, yet the others get ¹/₁₀ lb. more than they have paid for.
LECTURE IV.
THE FORCE OF GRAVITY.
Introduction.—Specific Gravity.—The Plummet and Spirit-Level.—The Centre of Gravity.—Stable and Unstable Equilibrium.—Property of the Centre of Gravity in a Revolving Wheel.
INTRODUCTION.
81. In the last three lectures we considered forces in the abstract; we saw how they are to be represented by straight lines, how compounded together and how decomposed into others; we have explained what is meant by forces being in equilibrium, and we have shown instances where the forces lie in the same plane or in different planes, and where they intersect or are parallel to each other. These subjects are the elements of mechanics; they form the framework which in this and subsequent lectures we shall try to present in a more attractive garb. We shall commence by studying the most remarkable force in nature, a force constantly in action, and one to which all bodies are subject, a force which distance cannot annihilate, and one the properties of which have led to the most sublime discoveries of human intellect. This is the force of gravity.
82. If I drop a stone from my hand, it falls to the ground. That which produces motion is a force: hence the stone must have been acted upon by a force which drew it to the ground. On every part of the earth’s surface experience shows that a body tends to fall. This fact proves that there is an attractive force in the earth tending to draw all bodies towards it.
Fig. 25.
83. Let a b c d ([Fig. 25]) be points from which stones are let fall, and let the circle represent the section of the earth; let p q r s be the points at the surface of the earth upon which the stones will drop when allowed to do so. The four stones will move in the directions of the arrows: from a to p the stone moves in an opposite direction to the motion from c to r; from b to q it moves from right to left, while from d to s it moves from left to right. The movements are in different directions; but if I produce these directions, as indicated by the dotted lines, they each pass through the centre o.
84. Hence each stone in falling moves towards the centre of the earth, and this is consequently the direction of the force. We therefore assert that the earth has an attraction for the stone, in consequence of which it tries to get as near the earth’s centre as possible, and this attraction is called the force of gravitation.