We have already had occasion to speak of mass. For purposes of daily life, mass is much the same as weight; the usual measures of weight—ounces, grams, etc.—are really measures of mass. But as soon as we begin to make accurate measurements, we are compelled to distinguish between mass and weight. Two different methods of weighing are in common use, one, that of scales, the other that of the spring balance. When you go a journey and your luggage is weighed, it is not put on scales, but on a spring; the weight depresses the spring a certain amount, and the result is indicated by a needle on a dial. The same principle is used in automatic machines for finding your weight. The spring balance shows weight, but scales show _mass_. So long as you stay in one part of the world, the difference does not matter; but if you test two weighing machines of different kinds in a number of different places, you will find, if they are accurate, that their results do not always agree. Scales will give the same result anywhere, but a spring balance will not. That is to say, if you have a lump of lead weighing ten pounds by the scales, it will also weigh ten pounds by scales in any other part of the world. But if it weighs ten pounds by a spring balance in London, it will weigh more at the North Pole, less at the equator, less high up in an aeroplane, and less at the bottom of a coal mine, if it is weighed in all those places on the same spring balance. The fact is that the two instruments measure quite different quantities. The scales measure what may be called (apart from refinements which will concern us presently) “quantity of matter.” There is the same “quantity of matter” in a pound of feathers as in a pound of lead. Standard “weights,” which are really standard “masses,” will measure the amount of mass in any substance put into the opposite scales. But “weight” is a properly due to the earth’s gravitation: It is the amount of the force by which the earth attracts a body. This force varies from place to place. In the first place, anywhere outside the earth the attraction varies inversely as the square of the distance from the center of the earth; it is therefore less at great heights. In the second place, when you go down a coal mine, part of the earth is above you, and attracts matter upwards instead of downwards, so that the net attraction downwards is less than on the surface of the earth. In the third place, owing to the rotation of the earth, there is what is called a “centrifugal force,” which acts against gravitation. This is greatest at the equator, because there the rotation of the earth involves the fastest motion; at the poles it does not exist, because they are on the axis of rotation. For all these reasons, the force with which a given body is attracted to the earth is measureably different at different places. It is this force that is measured by a spring balance; that is why a spring balance gives different results in different places.