In everyday language, when talking about the weight of anything, we have in mind its weight measured on the face of the earth. Every atom of the earth is pulling at the thing whose weight we are measuring, and the general effect produced by all these pulls acting against one another is what is named the weight of the thing. These pulls are in very different directions. Only those atoms which are on the shortest line between the thing in question and the middle of the earth are pulling it straight down. It is simple enough to see that all other atoms are pulling it down and sideways. But, as we have seen from experience,the effect of all those pulls is in the end straight down. A thing whose weight we are measuring has no tendency to motion in any sideways direction. This is what would naturally be looked for on a round body like the earth, because we see that any sideways pull, for example to the east, is made up for my an equal sideways pull to the west.
Not all the atoms of the earth are pulling at things with equal force, because the force of an atom's pull is dependent on its distance from a thing. If we are measuring the weight of something in London it is clear that a stone in Southend is pulling at it with a greater force than is a stone completely like it in Timbuctoo. Taking into account the different directions and distances of all the atoms of the earth, what would be their general effect ? The beautiful law was worked out by Sir Isaac Newton that the attraction of a round solid body on anything not inside it is the same as if the complete mass of the body was at its middle point. The effects of all the pulls, different in force and direction, are given in that statement.
Take, for example, the earth and the sun : Here we have two round solid bodies, and every atom of one is pulling at every atom of the other, and the other way round. But in working out the general effect, we may do so as if the complete mass of the sun was at its middle point, and the complete mass of the earth at its middle point. So that if we were able to say what the masses of the sun and of the earth are, we have only to have knowledge in addition of the distance between their middle points. The long and complex business of working out separately the pull of every atom on every other atom is made unnecessary by this simple law.
The complete pull of the earth on a thing whose weight we are measuring is the same as if the earth's mass was all at it middle point. So the earth's pull on anything is to the middle point of the earth. For a thing on the face of the earth this pint is about 4000 miles away. Anything higher than the face of the earth would be at a greater distance from the middle, and for this reason the earth's pull would be less ; that is to say, the thing would have less weight. At a great enough distance from the earth, far in outer space, the thing would have almost o weight at all.
We see, then, that the weight of anything is not an unchanging amount. Let us be clear that the weight of a body is different from its mass. Newton said that the mass of a body was the amount of substance in it. This is clearly the same if the body is on the face of the earth or far off in space. It is not dependent on the position of the body in relation to other bodies. The weights of two bodies will have a fixed relation to their measure if the weights are measured at the same place, and for this reason we frequently take weight as being equal to mass. We get butter by the pound, for example, because the weight is a true guide to the amount of butter we are getting. On Jupiter the weight of the same amount would be very much more. A man on Jupiter (if that was possible) would make the discovery that a meal of a half-pound of beef wouldn't go very far. It is, in fact, not the weight, but the amount or mass which he is interested in.
If, then, the weight of a body may be changed by conditions, while its mass is fixed, there is necessarily some way of measuring its mass other than through its weight. If we put force on a body, as by pulling or pushing it, then if he body is free to be moved, we give it motion. The greater the mass of the body the less is the motion we give it, so long, naturally, as we are using the same degree of force for the same amount of time. If we make the mass twice as great, we will give it half as much motion. And so on.
The masses of bodies may be measured in addition, by sending them against another body. A certain force is needed for stopping a body in motion. The greater the mass of the body, so long as the rate of motion is the same, the greater the force needed.
Now all these ways of measuring seem not to be dependent at all on their force of attraction. The masses of two bodies might be measured by sending them against one another without giving any attention to the attraction they have for one another. In fact, if the reader will give some thought to what we have said, he will see that the word "mass" seems to be used for two different qualities of a body. Because we said in one place that the pull between two bodies is in a fixed relation to their masses. In other words, by measuring their attractions, we might get at their masses. And later we have said that their masses might be worked out by sending them against one another. Are the masses talked of in these two tests the same ? We see no reason, outside experience, for the belief that they are the same, and, in fact, they have been given two different names -- the first being "gravitational mass" and the second, "inertial mass." But, on the other hand, the most detailed tests give no sign that they are in any way different. If it is seen from the test of sending them into one another that one body has twice the inertial mass of another, then it will be seen from the attraction test, that it has twice the gravitational mass. This completely parallel condition is quite unchanging, and seems to be, when one give thought of it, very strange. Because it seems quite a possible idea that substance might not have had force of attraction. If we came across a stone in outer space and gave it a blow with a stick it would be put in motion, and its rate of motion would be dependent on the force of the blow and on its inertial mass. But we never have the one without the other. Is it possible that "gravitation" and "inertia" are two names for the same thing ? This is a question which most men of science do not seem to have been troubled by. But one man was not only deeply troubled by it, but he got the answer ; and the outcome is the great turning-point in science named Einstein's Theory of Relativity.