94 THE UNIVERSE A VAST SYSTEM OF PARTS The "spring" ' tides are the highest because they occur when the pull of the sun and moon are acting together, in other words, when the sun and moon are on the same or opposite sides of the earth. The "neap" tides occur when the gravitational pull of the sun exerts the maximum neutralizing effect on the gravitational pull of the moon. The physiographic features of the earth's surface modify the intensity of the tides, delaying their arrival at different points. Because of the presence of the continents, the tides in the Atlantic, Pacific, and Indian oceans are secondary tides produced by the primary tides in the Southern ocean. The height of the tides varies from one foot to forty feet. Weight and Mass Are Proportional to, Other. but Not Identical with, Each It was pointed out at the beginning of this Section that all bodies in the universe attract each other with a force that is called gravitation. A special but very familiar example of this force is the force exerted on objects at the earth's surface. This is called their weight. This force, like every gravitational force, is proportional to the mass of the body, as stated in the expression of the general law of gravitation. is also proportional to the mass of the earth and inversely proportional to the square of the earth's radius, but these quantities do not vary much. It is true that a body weighs slightly less on a mountain top than it does at sea level, because there is a greater distance between the centers of gravity. But the force of gravity at the surface of the moon is only one-sixth of that for the same body at the earth's surface because the moon is so much lighter than the earth. On the moon, then, the weight of a body will be one-sixth of its weight on the earth. It is obvious, however, that there is something about an object that does not change, though its weight does. This unchanging property of matter is its mass, as already referred to in connection with the general law of gravitation. It is properly measured by the reaction of the body when it is acted on by a force, as will be discussed below in connection with Newton's second law of motion. In practice, the masses of two bodies are compared by their weights, to which they are proportional. The bodies are placed on the two pans of a balance, such as the chemist uses, and adjusted until the weights are equal. Then, by Newton's general law of gravitation, the masses are also equal. Balances are thus a device for comparing masses. Many food markets It ' " Spring" is a name in this case which has no relation to the spring season of the year.
NEWTON'S LAWS UNIVERSAL IN APPLICATION 95 use spring scales, in which the weight is balanced by the pull of a spring, whose elongation gives a measure of the force it exerts. If they were transported to the surface of the moon, the balances would still indicate a balance, for the masses are unchanged. The spring scale, however, would read only one-sixth as much, for the weight would be decreased in that proportion. Einstein Has Shown That Newton's Law of Gravitation Applies Rigorously Only to Matter at Rest. Newton's law of gravitation holds for matter at rest but is slightly inaccurate for matter in motion. Einstein's theory of relativity holds that mass increases as matter travels faster and that at the speed of light it would be infinitely great. Experiments with very small particles moving at great velocities show that Einstein is right — that they do increase in mass as they increase in speed. Einstein's theory of relativity considers time to be a fourth dimension of the calculation concerning time and space; the entire space-time system is considered to be curved into a spherical shape caused by the fairly equal distribution of the masses in the universe. There are no ways of testing many of the revolutionary ideas presented in Einstein's theory, but some of the conclusions based upon this theory have been tested and confirmed. For example, Einstein predicted that the mass of the sun would curve the space near the sun to such an extent that light passing through this space near the sun's surface would deviate from its normal path by L75 seconds of an arc. The British Royal Astronomical Society sent out two expeditions — one to Sobral in Brazil and the other to Principe in West Africa — to make observations of the eclipse of the sun on May 29, 1919. Photographs of positions of the stars appearing close to the edge of the sun were made, and the discrepancies observed in the positions of these stars were found to be in good agreement with Einstein's predictions. Later, in 1922, the Lick Observatory found the deviation to be 1.72 seconds, as compared with Einstein's predicted deviation of 1.75 seconds. Because of its speed, the path of light is curved only slightly, but the paths of less rapidly moving bodies would be curved to the extent that they would travel around the sun in hyperbolic, parabolic, or elliptical orbits, depending, respectively, upon their speeds. The paths of certain rapidly moving comets are nearly in agreement with Einstein's ideas. This theory has also explained some otherwise puzzling details in the motion of the inmost planet, Mercury.