AJI objects are made up of subatomic particles of a number of varieties. These particles fall into exactly three classes, however, with respect to electric charge:

1) Class A are those particles which, like the neutron and the neutrino, have no charge at all. Their charge is 0.

2) Class B are those particles which, like the proton and the positron, carry a positive electric charge. But all particles which carry a positive electric charge invariably carry the same quantity of positive electric charge what ever their differences in other respects (at least as far as we know). Their charge can therefore be specified as +I.

3) Class C are those particles which, like the electron and the anti-proton, carry a negative electric charge.

Again, this charge is always the same in quantity. Their charge is - 1.

You see, then, that an object of any size can have a net electric charge of zero, provided it happens to be made up of neutral particles and/or equal numbers of positive and negative particles.

For such an object q = 0, and no matter how large its mass, the value of qlm is also zero. For such bodies, Equation 7 tells us, FIF, is zero. The gravitational force is never zero (as long as the objects have any mass at all) and it is, therefore, under these conditions, infinitely stronger than the electromagnetic force and need be the only one considered.

This is just about the case for actual bodies. The over all net charge of the Earth and the Sun is virtually zero, and in plotting the EartWs orbit it is only necessary to con sider the gravitational attraction between the two bodies.

Still, the case where F. = 0 and, therefore, FIF,, = 0 is clearly only one extreme of the situation and not a par ticularly interesting one. What about the other extreme?

Instead of an object with no charge, what about an object with maximum charge?

If we are going to make charge maximum, let's first eliminate neutral particles which add mass without charge.

Let's suppose, instead, that we have a piece of matter com posed exclusively of charged particles. Naturally it is of no use to include charged particles of both varieties, since then one " of charge would cancel the other and total charge would be less than maximum.

We will want one object then, composed exclusively of positively charged particles- and another exclusively of negatively charged particles. We can't possibly do better than that as a general thing.

And yet while all the charged particles have identical charges of either + 1 or - 1, as the case may be, they pos sess different masses. What we want are charged particles of, the smallest possible mass. In that case the largest pos sible individual charge is hung upon the smallest possible mass, and the ratio qlm is at a maximum.

It so happens that the negatively charged particle of smallest mass is the electron and the positively charged particle of smallest mass is the positron. For those bodies, the ratio qltn is greater than for any other known object (nor have we any reason, as yet, for suspecting that any object of higher qlm remains to be discovered).

Suppose, then, we start with two bodies, one of which contains a certain number of electrons and the other the same number of positrons. There will be a certain electro magnetic force between them and also a certain gravi tational force.

If you triple the number of electrons in the first body and triple the number of positrons in the other, the total charge triples for each body and the total electromagnetic force, therefore, becomes 3 times 3, or 9 times greater.

However, the total mass also triples for each bod and the y total gravitational force also becomes 3 times 3, or 9 times greater. While each force increases, they do so to an equal extent, and the ratio of the two remains the same.

In fact the ratio of the two forces remains the same, even if the charge and/or mass on one body is not equal to the charge and/or mass on the other; or if the charge and/or mass of one body is changed by an amount different from the charge in the other.

Since we are concerned only with the ratio of the two forces, the electromagnetic and the gravitational, and since this remains the same, however much the number of electrons in one body and the number of positrons in the other are changed, why bother with any but the simplest possible number-one?

In other words, let's consider a Single electron and a simple positron separated by exactly I centimeter. This system will give us the maximum value'for the ratio of electromagnetic force to gravitational force.

It so happens that the electron and the positron have equal masses. That mass, in grams (which are the mass units we are using in this calculation) is 9.1 X 10-28 or, if you prefer, 0.00000000000000000000000000091.

The electric charge of the electron is equal to that of the positron (though different in sign). In electrostatic units (the charge-units being used in this calculation), the value is 4.8 x 10-111, or 0.00000000048.

To get the value qlm for the electron (or the positron) we must divide the charge by the mass. If we divide 4.8 x 10-10 by 9.1 X 10-28, we get the answer 5.3 x 1017 or 530,000,000,000,000,000.

But, as Equation 7 tells us, we must square the ratio qlm. We multiply 5.3 x 1017 by itself and obtain for (qlm)2 the value of 2.8 x 101,1, or 280,000,000,000,000, 000,000,000,000,000,000,000.

Again, consulting Equation 7, we find we must multiply this number by 15,000,000, and then we finally have the ratio we are looking for. Carrying through this multiplica tion gives us 4.2 x 1042, or 4,200,000,000,000,000,000, 000,000,000,000,000,000,000,000.

We can come to the conclusion, then, that the electro magnetic force is, under the most favorable conditions, over four million trillion trillion trillion times as strong as the gravitational force.

To be sure, under normal conditions there are no elec tron/positron systems in our surroundings, for positron virtually do not exist. Instead our universe (as far as we know) is held together electromagnetically by electron/ proton attractions. The proton is 1836 times as massive as the electron, so that the gravitational attraction is increased without a concomitant increase in electromagnetic attrac tion. In this case the ratio F,IF, is only 2.3 x 10il".

There are two other major forces in the physical world.

There is the nuclear strong interaction force which is over a hundred times as strong as even the electromagnetic force; and the nuclear weak interaction force, which is considerably weaker than the electromagnetic force. All three, however, are far, far strcinger than the gravitational force.

In fact, the force of gravity-though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate-is by far the weakest known force in nature. It is first and rearmost!

What makes the gravitational force seem so strong?

First, the two nuclear forces;ire short-range forces which make themselves felt only over distances about the width of an atomic nucleus. The electromagnetic force and the gravitational force are the only two long-range forces.

Of these, the electromagnetic force cancels itself out (with slight and temporary local exceptions) because both an attraction and a repulsion exist.

This leaves gravitational force alone in the field.

What's more, the most conspicuous bodies in the uni verse happen to be conglomerations of vast mass, and we live on the surface of one of these conglomerations.

Even so, there are hints that give away the real weak ness of gravitational force. Your weak muscle can lift a fifty-pound weight with the whole mass of the earth pull ing, gravitationally, in the other direction. A to magnet will lift a pin against the entire counterpufl of the earth.

Oh, gravity is weak all right. But let's see if we can dramatize that weakness further.

Suppose that the Earth were an assemblage of nothing but its mass in positrons, while the Sun were an assem blage of nothing but its mass in electrons. The force of at traction between them would be vastly greater than the feeble gravitational force that holds them together now.

In fact, in order to reduce the electromagnetic attraction to no more than the present gravitational one, the Earth and Sun would have to be separated by some 33,000,000,000, 000,000 light-years, or about five million times the diame ter of the known universe.

Or suppose you imagined in the place of the Sun a mil 108 lion tons of electrons (equal to the mass of a very small asteroid). And in the place of the Earth, imagine 31/3 tons of positrons.

The electromagnetic attraction between these two in significant masses, separated by the distance from the Earth to the Sun, would be equal to the gravitational at traction between the colossal masses of those two bodies right now.

In fact, if one could scatter a million tons of electrons on the Sun, and 31/3 tons of positrons on the Earth, you would double the Sun's attraction for the Earth and alter the nature of Earth's orbit considerably. And if you made it electrons, both on Sun and Earth, so as to introduce a repulsion, you would cancel the gravitational attraction al together and send old Earth on its way out of the Solar System.

Of course, all this is just paper calculation. The mere fact that electromagnetic forces are as strong as they are means that you cannot collect a significant number of like charged particles in one place. They would repel each other too strongly.

Suppose you divided the Sun into marble-sized fragments and strewed them through the Solar System at mutual rest.

Could you, by some manmade device, keep those fragments from falling together under the pull of gravity? Well, this is no greater a task than that of getting bold of a million tons of electrons and squeezing them together into a ball.

The same would hold true if you tried to separate a sizable quantity of positive charge from a sizable quantity of negative charge.

If the universe were composed of electrons and posi trons as the chief charged particles, the electromagnetic force would make it necessary for them to come together.

Since they are anti-particles, one being the precise reverse of the other, they would melt together, cancel each other, and go up in one cosmic flare of gamma rays.

Fortunately, the universe is composed of electrons and protons as the chief charged particles. Tbough their charges are exact opposites (-I for the former and +1 for the latter), this is not so of other properties-such as mass, for instance. Electrons and protons are not antiparticles, in other words, and cannot cancel each other.