The last fundamental dimensionful constant that we discuss is the one that was discovered historically first, and one that we have already seen. It is the constant that Newton found to describe gravity. As we saw in the last chapter, the most accessible but nontrivially powerful applications of Newton's understanding of gravity, in relating the falling of things like apples near the earth to the falling of other things like the moon that are much further away, does not obviously involve a fundamental constant, because both motions are induced by the presence of the earth, which can be considered an object of arbitrary size, in the sense that other planets have different sizes.

But the fact that all of the motions of the planets around the sun, as well as their moons around themselves, can also be related in scale to things like the motion of the earth's moon, quickly leads to the realization that there is another constant of proportionality that relates this empty-space property of gravity to the masses of the objects that induce it. This is Newton's constant G, described dimensionally in detail in the previous chapter.

Because, unlike the case of chemistry which gives a dimensionless (counting) notion of ``how much'' charge is present, there is no obvious basic ``unit of mass'' that has arisen in human experience so far, we can give no similarly simple description of its dimensional content to dimensionless numbers, as we could for the electric and magnetic constants. Therefore we simply follow the historical way to discuss it, essentially in the framework provided by Newton's way of expressing physical relations, which will be discussed in more detail in the next chapter. All of the relevant dimensional concepts have already been introduced. The Newtonian description of gravitational effects is conveniently made in terms of the ``force'' created on one object by another, which is a dimension that can be conveniently measured with compressed springs. In terms of this dimension, Newton found first, and the result has been much more precisely checked by Eotvos, Dicke (and others?) since, that this force scales as:

Since Force has the dimensions of , we see (again) that Newton's constant has the dimensions of .

For a long time that seemed to be about all there was to say about this constant as a dimensionful quantity. It had long been recognized as the single number that all gravitational effects have in common, but because there was no ``chemical''-type description of masses, there was no further expression of this constant in terms of other quantities. But like clues to a riddle that can have no obvious significance when considered apart, these constants, G complemented by c and later by h/, taken together, become remarkable.

Thu Aug 31 12:01:42 CDT 1995