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nature must start from some assumed law of nature, such, for instance, as the assumed law of the cost of building stated above. Accordingly, however accurately we have calculated that some event must occur, the doubt always remains—Is the law true? If the law states a precise result, almost certainly it is not precisely accurate; and thus even at the best the result, precisely as calculated, is not likely to occur. But then we have no faculty capable of observation with ideal precision, so, after all, our inaccurate laws may be good enough.

We will now turn to an actual case, that of Newton and the Law of Gravity. This law states that any two bodies attract one another with a force proportional to the product of their masses, and inversely proportional to the square of the distance between them. Thus if ${\displaystyle m}$ and ${\displaystyle M}$ are the masses of the two bodies, reckoned in lbs. say, and ${\displaystyle d}$ miles is the distance between them, the force on either body, due to the attraction of the other and directed towards it, is proportional to ${\displaystyle {\tfrac {mM}{d^{2}}}}$; thus this force can be written as equal to ${\displaystyle {\tfrac {kmM}{d^{2}}}}$, where k is a definite number depending ${\displaystyle d^{2}}$ on the absolute magnitude of this attraction and also on the scale by which we choose to measure forces. It is easy to see that, if we