Positivists and idealists have made great play with the fact that many laws of Nature, as formulated by scientists, have turned out to be inexact, and all may do so. But that is absolutely no reason for saying that there are no regularities in Nature to which our statements of natural law correspond. One might as well say that because no maps of England give its shape exactly it has no shape.

　　What is remarkable about the laws of Nature is the accuracy of simple approximations. One might see a hundred thousand men before finding an exception to the rule that all men have two ears, and the same is true for many of the laws of physics. In some cases we can see why. The universes is organized in aggregates, with, in many cases, pretty wide gaps between them. Boyle's law that the density of a gas is proportional to its pressure, and Charles' law that the volume is proportional to the temperature, would be exact if gas molecules were points which had no volume and did not attract one another. These laws are very nearly true for gases at ordinary temperatures and pressures, because

　　the molecules occupy only a small part of the space containing the gas, and are close enough to attract one another only during a very small part of any interval of time. Similarly, most of the stars are far enough apart to be treated as points without much error when we are considering their movements.

　　And most men manage to protect themselves from injury so far as is needed to keep both ears. Whereas trees cannot protect themselves form the loss of branches. It is very rare to see a completely unmutilated, and therefore completely regular tree. Mendel's laws, according to which two types occur in a ratio of 1： 1 in some cases and 3 ： 1 in others, are theoretically true if the processes of division of cell nuclei are quite regular, and if neither type is unfit so as to die off before counts are made. The first condition never holds, and the second probably never does. But the exceptions to the first condition are very rare. In one particular case a critical division goes wrong about one in ten thousand times. The effect of this on a 1 : 1 ratio or 3 ! 1 ratio could be detected only by counting several hundred million plants or animals. Differences in relative fitness are more important. But even so the Mendelian ratios are sometimes fulfilled with extreme accuracy, and are generally a good rough guide.

　　Jeffreys points out that in such cases it is often much better to stick to the theoretical law rather than the observed data. For example, if you are breeding silver foxes and a new colour variety occurs which, if crossed to the normal, gives 13 normal and 10 of the new colour, you are much more likely to get a ratio of about 1:1 than 13:10 if you go on with such matting, even though if you breed many thousands the 1: 1 ratio will not hold exactly. The mathematical theory which Jeffreys has developed concerning such cases is particularly beautiful, but can hardly be summarized here.

　　1. Ordinarily, gas molecules are so close that they attract one another for only a very short time.

　　2. The statement that atoms in the molecule H2O may be light or heavy is a sample of quantitative laws.

　　3. Human law is similar to natural law in essence.

　　4. Charles' law and Boyle's law are based on observations made at ordinary temperatures and pressures.

　　5. Since cell-division is sometimes irregular and certain types die off early, we sometimes get neither 3 ： 1 ratio nor 1 : 1 ratio.

　　6. Differences in relative fitness are more frequent than irregular cell-division.

　　7. We must see many human beings before stating the rule that all men have 2 ears.

　　8. Compared with human laws, laws of nature are accurate because they are expressed in the form of_______.

　　9. In considering the movements of stars, scientists need not consider their_______.

　　10. _______laws can serve as good guides.

　　I. Y 2. Y 3. N 4. N 5. Y 6. NG 7. N 8. approximation 9. distance 10. Qualitative ,

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