Laws of Nature, however, are not commands but statements of facts. The use of the same word is unfortunate. It would be better to speak of uniformities of Nature. This would do away with the elementary fallacy that a law implies a law-giver. Incidentally, it might just as well imply a parliament or soviet of atoms. But the difference between the two uses of the word is fundamental. If a piece of matter does not obey a law of Nature it is not punished. On the contrary, we say that the law has been incorrectly stated, It is quite probable that every law of Nature so far stated has been stated incorrectly. Certainly many of them have. Nevertheless, these inaccurately stated laws are of immense practical and theoretical value.

　　They fall into two classes-qualitative laws such as All animals with feathers have beaks, and quantitative laws such as Mercury has 13,596 times the density of water. The first of these is a very good guide. But it was probably not true in the past. For many birds which were certainly feathered had teeth and may not have had beaks. And it is quite possibly not today. There are about a hundred thousand million birds on our planet, and it may well be that two or three of them are freaks which have not developed a beak. But have lived long enough to grow feathers. It was thought to be a law of Nature that female mammals had mammary glands, until Prof. Crew of Edinburgh found that many congenitally hairless female mice lacked these organs, though they could bear young which other females could then foster.

　　And quantitative laws generally turn out to be inexact. Thus water is nothing definite. It is a mixture of at least six different substances. For in the molecule H20, one or both of the hydrogen atoms may be either light or heavy, and so may the oxygen atom. Similarly, mercury consists of several different types of atom. Thus the ratio of the densities of mercury and water is not fixed, though in the case of ordinary samples the variation is too small to be detected. But it can be detected if the water happens to have been taken from an accumulator which has been used for some time.

　　In his theory of Probability Jefferys has something new to say about induction. Two contradictory theories are in vogue as to the laws of Nature. The older view is that they are absolute, though of course they may have been inaccurately formulated. The extreme positivistic view, enunciated by Vaihinger, is that we can only say that phenomena occur as if certain laws held. There is no sense in making any definite statements, though it is convenient to do so.

　　Now Jeffreys points out that, if a number of observations have been found to conform to a law, it is highly probable that the next one will do so whether the law is true or not. In Jeffreys words A well-verified hypothesis will probably continue to lead to correct inferences even if it is wrong.

　　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.

　　Laws of Nature, however, are not commands but statements of facts. The use of the same word is unfortunate. It would be better to speak of uniformities of Nature. This would do away with the elementary fallacy that a law implies a law-giver. Incidentally, it might just as well imply a parliament or soviet of atoms. But the difference between the two uses of the word is fundamental. If a piece of matter does not obey a law of Nature it is not punished. On the contrary, we say that the law has been incorrectly stated, It is quite probable that every law of Nature so far stated has been stated incorrectly. Certainly many of them have. Nevertheless, these inaccurately stated laws are of immense practical and theoretical value.

　　They fall into two classes-qualitative laws such as All animals with feathers have beaks, and quantitative laws such as Mercury has 13,596 times the density of water. The first of these is a very good guide. But it was probably not true in the past. For many birds which were certainly feathered had teeth and may not have had beaks. And it is quite possibly not today. There are about a hundred thousand million birds on our planet, and it may well be that two or three of them are freaks which have not developed a beak. But have lived long enough to grow feathers. It was thought to be a law of Nature that female mammals had mammary glands, until Prof. Crew of Edinburgh found that many congenitally hairless female mice lacked these organs, though they could bear young which other females could then foster.

　　And quantitative laws generally turn out to be inexact. Thus water is nothing definite. It is a mixture of at least six different substances. For in the molecule H20, one or both of the hydrogen atoms may be either light or heavy, and so may the oxygen atom. Similarly, mercury consists of several different types of atom. Thus the ratio of the densities of mercury and water is not fixed, though in the case of ordinary samples the variation is too small to be detected. But it can be detected if the water happens to have been taken from an accumulator which has been used for some time.

　　In his theory of Probability Jefferys has something new to say about induction. Two contradictory theories are in vogue as to the laws of Nature. The older view is that they are absolute, though of course they may have been inaccurately formulated. The extreme positivistic view, enunciated by Vaihinger, is that we can only say that phenomena occur as if certain laws held. There is no sense in making any definite statements, though it is convenient to do so.

　　Now Jeffreys points out that, if a number of observations have been found to conform to a law, it is highly probable that the next one will do so whether the law is true or not. In Jeffreys words A well-verified hypothesis will probably continue to lead to correct inferences even if it is wrong.

　　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.