132 



NATURE 



[February 2, 1922 



to simple pelagic Coelenterates in which cell boun- 

 daries and cell layers may have played only a 

 secondary and belated part as the size of the 

 organism increased." 



The economic importance of th'ese organisms is 

 great, both as a food supply and also occasionally 

 as a destructive agency. It is well known that 

 they form a large pel-centage of the stomaqh con- 

 tents of sardines and other small fish. At times 

 they are the dominant forms of the plankton, and 

 have been recorded by Kofoid as the cause of out- 

 breaks of " red water " on the Calif ornian coast 

 and elsewhere which may be a menace to the 

 health and life of slow-moving or bottom-living 

 animals which, being unable to escape from the 

 infested area, die in quantity and are cast up in 

 masses on the shore. Such discoloration of the 

 water, due to species of Gymnodinium and 

 Gonyaulax, are recorded as extending sometimes 

 (August, 1917) for a hundred miles or more along 

 the coast. 



To point out a few slips in such a splendid 

 memoir may seem ungracious, but Prof. Kofoid 

 would probably prefer to have friendly criticism : 

 In the phylogenetic diagram on p. 84, have not 

 Protodinifer and Oxyrrhis exchanged places, 

 should not Protodinifer be Pelagorhynchus, and, 

 near the top of the diagram, should not Nema- 

 topsis be Nematodinium.' The text-figure on 

 p. 509 is evidently printed upside down, and in 

 Fig. F (p. 30) the numbers 2, 3, and 4 are mis- 

 placed. Some of the references to figures in the 

 text are not correct, but the careful reader will 

 notice these for himself and will readily discover 

 what is intended. 



So many species are described, redcscribed, or 

 discussed, and the synonymy and history are given 

 so fully, that the memoir is truly a monograph of 

 the group, and will be found indispensable by all 

 who work at these important lower organisms. 

 \V'. A, Herdman. 



The Theory of Probability. 



A Treatise on Probability. By J. M. Keynes. 

 Pp. xi + 466. (London: Macmillan and Co.' 

 Ltd., 1921.) 18^. net. 



DR. KEYNES'S book is a searching analysis 

 of the fundamental principles of the theory 

 of probability and of the particular judgments in- 

 volved in its application to concrete problems. He 

 adopts the view that knowledge may be relevant to 

 our rational belief of a proposition without amount- 

 mg to complete proof or disproof of it, and treats 

 the probability as a measure of this relevance. 

 NO. 2727, VOL. 109] 



Otherwise he does not attempt to define " prob- 

 ability," regarding it as a concept intelligible with- 

 out further definition. In this respect, as in several 

 others, he is in agreement with the views expressed 

 by Dr. Wrinch and the present reviewer {Philo- 

 sophical Magazine y vol. 38, 19 19, pp. 715-31), and 

 some comparison of the two presentations may not 

 be out of place. 



Previous writers have practically all assumed that 

 probabilities can be expressed by numbers, and this 

 assumption was put into precise form in the paper 

 mentioned. Dr. Keynes departs completely from 

 tradition on this point. Defining an " argument " 

 as the process of passing to knowledge about one 

 proposition by contemplation of it in relation to 

 another of which we have knowledge, he denies not 

 only that the probabilities of all arguments can be 

 expressed by numbers, but also that they can be 

 arranged in a one-dimensional series at all. Thus 

 the probability of one argument may be neither 

 greater than, equal to, nor less than that of another. 

 The difference in actual application between this 

 theory and ours appears likely to be slight, for the 

 definitions and hypotheses are such that practically 

 any two probabilities that one needs to compare are 

 comparable. From these the formal theory is 

 soundly developed. 



The principle of non-sufficient reason, or in- 

 difference, asserts that we assign equal probabilities 

 to propositions if we have no reason to do the 

 contrary. The author criticises severely many pre- 

 vious applications of this principle (so severely that 

 an unprepared reader is likely to be betrayed into 

 expecting him to reject the principle altogether). 

 He finally modifies it by saying that neither of the 

 propositions deemed equally probable may be ex- 

 pressible as the disjunction of two mutually incon- 

 sistent propositions, of the same form as itself, and 

 both consistent with the data. His precise state- 

 ment of this important principle makes it possible 

 to evaluate a large class of probabilities that could 

 otherwise be only estimated, and is a most useful 

 advance. 



Dr. Keynes rejects definitely the view of Jevons 

 and others that if any two alternatives are ex- 

 haustive and mutually exclusive, and we have no 

 reason to prefer one to the other, the probability 

 of each is \. His reasons for believing that this 

 view leads to contradictions, however, appear in- 

 correct. He says on p. 43 : " If, for instance, 

 having no evidence relevant to the colour of 

 this book, we could conclude that \ is the 

 probability of ' This book is red,' we could 

 conclude equally that the probability of each 

 of the propositions-, ' This book is black ' 

 and ' This book is blue,' is also \. So that we 



