February 2, 1922] 



NATURE 



33 



I 



are faced with the impossible case of three ex- 

 clusive alternatives all as likely as not." It appears 

 to us that each of these estimates is based on dif- 

 ferent evidence, and, therefore, that it is quite pos- 

 sible that the sum of the probabilities should he 

 greater than unity. A person who could recognise 

 only one colour, say, blue, all others appearing 

 alike to him, would estimate the probability that 

 the book is blue at ^. A person who could recog- 

 nise only red would make a similar estimate for 

 red. But one who could distinguish red, blue, and 

 black, and no others, would estimate each as having 

 a probability of J. In each case we follow the 

 author in assuming no previous knowledge of the 

 proportions of different colours among books. 



The point is worth insisting upon, for we believe 

 that the author has for such reasons refrained from 

 estimating prior probabilities in many cases where 

 such estimates would have been useful. In his dis- 

 cussion of sampling inference, for instance, he 

 refuses to admit that any plausible estimate of the 

 probable composition of a sample can be made, 

 however large a sample has already been examined, 

 unless we have further evidence that no disturbing 

 cause exists. Admittedly the inference depends on 

 the prior probabilities of different compositions, 

 but we have shown that in ordinary cases a wide 

 range of variation of the prior probability produces 

 little variation in the inference made with regard 

 to the composition of a large sample, and we think 

 this is the only justification required. The acquire- 

 ment of knowledge about a disturbing cause pro- 

 vides additional data and is valuable for that 

 reason; its absence is no reason for denying a 

 probability inference not based on it. 



The author's insistence on the desirability of 

 careful testing of the sample to see whether different 

 subclasses from it have compositions similar to the 

 whole is, however, very important on other grounds, 

 for his careful discussion indicates the precise use- 

 fulness of a kind of additional information that 

 is often obtainable and valuable. His con- 

 clusion (p. 426) that "sensible investigators only 

 employ the correlation coefficient to test or confirm 

 conclusions at which they have arrived on other 

 grounds " is an exaggerated statement, but perhaps 

 a salutary one. 



A form of the frequency definition is discussed 

 and rejected on the ground that it does not give any 

 basis for induction. According to this the proba- 

 bility of a proposition p on evidence q is to be 

 obtained by selecting a large number n of instances 

 of q. If m of these are also instances of f, the 

 probability of p given q is defined to be mjn. 

 This theory is taken too seriously; it would be 

 sufficient objection to point out that, unless mjn 

 is o or I, the probability would necessarily be 

 NO. 2727, VOL. 109] 



changed by having n-^i instances instead of n, 

 and would therefore be conventional. , In the form 

 of the frequency theory discussed (and also rejected) 

 in our paper the probability is defined as the limit 

 •of this ratio when n tends to infinity. This view, 

 though it has been seriously advocated, is not 

 mentioned by the author. 



The faults attributed to the book above are all 

 on the side of excessive caution, and the positive 

 contributions are extremely valuable. It is clearly 

 written, with a good index and a copious biblio- 

 graphy. The misprints are few. Whitehead and 

 Russell's " Principia Mathematica " is, however, 

 mentioned a few times as if it were by a single 

 writer. The work should be read by every student 

 of science who aims at a real understanding of his 

 subject. Harold Jeffreys. 



The Royal Society Catalogue. 

 Catalogue of Scientific Papers, Fourth Series 

 (1884-1900). Compiled by the Royal Society 

 of London. Vol. 17, Marc-P. Pp. v-f 1053. 

 (Cambridge: At the University Press, 1921.) 

 9Z. net. 



THE high standard set by the volumes already 

 published in this series is fully maintained 

 in the seventeenth volume of the Royal Society's 

 "Catalogue of Scientific Papers." The work of 

 preparing the material for the press and of proof- 

 reading was carried out by Miss Vagner and Miss 

 Barnard, and until December 1920 Miss Chapman 

 was also engaged upon the work. The Cam- 

 bridge University Press is to be congratulated on 

 the typographical excellence of the volume, the 

 small type which had to be used being quite easy 

 to read. 



The papers indexed are those published during 

 the seventeen years 1884 to 1900 by authors 

 whose names begin with the four letters M (from 

 Marc onwards), N, O, and P. No less than 

 10,662 names are indexed, the number of separate 

 papers being 57,474. Thus, on an average, each 

 author has published one paper every three years. 

 The volume brings up the total number of 

 authors* names already printed for the period 

 1884-1900 to 49,750, and the total number of 

 entries of papers published by authors whose 

 names begin with letters from A to P inclu- 

 sive to 279,902. The catalogue of papers by 

 authors whose names begin with letters from Q to 

 Z is still to be published. 



The Committee say that the difficulties in the 

 printing and publishing trade, which for a time 

 delayed the regular delivery of proofs, have now- 

 been overcome, so that they look forward with 



F 



