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NATURE 



[December 20, 1917 



part than it does elsewhere in Great Britain or 

 abroad, and the differences of opinion that from 

 the first existed between Koch and those Scottish 

 investigators whose material was obtained in 

 Edinburgh are thus, in all probability, accounted 

 for. This is a matter of great importance and 

 continues to receive attention. 



Dr. Cobbett, in summing up, contends that 

 the " bovine bacillus " is less virulent than the 

 " human bacillus " for man, man in this respect 

 differing from all other animals, " for, with the 

 exception of the apes and monkeys, which are 

 equally susceptible, and the dog, which is equally 

 resistant to either type, all other species, so far as 

 is known, are more severely affected with the 

 bovine than with the human bacillus." 



Finally, Dr. Cobbett concludes (i) that the 

 importance of tuberculosis is not to be measured 

 only by the deaths caused — above 50,000 per 

 annum in England and Wales alone, mostly " in 

 the prime of life or only a little earlier " — but 

 that, " in addition to these deaths, tuberculosis 

 produces a great number of cripples " ; (2) that 

 during the last fifty years " the number of 

 deaths caused each year by tuberculosis has 

 diminished steadily and substantially, and the 

 ratio of deaths to population has fallen by more 

 than 50 per cent.," that it is still declining rapidly 

 " and at an ever-increasing velocity." 



In a series of appendices a number of interest- 

 ing details concerning recent investigations are 

 given. Of these one of the most important is the 

 persistence of tubercle bacilli of human type in 

 the tubules of the cow's udder once it has made 

 its way, and gained a footing, there. This, with an 

 account of the general dissemination of tubercle 

 bacilli after subcutaneous injection, indicates the 

 danger involved in the attempt to immunise milch 

 cows against tuberculosis with living tubercle 

 bacilli. A brief account of the later studies of the 

 types of tubercle bacilli found in the lesions of 

 bone and joint tuberculosis, by which Dr. Cob- 

 bett has been led to the conclusion that the per- 

 centage of bovine infections is considerably 

 greater than set out earlier in the book, the per- 

 centage of bovine infections in England being: 

 14*7 and in Scotland 29-6, is of considerable 

 interest in that here we have a key to the value of 

 the work before us — the extreme impartiality and 

 open-mindedness of the author. 



All who are interested in tuberculosis will be 

 well repaid by a careful study — not merely a per- 

 usal — of this interesting work, a study rendered 

 far easier by the numerous excellent photoerraphs 

 illustrating points to which the author wishes to 

 direct special attention. 



MATHEMATICAL PUZZLES. 

 Anmsements in Mathematics. By H. E. Dudeney. 

 Pp. viii + 258. (London: T. Nelson and Sons, 

 Ltd.) Price 35. 6d. net. 



MR. DUDENEY is famous as a com- 

 poser of puzzles of a semi-mathematical 

 -character, and for some years questions by 

 NO. 2512, VOL. lOo] 



him of this kind have appeared regularly 

 in several English periodicals. He has now 

 collected a large number of them, added a 

 few new ones, and published the whole in book- 

 form classified under various heads. The ques- 

 tions, more than four hundred in number, range 

 over so wide a field that it is difficult to describe 

 them succinctly, but usually they consist of brief 

 statements, put in a picturesque form, of problems 

 that might conceivably occur. Of these conun- 

 drums, some are variations of familiar puzzles, 

 others are new, some are easy, others difficult, 

 but, broadly speaking, all are interesting, and 

 none can be answered without care and thought. 

 In a few cases the point of the problem depends 

 on the wording — a device open to criticism, though 

 one which, in his preface, Mr, Dudeney explicitly 

 defends. The solutions are given separately in 

 the latter part of the book, and no one acquainted 

 with Mr. Dudeney 's reputation will need the assur- 

 ance that they are ingenious and suggestive. 



The author — wisely for his purpose — generally 

 avoids lengthy discussions, but the permanent 

 value of the work would have been increased had 

 references to authorities who had treated ques- 

 tions analogous to those submitted been given 

 more freely. For instance, the problem of arrang- 

 ing the twelve members of a bridge club for eleven 

 days so that no two members play together as 

 partners more than once and each member meets 

 every other member as opponent twice is pro- 

 pounded, and Mr. Dudeney gives the bare answer ; 

 but there is no reference to Moore's paper of 1896 

 where the question for 4m players is discussed and 

 the theory set out. Again, one "compass" con- 

 struction is proposed, and the solution of the par- 

 ticular question is given ; but a reference to 

 Mascheroni's work of 1795 would have shown 

 that there is a theory of the subject and put the 

 reader on the track of scores of similar problems. 



Interspersed in the text are some scholia on 

 problems of particular types, with notes of 

 methods for attacking them. These seem to us 

 the most valuable part of the book, for collections 

 of miscellaneous questions, once read, are not 

 often looked at again ; but comments on methods 

 of solution and the past history of problems are 

 of permanent interest. We should have liked to 

 see further discussions of this kind, but with such 

 a feast spread before us it would be ungracious to 

 complain that more has not been given. In one 

 of these scholia there are diagrams of some 

 European labyrinths : Mr. Dudeney says he does 

 not know of any instance of such a figure 

 in an English church, so it may be pointed out 

 that there is one, outlined in marble, on the floor 

 of Ely Cathedral — probably it had not been laid 

 down in 1858, when Trollope wrote his standard 

 account of the subject. In the notes on magic 

 squares there is mention of a transerial or doubly 

 magic square of the eighth order, and it might well 

 have been added that similar squares of higher 

 orders are also known : the formation of such 

 squares is, however, a difficult problem and not 

 to be recommended to non-mathematical readers. 

 In another scholium the digital treatment of 



