February i6, 1922] 



NATURE 



201 



The work is divided into three parts. In the first 

 id longest of them the object is to fill, subject to 

 jrtain rules, a defined area by polygons all of the 

 ime shape and size, but each coloured or numbered, 

 like dominoes, according to a different scfieme. In 

 le second part arrangements made according to the 

 »ethods expoimded in the first part are " trans- 

 )rmed " so as to give a number of pieces of the 

 le colour but of shapes which are all different; 

 16 result is the production of a jig-saw puzzle. In 

 le third part we deal again with pieces all of the 

 le size and shape, and the object is to design 

 jpeating patterns which can be used to cover an 

 rea. 



The first part of the book involves the con- 

 ieration of how to fill in a certain way a prescribed 

 rea with wood or cardboard polygons, which may be 

 pgarded as super-dominoes. The shape of an ordi- 

 iry domino is a rectangle (the breadth of which is 

 imaterial) with two ends or faces, on which numbers 

 .pips can be inscribed, and, if we like, each number 

 jiay be taken to indicate a particular colour: by 

 sing n numbers we can get n{n+x)l2 different 

 lear dominoes. If our dominoes are triangular in 

 lape, and from some central point within the tri- 

 igle we draw lines to the angular points, we get 

 lominoes with three faces, on each of which numbers 

 or pips can be inscribed, and as before each number 

 may be taken to indicate a particular colour : by 

 using n colours we can get n{n^+2).lT^ different tri- 

 angular dominoes. Similarly, by using n colours 

 we can get n(n + j)(fi' - 71 + 2) / 4 different square 

 dominoes, n(n* + 4)l^ different pentagonal dominoes, 

 and so on. With each of these sets we can make 

 up puzzles. 



A particular instance will illustrate the kind of 



questions treated. Consider the case of equi- 



teral triangular dwninoes. If four colours are 



;d we get a set of twenty-four different dominoes, 



»d these can be put together (preferably fitting in 



■shallow box cut to the right size) to make a regular 



jxagon. Naturally the point in each domino from 



lich the lines radiate to its vertices Avill be taken 



it its centre, thus dividing each triangle into three 



}ual compartments, and facilitating the formation 



of symmetrical patterns. A consideration of what 



conditions can be imposed for arranging the dominoes 



next arises. For example, we may require the 



arrangement to be such that the colours of adjoining 



faces shall be alike, as also those of all the exterior 



faces; the solution, subject to this condition, is, 



smong others, given. 



The patterns formed are elegant, and the puzzle of 

 fitting the dominoes together according to some im- 

 posed condition is sure to interest a good many people, 

 ome of whom are likely to become enthusiasts 

 NO. 2729, VOL. 109] 



in the game. In the book the colours are indi- 

 cated by numerals, and thus the results appeal to 

 the mind rather than to the eye ; this is a loss. 



If the dominoes are right-angled triangles, we 

 get a hexagon arrangement of a different shape. 

 Further, we can play with sets selected from a par- 

 ticular full set and arranged in suitable geometrical 

 figures. Similar problems arise from the use of 

 square dcaninoes, hexagonal dominoes, etc. 



In the second part, the author concerns himself 

 with " transformations," necessarily unlimited in 

 number, of arrangements like those above described. 

 This is, in effect, an exposition of a method of 

 making jig-saw puzzles of a certain type. Probably 

 this has never before been reduced to a system, and 

 it may be doubted whether those who cut out such 

 puzzles will care to proceed by rule in the matter; 

 but, if they do, here are hints and directions for their 

 use. 



In the third part, the previous investigations are 

 applied to the formation of " repeating patterns," 

 built up by arranging sets of pieces which fit to- 

 gether. Here the author enters on a field of deco- 

 rative work in which there are already excellent tech- 

 nical books. He says that he has developed this 

 subject much further, and that he has in hand a 

 work entirely devoted to it. The subject is of im- 

 portance to architects and pattern-makers, and is 

 a recognised branch of arts and crafts. 



The results of the problems set out in the first 

 part of this book are singularly effective when 

 colours are used, and provide numerous novel and 

 interesting recreations of a certain type. We share 

 the author's disappointment that the cost of printing 

 nowadays has rendered it impossible to produce the 

 book in colour. The questions considered in the 

 second and third parts are of a more technical 

 character, and are likely to appeal to the specialist 

 rather than to the general reader : to the former they 

 will open new and interesting lines of development. 



The Fishing Industry and Scientific 

 Research. 



Ocean Research and the Great Fisheries. By 

 G. C. L. Howell. Pp. 2204-20 plates -i- 3 charts. 

 (Oxford : At the Clarendon Press, 1921.) 185. 

 net. 



THE reconstruction spirit of the years 1918-9 

 was nowhere more evident than in its relation 

 to the fishing industry. Even before the date of 

 the armistice the owners of trawling and drifting 

 vessels had met repeatedly and prepared a very 

 noteworthy memorandum, which was presented to 

 the President of the Board of Agriculture and 

 Fisheries later on. At that time emphasis was very 



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