April 24, 19 13] 



NATURE 



,87 



to be useful in photochemical work. The values 

 of the function e~ x are tabulated in thirteen pages 

 from .v = o to .v=io, and fifty-six pages are 

 assigned to tables by Dr. N. Rosanow showing 

 the reciprocal of the wave length and the fre- 

 quency for every Angstrom unit from \ 2000 to 

 A 8000. H. S. A. 



The Economics of Everyday Life. Part i. By 

 T. H. Penson. Pp. xiv+174. (Cambridge 

 University Press, 1913.) Price 3s. net. 



It is surprising how difficult it apparently is to 

 write a good short text-book of economics, but 

 Mr. Penson has been eminently successful in doing 

 so. He has fully grasped the fact that the first 

 need for such a book is to be simple and elemen- 

 tary as well as short. Where possible, he rightly 

 prefers the ordinary terms of everyday use to 

 the technical phrases of economics. For instance, 

 instead of production, exchange and distribution, 

 he talks of the "source of income," "buying 

 and selling," and the "individual income." These, 

 In my opinion, are far more intelligible to the 

 beginner. Moreover, his definitions are nearly 

 always both clear and adequate, those of demand 

 and supply affording a good example. 



The method of treatment follows, on the whole, 

 that of the modern school, of which Prof. Marshall 

 may be regarded as the head, and exchange is 

 treated before, and not after, distribution. The 

 subjects of consumption, taxation, trade unions 

 and cooperative societies are left to the second 

 part of this book, which has yet to be published. 



The present volume clearly marks Mr. Penson 

 as possessing great capacity as a teacher. He 

 chooses wiselv not only his terms, but the subjects 

 of which he treats. Omitting nothing that is 

 essential, he has avoided thorny and difficult sub- 

 jects likely to confuse the beginner. His defini- 

 tions, too, are both concise and complete. A new 

 and valuable feature of the book is found in the 

 simple tables and diagrams by which the argument 

 is rendered easy to understand, but mathematical 

 methods are rigidly, and in such a book rightly, 

 avoided. Occasionally, however, the author treats 

 unimportant matters somewhat too fully. Usually 

 he is neither too long nor too short, but, like 

 Sidney Godolphin, "is never in the way, and never 

 out of it." N. B. Dearle. 



Dent's Practical Notebooks of Regional Geo- 

 graphy. By H. Piggott and R. J. Finch. 

 Book i.. The Americas. Pp. 64. (London : 

 ]. M. Dent and Sons, Ltd., 1913.) Price 6d. 

 net. 



If every geography teacher set the same practical 

 exercises, this conveniently arranged notebook 

 would have a wide circulation ; but naturally a 

 teacher's exercises should reflect his own indi- 

 vidualitv. The little book may be commended, 

 however, as affording a good example of the way 

 in which pupils can be led to acquire an intelligent 

 knowledge of geography as the result of their 

 own activities. 



NO. 2269, VOL. 91] 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



An Application of Mathematics to Law. 



I have attempted to apply mathematical symbolism 

 to some of the difficult problems of patent law. The 

 question to be decided by the Court in a patent law- 

 suit is usually this : assuming that the alleged inven- 

 tion deals with "a manner of manufacture" (i.e. is, 

 or yields, something concrete), was there ingenuity 

 and utility in the step from what was already known ? 

 Ingenuity means inventive or creative ingenuity a> 

 apart from the normal dexterity of the craftsman, 

 which of itself is insufficient to support a patent, as 

 otherwise patents would unduly hamper industry. It 

 will be seen at once that it is a most subtle question 

 for any court to determine whether a given act, tin- 

 selection of one out of many alternatives, the 

 assemblage of various old elements, the adaptation of 

 old elements to new uses — whether such an act is one 

 which calls for ingenuity as apart from the expected 

 skill of the craftsman. 



To express the problem symbolically I will start 

 from an admirable dictum of Lord Justice Fletcher 

 Moulton (Hickton Pat. Syn. v. Patents Improvements). 

 He stated that invention might reside in the idea, or 

 in the way of carrying it out, or in both ; but if there 

 was invention in the idea plus the way of carrying 

 it out, then there was good subject-matter ' for a 

 patent. I express this by representing any idea as a 

 functional operator, and the way of carrying it out 

 (i.e. the concrete materials adopted) as a variable. 

 Calling result I : 



I =/(*>. 

 Here I represents what the Germans call the "tech- 

 nical effect" of the invention, or what Frost calls the 

 manufacturing "art," and we see at once that a patent 

 cannot be obtained for a mere principle or idea (/. 

 which is not concrete) unless some way of carrying it 

 out (x) is also given. But the invention may reside 

 either in / or in x. 



Let us express in general terms a manufacture (M) 

 which is not an invention. We will use / to represent 

 a known operator or idea, <i> to represent a new- 

 operator or idea, a, b . . . will represent known 

 variables, ways of carrying out an invention (e.g. . 

 valves, chemical substances, &c), and x, y, new vari- 

 ables. 



It is obvious that f(a) is not an invention, nor will 

 it normally be an invention to add fib) to it. More- 

 over, the craftsman is not to be tied down to this. 

 He is at perfect liberty, within limits, to make varia- 

 tions in his variables, to alter the size of a crank, to 

 substitute one alkali for another, and so on ; in other 

 words, he can take f(a + &a). 



Generalising, we may say : 



M=2/(a+8«). 

 Developing this by Taylor's theorem, and proceeding 

 from an infinitesimal to a finite change, we have, 

 neglecting quantities of the second order : 



M = 2/(rt)+2S/(tf). 

 This is the general equation for a manufacture which 

 is not an invention. To be an invention, ingenuity 

 (»') must be involved. 



I = M+/ or I = ^(M), 

 thus : 



I = \ft2/(rf) + 28/(rt)] = 2/"(<t) + 28/7 a) + 1. 



