August 3, 19 16] 



NATURE 



459 



These " Ic^arithms " serve for rule of three 

 sums, but they are not suitable for simple multi- 

 plications or divisions. Briggs appears to have 

 seen how to amend the system by choosing- lo 

 for the base, and i as the antilogarithm of zero. 

 Whether the same idea had occurred to Napier 

 is uncertain ; at any rate, after consultation, the 

 two men agreed upon the usefulness of the trans- 

 formation, and Briggs performed the necessary 

 computations. On all points in this connection 

 Prof. Gibson's paper is very convincing and in- 

 structive. We do not suppose that either Briggs 

 or Napier consciously thought of a base or a 

 unit as we do, but they probably realised the 

 meaning of a formula, 



A(x) = ^log(x) + q, 



where A.(^), log {x) are logarithms of the same 

 number in two related systems. Here, again. 

 Prof. Gibson's paper should be consulted. 



We now come to the question of priority, which 

 ought never to have been raised; it is astounding 

 that even M. Cantor should prolong this idle 

 controversy. Burgi's table of antilogarithms 

 appeared in 1620; his calculations appear to have 

 been finished by 1610 (p. 209); Napier's table of 

 logarithms appeared in 1619. Each table was 

 the result of years of work; to convert either 

 into the other, fraudulently, would involve a vast 

 amount of labour; and there is not a shred of 

 evidence that either man had access to the MS. 

 of the other. It is the case of Newton and Leib- 

 niz over again in another form. So far as actual 

 priority in publishing a table of logarithms is 

 concerned, Edward Wright has a claim superior 

 to that of either Napier or Burgi ; but he was 

 sensible enough to know the difference between 

 a special table constructed for use with Mercator's 

 chart (essentially a log tan|^ table) and one 

 adapted for general computation ; even supposing 

 that he knew, before the "Canon " was published, 

 that his own table was a table of logarithms — 

 which is extremely unlikely. Finally, Wright 

 paid ample tribute to the genius of Napier, and 

 never made any claim on his own account. This 

 was reserved for the eccentric Benjamin Martin. 



Among the other papers may be noted Dr. 

 Glaisher's excellent paper on logarithms and 

 computation; Prof. Sampson's careful biblio- 

 graphy of books exhibited ; Dr. Knott's account 

 of Edward Sang and his logarithmic calculations; 

 Prof. d'Ocagne's notes on nomograms and multi- 

 plying machines; Mrs. E, Gifford's account of 

 her new table of natural sines ; papers on prob- 

 ability by Messrs. Erlang and Quiquet; and one 

 on the arrangement of mathematical tables by 

 Dr. J. R. Milne. In its way, the last is of. out- 

 standing importance, because everything possible 

 should be done for those who have to use tables 

 daily and for hours together; such things as 

 paper, colour, typography, etc., are not the trifles 

 they may seem to the amateur. 



The general appearance of the volume is ex- 

 cellent; it is well printed, and the illustrations 

 (two in colour) are most interesting; the indexes 

 are ample, and the price is not extravagant. The 

 NO. 2440, VOL. 97] 



biography of Napier has been well done by Dr. 

 P. Hume Brown, and Mr. G. Smith has con- 

 tributed a careful account of Merchiston Castle. 

 The editor (Dr. Knott) may be congratulated 

 on the result of his labours. G. B. M. 



AN AGRICULTURAL POLICY. 

 Agriculture after the War. By A. D. Hall. Pp. 



vii + 137. (London : John Murray, 1916,) 



Price 35. 6d. net. 

 TN this little book Mr. Hall sets out his views 

 -*- as to the methods to be adopted after the 

 war in order to develop agriculture to the full 

 extent demanded by the national necessities. Mr. 

 Hall insists that more food must be grown at 

 home as an insurance in time of war, to develop 

 our resources and reduce our foreign indebted- 

 ness, and to increase the agricultural population 

 as a specially valuable element in the community. 

 This can be attained only by bringing more land 

 under the plough. Farmers will not on their 

 own responsibility plough up grass land : to do so 

 is to destroy a certain, though small, source of 

 profit for the sake of a more risky, but possibly 

 larger, one. Mr. Hall considers that the old 

 laissez-faire policy will no longer meet the case : 

 the State may be driven to adopt some system of 

 bounties or protective duties to make the profits 

 more certain and the inducements more tangible. 

 Five methods are outlined for obtaining a more 

 intensive cultivation of the soil : the establish- 

 ment of large industrial farms working on a 

 considerable area with all the economic advan- 

 tages of organisation and scientific management; 

 the establishment under certain conditions of 

 colonies of small holders working under co- 

 operative organisation ; the intensification of 

 existing methods; the reclamation and settlement 

 of waste and undeveloped areas ; and the estab- 

 lishment of certain subsidiary industries. 



Mr. Hall's writings are always marked by 

 breadth of view and saneness of outlook, and it 

 is gratifying to know that these have not deserted 

 him since he left the country for Dean's Yard. 

 He has never hesitated about a proposal because 

 it happened to be rather revolutionary, nor does 

 he do so here. The scheme suggested is com- 

 prehensive and logical, but it has its revolution- 

 ary aspect, and the final solution, in his own 

 words, is "for the State to become the ultimate 

 landowner. " 



It is undeniable that the land is not producing 

 as much as it might do. It is equally undeniable 

 that no comprehensive attempt has been made 

 to get it to do so. Almost ever}' estate has an 

 amenity value and a sporting value in addition 

 to its agricultural value — ^thus the land has to 

 serve three masters. Trees, hedgerows, grass, 

 parks, plantations, warrens, are all kept up, 

 even when they are in direct conflict with the 

 agricultural productivity of the land. To make 

 matters worse, the farmer lacks the manufac- 

 turer's certainty of return. The manufacturer 

 works on a contract ; he knows precisely how 

 1 much he will be paid, and what output he may 



