324 



NATURE 



[December 27, 191 7 



OUR BOOKSHELF. 



Elliptic Integrals. By Prof. Harris Hancock. 



Pp. 104. (Mathematical Monographs, No. 18.) 



(New V'ork : John Wiley and Sons, Inc. ; 



l^ondon : Chapman and Hall, Ltd., 1917.) 



Price 6s. net. 

 Inspired by Sir G. Greenhill, to whom he makes 

 due acknowledg-ment, Prof. Hancock has compiled 

 a very useful monograph, compact, well arranged, 

 and apparently accurate. Chap. i. is on elliptic 

 integrals, properly so called, and their reduction 

 to Legendre's normal forms; it is illustrated by 

 appropriate graphs. Chap. ii. is on the sn, en, dn 

 functions, and gives the period-pavement for each. 

 Chap. iii. gives a well-arranged list of integrals 

 involving elliptic functions. Chap. iv. is on com- 

 putation, and follows Jacobi and Cayley in the 

 main. It begins with Jacobi's two-circle proof of 

 the addition theorem, goes on to the Landen trans- 

 formation, and then gives worked-out examples, 

 using the descending scale of moduli {k, k^, k^, 

 . . .) as Jacobi does. The algorithm of the arith- 

 metico-geometric mean is explained and applied, 

 and there is a particularly neat discussion (p. 79) 

 of integrals of the second kind. There are three 

 tables, all to five places : (i) Complete integrals 

 K, E with fe = sin^°, and 1° stepfor^°; (ii) elliptic 

 integrals F(fe,^) with k as above, step 5° for 6° 

 and 1° for «}i°; (iii) elliptic integrals E(fe,<^) with 

 k,cf) as for (ii). All these tables were reproduced 

 from Levy's " Th6orie des fonctions elliptiques "; 

 they are well printed and properly spaced. 



It is unfortimate that restrictions of space pre- 

 vented Prof. Hancock from giving any formulae 

 relating: to the first-stage functions ^J, f'. It is 

 true that in numerical applications we have to use 

 a modulus k instead of two invariants, but in 

 many parts of tTieory Weierstrass's functions are 

 the proper ones to use. G. B. M. 



Farm. Forestry. By Prof. J. A. Ferguson. Pp. 



viii + 241. (New York: J. Wiley and Sons, 



Inc.; London: Chapman and Hall, Ltd., 1916.) 



Price 65. net. 

 Scattered all over the United States, amidst 

 the farm land, there are numerous small 

 woods, which are in most cases remnants of the 

 original virgin forest. These wood-lots, as they 

 are called, are said to cover in the aggregate as 

 many as 200,000,000 acres. Though, as a rule, 

 poorly stocked with timber at present, the wood- 

 lots are of great value to the rural population, as 

 they provide cheaply the fuel, posts, fencing, and 

 timber required on the farm. Under proper care 

 and management their productive capacity is 

 capable of great expansion, and it is estimated 

 that all the timber necessary for the manifold 

 industries of the United States might be grown 

 on the wood-lots alone. Great efforts are now 

 being made by the Department of Agriculture at 

 Washington and by the agricultural experiment 

 stations in each State to encourage the farmer to 

 take a greater interest in his wood-lot. 



The importance of forestry as a subject of in- 

 struction in agricultural colleges and in high 

 NO. 2513, VOL. 100] 



schools is now universally acknowledged. The 

 present volume is a suitable text-book for agri- 

 cultural students and for owners of small wood- 

 lands, as it covers in a simple way the whole 

 subject of farm forestry. It consists of a series 

 of readable chapters on the economic value of 

 the wood-lot and on the principles of sylviculture 

 as applied to small woods. 



The Yearbook of the Universities of the Empire, 

 1916 and 1917. Published for the Universities 

 Bureau of the British Empire. Pp. xvi-f-4i2. 

 (London : Herbert Jenkins, Ltd.) Price 75. dd. 

 net. 

 For reasons of economy the Yearbook was not 

 published last year. Since the commencement of 

 the war few changes have been made in the regu- 

 lations of the universities, and the information 

 regarding the conditions of admission, faculties,, 

 degrees, scholarships, and publications of the 

 various universities contained in the 191 5 issue 

 continue to be substantially correct and are not 

 repeated here. In view of the fact that there are 

 certain matters to which it is forbidden to refer, 

 the part which the universities have taken in 

 national service of all kinds is not summarised in 

 the Yearbook ; this subject is postponed until the 

 conclusion of hostilities. Three appendices added 

 to the present volume give full particulars of the 

 Beit fellowships, the scholarships awarded by the 

 Royal Commissioners for the Exhibition of 1851, 

 and the Rhodes scholarships. 



The Yearbook provides a very useful summary 

 of university activities throughout the Empire. 



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.] 



Labyrinths in English Churches. 



As the author of "Amusements in Mathematics," 

 reviewed in Nature of December 20, says that he does 

 not know of any instance of a labyrinth in an English 

 church, it may be mentioned that one is represented 

 in one of the bosses of the north aisle of the nave of 

 St. Mary Redcliffe, Bristol. The style is Somerset 

 Perpendicular, the date probably about 1420. 



C. S. Taylor. 



Banwell Vicarage, December 21. 



An Optical Phenomenon. 



In physiological laboratories several routine experi- 

 ments are in use for demonstrating phenomena of the 

 kind described by Capt. C. J. P. Cave (Nature, De- 

 cember 13, p. 284). These phenomena all support 

 Hering's theory of the reciprocal after-effects of stimu- 

 lation (see W. H. R. Rivers in Schafer's "Text-book 

 of Physiology," vol. ii., pp. 1146-47, especially fourth 

 paragraph, p. 1147). The seat of illusion begins at the 

 retina, but (as hinted in my letter on p. 165, Novem- 

 ber i) involves all the intricate labyrinth of nerve 

 tissue from the retina to the highest sensory and motor 

 centres. 



The way in which the reciprocal after-effects operate 

 in the cases under consideration cannot be fully dis- 



