Books Received | Published:

Elliptic Integrals

Nature volume 100, page 324 (27 December 1917) | Download Citation



INSPIRED by Sir G. Greenhill, to whom he makes due acknowledgment, 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 computation, 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 transformation, and then gives worked-put examples, using the descending scale of moduli (k, kv kz, …) as Jacobi does. The algorithm of the arithmetic 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 6°, and i° step for 9°; (ii) elliptic integrals F(k,) with k as above, step 5° for 6° and i° for 4>°; (iii) elliptic integrals E(k,) with k, as for (ii). All these tables were reproduced from Levy's “Theorie des fonctidns elliptiques “; they are well printed and properly spaced.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

About this article

Publication history




  1. Search for G. B. M. in:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Newsletter Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing