i66 



NATURE 



[October 15, 1914 



searches into African myths and beliefs. I single 

 out one point for comment. The Ibo name is 

 given of the Spitting-cobra, that African cobra 

 which seldom strikes at man directly with its 

 fangs, but by a muscular compression of the 

 poison-bag ejects the venom through the hollow 

 tooth to a considerable distance, aiming generally 

 at the eyes of the person it is striking. The 

 Spitting-cobra was, I believe, first heard of in 

 South Africa through the Dutch colonists in the 

 eighteenth century, and it was regarded for a 

 long time as a zoological fable. During the last 

 twenty or thirty years, however, the fact that 

 this cobra {Naja haje, or more likely Naja 

 nigricollis) can and does really eject its venom 

 with deliberate aim was attested by the present 

 writer and by many other African explorers, and 

 is now a proved fact. This spitting snake is 

 credited with another accomplishment, not merely 

 in Iboland, but in the beliefs of the natives of 

 East Africa, of, Nyasaland, of the Gaboon, the 

 Congo basin, and the Cameroons. It is said to 

 utter a sound like the crowing of a cock. 

 [I have heard this allegation sometimes made in 

 regard to the Tree-cobras, Dendraspis.] In Mr. 

 Thomas's Ibo Dictionary the cock-crowing is 

 attributed to the Spitting-cobra, as it is in some 

 other parts of Tropical Africa. It is, at any 

 rate, a curious coincidence that this story should 

 be told of one or other of the cobras in Africa, 

 independently, and without any possible collusion 

 between the Europeans who record these state- 

 ments. At the same time, I do not know that 

 proof has been adduced that this or any other 

 snake could utter any cry but a hiss. If, however, 

 it is shown that the native stories are true, and 

 that there is a snake in Africa which crows like 

 a cock, it may be at the base of the old Greek 

 stories of the Basilisk. H. H. Johnston. 



AMERICAN LECTURES ON MATHE- 

 MATICS. 



American Mathematical Society. Colloquium 

 Lectures. Vol. Iv., "The Madison Colloquium, 

 1913-" (i-) On Invariants and the Theory of 

 Numbers. By L. E. Dickson, (ii.) Topics in 

 the Theory of Functions of Several Complex 

 Variables. By W. F. Osgood. Pp. iii + iii + 

 iio + iii+ 111-230. (New York: American 

 Mathematical Society, 1914.) 



Elementary Theory of Equations. By Prof. L. E. 

 Dickson. Pp. v + 184. (New York: J. Wiley 

 and Sons, Inc. ; London : Chapman and Hall, 

 Ltd., 1914.) Price 75. 6d. net. 



THESE works are very different in scope, 

 but may be noticed together as examples 

 of the way in which mathematics is studied in the 

 NO. 2346, VOL. 94] 



United States. Prof. Dickson's treatise on the 

 theory of equations is suited for the average 

 university student, and it is interesting to see 

 how an accurate and distinguished mathe- 

 matician like the author chooses and discusses his 

 topics. He begins with graphics; and here he 

 does what so many fail to do — gives a warning 

 example to show the risk of drawing wrong con- 

 clusions from free and easy plotting. Graphical 

 methods are very useful in this theory in connec- 

 tion with such things as Fourier's theorem, 

 Newton's approximation rule, etc. ; they are not 

 trustworthy substitutes for calculation when the 

 real roots of a given equation have to be found. 

 Other things dealt with are the elementary theory 

 of cubics and quartics, symmetric functions, 

 separation and calculation of real roots, deter- 

 minants, systems of linear equations, resultants. 

 The proof of the fundamental theorem for 

 symmetric functions is the proper one : namely, 

 by establishing the one-one correspondence of the 

 highest part of any given symmetric function to 

 that of a definite product of coefficients — not 

 using the theorem about the sums of powers of 

 the roots. The proof that every equation has a 

 root is substantially that of Gauss; this is a 

 rather noteworthy fact. The omission of the 

 Galois theory is quite natural ; but we are inclined 

 to regret that the author did not comment on the 

 solutions of the cubic and quartic so as to show 

 their common features, and prepare the way for 

 group-theory. 



The same author's lectures in the Madison 

 Colloquium are addressed to experts, and ex- 

 pound what may be called in the first instance 

 a new and amusing mathematical game. Forms 

 and linear transformations are considered, not 

 absolutely, but with reference to an ordinary 

 integral modulus; the result is to change the 

 problem of finding a complete system of co- 

 variants and invariants into one of an entirely 

 different character. Connected with this we have 

 a theory of "modular geometry," and in such 

 things as group-study and the study of configura- 

 tions this seems likely to be of considerable ser- 

 vice. The theory is worked out in detail for a 

 quadratic form in m variables to modulus 2. 



Prof. Osgood's course is on the very difficult 

 theory of analytical, and in particular algebraic, 

 functions of two or more independent variables. 

 So far as the subject admits, it is an admirably 

 clear and interesting account of the principal 

 results hitherto attained; in particular, those due 

 to E. E. Levi. A remarkable result of recent in- 

 vestigations is to show that a theorem of 

 Weierstrass's about essential singularities is in- 

 correct. It should also be noted how, here and 



