656 



NATURE 



[January 20, 192 1 



The paper of Ferrers {Q.J.M., vol. xii., 1873) ap- 

 peared six years after the publication of Thomson 

 and Tait's "Natural Philosophy," but it is curious 

 that there is not in the second edition (1883) of 

 that treatise any hint of the existence of the 

 peculiar systems of which Ferrers gave examples. 

 In his review of the second edition of the " Natural 

 Philosophy" (Nature, vol. xx., 1879), Clerk-Max- 

 well, in his own inimitable way, directed attention 

 to the introduction in that work of the method 

 of Lagrange. "The two northern wizards were 

 the first who, without compunction or dread, 

 uttered in their mother tongue the true and proper 

 names of those dynamical concepts which the 

 magicians of old were wont to invoke only by the 

 aid of muttered symbols or inarticulate equations." 

 The spell of the " northern wizards " was not free 

 from defect, but either their good fortune or their 

 instinct preserved them from the examples in 

 which the use of an incantation insufficiently 

 guarded in its terms might have led to disaster. 



This has not been the fate of every wielder of 

 the magic wand of Lagrange. In the first issue, 

 about twenty years ago, of an important 

 treatise on " Rational Mechanics " a discussion 

 of the motion of a coin rolling and spin- 

 ning on a horizontal table appeared, in which 

 the method of Lagrange was used with erroneous 

 results. The error led the distinguished author to 

 the invention of a new method, in which a set of 

 general dynamical equations, which could be used 

 instead of those of Lagrange, and were applicable 

 in all cases, was set up. The error thus had the 

 fortunate effect of enriching 'dynamical science. 

 It is not, alas ! the fate of all who make mistakes 

 to rise on the stepping-stones of their errors to 

 higher and better things. 



In our opinion, recourse is had to the method of 

 Lagrange in far too many cases. The student 

 flies to it on the appearance of the least difficulty. 

 A proper training in dynamics, which should 

 be experimental as well as mathematical, 

 would give students the power of solving 

 problems of all kinds by the direct applica- 

 tion of first principles. The use of La- 

 grange's equations does not develop this — indeed, 

 it has a directly contrary effect. In this power 

 the dynamical students and graduates of our uni- 

 versities are sadly deficient. 



A good account of Lagrange's method is fol- 

 lowed in Prof. Lamb's book by an exposition of 

 Hamilton's dynamical method, and this in its turn 

 leads to Jacobi's discussion of the integration of 

 Hamilton's canonical equations by means of the 

 complete integral of Hamilton's partial differential 

 equation fulfilled by his so-called principal function 

 NO. 2673, VOL. 106] 



S. The corresponding function S' connected with 

 S by the relation S+S' = 'S,{pq) does not seem to 

 be mentioned. A partial differential equation 

 similar to, and yet curiously different from, that 

 for S also holds for it. S is a function of the 

 qs, t, and as many constants, which depend on 

 the initial co-ordinates of the system, as there 

 are independent co-ordinates ; S' is a function of 

 the ps, t, and the same number of constants as 

 before, which, however, depend on the initial 

 motion. 



One or two examples of the solution of these 

 partial differential equations — for example, 

 Jacobi's discussion of the elliptic motion of a 

 planet referred to three co-ordinates — would have 

 added to the interest of what is in itself a very 

 interesting chapter of an excedingly interesting 

 book. A. Gray. 



Maya Civilisation. 



The Inscriptions at Copan. By Sylvanus Griswold 

 Morley. (Publication No. 219.) Pp. xii -1- 643 -f 

 33 plates. (Washington : The Carnegie Institu- 

 tion of Washington, 1920.) 

 IN this large quarto volume of more than six 

 hundred pages, efficiently illustrated. Dr. S. G. 

 Morley has produced a work which may justly 

 be regarded as of the highest importance. It is 

 necessary to enforce this statement, almost with 

 a feeling of shame, because there are so few in- 

 dividuals in this country who have the faintest 

 idea what enormous strides have been made in 

 the elucidation of Central American archaeological 

 problems since our own countryman. Dr. 

 Maudslay, published the results of his explora- 

 tions in a series of volumes, which Dr. Morley 

 generously, but no less justly, describes as "easily 

 the most important field contribution to Maya 

 archaeology." Those volumes might have been 

 expected to give a lead to British archaeologists 

 and explorers ; as a matter of fact, not only did 

 no one appear in this country to carry on 

 Maudslay 's work, but the fine series of moulds of 

 the principal Central American carvings, which 

 he made at the cost of enormous labour and ex- 

 f>ense, lie buried in the cellars of the Victoria and 

 Albert Museum, and not even an approximately 

 representative series of casts taken from them is 

 available to British students. 



It follows that such a work as this is almost 

 the despair of the reviewer. Most people have 

 heard of the Aztec, but the earlier Maya civilisa- 

 tion is familiar to few even by name. Yet the 

 Maya had evolved a remarkably fine art, an 

 elaborate hieroglyphic script, and a very highly 



