April 9, 1885] 



NA TURE 



527 



the pressure of a gas or the electric resistance of a wire 

 "comes out" negative ! To such men the recent intro- 

 duction of the subjects of heat and electricity by the 

 Board of Mathematical Studies, and the appearance of 

 Thomson's Electrical Papers, Maxwell's splendid trea- 

 tises, and other kindred books, have been happiness 

 indeed. Open any one of these books, at any place, 

 and concoct from it by whatever assumptions (however 

 unphysical) are necessary, a problem which shall lead to 

 an elliptic integral or a Bessel's function, and there you 

 are ! This cannot long go on without seriously impairing 

 the progress of physical science in our great mathematical 

 university. Mathematics is, in itself, a right noble and 

 worthy study ; but the embryo physicist should, from the 

 first, be taught to regard it as (for him) an indispensable 

 auxiliary only, not a source of natural (?) laws. The whole 

 procedure is thoroughly characteristic of the Cambridge 

 of to-day. It has, among its professors and elsewhere, 

 many of the foremost of living physicists and mathe- 

 maticians, as well as others destined in time to take 

 similar rank : — but does not utilise them. Even its one 

 real test of mathematical merit, real because conducted 

 by such men, the Smith's Prize Examination, has just 

 been abolished ! So, it has a magnificent boat at the 

 " head of the river," but not one member of that crew is 

 sent to encounter Oxford at Putney ! What can be 

 expected, either in the boat-race or in the more arduous 

 toiling over the scientific course, but thorough and most 

 deserved defeat ? 



Differential Calculus for Beginners, with a Selection of 

 Easy Examples. By Alex. Knox, B.A. (London": 

 Macmillan and Co., 18S4.) 



This little book deserves hearty welcome from those who 

 are engaged in leading forward students to the higher 

 mathematics ; not so much as a substitute for anv other 

 work at present in use, but as presenting a carefully- 

 selected set of illustrations of infinitesimals, limits, and 

 differential coefficients, which a student may profitably- 

 work through before entering upon the usual formal 

 treatises on the calculus. 



We know of no work in English comparable with the 

 present since De Morgan's " Elementary Illustrations of 

 the Differential and Integral Calculus." 



The special symbols of the subject are not introduced 

 into the work before us, attention being directed to the 

 new principles involved in the method of the calculus ; 

 indeed, the chief aim of the author throughout is to give 

 the learner a firm grasp of the idea of a differential co- 

 efficient—a fundamental notion which, in the minds of 

 beginners, is usually shrouded in a haze. Care is taken 

 to deal one at a time with the difficulties which present 

 themselves in this subject. The book is divided into 

 twenty sections, the latter two or three dealing with suc- 

 cessive differentiation, Maclaurin's theorem, and maxima 

 and minima. 



But before new principles or processes are introduced, 

 an endeavour is made to insure a precise comprehension 

 of the meaning of terms already employed by the student. 

 And the freshness of treatment, as well as the clearness 

 with which the author brings before the mind the exact 

 meaning of such terms as " point," " line," " superficies," 

 in the first section of this book, will awaken the interest 

 and arrest the attention of even an indifferent learner. 



Many of the sections are independent of each other. 

 There is much variety of illustration, the central principle 

 being looked at from different points of view. A distin- 

 guishing feature is the great use made of arithmetical 

 calculations, many examples of the method of finite 

 differences occurring. 



Besides the usual geometrical treatment based on New- 

 ton's " Lemmas," the ideas of time and motion are freely 

 introduced, and illustrations taken from elementary 

 kinematics. 



The book closes with a set of examples worked out in 

 full, and a series of one hundred easy exercises, the 

 answers to which are appended. A. R. VV. 



LETTERS TO THE EDITOR 



[TkeEditordoesnot hold himself responsible for opinion sexpressea 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications . 



[The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 thai it is impossible otherwise to insure the appearance even 

 of communications containing interesting and novel facts.] 



Rock-Pictures in New Guinea 

 A few years ago I mentioned in a paper in Globus (lxiii. 94) that 

 Mr. Th. B. Leon had reported the existence of pictures on rocks 

 he had seen in the Ogarand Arguni groups of islands (south part 

 of McCluer inlet), and that the officer in command of H.N.M.S. 

 Batavia, who had been charged to make further inquiries, had 

 not been able to find them. At that time Mr. Leon's account 

 had not been published in the regular issue of the Batav. Genoot- 

 schap. Since then, however, explorations by Mr. van Braam Morris, 

 whilst on his voyage in New Guinea in 1S83, and by some of the 

 officers of H.N.M.S. Samarang, have resulted in the discovery of 

 rock-pictures similar to those spoken of by Mr. Leon. The 

 papers giving an account of these explorations (including Mr. 

 Leon's) have been published in a recent number of the Tijdschrift 

 voor Indische Land-, Taal-, en Volkenkunde (xxix. pp. 582-591), 

 and an abstract of their contents may be interesting. 



One day Mr. Leon set out from the kampong (village) oi 

 Arguni, situated on the island of that name, for the purpose of 

 fishing. In the beginning, on account of the surf, he kept at 

 a great distance, but the third island of the group he was able to 

 approach. He perceived the distinct representation of a human 

 hand, painted in white, and surrounded with red spots, and 

 other drawings in white, which appeared to be meant for letters, 

 though traced in characters unknown to him. Afterwards, on 

 penetrating between two other islands of the group, he saw 

 several hands, all similar to the first, and accompanied by similar 

 drawings. He was not able to land ; he estimated the height of 

 the place at which they were drawn on the rock to be from 

 75 to 150 feet above sea-level, the hands being about three- 

 quarters of the way up, and the other figures about 10 feet 

 higher still. The hands were of all sizes, representing those of 

 children, of full-grown men, of giants, and were in great 

 numbers. He fancied the characters bore some resemblance to 

 the written signs in use amongst the Orang Kling, the Orang 

 Bugis, and the Orang Mangkasser; they were certainly not 

 Javan or Malayan. He was greatly puzzled as to how they 

 could have come there, since the face of the rock was perfectly 

 perpendicular, and without any projections or caverns, so far as 

 he could perceive. The only explanation he can suggest is that 

 they must have been done at a time when that part of the rock- 

 surface was nearer to the level of the sea, or the outward form 

 of the rock must have been changed on that side by losing 

 ledges or projections by which the native draughtsmen may 

 have approached the place. It will be readily understood that 

 the natives attribute these drawings to Kasuak, the prince of 

 evil spirits, who, in their opinion, has his dwelling in one of the 

 small islands, and of whom they are naturally greatly afraid. 

 On another island Mr. Leon discovered a huge stone, which 

 would probably require half a dozen men to lift it, rudely shaped 

 like a bullock, and surrounded with several other stones, 

 evidently arranged on some fixed plan. 



Mr. van Braam Morris says : — On September 16, 18S3, I 

 came to McCluer inlet, and was told by the native chiefs 

 that the figures I was in search of were to be found on Arguni, 

 or the islands to the west of it. I discovered them on a 

 small island a few hundred yards from the mainland. The 

 shores of both the island and the mainland rose perpendicu- 

 larly from the water, and in the rocky face of the former. 

 about 5 feet above high-water mark, the surf had eaten out 

 an excavation from 3 to 5 feet wide, thus leaving a narrow 

 platform, on which several small prahus were deposited, some 

 of them being 3 feet long. Various figures were drawn on the 

 rock above, especially hands, both of full-grown people and of 

 children. A hand had evidently been sketched in outline from 



