6i8 



NATURE 



[Oct. 28, 1880 



conditions of equilibrium of mixtures of alcohols aud mineral 

 acids. He considers in detail the velocity, and limits of etherifi- 

 cation of the more important mineral acids, and arrives at many 

 valuable results. 



GEOGRAPHICAL NOTES 

 At the last meeting of the Berlin Geographical Society news 

 was received through a German trade house in Tangier that Dr. 

 Lenz had reached Timbuctoo, and that he hoped to be at St.' 

 Louis, in Senegal, in the month of July. If this is correct Dr. 

 Lenz has made a rapid journey in this direction, as he only 

 left Tangier on December 22 List. Caille, however, in 1S28, 

 travelled from Timbuctoo to Fez in four months. The last 

 letter received from him by the Society was from Tenduf, in 

 the beginning of May, twenty days' journey from Timbuctoo. 



The Zcitschrift of the Berlin Geographical Society, Nos. SS, 

 S9, has a valuable map by Herr Richard Kiepert, showing the 

 work done in Angola in 1S76 by Dr. H. von Earth in the region 

 of the Bengo and Lucalla, and of Herr Otto Schiitt in i87f-79 

 on the Lower Quanza. Dr. von MoUendorff discusses the 

 methods of transcribing Chinese geographical names, and con- 

 cludes that the Pekin form of the Guan-hua, or so-called Man- 

 darin dialect, would be best for general purposes. But Dr. vnn 

 MoUendorff asks whether, while selecting this form generally, it 

 is advisable to make exceptions in certain cases. Such names 

 for example, as already exist in familiar forms might be excepted, 

 as Pekin, Canton, Hongkong, Swatow, &c. With other names, 

 especially for special maps, a change from the uniform method 

 of writing might be adopted. Maps of districts for the use of 

 travellers would evidently be of greatest service when the local 

 forms of names were given. Perhaps the Guan-hua might be used 

 for the names of great towns, large rivers, and mountains, while 

 stnaller places might have the local forms of their names. 

 For a map of the whole of China, or of the greater part 

 of it, containing little more than the district towns, evidently 

 the Guan-hua would be the preferable form. \\\ book's 

 It would perhaps be best to give both forms. It is, no 

 doubt, high time that some attempt at uniformity should 

 be ^ made, but the difficulty is by no means easy of solution, 

 ovvmg partly to the letters of the alphabet not being sounded 

 uniformly in all European languages. Herr von MoUen- 

 dorff instances the absurdity of the present want of system 

 by the ways in which the Cliinese name of the Yellow River is 

 spelled. These are confusing enough, but what uill he say w^hen 

 he sees " Houan He" (for Hwang-ho) at the head of the 

 interesting communication just received from Col. Prejevalsky? 

 We cannot entirely concur in Herr von Mollendorff's definition 

 of "Kwan-hwa," popularly translated "Mandarin dialect," and 

 he himself makes the orthographical jumble much worse by 

 writing "Guan-hua," which we should imagine few sinologues 

 would attempt to defend. The vexed question, however, may 

 find a solution before long in an unexpected quarter, for the 

 Statistical Department of the Chinese Maritime Customs at 

 Shanghai, we believe, have under consideration a system of 

 spelling for adoption in their reports and other publications, and 

 this, if adopted, will probably come by degrees into general use. 

 Dr. Hildebrandt gives an account of a visit he made to the 

 Amber Mountains in the north of Madagascar ; Herr K. Himy 

 continues his elaborate paper on the region around theKara-Kul, 

 and much of tlie number is occupied with the journal in North 

 Africa of the late Dr. Erwin von Bary. 



The new number of the Lyons Geographical Society's Bulletin 

 contains several items of interest. M. Morice's paper on French 

 Cochin-China is published with a sketch map, followed by some 

 notes by the Abbe Desgodins on the hydrography and orography 

 of Tibet, and a communicatio 1 by the Abbe Faure on Potosi in 

 Bolivia. Among the other contents are Pcre Brucker's notes on 

 the geographical positions in Eastern Turkistan and Jungaria 

 determined in 1876 by two Jesuit missionaries, and the report on 

 Col. Flatters' explorations in the Central Sahara last spring. 



M. Venuikoff has just published at Geneva an historical 

 sketch of the geographical discoveries made in Asiatic 'Russia 

 from the most remote times to our own days, illustrated by 

 Perthes' map of North and Central Asia. 



The China Inland Mission have been informed by Mr. Samuel 

 Clarke, one of their agents in the Chinese province of Szechuen, 

 that, in company with Mr. Mollman, of the British and Foreign 



Bible Society, he lately made a journey from Chungking, on the 

 Upper Vangtsze-kiang, to Chengtu-fu, the capital of the province, 

 on which he travelled by unfrequented roads, where, so far as he 

 could learn, no foreigner had ever been seen before ; several 

 previously unvisited towns were also entered. Mr. Clarke calls 

 especial attention to the commercial activity prevailing along his 

 route, and the frequency with which markets were held. 



The Asiatic Society of Bengal have just published, as an 

 extra part of their Journal, a "Vocabulary of the Langua<'e of 

 Eastern Turkistan," by the late Mr. R. B. Shaw, the well-known 

 traveller, supplemented by two Turki vocabularies of birds and 

 plants by Mr. J. Scully, lately on special duty at Kashgar. 



From the Vienna Allgemeine Zeitung we gather that Dr. 

 Emil Holub contemplates undertaking another lengthened journey 

 in Central South Africa, provided that he can obtain the neces- 

 sary funds. It is estimated that 50,000 florins will be required 

 for the purpose, and it is proposed to raise this sum by a public 

 subscription, the Austrian Geographical Society heading the 

 list. 



The September number of the Boktin of the Madrid Geo- 

 graphical Society contains a detailed account of the Marquesas 

 Islands, with map, by D. Ricardo Beltran of Rozpide. 



It is stated that the Gulnare, with Capt. Hovi'gate's expe- 

 dition, landed at Riltenbank in Greenland, Dr. Pavy and Mr. 

 Clay, whose intention is .stated to be to make natural history 

 collections and explore the northern limits of Greenland. This, 

 we believe, is the same M. Pavy (a Frenchman) whose projected 

 polar expedition suddenly collapsed in San Francisco seven years 

 ago. 



The Austrian Monatsschrift ficr dm Orient for October con- 

 tains an article by Prof. Vambery on the commercial importance 

 of the Upper Oxus, in which he endeavours to show that there, 

 and not on the Lower O.xns, is trade likely to be developed. 

 Dr. Paulitschke gives an interesting sketch of the progress of 

 African exploratiun during the past seventy years. 



ON MAXIMUM AND MINIMUM ENERGY IN 



VORTEX MOTION'^ 

 L A FINITE volume of incompressible inviscid fluid being 

 given, in motion, filling a fixed, simply continuous, rigid 

 boundary, the fact of its being in motion implies molecular rota- 

 tion, or (as it may be called for brevity) vorticity. Helmholtz's 

 law of conservation of vorticity shows that, whether the boundaiy 

 be kept fixed as given, or be moved or deformed in any way, 

 and brought back to its given shape and position, there remains 

 in every portion of the fluid which had molecular rotation a 

 definite constant of vorticity ; and his formula for calculating 

 cne]-gy for any given distribution of vorticity allows us to see 

 that the energy may be varied by the supposed operation on the 

 boundary. 



II. The condition for steady motion of an incompressible in- 

 viscid fluid filling a finite fixed portion of space (that is to say 

 motion in which the velocity and direction of motion continue 

 unchanged at every point of the space within which the fluid is 

 jjlaced) is that, with given vorticity, the energy is a thorough 

 maximum, or a thorough minimum, or a minimax. The 

 farther conditition of s'.ability is secured by the consideration of 

 energy alone for any case of steady motion, for wliich the energy 

 is a thorough maximum or a thorough minimum ; because when 

 the boundary is held fixed the energy is of necessity constant. 

 But the mere consideration of energy does not decide the ques- 

 tion of slability/or any case of steady motion in which the energy 

 is a minimax. 



III. It is clear that, commencing with any given motion, the 

 energy may be increased indefinitely by properly-designed opera- 

 tion on the boundary (understood that the primitive boundary is 

 returned to). Hence, with given vorticity, there is no thorough 

 maximum of energy in any case. There may also he complete 

 annulment of the energy by operation on the boundary (with 

 return to the primitive boundary), as we see by the following 

 illustrations : — 



I. The case of two equal, parallel, and oppositely rotating 

 vortex columns terminated perpendicularly by two fixed parallel 

 planes, which, by proper operation on the boundary, may be so 



■ By Sir William Thomson, British Associ.ition, Swansci, Section A, 

 Saturday, August 28. 



