December 20, 1894] 



NATURE 



175 



character, that it is difficult to believe that so many 

 minds are necessary for its construction. The contribu- 

 tors are Sir Herbert Maxwell, Mr. O. V. Alpin, Mr. 

 John Cordeaux, Mr. Cecil Warburton, Dr. J. Nisbet, 

 and Mr. C. 15. Whitehead. Each tells his tale in his 

 own way, and the editor amplifies the information here 

 and there by means of foot-notes. Farmers will find 

 the book a handy and simple guide, and one which will 

 enable them to know their friends and enemies among 

 the " varmints." 



LETTERS TO THE EDITOR. 



[The Eililor doet not hold himself responsible for opinions ex- 

 pressed ty his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.^ 



The New Cypress of Nyasaland. 



The interesiing accnunt of Widdringtonia whytei (Nature, 

 Nova ' t)cr 22, pp. 85-87) discovered by Mr. Whyle on the 

 Milanji plale lU, suygrsls a few brief comments. 



(1) Ii is said lo extend "the geographical range of the 

 genus hi'herlo known only from South Africa, Madagascar, 

 and Mauritius into tropical Africa." As far as the latter state- 

 ment is concerned, this is no doubt true. But the existence of 

 any spi^cics of the genus in Madagascar or Mauritius seems to 

 be wanting in sufficient evidence, though repeatedly cited by 

 authorities. Thus Madagascar is given in the geographical distri- 

 bution for the aggregate genus Callitris in Hem ham and Hooker, 

 "Genera flunlarum," vol. iii. p. 424; Dr. Masters, jfourn. 

 Linn Soc. Bot vol. xxx p. 17, says "one (IViddringtonia) has 

 been di-cuvcrt-d in Madagascar"; Mr. Rendle, Trans. Linn. 

 Soc. (2nii series) Hot. vol. iv. p. 61, speaks of the " South 

 African and Mascarene IViddringtonia." 



All these statements aie based on a species, IViddringtonia 

 Commersonii, which was cultivated at Rtiduit, Mauritius, and 

 of whiv:h the native country was assumed to be Madagascar, 

 though this has never been confirmed. 



In 1S06, it is referred to in the " Nouveau Duhamel," vol. 

 iii. p. 10, as Thuya quiulrangularis, with the following remark: 

 "Habile I'tsle dc Madagascar; depui> quelques annees on le 

 ■cultive au rc'tuit, jardin de botanique a I'lsle de France." 



The Madagascar habitat was apparently purely conjectural. 

 And though the island has of late years been pretty assiduously 

 worked by French, German, and English botanical collectors, 

 no contfi-r ha> been delected in it except Podocarpus. 



In l8j3 the ■ evelopment of the myth went a step further. 

 Brongiii.in cites the species in the Ann. des Sc. Nat., series I, 

 vol. xxx. y. 19a, under the name of Pachylepis Commersonii, 

 with the lemark : " llab. in Insula Mauritii in loco dicto Le 

 Rcduil (Commerson, 1 769)." 



Thus ii will be seen that, starling as an introduced Mada- 

 gascar spe'ies cultivated in a botanic garden in Mauritius, it 

 finishes wnh beipgtreaied as an undoubted nauve of that island. 



It i^, however, to be noted that from "Biker's Flora of 

 Mauri tus and the Se>chelles" (1877) the Coniferce appearto be 

 entireb ab-ent from 'lie Mascarene Islands. 



(2) 1 hete is iio'.hing improbable in a IViddringtonia oc- 

 curring in Mailaga'Car. But none has yet been detected with 

 any cett.iinty. It seems not improbable that Commerson's 

 plant was really derived from S uth Africa. This would seem 

 to be the conclusion at which Carricre arrived in 1867, 

 "Contieres." ed. ii. p. 67: — " Cette prciendue espcce me 

 parail c le a peine une forme de la precc'dente." ( /('. 

 ctiprcssoides, one f the two South African species). 



(3) Ti e Conifer, c lor the most part can hardly be regardeil as 

 other than a veiy ancient and a decaying group. Their existing 

 distribution is therefore peculiarly interesiing. Bentham and 

 Hooker unite under Callitris a number of small genera which 

 practically only difTc in he number of their ovule-hearing scales 

 andin ihcir ncMgrajihic 1 distribution. They divide the genus so 

 reconstituted inio four sections, of which two are broadly 

 Australian, iwo are African. Other instances of parallelism 

 between ihe .\u-.lralian and .\fiicin floras are well known and 

 are full ot inietest. Of the .\frican sections one is confined to 

 the norih, wnh one species, Callitris quadrivalvis , which yields 

 the gum Sandarach of modern ommerce, and produced the 



NO. 1312, VOL 51] 



Thyine wood once so prized by the Romans ; the other 

 section, with two species, is confined to the south. The oc- 

 currence of a third species on the Milanji highlands is entirely 

 in harmony with whal we know of the distriimtion of plants in 

 Tropical Africa. As has been shown now in numerous cases, a 

 temperate and possibly more ancient flora more or less overlies 

 at elevations where it can exist, the lower lying tropical one, 

 and it forms a series of broken links by which the connection 

 of the temperate flora of Europe and of the Meiiiterranean basin 

 with that of South Africa, and even of the Madagascar uplands, 

 are at least indicated. 



It may be remarked that another coniferous genus, Podocarpus, 

 behaves much in the same same way as Callitris. Four of the 

 five African species occur at the Cape, and two on Kilima-n'jaro. 

 funiperus, on the other hand, though well represented in 

 Northern Africa, occurs in Abyssinia and the Msisai country, 

 but yet does not reach South Africa. 



W. T. Thiselton-Dyer. 



Royal Gardens, Kew, December 10. 



The Kinetic Theory of Gases. 



I SHOULD like to ask Mr. Culverwell what are the "other 

 considerations " from which we know that in a system of elastic 

 spheres the error law gives the only permanent slate. 



I will endeavour to extend the proof of the Htheorem which 

 I gave for elastic spheres to a more general, but not the most 

 general, case, 



The coordinates of a molecule are x,y, z, defining its position 

 in space, and '/,... qn-^^ the momenta are /, . . . A. ; and 

 different values ol the same variables shall be denoted by PQ 

 and, as the case may require, by accented letters ;5'P', &c. The 

 number per unit volume of molecules, for which the variables/ 

 and tj are between assigned limits, \^ fdq dp, andy is a function 

 of the/'s and i/'s independent of .xyz. 



The number of pairs for which one molecule has variables 

 P'O' between assigned limits, i.e. is in the state P'Q', and the 

 other /'(/' between assigned limits, i.e. is in the stale p'q', is 

 YfaV'dfYdp'dq'. 



Each molecule has a centre of gravity. It is possible to 

 describe a sphere about that point as centre, such that if the 

 centre of gravity of another molecule be on or beyond that 

 sphere, no appreciable force is exerted between the two 

 molecules. Let a • e the least radius of such a sphere. Then 

 when the centre of one molecule is on the sphere of radius a 

 described round the centre of another, an encounter begins or 

 ends between the two molecules. 



Now suppose an encounter to take phce between a pair of 

 molecules one of which is in the state P'Q', and the other in the 

 state /'.y'. As the result of the encounter the variables P'. . . q' 

 assume new values, but what particular values they shall 

 assume, given P''J'/''/ before encounter, depends on the two 

 coordinates ffip' defining the position of the centre of one of the 

 two molecules on the " a" sphere describe! about the centre of 

 the other at the commencement of the encounter. 



Inasmuch as no work is done in moving the centre of one 

 molecule on the surface of this sphere, it is evident that the 

 "sorting demons" can make the result of the encounter 

 anything that they please, conservatis conservandis. 



Let us suopose thit if these spherical coordinates lie between 

 the limits 6' and 8' -t- d6', <p' and </>' -f d<p', the variables will 

 after encounter lie between the limits P . . . P -f i/H, &c., that 

 is, the pair will be in the slate Vq, and B'(p' will have become 

 . . . e i- de and (j> . . . (p + d<l>. 



I will now assume (condition A) that the coordinates 6'(p' are 

 taken at haphazard without regard ti the variahles \"q' ; if that 

 be so, the chance that, for given P'q' before encounter, the pair 

 of molecules shall be in the Vqe(p state afler encounter is 

 de'd<ti' 



4ir 



But the number of pairs which now are in the state P'q' is 



F'/WP' . . dq' 

 And therefore the number which after encounter will be in the 

 state PqSip, having passed thereto from the state P'q', will be 



r/'dP'dQ'dp'dq'!'^'''^' 



which is equal to 



4» 



47r 



' dPdQdpdqdedii.F'f. 



