240 



NATURE 



[January 10, 1S95 



well be doubted whether such a definition can be framed in the 

 present state of knowledge. What Mr. Galton's definition or 

 |ihrase does accomplish, is to point out jt'OT,r characters which 

 may certainly be classtd as "acquired" and not "inherited," 

 and from the study of which we may accordinjjly start in the 

 inquiry as to whether or not the acquired characters of one 

 generation may become inherited in a sub^equent generation. 

 "Characters," writes Mr. Gaiton, "are said to be acquired 

 when, &c." This by no means asserts that there are not other 

 characters which should be rej;ardcd as acquired, if we knew 

 fully about their history; for instance, at the very moment when 

 our observation is being made on a group of individuals, some 

 might conceivably be exhibiting a character inherited from the 

 last generation, and other specimens might be exhibiting exactly 

 the same character acquired de novo. Such cases (supposing 

 that they ever occur) would not help us at all m the attempt to 

 determine whether acquired characters are transmissible; and 

 the fact that they are not included in Mr. Gallon's definition 

 (though their existence is not expressly denied) renders that 

 definition a more practical one, and more useful to the experi 

 mental naturalist than a more comprehensive definition which 

 could not be brought to a practical issue. 



Lastly, it seems to me that Mr. Gallon's definition is pre- 

 cisely what Lamarck pointed to in his " Premiere loi " and the 

 first sentence of his " IJeuxicme loi." The reciprocally 

 dcitruciive nature of the propositions contained in those 

 two laws I pointed out, in a former letter, and have not yet 

 had the pleasure of seeing, in reply, any defence of Lamarck's 

 position from one of his adherents. E. Ray LaNKESTER. 



Oxford, January 4. 



Boltzmann's Minimum Theorem, 



The remarkable differences of opinion as to what the 

 Hlheorem is, and how it can be proved, show how necessary 

 is the discussion elicited by my letter on the oversight in Ur. 

 Wa'son's proof. Each of the four authorities who have replied 

 takes a different view. 



Dr. Larmor enforces the view I put forward at the close of 

 my letter, and says that the theorem is what I said appeared an 

 ii /'riori po-sibility ; and I may here point out that his letter is a 

 complete answer to the argument I used in the Phil, Mag. 

 1890, p. 95, urging that, as there were as many configurations 

 which receded from the permanent state as approached it, there 

 was an u priori improbability that a permanent slate would 

 ever be reached. This argument was criticised at some length, 

 not really answered, in Messrs. Larmor and Bivan's Report 

 on Thermodynamics (British Association Report, 1891), but the 

 suggestive remarks there given helped me, I think, to arrive (inde- 

 pendently) at the complete answer given in Dr. Larmor's recent 

 letter. But my present use of the argument is not that which Dr. 

 Larmor criticises ; I now use it as a test of a particular proof 

 of the H-iheorem. I say that if that proof does not somewhere 

 or other introduce some assumption about averages, probability, 

 or irreversibility, it cannot be valid. 



Mr. Burbury appears to consider that the theorem can only be 

 proved if we assume that some element of the distribution does 

 tend to an average (quite a different position from Dr. LarmorV), 

 and he is as yet unable to state the appropriate assumption 

 except for the case of hard elastic spherical particles colliding 

 or " encountering ' (for since a is constant in his last letter, 

 it seems as if the ./,... ,i„_^ cooidinales are really dummies). 

 Yet Mr. liurbury his already given what purports to be a 

 general proof of the theorem for any number of degrees of 

 freedom. 



.Mr. Uryan thinks that a condition which excludes the reversed 

 motion is implied in Dr. Watson's proof, for he says that in 

 taking unaccented letters K/as proportional to the number of 

 molecules passing from one configuration to another in the 

 reversed motion, I make a less " natural "supposition than Dr. 

 Watson, who lakes accented letters ¥' /'. I cannot see what 

 virtue there is in putting accent* on or leaving them olT, and 

 after a very careful study of Mr. liryan's letter, I can only think 

 that he has fallen into some confusion owing to the way in 

 which he use* al one lime aarnltil and at another lime ttn- 

 (Uiented differential i, although (as he himself remarks) there is 

 no difference whatever between their accented and unaccented 

 prodiutt. Hut iven if .Mr. bryan be right, would he put us any 

 " forrarder "? What we want is a f-roof that the cdlisions will 

 make II decrease, and we can hardly be satisfied with a proof 



NO. 1315, VOL. 51] 



which depends on the previous assumption that the particles do 

 " naturally " tend to move in the desired way. 



Dr. Watson meets my reversibility argument by saying that 

 H decreases even in the reversed motion, when the system is 

 confessedly receding from its permanent state. No other 

 corre-pondent agrees with him in this view, which would 

 indeed take a-Mij' all fhysiiol meaning from the H theorem, 

 for the decrease of II would then be quite unconnected with the 

 approach to a permanent slate. As to the other point. Dr. 

 Watson does not amend his proof himself, but says it is " easy ' 

 to do, and so does .Mr. Hryan. Vet one has an instinctive dis- 

 trust of things which are said to be "easily seen,' and al all 

 events Dr. Watson's reference to the case in which the theorem 

 is aj<flied does not help one in the froof, ^Oiere it is necessary 

 to express separately the products of the differentials expressed 

 by the small and capital letters respectively in his "Kinetic 

 Theory. ' 



Mr. Burbury asks why I say ihe error law has been proved 

 for the case of hard spheres without the use of Boltzmann's 

 Minimum Theorem. I thought Tail had done so ( Trans. R. S. E. 

 18S6), and at all events I thought the ordinary investigation 

 showed that there was but one solution, that of the error law, 

 in that ca-e ; but perhaps I am mistaken. 



Mr. Hryan says Lorenz gives the clearest account of the as- 

 sumptions in Boltzmann's theorem, lie would earn our gratitude 

 if he would slate them in his next letter. 



Edw. p. Cui.verwell. 



Trinity College, Dublin, December 29, 1894. 



Aurora of November 23, 1894. 



Observations of this aurora, by Mr. James T. Pope, at 

 Dingwall, in the north of .Scotland, have been sent to me by 

 Mr. II. Corder, of Bridgwater, a few particulars having also 

 been recorded here of the appearance, which, although the dis- 

 tance of this place from Dingwall falls but veiy little short of 

 400 miles, yet showed some very excellent agreements with 

 Mr. Pope's description. 



Beginnings of the aurora were seen by Mr. Pope between 6 

 and 7 p.m., as a glow which brightened gradually along 

 the eastern, and sent up a few faint streamers from the western 

 parts of the horizon towards the north, until 6.30, gradu.ally 

 fading out, after that, till nearly 7 p.in. The glow then gradually 

 reappeared as a bright band, brighter in the east than in its 

 western half, stretched across the sky from east to west, some- 

 what southward from the zenith. This band of light continued 

 very bright for some time, but f.aded out gradually towards 

 7.30, the streamers in the north-west at the same time increasing 

 continually in brightness. 



Near Slough the dispKay was first noticed about 7.15 p.m. as 

 a low ill-defined while bow, stretching, at about half the altitude 

 of those stars above the horizon, from under (," to under v Ur £b 

 Majoris (altitudes 19 and 24^ azimuths 13 W. and 16 E.) 

 from north). -V little later, towards 7.30 p.m., this arc had 

 become a bright narrow band, a degree or two in width, and 

 about 25° long, extending from j; Ursa; Majoris in the west 

 (altitude 15 , 19 W. of north) to a few degrees under 7 and 3 

 Ursa: Majoris (altitudes 16 and H) , 2' W. and 6 E. of north) 

 on a slightly downward slope lo some degrees eastward from 

 the latlerstar. It faded out partially about 7.30p.m., leavinglwo 

 bright remnants across 77, and under 3 Ursre M.ajoris, eaih about 

 8 long, while a third just similar wisp of light apiieared on the 

 same line's far Icl'tward prolongation ; this western offshoot of the 

 band continued with the other two short segments till all had 

 faded out at 7.45 or 7.50, marking the arc's considerable bul 

 not otherwise lraceablec<tension westwards, across «,C Ilerculis 

 (altitudes 17' and 15 , 60 and 55 W. from north). 



Dingwall is about 390 miles distant from Slough, in Ihe 

 direction 18" or 19' west from north; so that it appears 

 that Ihe strong part of the glow-band sei-n most brightly in the 

 east from Dingwall, was alone observable here (if we except 

 the light-wisp in Hercules towards the west, at last), in the 

 vapoury sky near the horizon. 



lirginning with an average altitude of between 9^" and xi", 

 or of about II , at 7.15, the band in growing stronger reached 

 an altitude, at Slough, of 14° or 15' towards 7.30, during 

 about the space of time when it was most distinct, and seen 

 most strongly in the east at Dingwall rxtending from east to 

 west somewhat southward from the zenith. If its altitude 

 there w.is at that lime about 60", and at Slough about 13° 



