December 13, 1894I 



NA TURE 



■OJ 



which this function has finally attained its minimum, and is thus 

 the unique steady state : it still being borne in mind that this is 

 only a proposition of averages derived from a great variety of in- 

 stances in which nothing is conserved in encounters except the 

 energy, and that exceptional cases may exist, comparatively very 

 few in number, in which the trend is, at any rate temporarily, 

 the other way. . 



Such an exceptional case is in fact the very striking one, 

 pointed out by Maxwell and Helmholtz, in which the motions 

 of the system are all at some stage precisely reversed, so that it 

 retraces its previous history backwards, and the trend of the 

 reversed system is therefore in the opposite direction to the one 

 which would lead towards the steady state. Now it has been 

 assumed, at first sight plausibly, that there are just as many 

 cases of this reversed motion as there are of the direct motion ; 

 and if that were so, it would undoubtedly go hard with the distri- 

 bution theorem. But a fallacy underlies such an assumption, as 

 indeed the other accepted proofs of simple cases of the distribu- 

 tion theorem would lead us to expect. Consider an arbitrary distri- 

 bution of velocity and configuration of the system to begin with ; 

 and let it settle down for a time towards the final state, whatever 

 that may be. Suppose at the end of that time that its velocities 

 are all reversed ; the system will retrace its course up to the 

 initial state, but when it has got there, it will presumably go on 

 settling down towards the final state by another route, because 

 there is no longer any reason for exceptional behaviour. Thus 

 there will be only a temporary aberration in the course of the 

 reversed system ; and further, if the original progress towards a 

 steady state was at all rapid, this aberration will be sensible only 

 for a brief time, the remainder of the history of the reversed 

 motion corresponding nearly to the steady stale. It is true that 

 if the whole universe were thus reversed, the aberration would 

 be permanent ; but then the whole universe i> a permanently 

 dissipative system, and there is no question of a steady state 

 being attained by it in measurable time. For a finite system, 

 like a mass of gas imagined as bounded by a rigid envelope, 

 the case would be different. 



Tims even if these reversed states amounted to half the 

 possible states, there would still be a preponderating, though 

 not immense, probability in favour of a final settling down. Bat 

 are these reversed states half the total number ? The character- 

 istic of such a state is that it is derived from an entirely for- 

 tuitous initial distribution by a process of change which is in 

 the direction of the final steady state, whatever that may be, 

 and much in that direction if the time concerned be consider- 

 able. It seems then that the number of configurations which 

 can retrace their history for a sensible time is very much more 

 limited than the total number of possible configurations, and 

 that they are simply the exceptions which do not disprove the 

 rule. For a theorem of average, derived from a very great 

 number] of instances, is of course not invalidated by picking 

 out a comparatively small number of instances which depart 

 widely from the average. J. L.\RM'jR. 



Cambridge, December 4. 



" Peculiarities of Psychical Research. 



Mr. II. G. Wells disposes very aptly of most of the claims 

 set up by Mr. Podmore and his colleagues to be real scientific 

 investigators. But, I think, he rather disguises the significance 

 of the card-drawing experiments to which he refers. The 

 experiments of M. Kichet and those of the .S. P. R. belong to 

 two very different categories. In the former case, 7S9 correct 

 guesses were made in 2927 trials, or a deviation from the most 

 probable result of 57 or 58 ; this is about 24 times the 

 standard deviation, or the odds against a deviation in excess of 

 this amount are only about 100 to I, or odds of only about 50 

 to I of a deviation of this magnitude either way. 



On the other hand, in the S.P. R. trials we have a deviation 

 from the most probable of 347, about six times the standard devia- 

 tion. That is to say, the odds against such a result are in round 

 numbers about 2,000,000,000 to 3 \ Now, this is of a totally 

 different order to that given by M. Richet's numbeis. I have ob- 

 tained odds as great as 100 to I against the results of very care- 

 fully conducted lottery experiments. There is in reality nothing 

 significant about such odds. But the odds against the S. P.R. 

 experiments are almost equal to the odds against the Monte 

 Carlo roulette returns! The experiments are significant, very 

 significant — not to my mind, however, of telepathy, but of the 

 want of scientific acumen in the psychical researchers. The 



NO. 131 I, VOL 51] 



interesting point as to whether an abnormal distribution was 

 also in the cards turned up as well as in the percipient, does not 

 appear to have been recorded. Mr. \Yell5has, however, passed 

 over the difference between the two cases, and given, I fear, 

 the psychical researchers the chance of a little self-glorification 

 on their due appreciation of the significant. 



University College, December S. Karl Pearson. 



Chronometer Trials. 



The Mersey Docks and Harbour Board have, by an Order 

 dated November 29, 1894, modified the regulations under which 

 they are prepared to issue certificates to those who deposit 

 chronometers and other scientific apparatus at their Observatory 

 for test and examination. Under the new regulations, instru- 

 ment-makers can re-submit their apparatus within a twelvemonth 

 of first deposit, without any additional fee. In the case of 

 chronometer-makers this concession will probably be welcomed 

 for the following reasons. Hitherto, the certificates granted 

 have simply been regarded as a protection to the public, and 

 the makers have had 10 apply their own tests to ensure accurate 

 performance before submitting them to independent examina- 

 tion. But it will now be possible for makers to spare, in some 

 degree, their own rigorous control, since the certificate granted 

 will show the direction in which correction must be made, 

 and a second certificate will be granted without fee to 

 the improved instrument. If no alteration be needed, the 

 time required for the additional trial is of course saved. 

 Another modification, which will be appreciated by those who 

 seek certificates for watches, is that affecting the condition under 

 which these certificates are granted. The alteration will be 

 best shown by an example. Suppose a watch to have a normal 

 rate in the first position of trial of nine seconds a day, and 

 under the various tests to which it is submitted the rate increase 

 more than a second daily. Such a watch or chronometer, under 

 the old regulations, would be refused an " A " certificate because 

 the daily rate increased to more than ten seconds from mean 

 time. But the watch might evidently be superior to one 

 with a normal rate of two seconds, and which varied some five 

 or six seconds in the various stages of its trial. The alteration 

 in the regulations sanctioned by the Board will n^w permit the 

 variations to be reckoned from the normal rate, and not from 

 mean times. William E. Plummer. 



Liverpool Observatory, December 10. 



Indo-Malayan Spiders. 



In* your issue of November 29, Mr. R. I. Pocock, 

 reviewing Mr. and Mrs. Workman's book on "Malaysian 

 Spiders," states: "But the pine-apple is a native of South 

 America, and has only of late years been introduced into 

 Singapore ; &c." Now, twenty years ago it was as common at 

 Singapore as any other fruit, more so than many indigenous 

 ones. How long before it may have been introduced I am 

 unable to say, but that also should surely be stated "Before 

 such a conclusion, however, can be looked upon as an estab- 

 lished fact." I quite grant that in all probabiUly the plant and 

 spider were introduced simultaneously. 



New Club, Grafton Street, W. B. .\. MuiRHEAD. 



Death-feigning in Snakes. 



In Nature of November 29, p. 107, L. C. Jones asks 

 whether death-feigning is, among snakes, confined to Hcterodon 

 plalyrriiinus. 



A writer in the American Naturalist, November 1894, 

 pp. 966-8, tells almost precisely the same story of the 

 " Moccasin " snake (Ancisirodon) and of " a black or blowing 

 viper." 



He also finds " letisimulation " in the toad, and in certain 

 arthropods, worms, and protozoa. 



December i. Gerard W. Butler. 



The alleged Absoluteness of Motions of Rotation. 



Proi". Gkelnhill's remarks on my letter on this subject 

 {Nature, November 29), admitting that he is unconverted, and 

 throwing out a suggestion that further arguments or explana- 

 tions are desirable, appear to open a wider question than can 



