December 



1891] 



NATURE 



'99 



Special example : — 



123x456x789 



I 23 

 456 

 789 



First figure.— 3x6x9=162 2 



Second figure.— 16 + 2 .6.9 + 5.9. 3 + 8 3 • 6=403 . . 32 

 Third figure.— 40 + 1 . 6 . 9 + 4 . 9 . 3 + 7 . 3 . 6 + 2 .5.9 



+ 5.8.3+8.2. 6 = 634 432 



Fourth figure.— 63 + 1 . (5 . 9 + 8 . 6) + 4 . {2 . 9 + 8 . 3) 



+ 7.(2.6 + 5 . 3) + 2. 5 .8 = 593 . . . .3432 



Fifthfigure.— 59 + 1 . 4 • 9 + 4 ■ 7 • 3 + 7 i • 6 



+ 1.5.8 + 4.8.2 + 7.2.5 = 395'. . .53432 

 Sixth figure.— 39+1 . 4 . 8 + 4 . 7 . 2 + 7 . i . 5 = 162 . 253432 

 Seventh and eighth figures.— 16 + 1 . 4 7 = 44 • • -44253432 



K. Haas. 

 Vienna, VI., Matrosengasse 8. 



The Migration of the Lemming. 



Having resided during the summer months for more than 

 twenty years on the plateau from which the migrations of the 

 Norwegian lemming are supposed by many to take their origin, 

 I can speak from personal observation. Some years ago I had 

 the honour to read a rather lengthy paper before the Linnean 

 Society on these animals, and, with one exception, to which 

 reference will be presently made, I am happy in having nothing 

 to alter or recant. The increase of the Lemmings is not 

 cumulative, but rather periodic, as indeed is usual among the 

 voles as well as among many other forms of life. The 

 migrations are not caused by insufficient food nozv, whatever 

 they may formerly have been, and this is evident from the fact 

 that the swarms pass through, but do not exhaust the fertile 

 districts which they encounter on their nilgrimage. Nor are 

 they affected by any personal struggles between these most 

 pugnacious of animals, for the young litters, when reared, go 

 singly on the journey from which none have ever been observed 

 to return. They do not follow the watershed, and they do not 

 always migrate to the west — an error into which I was betrayed 

 by trusting to common report and insufficient personal experience. 

 But they do go straight. It is well known that the eyes of the 

 lemming are so placed on the top of the head as to render it 

 impossible for the animal when swimming, to discern any object 

 not far above the plane of its horizon. On a calm morning last 

 summer, I often placed my boat in the path of the swimmers, 

 and noticed that they crossed my lake in an absolute "bee-line," 

 and that they could not discern my presence until the angle sub- 

 tended by the boat was infinitely higher than that of the 

 opposite shore. This latter migration was south-east, and in 

 the late autumn the steamer on Lake Mjosen made its way through 

 thousands of these hapless wayfarers; whilst, still later, large 

 numbers were to be seen close to Christiania ; but I venture to 

 prophesy that none will be found in that neighbourhood next 

 year, nor, for tie matter of that, in Heimdalen itself, though 

 it is obvious that some must remain. Probably the ex- 

 planation of these apparently capricious and suicidal migra- 

 tions may be that they are the result of hereditary instinct, 

 which formerly was of service if not necessary to the species. 

 The straight course which they pursue must be owing to 

 the sense of direction common to migrants, and I would hazard 

 the conjecture that the changes of destination may be due to an 

 instinct which, owing to its present inutility, is gradually dimin- 

 ishing in precision and intensity. W. Duppa-CroTCH. 



Asgard, Richmond, December 24. 



The Recent Earthquake in Japan. 



Dans la lettre de AL J. Milne, Tokio, 7 novembre, sur le 

 Iremblement de terre du Japon du 28 octobre, 1891 (Nature, 

 xlv. 127), il y a entr'autres un fait interessant : c'est la mise en 

 oscillation de I'eau d'un bassin de 60 pieds de longueur sur 25 

 pieds de profondeur. II est rare que dans un tremblement de 

 terre I'eau des elangs ou des lacs soit mise en mouvement ; le 

 rythme des vibrations du sol ne correspond pa.s, le plus souvent. 



au rythme de I'oscillation de I'cau. Dans le cas actuel, lea 

 vagues ayant atteint une hauteur de 3 a 4 pieds, il est certain 

 que I'eau a pris un mouvement de balancement. 



Le formule d'un tel mouvement d'oscillaiion pendulaire, si le 

 bassin a un fond horizontal, est : 



/ = 60 pieds = i8*29m., 

 h = 25 pieds = 7 •62m., 

 / = 4*2 secondes de temps.' 



II serait interessant de savoir si le rythme des vibrations du 

 tremblement de terre a Tokio a correspondu a une duree aussi 

 lenie ; ou peut-eire a la moitie de cetle duree, soit 2"i". Ce 

 serait deja des vibrations extraordinairement lentes pour un 

 tremblement de terre. F.-A. Forel. 



Morges, 12 decembre. 



ON THE VIRIAL EQUATION FOR GASES 

 AND VAPOURS. 



A LTHOUGH I had, some time ago, written to Lord 

 -^~*- Rayleigh to the effect that I did not intend to pro- 

 long the discussion of this question, it may perhaps be 

 expected that I should say a few words with reference ta 

 Prof. Korteweg's paper in the last issue of Nature. 



1. I do not agree with Prof. Korteweg's statement 

 that Van der Waals's method, if it could be worked 

 out with absolute rigour, would give the same result 

 as the direct method. There is but one way of dealing 

 with the virial equation : — if we adopt it at starling 

 we must develop its terms one by one, and inde- 

 pendently. In this connection I may refer to Lord 

 Rayleigh's statement (Nature, 26/11/91) : "It thus ap- 

 pears that, contrary to the assertion of Maxwell, p is 

 subject to correction." I cannot admit that p is " cor- 

 rected" ; it is not even changed either in meaning or in 

 value. It is introduced as, and remains (at the end of 

 any legitimate transformations of the equation) the value 

 of the pressure on the containing vessel. This, of course, 

 depends upon what is going on in the interior. Other 

 terms in the virial equation, which happen to have the 

 same factor, may be associated with ^ for convenience ; 

 they assist in finding its value, but they do not change 

 its meaning, nor do they " correct " it. 



2. I do not think that much aid can be obtained by 

 analogy, at least in the present question, from the case 

 of one-dimensional motion. For the latter may be looked 

 on as virtually the to-and-fro motions between fixed 

 boundaries of a number of particles, each of which keeps 

 its speed forever unchanged, except at the moments when 

 two instantaneously pass through one another. From 

 this point of view the result of Lord Rayleigh and of 

 Prof. Korteweg follows at once. Make the particles 

 mere points, and diminish their free range by the sum 

 of their original lengths, and everything will go on prac- 

 tically as before. Can a corresponding statement be 

 made for three dimensions ? Agam, there is in the one- 

 dimensional case a perfectly arbitrary set of speeds, 

 which remains unchanged :— there is nothing analogous 

 to the beautiful statistical distribution of Clerk-Maxwell. 

 And what would be the result if molecular forces were 

 introduced ? 



3. Prof. Korteweg seems not to have noticed the fol- 

 lowing sentence in my second letter to Lord Rayleigh 

 (Nature, 29/10/91, p. 628) : — "The true mode of gettmg 

 a cubic here . . . \i.e. in Prof. Korteweg's notation, 



Af = i2(/««=')(i + |)] 



is to write ^l{v - y) instead of ^Iv. This can, to a 

 certain extent at least, be justified ; the other method 



NO. 115;, VOL. 45] 



