546 



NATURE 



[October 8, 1891 



of boilers and engines, when it is very doubtful if even 

 the present story can be wholly utilized for a long time to 

 come ; rows of boilers and furnaces were erected some 

 two or three years ago to supply steam to drive dynamos 

 which are not yet made ; tens of thousands of pounds 

 have been expended on machinery to be employed in 

 'Constructing two ten-thousand horse- power dynamos, and 

 the armature of one of them, 43 feet in diameter, has had 

 to be left abandoned only half finished, because there is 

 neither money nor present need for such a dynamo at 

 Deptford. 



And while all these provisions for the future electric 

 lighting of London on a vast scale were slowly proceeding, 

 the present customers were left sometimes for hours, some- 

 times for days, and occasionally even for weeks in darkness; 

 what wonder is it, then, that all over London there have 

 have been growing up central stations supplying a direct 

 current at low pressure, and that many of the house- 

 holders who formerly received current from the over- 

 head wires of the London Electric Supply Corporation 

 have had their houses connected instead with the low- 

 pressure underground mains of other companies ? 



To the world at large, however, the Deptford under- 

 taking has been of immense value, for it has shown the 

 possibility of practically using the very high potential 

 differences absolutely necessary for economically trans- 

 mitting power over such distances as that between 

 Lauffen and Frankfort. Hence, maintaining 20,000 volts 

 between bare wires running for 109 miles along the side 

 of the Neckar railway, at a height of only 16 feet from 

 the ground, sounds much less startling now than did Mr. 

 Ferranti's proposal made and acted on five years ago to 

 bring only one-tenth of this pressure, by means of india- 

 rubber covered conductors, into locked transformer rooms 

 built of brick in the basement of the houses supplied 

 with current from the Grosvenor Gallery. 



In fact, the results that have been attained through Mr. 

 Ferranti's undaunted courage, and the well-filled purses 

 of his friends, have led people to look on a pressure of 

 20,000 volts as they regard a velocity of 70 miles an hour, 

 so that to day, in order to prevent boys climbing up any 

 one of the 3000 ordinary telegraph poles which carry the 

 wires from Lauffen to Frankfort, it is thought sufficient 

 to merely paint a skull and cross-bones on every post as 

 an indication of the deadly fate that awaits the climber.^ 

 ( To be continued) 



ON VAN DER WAALS'S TREATMENT OF 



LAPLACE'S PRESSURE IN THE VI RIAL 



EQUATION: IN ANSWER TO LORD 



RA Y LEIGH. 



TYJ Y DEAR LORD RAYLEIGH,-As you are aware, 



■'■*-*■ I did not see your letter of September 7 (Nature, 



24/9/9O till a fortnight after its date ; and my reply has 



been further delayed for a week in consequence of the 



closing of Edinburgh University Library at this season. 



Even now I can refer only to the German version of Van 



der Waals's pamphlet. 



Partly on account of its unfamiliar language, but more 

 especially on account of a very definite unfavourable 

 opinion expressed by Clerk-Maxwell (Nature, 15/10/74) 

 1 did not attempt to read the pamphlet when it appeared ; 

 and it was not till 1888 that, in consequence of some hints 

 from Dr. H. Du Bois, I hastily perused it in its German form. 



The passage which you quote from my paper (where, 

 by the way, the printers have unfortunately put resisfance 

 for resilience) is certainly not a very accurate description 

 of Van der Waals's method, but it represents faithfully the 

 difficulties which I felt on first reading the pamphlet. I 

 said that Van der Waals's " justification of the introduction 

 of the term ajv"^ into an account already closed, as it were, 



' We have to thank the Electrician and the Electrical Review for some 

 Of the illustratuns used in this article. 



K o. J ]45, VOL. 44] 



escapes me." And I am not surprised that it did so. 

 For the statement of Clerk-Maxwell had prepared me to 

 look for error ; and when, at the end of Chap. VI., I 

 met with the formula 



p{v -b) = R(i + at), 

 which, a couple of pages later (nothing but general 

 reasoning intervening), somehow developed itself into 



{p + ~^{v-b) = n^+at), 



I naturally concluded that this was the matter adverted 

 to. I spoke of the first of these equations as a " closed 

 account," because of the process by which b had been 

 introduced. To this point I must presently recur. 



I had not examined with any particular care the 

 opening chapters, to which your letter chiefly refers ; 

 probably having supposed them to contain nothing 

 beyond a statement and proof of the Virial Theorem (with 

 which I was already familiar) along with a reproduction 

 of a good deal of Laplace's work. 



Of course your account of this earlier part of the 

 pamphlet (which I have now, for the first time, read with 

 care) is correct. But I do not see that any part of my 

 statements (with perhaps the single exception of the 

 now italicized word in the phrase " the ivhole procedure 

 is erroneous") is invalidated by it. No doubt, the sudden 

 appearance of ajv'^ in the formula above quoted is, to 

 some extent at least, accounted for ; but is the term 

 correctly introduced .' 



The formula you give would lead, on Van der Waals's 

 principles as to the interpretation of |2(;«V'-), to 



v{p + K) = R(i + at), 

 or 



{/ + ^,)=R(l+a/). 



But how can the factor {v - b)lv, which Van der Waals 

 introduces on the left in consequence of the finite dia- 

 meters of the particles, be justifiably applied to the term 

 in K as well as to that in p ? Yet to apply it so is essential 

 to Van der Waals's theory ; for without it the resulting 

 equation will not give a cubic in v, and cannot therefore 

 be applied to the isothermals for which it is required. 

 And, in any case, it could scarcely be said that the K 

 term, after being manipulated in this manner, is, in any 

 strict sense, " extracted from the term 2(Rr)." 



A very strange thing appears, in this connection, in the 

 German version. A result, due it seems to Lorentz 

 (which, in ignorance of his work, I had reproduced and 

 published in the first part of my paper), leads directly to 

 the equation 



/2/ = R(l+a^;(l-f ^J; 



which is then put in the confessedly approximate form 

 P{v -b) = R(l -f at). 



Of this it is remarked :—" was genau mit dem obigen 

 Resultate [that obtained by the use of the factor 

 (7/ — b)lv] iibereinstimmt." It is obvious that, when we 

 have to divide both sides hy v — b, we ought to restore 

 the proper factor on the right ; and thus that the equatioH 

 ought to take the final form 



V -\- b 



v 



R(I + at) 



instead of the more convenient form 



^ ^ t/2 v~b ' 



in which Van der Waals employs it. But then it would 

 not give the required cubic in v ! 



I think that the mere fact of Van der Waals's saying 

 (in a passage which is evidently applicable to his own 



