December 14, 1893] 



NA TURE 



151 



assumption. J- J- Thomson subsequently condders the case of 

 X being a function of T as well as of & (p. lOo). But he does not 



in this case make -^ a complete differential. 



I think that in the general case we must regard x as a func- 

 tion of the unconstrainable coordinates, and as varying from 

 one configuration to another, through which the system passes 

 in the same stationary motion with constant v. When v 

 becomes v ■\- dv we do work in two ways. Firstly, we alter 

 the value of x for each configuration, doing thereby on the 



whole an amount of work equal to ^—^v. Secondly, we alter 



dv 



the comparative frequency of different values of x ii^ the 

 stationary motion. This is essential ; for without this the 

 system would not be in stationary motion with the altered 

 values of T and v. I think J. J. Tnomson had this in his mind 

 when he madex a function of T as well as v (p. lOo). 



Let, then, fitx^ ... dxn or/da denote the frequency of the con- 

 figuration Xj ... x„, so that 



f^"" t- 



and 



j'i-'" 



dx = ljdx'^<^ + j xdifda) 

 ddc refciring to variation of the limits of integration 



= / xd'J'^T) + 'l^^v. 



and so 



and 



■I 



Now how to make 



av J 



^^ = 2Na log (.T) + ljxd[fd<T). 



\ fxd:/d<r), 



]^Mfd<r), 



a complete differential ? 

 If 



B= //(log/- i)d<r 



(Boltzmann's minimum function), 



/ log/a (/da) = 33 + N3 log z', 



and is a complete differential. 



Hence one solution, and probably the only general solution, 

 of the problem is obtained by making log C/ proportional to 



^, or 

 T 



where 



is numerical. 



r 



That gives -j^^ 

 2Naiog(zT)-i9B - 



N 



d log z'. 



Since 2/T is the Action of the system during the definite 

 time i, we see that the second law stands in a certain relation 

 to the principle of least Action. But I think the complete treat- 

 ment of it must be based on the virial equation. And it may 

 be regarded as the law of the variation of B when T and the 

 controllable coordinates vary. S. H. Burbury. 



THE LOSS OF H.M.S. ''VICTORIA:''^ 



III. 



T AST week we discussed the opinions expressed by the 



■L^ Board of Admiralty, in their Minute of the 30th of 



October, upon certain points that relate to the construc- 



1 Continued from p. 127. 



NO. 1259, VOL. 49] 



tion and stability of the Victoria; but the remainder was 

 left for consideration in the present concluding article. 



7 /te vali(e of aft armour- belt at the cuds for resisting 

 damage. — Their lordships say " the fact that the Victoria 

 was not armour-belted to the bow had no influence upon 

 the final result of the collision. Ino armour-belt could 

 have prevented the ripping open of the bottom below 

 water by the ram-bow of the Camperdown,ar\6. the flood- 

 ing of the compartments to which water could find access 

 through the breach." Mr. White argues strongly against 

 the assertion, which he states has been made, that if a 

 strong armour-belt had existed at the place where the 

 blow was struck, the damage might have been greatly 

 reduced and the ship kept afioat. He considers that all the 

 most important compartments which were flooded in the 

 Victoria must have been thrown open to the sea under 

 the conditions of the collision, even if there had been such 

 a belt. " The breach in the side might have been different 

 in form and possibly less extensive, especially above 

 water ; but it must in any case have been of large extent, 

 and have admitted very large quantities of water in a 

 short time." Mr. White proceeds to argue that the 

 extent to which the Caniperdoun penetrated into the 

 interior of the Victoria was not altogether a disadvantage, 

 as the Camperdoivfi's bow thus became virtually locked 

 in the protective deck of the Victoria, till the relative 

 forward movement of the latter ship was destroyed and 

 the tearing action of her spur upon the side of the Victoria 

 was thereby prevented. " Under the assumed condition of 

 a non-peneti able armour-belt, this relative forward move- 

 ment and tearing action must have taken place." But the 

 Admiralty cannot admit the assumption of impene- 

 trability. Reference is made to cases of collision, such 

 as those between Vanguard and Iron Duke., and between 

 Grosser Kiirfiirst and /\onig J Vi//ic///i , which prove, m Mr. 

 W'hite's opinion, that "the existence of an armour-belt is 

 no sufficient safeguard against injuries resulting from 

 serious collision.'' 



The objections tliat have been made to leaving so 

 much of the ends of some of our first-class battleships 

 unprotected by armour, have been mainly in connection 

 with their defence against gun-fire. The gun is, and 

 appears likely for some time to be, the weapon of attack 

 which a battleship must be designed primarily to resist. 

 The attack of the ram can often be evaded by speed or 

 skilful handling ; and thatof the torpedo by watchfulness, 

 tactical resource, and smart conduct on the part of the 

 officers in command. The real defence against rams 

 and torpedoes lies at present much more in the judgment 

 and skill with which a ship can be safeguarded or 

 manoeuvred by her officers, than in her own intrinsic 

 power of resistance. 



At the same time, it is obviously desirable that every- 

 thing possible should be done to mcrease the amount of 

 resistance that can be offered by a ship's hull to attack 

 from ram or torpedo. The Admiralty say that an armour- 

 belt would have no influence upon the final result of ram- 

 ming. This statement is based upon two assumptions : 

 (i) that " under a blow of such energy as was delivered on 

 the Victoria the strongest armoured side ever constructed 

 must have yielded and been driven in. Its water-tight- 

 ness and that of the bulkheads, &c., within it adjacent to 

 the place where the blow was struck, must have been 

 destroyed, and the ultimate result (as regards the admis- 

 sion of water) would have been practically as serious 

 under the same conditions of open water-tight doors, (S:c. 

 as that which actually occurred in the Victoria''; and 

 (2) that if the Camperdozinis bow had been prevented 

 by an armour-belt from penetrating to so great a depth 

 as was stated into the side of the Victoria, her spur would 

 have torn away much more of the bottom plating than it 

 actually did. 



The truth of both these assumptions appears very 



