32 



NATURE 



tion. This animal "never tries to run away, but stands 

 and hisses, distending its stomach to an abnormal size." 

 The dog hates it cordially ; and very naturally, for, when 

 the dog is approaching to the attack in front, " the lizard 

 suddenly brings his tail round and gives the unwary dog 

 a most tremendous wipe across the side of the head." 

 " The first interview between a dog and one of these 

 animals is very amusing — the dog is always so utterly as- 

 tonished at this unexpected attack On the lizard's part, 

 and also so hopelessly wroth." We may note that in a 

 pocket at the end of the volume there are two maps — 

 a map of the north-west frontier of Afghanistan, and a 

 sketch-map showing the routes traversed by the Boundary 

 Commission during 1884, 1885, and 1886. 



By Leafy Ways. 

 Elliot Stock, 1 85 



By 



Francis A. Knight. (London : 



This volume is made up of " brief studies," which 

 originally appeared as articles in the Daily News. The 

 author's object is not to present scientific conclusions 

 about Nature, but to convey some idea of the impressions 

 which have been produced upon him by various elements 

 of the external world. He is an ardent lover of every- 

 thing in Nature that appeals to what may be called the 

 artistic sense ; and he has the secret of suggesting, by 

 means of brief and simple descriptions, very vivid pictures 

 of scenes in which he himself has found delight. No one 

 who wants to be intellectually instructed should trouble 

 himself to read the volume ; but it will give much pleasure 

 to persons who like to be reminded of some of the in- 

 numerable aspects in which the country reveals itself to 

 sympathetic observers. The volume is prettily illustrated 

 by E. T. Compton. 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible jor opinions ex- 

 pressed by his correspondents . Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonymous communications. ] 



On an Electromagnetic Interpretation of Turbulent 

 Liquid Motion. 



The equations of rate of increase of momentum F, com- 

 ponents X, Y, Z, per unit volume of a liquid (density = l) 

 are — 



X 



du 



du 



. au , du , du , dp 

 dt dx dy dz dx 



and corresponding terms for Y and Z. If the liquid be 

 incompressible, 



du , dv , d'cv 



-, + V- + — = O- 



dx dy dz 



Mulip ying this by u, and adding to X, we get — 



Xdu , d , ns , d , s , d , ^ , dp 

 dt dx dy dz dx 



and similar ones for Y and Z. 



It is at once obvious that these could be written down at once, 

 for t<", uv, and uiv are the momenta per second carried into the 

 element through its faces as in the kinetic theory of gases ; and it 

 is evident that the equation is the same as for a strained solid 

 where these are the superficial normal and tangential forces. 



If we now take the average values of these throughout any 



small region, and write for 'the average of -7- = ,-, we 



have- 



X 



dx 



du , dii- duv , duw , dp 

 + , - -t- , - + - . — -i- ^ • 



dx' 



dt 



dx 



dz 



dx 



{May 9, 1889 



Comparing this with Maxwell's stress in the ether, we must 

 take (" Electricity and Magnetism," vol. i. § 105) — 



dii- 

 7x 



d 

 dx 



(d^W 



d 



\fx 



___ K^-dx^'^^-^'^-d.^'-'^-^, 



dy dy \dx • dy) ^ dy ^^ ^ Ty • "^' 

 duw _ d (d'i^ d^\ , ^ Tjr> , d 



if: - TzKjx • -dz) ^ dz ^^^ dz' «T'' 



adding these together, and comparing with the equation for X, 

 we get — 



■v^ _ du _ dp 

 ft dx 



- dx I \dxj \dy) \dz) ) dx( dx' dy- uz' ) 



IdP ^-dQ + ^\ . q/^Q _ dP\ ^^(<ll ^ dR\ 

 \dx dy az ) ^ \dx dy ) \ dz dx ) 



+ P 



and 



J± + «'^ + dy\ _^/d0 _da\^ (da _ dy\ 

 \dx dy az) \dx dy) \dz dx) 



Iving Y and Z. 



and two similar ones involving Y and Z 

 Now, assuming 



we get — 

 X - 



d-\\/ d-\j/ d-iii 



If'-^ff-^d^^^ °' 



d? dQ ^ d^ 



ax dy dz 



da , d^ , dy 



■ . + -7- -1- f = vi, 



ctx dy dz 



.^ Idq d?\ ^ ,. dV d\\\ 

 ^ \dx dy ) \ dz ay / 



-^ 



+ 7 



and two other similar ones. 



li vis now assume as the relations connecting P, Q, R and 

 a, ff, y with a velocity V — 



\dy dz) dt \dy dz] 



dy 

 and the corresponding others, we get — 



d? 

 It' 



1' du _ 



X - = Pf + am + 



dt 



dt 



(Q7-R3), 

 du 



which, if we suppose the motion steady, so that "" = o gives 



dt 

 exactly the right expression for the mechanical force due to an 

 electric charge, e, and a magnetic charge, m, and to an electric 



dP dO dK 

 current with components - ,. ',,' A • 



In order to justify the assumed relation between c, fi, y and 

 P, Q, R, compare with Sir ^Villiam Thomson's equations of 

 propagation of disturbance in a turbulent liquid (Fhil. Mag., 

 October 1887, p. 342). 



In his case everything is a function of y only, and in that case 

 my equations become, when there is no mechanical force — 



= Q 



du 

 dt 



dV 

 dy 



V dt 



(R/3 



- R '^^^ + ;8 



da 



dy 



dy 

 dy 



Now under the circumstances contemplated, R and 7 are not 



functions of j; — 



. du r\dP , ada 



. . - — ^ , + P , • 



dt dy dy 



