of Electrons in an Elastic Solid ^Ether. 137 



hypotheses treated, the second very briefly, below. By 

 differing interpretations the one diagram is made to represent 

 both, but we will speak o£ it here principally in connexion 

 with the first. The curves of the diagram are the contour 

 lines at equal vertical intervals (the dotted curves excepted) 

 of the surface 



z = n,(*-!)T + c(x + 2yf-6xf, . . . (21) 



where b and c are positive constants, and in the actual 

 drawing c is taken equal to 2b. The axis of z is perpendicular 

 to the plane of the paper and upwards; x will be spoken of 

 as pointing east and y as pointing north. In our first 

 hypothesis we suppose c really to be very large compared 

 with b, say c is thousands or millions of times b, but so long- 

 as c is greater than b the characteristics of the surface do 

 not for our purposes change. The shaded region of the 

 figure will be called the lake, the regions V and AY the 

 north and south valleys, A the amphitheatre, and H the ridge. 

 The points S x and S 2 will be called the north and south 

 saddles. 



In order that the height of such a surface or mapped 

 country may represent ic, iv must be a function of two 

 variables only; this is the imperfection of the representation. 

 It is assumed that /=</, and the height of the surface repre- 

 sents wasa function of" e and /. w is proportional to z ; in 

 the second hypothesis e and / are proportional to x and y 

 respectively ; but in the first hypothesis 



e= + 2y, f=g=+(x+y). . . . (25) 



The ambiguity of sign implies an ambiguity accepted at first 

 in the first hypothesis. [Beyond the limits of the paper we 

 may suppose the true surface to turn upwards, by adding to 

 the right of (24) such a term as h(x* + 2// 2 ) c , h being positive 

 and as small as we please.] 



We suppose that throughout vastly the greater portions 

 of space, the elastic solid is in the state represented by fl 

 point very near to the lake bottom at the origin. The oscil- 

 lations about that state serve to convey light and, perhaps, 

 gravitation. In certain localities the state is represented by 

 a point in the south valley, and it is never represented by a 

 point in the north valley, because the north saddle is so high 

 that in the most violent disturbances that ever take place 

 the north saddle is not crossed. The original cause of the 

 south valley conditions may be supposed to be an initial 

 state of violent irregular motion throughout the solid 

 generally. 



