1878.] Solution of Simultaneous Linear Equations. Ill 



screen : the light by which the eye then sees the screen is, of course, 

 nndulatory. 



The phenomena in these exhausted tubes reveal to physical science 

 a new world — a world where matter exists in a fourth state, where 

 the corpuscular theory of light holds good, and where light does not 

 always move in a straight line ; but where we can never enter, and 

 in which we must be content to observe and experiment from the 

 outside. 



II. " On a Machine for the Solution of Simultaneous Linear 

 Equations." By Sir William Thomson, LL.D., F.R.S., 

 President of the Royal Society, Edinburgh. Received 

 August 30, 1878. 



Let Bj, B 2 , . . . B w be n bodies each supported on a fixed axis (in 

 practice each is to be supported on knife-edges like the beam of a 

 bal ance). 



Let Pn, P 2 i, P 3 i, . . . P wi , n pulleys each pivoted on Bi ; 



P12, P221 P321 



Pl3, P23j P33j 



Ci, C 2 , C3, . . 



Dl, P n , P13, P 



D 2 , P 21 , P 22 , P 2 



P«2 

 P«3 



B> 



n cords passing over the pulleys ; 

 . P 1B , Ei, the course of Ci ; 

 • P2«, E 2 , ,, C 2 ; 



Di, Ei, D 2 , E 2 , . . . D w , E„, fixed points ; 



li, L, Z 3 , . . . l n the lengths of the cords between D x , Ei, and D 2 , E 2 , 

 . . . and D w , E«, along the courses stated above, when B x , B 2 , . . . B /i; 

 are in particular positions which will be called their zero positions ; 



li + e h Z 2 + e 2 , . . . l n + Gn, their, lengths between the same fixed 

 points, when Bi, B 2 , . . . B w are turned through angles x i} x 2 , . . . a'n 

 from their zero positions ; 



fll), (12), (13), . . . (1*0, 

 (21), (22), (23), . . . (2«), 

 (31), (32), (33), . . . (3*0, 



quantities such that 



(11> 1 + (12>2+ . . . +(ln)x n =e l 



(21>i + (22> 2 + . . . +(2w)afc=u 8 



(31>i + (32> 2 + . . . +(3»)as»=e a 



• (I) 



(nV)x x + (%2)a5 2 + . . . + (3n)x n =e n . 

 We shall suppose x h x> z , . . . x n to be each so small that (11), (12), 



