274 Prof. Sir W. Thomson on general [Feb. 3, 



so as to move with the same speed, and let t be the displacement of any 

 one of them from any particular position. Let 



x,y i x' i y\x" i y" i ...x^\y^\ 



be the displacements of the second cylinders of the several double inte- 

 grators. Then (the second globe-frame of each being connected to its 

 first cylinder) the displacements of the first globe-frames will be 



d 2 x d 2 y d 2 x' d 2 y' „ 



W W 3F* W 



Let now X, T, X', T', &c. be each a given function of 



&> y> x \ y'> °°'\ &c - 



By proper mechanism make the first globe of the first double integrator- 

 frame move so that its displacement shall be equal to X, and so on. 

 The machine then solves the equations 



For example, let 



> X=(x'-x)f{(x'-xf + (y'-yf} 

 + ^>-x)f{{x"-x) 2 + (y"-y) 2 } 

 + 



¥=(y'-y)fW-*) 2 +(y'-m 

 +(y"-y)f{(*"-*yHy"-yy} 

 + 



X' = &c, T'=&c, 



where / denotes any function. 



Construct in (frictionless) steel the surface whose equation is 



*=*/(? W) 



(and repetitions of it, for practical convenience, though one theoretically 

 suffices). By aid of it (used as it were a cam, but for two independent 

 variables) arrange that one moving auxiliary piece (an ^-auxiliary I 

 shall call it), capable of moving to and fro in a straight fine, shall have 

 displacement always equal to 



(x'-x)f{(x'-xy+(y'-y) 2 }, 



