32 SCIENTIFIC APPARATUS. 



which was obtained by the invention of logarithms, has completely 

 outrun the present capabilities of geometrical methods ; and these 

 methods are now seldom used, except for obtaining rough first 

 approximations. Thus it is that the degree of perfection which has 

 been given to analysis has enabled it to dispense with mechanical 

 aids ; although instances are not wanting which may serve to show 

 that the mechanical methods may yet receive a great future deve- 

 lopment. In addition to the applications of the Peaucellier 

 movement, to which we have already referred, we may also men- 

 tion that Sir William Thomson has recently planned an integrating 

 machine which will integrate mechanically any differential equation, 

 or set of simultaneous differential equations, containing only one 

 independent variable. In the important case of the linear equa- 

 tion of the second order with variable coefficients, the actual con- 

 struction of the requisite mechanism would, in the opinion of Sir 

 William Thomson, present no insuperable difficulty. The kine- 

 matical principle employed in this integrating machine is due to 

 Professor James Thomson, and consists in the transmission of 

 rotation from a disk or cone to a cylinder by the intervention of a 

 loose sphere, which presses by its weight on the disk and cylinder,, 

 or on the cone and cylinder, as the case may be; the pressure 

 being sufficient to give the necessary frictional coherence at 

 each point of rolling contact. Sir William Thomson proposes to 

 apply this principle to the construction of a machine adapted to 

 calculate the harmonic constituents of any given function ; and he 

 believes that by employing such a machine in the analysis of the 

 ides a single operator will be enabled to find, in an hour or two, 

 my one of the simple harmonic elements of a year's tides recorded 

 In curves by an ordinary tide gauge in the usual manner, a result 

 which hitherto has required not less than twenty hours' computa- 

 tion by skilled arithmeticians. As another indication of the same 

 tendency to substitute (wherever it maybe found possible) mecha- 

 nical or graphical contrivances for abstract calculations, we may 

 refer to an excellent German treatise, the " Graphische Statik " of 



