HERMANN VON HELMHOLTZ 



parts is more or less gradually destroyed by virtue of 

 viscosity or fluid friction. In a viscid fluid there is 

 a great internal friction ; and from this extreme case 

 we can pass by gradations to fluids of less viscosity 

 until we arrive at a very mobile fluid like sulphuric 

 ether. This suggests the abstraction of a perfectly 

 frictionless fluid, in which there is no tangential stress 

 between elements sliding past one another. The 

 greater part of the theory of hydrodynamics deals with 

 such an ideal fluid, for the simple reason that our 

 mathematical methods are insufficient to attack the 

 general problem of the motion of a viscous fluid. Al- 

 though no known fluid is even approximately friction- 

 less, nevertheless the study of the ideal frictionless fluid 

 leads to important results and must ultimately enable 

 us to understand better the effects of fluid friction. 

 In 1858 Helmholtz investigated, mathematically, the 

 laws of vortex motion in a frictionless fluid. In 

 addition to the very remarkable theorems in hydro- 

 dynamics, to which Helmholtz was led and on which 

 Lord Kelvin and others have based whole theories of 

 the ultimate constitution of matter, the investigation 

 has another important side. The mathematical for- 

 mulae are identical with certain formulae in electro- 

 magnetism, so that, as Helmholtz himself pointed out, 

 there is a striking analogy between the two apparently 

 distinct classes of phenomena, hydrokinetics and electro- 

 kinetics. Indeed all mechanical models that aim at 

 explaining the reciprocal relations of electricity and 

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