AT THE PHYSICO-TECHNICAL INSTITUTE 391 



however small, of the form of equilibrium will be augmented, 

 and the equilibrium will become unstable, as appears with 

 real water-waves in the foaming and breaking of the wave- 

 crests. With increased force of wind, and propagation of 

 the waves along the water, the absolute minimum must 

 eventually cease to exist, and the equilibrium becomes labile, 

 so that with increasing currents stationary waves of given 

 wave-length become impossible. It follows that stationary 

 waves of prescribed wave-length are only possible in the case 

 of current velocities lying below certain limits, while the value 

 must also exceed certain minimum limits. One velocity of 

 current determines the rate of wave transmission along the 

 water, the other the velocity of the wind relative to the 

 waves. The application of the analytical expressions thus 

 determined shows, in conformity with experience, that wind 

 of constant intensity which impinges upon a quiescent surface 

 produces faster, that is longer, or higher, waves when it has 

 been blowing for some time upon the waves first produced, 

 and has accompanied them for some distance along the surface 

 of the water : with constant wind, the waves can only increase 

 if the wind goes forward in the same direction more rapidly 

 than they do themselves. From observations made at Cap 

 d'Antibes in April, with a small portable anemometer for 

 measuring the strength of the wind, he was, generally 

 speaking, able to confirm the theoretical statement that so 

 long as the wind outruns the waves it augments the total 

 energy and the momentum of the wave-motion. So long as 

 the energy calculated for stationary waves diminishes, and 

 produces a still lower minimum, the tendency towards the 

 form of minimal energy, under the influence of all the little 

 disturbances produced by the other concurrent waves in actual 

 cases, also co-operates. This eventually tends to a maximum 

 value, and the breaking of the crest, if this can be reached 

 at the given velocity of the wind. 



Helmholtz now became engrossed in his work at the -\ 

 Reichsanstalt. On December 13, 1890, he published a ' Memoir of 

 the Work hitherto accomplished at the Physikalisch-Technische 

 Reichsanstalt', to be laid before the Reichstag, which bore 

 witness to the zeal and energy with which he had endeavoured 

 to fulfil all the duties of his position. The physical portion 



