PROFESSOR AT HEIDELBERG 187 



round the direction of gravity. He analyses this function, 

 which characterizes the angular velocity of the rotation, into 

 an exponential function lineally dependent upon the time, 

 and another that depends only upon the distance, and is 

 independent of the time, and thence deduces the general 

 integral of the normal differential equation, characteristic of 

 this second factor; after this it is a simple matter to deter- 

 mine the integrals of the equations of motion for a fluid 

 mass, subject to friction, within a hollow sphere. Since it 

 was assumed that no force, beyond gravity, was acting inside 

 the mass of water, the forces which set it in motion can 

 only act upon the outermost layer, and this is actually set 

 in motion by the friction of the vessel with which it is in 

 contact. It does not adhere to the inner wall of the vessel, 

 but glides along it. 



As the analytical function for the components of the force 

 with which a fluid in motion acts upon a superficial layer was 

 known, it was evident that the force which the moving water 

 exerts upon its outermost layer must be balanced by the force 

 exerted by the wall of the vessel on the outermost layer of 

 water ; hence it appeared in the first place that the motion in the 

 vessel described by the integrals arrived at fulfilled the condi- 

 tions of Piotrowski's experiments. Helmholtz was next able, by 

 comparison of these experiments and the theoretical functions, 

 to calculate the constants for the internal friction of different 

 fluids, their value differing according to the nature of the fluid 

 and its temperature. The experiments, however, presented 

 great difficulties, since they seemed to show that the chemical 

 composition of the wall of the tube was not in every case with- 

 out influence upon the motion of the fluids. 



Immediately after this, Helmholtz gave a lecture to the Med. 

 Nat. Hist. Verein, on 'Contrast Phenomena in the Eye', in 

 which he endeavoured to distinguish contrast phenomena 

 from after-images, and to demonstrate a method by which the 

 true simultaneous contrast-images could be investigated apart 

 from after-images. In trying to determine the most favourable 

 conditions for the appearance of the familiar phenomena of 

 contrast, he finds that all the conditions are fulfilled in the 

 phenomenon of coloured shadows. When these are observed 

 through a blackened tube, the eye retains an impression of 



