

1888.] President's Address. 57 



motion of water shall be direct or sinuous, or, in other words, regular 

 and stable, or else eddying and unstable. The dimensions of the terms 

 in the equations of motion of a fluid when viscosity is taken into 

 account involve, as had been pointed out, the conditions of dynamical 

 similarity in geometrically similar systems in which the motion is 

 regular ; but when the motion becomes eddying it seemed no longer 

 to be amenable to mathematical treatment. But Professor Reynolds 

 has shown that the same conditions of similarity hold good, as to the 

 average effect, even when the motion is of the eddying kind ; and 

 moreover that if in one system the motion is on the border between 

 steady and eddying, in another system it will also be on the border, 

 provided the system satisfies the above conditions of dynamical as 

 well as geometrical similarity. This is a matter of great practical 

 importance, because the resistance to the flow of water in. channels 

 and conduits usually depend mainly on the formation of eddies ; and 

 though we cannot determine mathematically the actual resistance, 

 yet the application of the above proposition leads to a formula for the 

 flow, in which there is a most material reduction in the number of 

 constants for the determination of which we are obliged to have 

 recourse to experiment. 



There are various other investigations of Professor Reynolds's 

 which time would not allow me to enter into, and I therefore merely 

 mention his investigation of the relation between rolling friction and 

 the distortion produced by the rolling body on the surface on which 

 it rests, that of the effect of the change of temperature with height 

 above the surface of the ground on the audibility of sounds and his 

 explanation of the effect of lubrication as depending on the viscosity 

 of the lubricant. 



The Davy Medal has been awarded to Mr. Crookes for his investi- 

 gations on the behaviour of substances under the influence of the 

 electric discharge in a high vacuum. 



Mr. Crookes 's remarkable series of researches which conducted him 

 to the invention of the radiometer led him to work with excessively 

 high vacua. In connexion with this he found that an electric 

 discharge in such vacua is capable of exciting effects of phospho- 

 rescence apparently quite different in their origin from those produced 

 in the ordinary way by such discharges. The latter are clearly 

 referable to the action of the ethereal undulations which are propa- 

 gated from the seat of the discharge. But the former involve in 

 some way the effect of the actual transference of the molecules of 

 ponderable matter. These phenomena, in the hands of Mr. Crookes, 

 opened up a new means of discrimination between different bodies, 

 and he has applied them as a test for the discrimination of groups of 

 rare earths, not yet fully investigated. The test went hand in hand 

 with processes of chemical separation. But here a great difficulty 



