GO Professor H. S. Hele-Shaw [Feb. 10, 



that is done, we find that the flow absolutely agrees with that pre- 

 dicted by Professor Lamb, the central line which meets the plate, 

 leaving it exactly with the same form at a corresponding point on 

 the back, the curves of each being hyperbolas. This effect is, of 

 course, produced by the central line dividing on the plate, a portion 

 flowing upwards and a portion downwards, reuniting at a correspond- 

 ing point behind, from whence it flows away. 



Such a state of thing? would be absolutely impossible to conce've 

 by most of us, but by turning the plate at an angle in the lantern, we 

 are able to approximately represent, even without artificial border lines, 

 this condition of flow. You are thus able to see a striking example 

 of the absolute accuracy of mathematical prediction, and to feel every 

 confidence, that the original experiment in the channel, or indeed any 

 others with thin viscous films, should give us indeed a correct picture 

 of wliat we can never hope to see, viz. the motion of a perfect liquid. 



It is satisfactory to know that the principle of the thin films has 

 been examined by probably the greatest authority on the subject, and 

 as a result, Professor Sir G. Gabriel Stokes states, that " they afford a 

 complete graphical solution, experimentally obtained, of a problem 

 which, from its complexity, baffles the mathematician except in a few 

 simple cases." 



Whilst I have been dealing with the stream-lines of a perfect 

 liquid, your minds will doubtless have turned to the lines along 

 which magnetic and electrical forces appear to act. We are possibly 

 further from realising the actual nature of these forces, than from a 

 correct conception of the real nature of a liquid. We have long 

 agreed to abandon the old ideas of the electrical and magnetic fluids 

 flowing along these lines, and to substitute instead the idea, that these 

 lines represent merely the directions in which the forces act. Now 

 we can easily see that this conception is quite a reasonable one, for in 

 the case of the model it is not necessary to have the row of balls 

 actually moving, in order that the effect may be transmitted along 

 the different lines they occupy. If I attempt to raise the plate upon 

 which they rest, the pressure is instantly transmitted through the 

 whole row to the top ball along each line, whatever curve the line may 

 take. In the same way, you will remember that it was not necessary 

 to have the colour bands actually in motion, for, though apparently 

 free to move in any direction, they retain their form for a considerable 

 time, and the path along which they would influence each other as soon 

 as the tap is opened, would be along those lines in which the liquid was 

 flowing before it was brought to rest. Hence it is possible, with some 

 suitable means, to cause a viscous liquid to reproduce exactly the lines 

 of magnetic and electrical induction. In the case of magnetism and 

 electricity, it is of course possible, by means of a small magnetic 

 needle or a galvanometer, by exploring the whole surface through 

 which magnetic induction or electrical flow is acting, to plot the lines 

 of force for innumerable cases, where we can work in air or on the 

 6urface of the solid conductor. 



