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



thinner, less particles will be able to dispose of themselves in the 

 shallow portion of the film, and hence the lines of flow will be 

 pushed away from this portion, giving us exactly the same forms 

 as magnetic lines of force in a magnetic field in proximity to a dia- 

 magnetic body. 



Here, again, mathematical methods have enabled lines of actual 

 flow to be predicted, and you may compare the actual flow for tho 

 case of a cylindrical para-magnetic body, which was worked out some 

 years ago. 



You will doubtless not be inclined to question the practical value 

 of stream-lines in the subject which we have just been considering, 

 because, unlike the flow of an actual liquid, magnetic lines of force 

 can never be themselves seen, and because there is no doubt as to 

 the correspondence of the directions to the lines of a perfect liquid. 

 It was the conception of these lines in the mind of Faraday, and moro 

 particularly their being cut by a moving wire, that enabled him to 

 realise the nature of the subject more clearly than any other man at 

 the time, and to do so much towards the rapid development of electrical 

 science and its practical applications. 



When we come to consider the relation of the study of the motion 

 of a perfect liquid with hydromechanics and naval architecture, it 

 must be almitted that the matter is a difficult one. 1'r >bably one of 

 the most perplexing things in engineering science is the absence of 

 all apparent connection between higher treatises on hydrodynamics 

 and the vast array of works on practical hydraulics. The natural 

 connection between the treatises of mathematicians and experimental 

 researches of engineers would appear to be obvious, but very little, if 

 any such connection exists in reality, and while at every step electrical 

 applications owe much to the theories which are common to electricity 

 and hydromechanics, we look in vain for such applications in con- 

 nection with the actual flow of water. 



Now the reason for this appears to be the immense difference 

 between the flow of an actual liquid and that of a pet feet one owing 

 to the property of viscosity. A comparison of the various experiments 

 which you have seen to some extent indicates this. 



In the first place let us consider for a moment some of the things 

 which would happen if water were a perfect liquid. In such a case, 

 a ship would experience a very different amount of resistance, because, 

 although waves would be raised, owing to the reasons which we have 

 already seen, the ch : ef causes of resistance, viz. skin friction and 

 eddying motion, would be entirely absent, and of course a submarine 

 boat at a certain depth would experience no resistance at all, since 

 the pressures fore and aft would be equal. On the other hand, 

 there would be no waves raised by the action of the wind, and there 

 would be no tidal &o\v, but to make up for this rivers would flow with 

 incredible velocity, since there would be no retarding forces owing to 

 tho friction of the banks. But the rivers themselves would soon 

 cjase to flow because there would be no rainfall such as exists at 



