THE RECENT PROGRESS OF PHYSICAL SCIENCE. 749 



in the case of fair-shaped bodies, we have to deal almost entirely with 

 resistance dependent upon skin-friction, and at high speeds upon the 

 generation of surface-waves by which energy is carried off. At speeds 

 which are moderate in relation to the size of the ship, the resistance is 

 practically dependent upon skin-friction only. Although Professor 

 Stokes and other mathematicians had previously published calculations 

 pointing to the same conclusion, there can be no doubt that the view 

 generally entertained was very different. At the first meeting of the 

 Association which I ever attended, as an intelligent listener, at Bath, 

 in 1864, I well remember the surprise which greeted a statement by 

 Rankine that he regarded skin-friction as the only legitimate resist- 

 ance to the progress of a well-designed ship. Mr. Froude's experi- 

 ments have set the question at rest in a manner satisfactory to those 

 who had little confidence in theoretical prevision. 



In speaking of an exj)lanation as satisfactory in which skin-friction 

 is accepted as the cause of resistance, I must guard myself against be- 

 ing supposed to mean that the nature of skin-friction is itself well 

 understood. Although its magnitude varies with the smoothness of 

 the sui'face, we have no reason to think that it would disappear at any 

 degree of smoothness consistent with an ultimate molecular structure. 

 That it is connected with fluid viscosity is evident enough, but the 

 modus operandi is still obscure. 



Some important work bearing upon the subject has recently been 

 published by Professor O. Reynolds, who has investigated the flow of 

 water in tubes as dependent upon the velocity of motion and upon the 

 size of the bore. The laws of motion in capillary tubes, discovered 

 experimentally by Poiseuille, are in complete harmony with theory. 

 The resistance varies as the velocity, and depends in a direct manner 

 upon the constant of viscosity. But when we come to the larger pipes 

 and higher velocities with which engineers usually have to deal, the 

 theory which presupposes a regularly stratified motion evidently ceases 

 to be applicable, and the problem becomes essentially identical with 

 that of skin-friction in relation to ship-propulsion. Professor Rey- 

 nolds has traced with much success the passage from the one state of 

 things to the other, and has proved the ajoplicability under these com- 

 plicated conditions of the general laws of dynamical similarity as 

 adapted to viscous fluids by Professor Stokes. In spite of the difiicul- 

 ties which beset both the theoretical and experimental treatment, we 

 may hope to attain before long to a better understanding of a subject 

 which is certainly second to none in scientific as well as practical in- 

 terest. 



As also closely connected with the mechanics of viscous fluids, I 

 must not forget to mention an important series of experiments upon 

 the friction of oiled surfaces, recently executed by Mr. Tower for the 

 Institution of Mechanical Engineers. The results go far toward up- 

 setting some ideas hitherto widely admitted. When the lubrication is 



