On the Stability of the Floiv of Fluids, 59 



to the parabola which is being constructed. The curves so 

 drawn may be used for the production of templates for lenses 

 or mirrors, and they could be drawn small and then magnified 

 either by photography or by a pantagraph arrangement. 



This instrument is a combination of well known link move- 

 ments, but I do not think they have ever before been applied 

 to the production of a parabolic curve from a single straight 

 line motion. 



The instrument may be so constructed that any play be- 

 tween the sliding pins and the slot may be avoided by pressing 

 the handle down towards the lower side of the slot, which 

 thus becomes a ruler. In the event of any machine being 

 constructed on this principle, gravity itself might make this 

 pressure. 



20 Bartholomew Villas, Kentish Town, N.W., 

 February 2, 1892. 



VIII. On the Question of the Stability of the Flow of Fluids. 

 By Lord Rayleigh, Sec. E.S.* 



IT is well known that while Sir G. Stokes's theory of viscous 

 flow gives a completely satisfactory account of what is 

 observed in the case of capillary tubes, no theory at present 

 exists to explain the complete change in the laws of flow 

 which supervenes when the tubes are of larger diameter and 

 the velocities not very small. Prof. Osborne Reynolds f has 

 applied the theory of dynamical similarity to this question, 

 and has shown both by theory and experiment that the change 

 in the law of resistance occurs when cpw/p, has a certain value, 

 where c is a linear parameter such as the diameter of the tube, 

 w is the velocity, p, the coefficient of friction, and p the 

 density. The conclusion is perhaps most easily reached by 

 applying the method of dimensions to the expression for the 

 ratio (P) of the difference of pressures at two points along 

 the length of the tube to the distance between the points. 

 The dimensions of this ratio are those of a force divided by a 

 volume ; and if we assume that it may be expressed in terms 

 of v% (equal to p>/p) } c, p, and w in the form 



c x v y p z W n j 



* Communicated by the Author. 



t Phil. Trans, clxxiv. p. 935 (1883). 



X Of which the dimensions are 2 in space and — 1 in time. 



