1883.] 



On the Motion of Water. 



87 



is a quantity of the nature of the product of a distance and a velocity ; 

 and to point out that the establishment of a dependence of the character 

 of fluid motion on a relation between the linear size of the space, the 



velocity of the fluid, and -, would be equivalent to establishing the 



P 



existence of two physical constants, one a distance and the other a 

 velocity or a time, as amongst the properties of fluids. Using the 

 term dimension as implying measures of time as well as space, these 

 constants may well be called dimensional properties or fluids. Similar 

 constants are already recognised ; thus the velocity of sound is such a 

 velocity constant, and the mean paths of gaseous molecules, or the 

 mean range, are such linear constants. 



It is always difficult to trace the dependence of one idea on another; 

 but it may be noticed that no idea of dimensional properties, as 

 indicated by the dependence of the character of motion on the size of 

 the tube and the velocity of the fluid, occurred to me until after the 

 completion of my investigation on the transpiration of gases, in which 

 was established the dependence of the law of transpiration on the 

 relation between the size of the channel and the mean range of the 

 gaseous molecules. 



6. Evidence of Dimensional Properties in the Equations of Motion. — 

 The equations of motion had been subjected to such close scrutiny, 

 particularly by Professor Stok es, that there was small chance of dis- 

 covering anything new or faulty in them. It seemed to me possible, 

 however, that they might contain evidence which had been overlooked, 

 of the dependence of the character of motion on a relation between 

 the dimensional properties and the external circumstances of motion. 

 Such evidence, not only of a connexion, but of a definite connexion, 

 was found, and this without integration. 



If the motion be supposed to depend on a single velocity parameter 

 U — say the mean velocity along a tube — and on a single linear 

 parameter c, say the radius of the tube ; then, having in the usual 

 manner eliminated the pressure from the equations, there remain two 

 types of terms in one of which — 



TP 

 c 3 



is a factor, and in the other — 



is a factor. So that the relative values of these terms vary respectively 

 as U and — 



c P ' 



This is a definite relation of the exact kind for which I was in 



