Me maxwell, ON FARADAY'S LINES OF FORCE. : 31 



even a hypothetical fluid which is introduced to explain actual phenomena. It is merely a 

 collection of imaginary properties which may be employed for establishing certain theorems in 

 pure mathematics in a way more intelligible to many minds and more applicable to physical 

 problems than that in which algebraic symbols alone are used. The use of the word " Fluid" 

 will not lead us into error, if we remember that it denotes a purely imaginary substance with 

 the following property : 



The portion ofjluid which at any instant occupied a given volume, will at any succeed- 

 ing instant occupy an equal volume. 



This law expresses the incompressibility of the fluid, and furnishes us with a convenient 

 measure of its quantity, namely its volume. The unit of quantity of the fluid will therefore 

 be the unit of volume. 



(2) The direction of motion of the fluid will in general be different at different points of 

 the space which it occupies, but since the direction is determinate for every such point, we 

 may conceive a line to begin at any point and to be continued so that every element of the line 

 indicates by its direction the direction of motion at that point of space. Lines drawn in such 

 a manner that their direction always indicates the direction of fluid motion are called lines of 



jluid motion. 



If the motion of the fluid be what is called steady motion, that is, if the direction and 

 velocity of the motion at any fixed point be independent of the time, these curves will repre- 

 sent the paths of individual particles of the fluid, but if the motion be variable this will not 

 generally be the case. The cases of motion which will come under our notice will be those of 

 steady motion. 



(3) If upon any surface which cuts the lines of fluid motion we draw a closed curve, 

 and if from every point of this curve we draw a line of motion, these lines of motion will 

 generate a tubular surface which we may call a tube of fluid motion. Since this surface is. 

 generated by lines in the direction of fluid motion no part of the fluid can flow across it, so 

 that this imaginary surface is as impermeable to the fluid as a real tube. 



(4) The quantity of fluid which in unit of time crosses any fixed section of the tube is 

 the same at whatever part of the tube the section be taken. For the fluid is incompressible, 

 and no part runs through the sides of the tube, therefore the quantity which escapes from 

 the second section is equal to that which enters through the first. 



If the tube be such that unit of volume passes through any section in unit of time it is 

 called a unit tube ofjluid motion. 



(5) In what follows, various units will be referred to, and a finite number of lines or 

 surfaces will be drawn, representing in terms of those units the motion of the fluid. Now 

 in order to define the motion in every part of the fluid, an infinite number of lines would have 

 to be drawn at indefinitely small intervals ; but since the description of such a system of lines 

 would involve continual reference to the theory of limits, it has been thought better to suppose 



