THE RATIO OF THE SPECIFIC HEATS OF GASES. 285 



we require to know how the ship's head is pointing. This 

 is usually defined by reference to the points of the compass, 

 but we might more simply state the angle the ship's head 

 makes with some fixed line, say the N. and S. line. 

 Finally, it may be a matter of interest to know whether 

 the ship is heeled over, and whether the line joining the bow 

 and stern is tilted up or not. For this purpose we require 

 two more co-ordinates, say the angle the plane through the 

 masts makes with the vertical plane, and the angle a line 

 along the deck from stem to stern makes with the horizon- 

 tal plane. If the ship is a rigid body, so that its parts do 

 not move relatively to one another, and if the sea is wave- 

 less, so that the centre of gravity of the ship does not move 

 up or down, the position will be completely fixed by these 

 five co-ordinates, and cannot be fixed by any smaller 

 number than five, however they may be chosen. More- 

 over, a moment's consideration will show that the ship can 

 be moved in such a way as to alter any one of these co- 

 ordinates without change in any of the others — hence the 

 name, degrees of freedom. 



If we were defining the position of a balloon instead of 

 a ship, we should need to know its height above the earth 

 in addition to the five co-ordinates already given, so that a 

 rigid body free to move in any direction, and to rotate in 

 any way, has six degrees of freedom. 



Each of these co-ordinates may at any moment be 

 changing, so that corresponding to each co-ordinate will be 

 a rate of change or velocity, and if we know all the co- 

 ordinates and all the corresponding velocities at any 

 moment, the position and motion of the body or system 

 will be completely specified. 



The most general conception of the constitution of a 

 gas is to regard it as made up of a number of molecules, 

 each of which is a dynamical system with a definite number, 

 say q, degrees of freedom. 



Three of these fix the position of the centre of gravity, 

 and the remaining q - 3 show how the parts of the molecule 

 are arranged at any moment with reference to the centre of 

 gravity. 



