SYSTEM OF UNITS. 5 



3. Units Used in Dynamics of Continuous Media. In elementary dynam- 

 ics definite masses are considered, to which the above-mentioned quantities are 

 referred. In the dynamics of continuous media we have to deal with continuous 

 distributions in space of mass, as well as of the quantities serving to define the static 

 or the dynamic state of this distribution of mass. We then meet with the idea of 

 fields of scalar as well as of vectorial quantities. 



The purely kinematic quantities velocity and acceleration can be used at once 

 for the description of fields in continuous media. But the quantities involving the 

 idea of mass are not immediately serviceable. They must be referred either to 

 unit-mass or to unit-volume of the medium. 



The distribution of mass itself is described either by the volume per unit-mass 

 or by the mass per unit-volume of the medium. The first of these quantities is the 

 specific volume [Jlf' 1 !, 3 ], the second is the density [AfL~ z ]. They are reciprocal 

 to each other, and the units in the m.t.s. system are the same as in the c.g.s. system. 



Referring a mechanical quantity once to unit-mass and once to unit-volume of 

 the medium, we arrive at two corresponding quantities. The passage from a 

 quantity referred to unit-mass to the corresponding quantity referred to unit-volume 

 involves the multiplication by a density, while the return involves the multiplica- 

 tion by a specific volume. 



Most investigations in the dynamics of continuous media have been restricted 

 to the case where the media are homogeneous. Then the fields of the correspond- 

 ing quantities do not differ essentially from each other in their geometrical feature. 

 This is the reason why the correspondence mentioned has attracted no greater 

 attention hitherto. But in the problem now before us we shall have to treat the 

 dynamics of essentially heterogeneous media. In this case the fields of correspond- 

 ing quantities may differ widely from each other, and it is important to notice the 

 analogies as well as the contrasts in these fields. 



Momentum when referred to unit-mass leads back to the velocity, while 

 momentum per unit-volume or specific momentum [ML~~T~ l ] is the product of 

 a velocity by a density. The m.t.s. unit of specific momentum is equal to 100 

 c.g.s. units of the same quantity, just as in the case of velocity. Velocity and 

 specific momentum are the two corresponding quantities serving to describe the 

 fields of motion in a continuous material medium. 



Force when referred to unit-mass leads back to accelerating force, or accelera- 

 tion, while force per unit- volume [J/Z _2 y -2 ] is equal to the product of an accel- 

 eration by a density. The m.t.s. unit of force per unit-volume is equal to 100 c.g.s. 

 units of the same quantity, just as in the case of force per unit-mass. For the 

 description of fields of force, the two defined kinds of force are theoretically equiv- 

 alent to each other. The acceleration of gravity, used generally to describe the 

 gravitational field of force, is a force per unit-mass. The gradient serving to 

 describe the field of force due to a distribution of pressure in a fluid is a force per 

 unit-volume. But for special reasons it may also be useful occasionally to describe 

 the gravitational field by the force per unit-volume, and the field due to the pressure 

 by the force per unit-mass of the medium. 



