1895.] on the Absolute Measurement of Electrical Resistance. 603 



have such relations between lengths, areas, and volumes ; in kine- 

 matics, relations between these mathematical quantities and times, 

 velocities, and accelerations ; in dynamics, between these mathe- 

 matical and kinematical quantities and mass, momentum, force, work, 

 and energy ; in electrical and magnetic science, relations between the 

 foregoing quantities and electrical and magnetic magnitudes ; and 

 so on. 



These relations of interdependence are expressed in equations, and 

 it is of obvious advantage, both for ease of arithmetical calculation 

 and clearness of thought, to rid these equations as far as possible of 

 superfluous arithmetical constants. This may be done by a judicious 

 selection of units, by making the units of the quantities that appear 

 most complex in their relations of interdependence depend upon the 

 units of the quantities that appear in their nature to be simplest. A 

 unit of any quantity so defined wdth reference to the units of quanti- 

 ties apparently simpler is called a derived unit with reference to the 

 latter units as fundamental. 



Thus, the attraction of the earth on a mass of 1 lb. — the weight 

 of 1 lb. — is an arbitrary unit of force. The force that, acting on a 

 mass of 1 lb., increases its velocity by 1 ft. per second every second 

 is a derived unit of force with reference to the units of length, time, 

 and mass, as fundamental. It is usually called the absolute unit of 

 force on the pound-foot-second system ; and by the very nature of its 

 definition it gets rid of an arbitrary constant in the relation between 

 force, mass, and acceleration. If the arbitrary unit of force mentioned 

 above — the gravitation unit — is used instead of the absolute unit, our 

 dynamical equations are uselessly complicated by the introduction of 

 " #," the acceleration of gravity at the particular point of the earth's 

 surface at which we happen to be, and at the particular time when 

 our measurements happen to be made. 



2. The second condition of prime importance to a scientific system 

 of units is that the units of all quantities should be invariable, un- 

 affected by conditions of time and place, and independent of the 

 properties of particular bodies, i. e. they should be absolute. The 

 word " absolute "is in philosophy opposed to " conditioned." When 

 it is applied to a unit in science the implication should be that the 

 unit is the same at all times and in all places, and that it is uncon- 

 ditioned by the properties of any specified body or bodies, i. e. that its 

 magnitude is brought into relation with and depends upon only the 

 most permanent phenomena of the universe. 



The modern system of absolute units goes far to fulfil the first 

 of our two requirements ; it only very partially fulfils the second. 



When we speak of an absolute unit at present we mean a unit 

 the magnitude of which depends on nothing else than the units of 

 length, time, and mass, and the properties of the ether. The latter 

 may be regarded as universal enough, but the units of length, mass, 

 and time are arbitrary standards. The metre depends on the pro- 

 perties of a particular bar, the gramme on the properties of a particular 



