the Systems of Scientific Units of Measurement. 181 



I have myself not seen such reduction-formulse elsewhere, 

 and under the present systems I think they may be found 

 of use. 



But it would be far better than employing such formulae to 

 have but one system for all measurements, and do away with 

 this inconvenient bimetallism in the currency of science. 



And in this case the way out of the difficulty is easy. We 

 have only to adopt " v " as the unit of velocity. With this 

 one restriction any magnitude will be expressed in a system 

 based upon any units by the same number in either system. 

 Such a system would be a veritable coalition, and for distinc- 

 tion might be so called. 



A coalition system, then, merely requires that the unit of 

 velocity shall be a certain one, which is also a natural one. 

 It reduces the degrees of freedom in the choice of units by 1, 

 and, without prejudice to Prof. Rlicker's method of formula- 

 tion, will allow us to fix almost any two other units arbitrarily. 

 The two cannot of course be time and length, for velocity 

 simply involves these alone. If the second were retained, the 

 unit of length would be SO quadrants. If the quadrant were 

 retained, the unit of time would be 3*0 of a second. 



If it be urged that a velocity of 30 quadrants per second is 

 a large one, I would reply that it is only 30 times the present 

 unit of velocity in the practical system ; and that experience 

 shows that extremely high or low units do not materially aficct 

 calculations. The unit of capacity is a million times the 

 microfarad of our laboratories, and that of velocity about a 

 million times the speed of an express-train. The use of mega- 

 and micro- has now been found by experience to present no 

 difficulty or objection. 



Thus this change in the unit of velocity would not introduce 



inconvenience in itself ; but unfortunately, since v ■= -, its 



change would necessitate one indirectly in either length or 

 time, and clocks and meters are so commonly in use that any 

 interference in their present constructions would be felt a 

 serious thing. Of the two changes, that of the time unit 

 seems to me simplest. To take s'o of a thing which itself is 

 g^Q of a minute, that again being g^j of an hour, does not 

 appear so very radical an operation. 



If we calculate the various units obtained by this change in 

 the time unit and compare them with the quadrant-volt- 

 second units, we shall find (column V.) that mass, length, and 

 quantity of electricity remain unaltered ; time and conduc- 

 tivity become ^q ; velocity, momentum, current, resistance, 

 magnetic field, pole, and magnetic moment, 30 times ; force, 



