382 Dr. Gr. Johnstone Stoney on the 



2. Hitherto the practice of mathematicians has been governed 

 by the demands of the science of mechanics, in the greater 

 part (though not in the whole) of which science it is possible 

 to derive the units of all the other kinds of quantity from any 

 three which may be chosen. A system built in this way upon 

 a foundation which is arbitrarily assumed is necessarily an 

 artificial system. The units which are usually selected as the 

 fundamental units of a series of arbitrary systematic measures 

 are : — 



the metre* for lengthine, or unit of length ; 

 the gramme for massine, or unit of mass ; and 

 the solar second for timine, or unit of time. 



These three, and all the units which may be derived from 

 them, may be called the metric series of units ; and in this 

 investigation they will be represented by small letters. Thus, 

 the fundamental metric units being 



t 1} the metre, the metric lengthine, or unit of length ; 

 t 1} the solar second, the metric timine, or unit of time ; 

 m x , the gramme, the metric massine, or unit of mass ; 

 some of the derived units will be: — 



Vij the metric velocitine, or unit of velocity, which is a velo- 

 city of one metre per second ; 

 f lf the metric forcine, or unit of force, which is the hyper- 

 decigramme | — this being the force which, if it acted in 

 a fixed direction on a mass of one gramme for a second, 



* Since this paper was written the centimetre has been suggested as a 

 unit of length, and has been largely made use of. 



t The hyper-decigramme means the gravitation or downward force 

 towards the earth of a mass which exceeds a decigramme in the ratio of 



10 



— , where g is the acceleration of gravity measured in metres per second per 



second. The appropriateness of the term hyper-decigramme arises from the 



10 

 circumstance that the coefficient — everywhere exceeds unity, whether 



within the earth, outside it, or on its surface ; and the convenience of the 

 term arises from the circumstance that on the earth's surface the coefficient 

 nowhere exceeds unity by more than a small fraction, so that the hyper- 

 decigramme is a force which but little differs in value from that gravita- 

 tion or weight of a decigramme with which we, inhabitants of the earth, 

 have become familiar ; so that the name suggests to us the amount of the 

 force. Gravitation is the downward force, and gravity is the downward 

 acceleration towards the earth as observed. They are chiefly due to the 

 attraction of the earth, and in a small degree, when the observation is 

 made on or within the earth, to the earth's rotation. This is the meaning 

 of the word gravity as it is used by the classical writers on mechanics (see 

 Pouillet's Mecanique, passim) ; and the practice of some modern writers, 

 who use this term to designate a force instead of an acceleration, is to be 

 deprecated. 



