Systems of Physical Units. 109 



of heat Q, 



A=Qw. 



The dimensions of Q are 



[A] 



M 



"We usually put 



„ _ metre x kilogramme (force) 



kilogramme (^mass) x degree 0. x capacity of water 

 = 424 X 3-281x|( = 773) F English foot x English poundfforce) _ 

 9V J Engl.pouncl(mass) x deg.l . X capac.oi water 



This value does not agree with either of the two ordinary 

 mechanical systems, since both the unit of force and the unit 

 of mass are here fundamental units. But if we introduce either 



_ -, ., ,„ x A d-i metre x kilogr. (mass) 



1 kilogramme (force) = 9-81 x -, ^W -t 



° v J (second) - 



or 



„ , ., , N 1 (second) 2 x kilogr. (force) 



1 kilogramme (mass)= -^-^ * — : — -^ — s -> 



° v J 9-81 metre 



we obtain in both cases 



Q=424x9'81(=4160) — — ■. ^etre) 2 



v sec. - x degree U. x capacity of water 



which value may be employed either with the Grauss-Weber 

 system or with the gravitation system. 



In stating physical magnitudes, we frequently see arbitrary 

 units employed besides the absolute units: it is important in 

 using such units to state their names completely, the names 

 being often formed according to the theory of dimensions. 



Example. — Electrolytic (chemical) unit of current 



cubic centim. of electrolvtic gas milligramme copper 



= -. — - l ^- or 5 — -. — - £±— . 



minute minute 



The rules for the reduction to new units are then always 

 applicable, as the above examples in heat show, and render the 

 calculation rapid and certain. 



Helsingfors, January 1881. 



Postscript. — After the above was in type the author became 

 acquainted with Dr. Herwig's work, Physikalische Begriffe und 

 absolute Maasse (Leipzig, 1880). The units of the science of 

 heat are stated somewhat differently by Herwig : the equiva- 

 lent Q is first eliminated, so that the units of quantity of heat 

 and of work become identical] secondly, the capacity of water 

 is taken as a conventional unit, and its name is omitted from 

 the dimensions. 



