Systems of Physical Units. 103 



where e is to be taken in accordance with equation (42). The 

 fundamental law may then also be written 



9. Systems with two fundamental units result by elimina- 

 ting one constant from the fundamental equations for systems 

 with three units. Various systems with two fundamental 

 units may be formed by elimination of the constant of attrac- 



'615 metre 3 



sec. 2 x kilogr. 

 put 



n , ... 615 metre 3 615 millim. 3 .... 



tion. If in the value of this constant ( ^7^ ~i — n ) we 



V10 id sec/x kilogr./ 



this constant becomes unity, and we obtain a system with the 

 two fundamental units of length and time. The unit of mass 

 derived from the metre and the second is consequently 



- metre 3 10 13 , ., 



1 tk = 773-^ kilogramme. 



second 2 615 & 



The unit of force 1 kilogramme (Paris) 



— q «n«^°» r ' x me ^ re _ 9*808 x 615 metre 4 

 - J ' W * ( secon d)* ~ TO 11 "s^cT" ; 



consequently the new unit of force is 



, metre 4 10 13 .'„ /-p • \ 



1 ^nd 4 " = 9-808x615 kllo g™ mme ( Pa ™)- 



This system is employed for attraction-problems by Thomson 

 and Tait (< Theoretical Physics/ § § 459, 774)*. The densityf 



of water ( = 1000 — 7^-3') becomes in this system ^^ ~ 



v metre 3 J 10 10 sec. 2 



(thus independent of the unit of length). In order to com- 

 pare this number with the number given by Thomson and Tait 



(§ 774) we must multiply it by ■%-=, since Thomson and Tait 



put the mean specific gravity of the earth equal to 5"5. We 



* Compare also H. Weber and Kohlrausch (Zollner, Prineipien einer 

 eleMrodynamischen Theorie, p. 129); Maxwell, 'Treatise on Electricity 

 and Magnetism,' vol. i. p. 4. 



t Density is here taken to mean mass of unit volume of the substance 

 (Maxwell, p. 5). 



