Resistance according to an absolute Standard. 267 



absolute unit of measure of the momentum of rotation (the pro- 

 duct of a millimetre into that force which in one second imparts 

 to the mass a milligramme, the absolute unit of measure of 

 velocity), if M is the absolute unit of measure of the magnetic 

 fluid, and J is the absolute measure for intensities ; if, further, P', 

 M f , and J' are the measures actually used, 



PM'J' 

 ^~ P'MJ ; 



consequently, using the absolute measure, /3=1. 



3. Ampere's fundamental law of electrodynamics represents 



the electrodynamic force of attraction F as an expression of the 



intensities of two elements i and i', and of a number which is 



fixed by the relations of the lengths of the two elements to their 



ds ds 

 distance — , — ; and by the three angles e, 0, 6\ which ds and 



ds' form with one another and with r ; that is, if the constant 

 whose value is to be determined from the given measures is 

 designated by 7, 



F = 



.., dsds' I 3 a a \ 



7 . iv . ( cos e — - cos cos & ). 



rr \ 2 / 



The constant 7 has the following signification : — If F is the abso- 

 lute measure of force (that force which in a second imparts to 

 the mass of a milligramme a velocity of a millimetre in a 

 second), if J is the absolute measures for intensities, and F', J' 

 the measures actually used, we get 



7 = 



FJM' 

 F'JJ 



hence using the absolute measure, 7 = ?*. 



4. The fundamental law of magneto-induction represents the 



electromotive force e as an expression of the mass of magnetic 



fluid /A, of the velocity of induced motion c, of the length of 



the induced element ds, and of its distance r from /j,, and of a 



number given by the two angles <f> } ty which ds makes with r 



and c with the normal to the plane rds ; that is, if the constant 



whose value is to be determined from the measures chosen is 



called S, 



steeds . , , 



e = o sin d> cos -dr. 



rr ' 



The constant 8 has the following signification : — If E is the abso- 

 lute unit of measure of electromotive force, M the absolute unit 

 of measure of magnetic fluid, S the seconds of time, and E',M',S' 



T2 



