Dimensions of Physical Quantities. 109 



M, L, T, and of either electrical quantity or the strength of a 

 magnetic pole. My suggestion amounts to nothing more 

 than that we should use a similar list in which the unknown 

 quantities are K and fi instead of e and m. The dimensions 

 in terms of L, M, and T will then be those in the electrostatic 

 and electromagnetic systems, and, instead of suppressing K and 

 /i, we should retain them as representing dimensions which are 

 unknown in terms of the fundamental units. 



In cases where it is necessary to indicate whether the 

 quantity represented by a symbol is understood to be expressed 

 in terms of K or /a, we may use the letters s and m subscript 

 to distinguish between them. Thus eg and Bm are not quantities 

 whose dimensions are fundamentally different, but quantities 

 the dimensions of which are unknown and are expressed in dif- 

 ferent ways in terms of other unknowns. The letters s and m 

 indicate which of the two methods which are in practical use 

 is employed. 



By equating two such expressions for the same quantity, or 

 by using any general relation between any two of the derived 

 quantities, we get a necessary relation between the dimensions 

 of the secondary fundamental units in terms of the primary 

 fundamental units of length, mass, and time. 



Thus we have from any one of Maxwell's equations (1) to 

 (12) (p. 241) the general relations 



[em] = [ML2T-i]. 



If we choose to express e in terms of K and m in terms of 

 /Lt, the relation still obtains, and thus 



[e m] = [M^ L^ T-i K^] x [M' L' T-^ /a*] = [M P T'^] ; 

 .-. [K-i^-] = [LT-^]. 



It is obvious that there must be such a relation, for since 

 only one equation is wanting for the complete determination 

 of the dimensions in terms of L, M, and T, we cannot have 

 two independent methods of expressing them. 



If, then, we use the letters s and m subscript in the sense 

 above explained, 



{es mm ] = [M^ L^ T-i K^] X [M* L^ T-i fx^], 

 [bs m,] = [M* L^ T-i K*] X [M* L^ K"^], 

 [e^?n,] = [M^L>-^] X [M^L*K-*], 

 [e^ m„] = [M' 11 ^-^] X [M^ L"^ T-i /.*] ; 



