256 Mr. W. Williams on the Relation of Dimensions 



6. A=ET=/* I [M I RT- 1 (X-*Y~*Z 1 )]. 



7. C =HY= A 6-*[M"RT- 1 (X" i Y l Z-*)]. 



8. C =C(YZ)- 1 =^[M*RT- 1 (X- | Y- | Z- i )]. 



9. e =CT=^[M*R(X- | Y*Z- 1 )]. 



10. D =CT=^(YZ)- 1 = . w - | [M*R(X-*Y-^Z- f )]. 



From 5 and 10 we have 



and substituting & -1 [Z _2 T 2 ] for p all through in the above 

 we get for each quantity its electrostatic dimensions, the 

 results being identical with those obtained directly as below. 



II. Electrostatic System : — 



w=MR a ar i (XYZ)- 1 . 



1. E = ^[M^RT-^XYZ)-*]. 



2. D =kE = ^[M^RT-^XYZ)" 1 ]. 



3. e =D(YZ)=#[M I RT- 1 (X- | Y I Z 1 )]. 



4. C=^T" 1 =:#[M*RT- 2 (X- | Y I Z 1 )]. 



5. C =C(YZ)~ 1 = ^rM^RT-^X-^Y-'Z" 1 )]. 



6. H = C(Y~ 1 ) =^[M I RT- 2 (X" § Y- | Z 1 )]. 



7. E =E(X)=^[M § RT- 1 (X*Y- | Z- 1 )]. 



8. m =p=ET= ^-*[M I R(X*Y-*Z-*)]. 



9. B =w(XZ)" 1 =^- | [M l E(X- | Y- | Z- 1 )]. 



10. A =ET=* _l [M l R(X- | Y-*Z-i)]. 



From 6 and 9 we have 



and by substituting /«,— x [Z~ 2 T 2 ] all through for h in the 

 above, we recover the electromagnetic dimensions previously 

 deduced. 



The following are examples of the manner these formulae 

 work out : — 



