Quantity 
Physical law 
Variation equation 
Definition of derived unit 
Derived unit 
Dimensional equation 
Length, l Mass, m Time, t 
FUNDAMENTAL ARBITRARY UNITS 
Centimetre, cm Gramme, gm Second, sec


Area, A. 
The areas of similar figures are proportional to the second power of their linear dimensions. 
A l^{2} 
The area of a square the length of a side of which is i centimetre. 
Sq. cm. 
[A]=[L]^{2} 
Volume, V. 
The volumes of similar solids are proportional to the third power of their linear dimensions. 
V l^{3} 
The volume of a cube the length of a side of which is 1 centimetre. 
C.c. 
[V]=[L]^{3} 
Density, d 
The mass of a body is proportional to its volume and its density conjointly (Definition of Density). 
m v d 
The density of a body of which the mass of 1 cubic centimetre is 1 gramme. 
Gm. per c.c. 
[D]=[M][L]^{3} 
Velocity, v. 
The space passed over by a body moving uniformly is proportional to the velocity and the time of passage. 
s v t 
The velocity of a body moving so that it passes over 1 centimetre in a second. 
Cm. per sec. 
[v]=[L][t]^{1} 
Acceleration, a 
The increase in the velocity of a body moving with a constant acceleration is proportional to the acceleration and the time, during which the motion has been accelerated. 
v a t 
The acceleration of a body whose velocity is increasing every second by 1 cm. per sec. 
Cm. per sec. per sec. 
[a]=[L][T]^{2} 
Force, f 
The force which produces change of motion in a body is proportional to the rate of change of momentum produced (the rate of change of momentum being measured numerically by the product of the numerical measure of the mass of body, and the numerical measure of the acceleration produced (second law of motion) 
f m a 
The force which acting upon 1 gramme produces per sec. an acceleration of 1 cm. per sec. 
Dyne 
[F]=[M][L][T]^{2}.

Work or energy, w 
The work done by a force is proportional to the force and to the distance through which it moves its point of application. The energy of a body is its capacity for doing work, measured by the work to which it is equivalent. 
w f l 
The work done by a dyne when it has moved its point of application through 1 centimetre. 
Erg. 
[W]=[M][L]^{2}[T]^{2}

Pressure, (tension), p 
The force exerted by a fluid upon a given area is proportional to the area and to the pressure of the fluid at any point of the area, this pressure being supposed uniform over the area. 
f p A 
The pressure exerted when the force on every sq. cm. of area is 1 dyne. 
Dyne per sq. cm. 
[P]=[M][L]^{1}[T]^{2} 
Volume elasticity, e 
The fractional diminution in volume of a fluid under increased pressure is proportional directly to the increase of pressure and inversely to the elasticity of the fluid. 
(v_{1}v_{2})/v_{1} = (p_{2}p_{1})/e 
The elasticity of a body such that an unit diminution of pressure would double the volume. 

[E]=[P]=[M][L]^{1}[T]^{2} 

MAGNETIC UNITS. 




Strength of magnetic pole, μ 
The force between two magnetic poles is proportional to the product of the strengths of the poles and inversely proportional to the square of the distance between them. 
f μμ'/l^{2} 
That pole which repels an equal and similar pole at a distance of 1 cm. with a force of 1 dyne. 
C.G.S. unit magnetic pole. 
[μ]=[M]^{0.5}[L]^{1.5}[T]^{1} 
Strength of a magnetic field, H. 
A magnetic pole, when placed in a magnetic field, is acted upon by a force proportional to the strength of the pole and the strength of the field. 
f H μ 
That field in which a C.G.S. unit magnetic pole is acted upon with a force of 1 dyne. 
C.G.S. unit magnetic field. 
[H]=[M]^{0.5}[L]^{0.5}[T]^{1} 
Magnetic moment of a magnet, M. 
The magnetic moment of a solenoidal magnet is proportional to the strength of each pole and the distance between them. 
M μ l 
The moment of a solenoidal magnet with poles of 1 C.G S. unit strength and length 1 centimetre. 
C.G.S. unit of magnetic moment. 
[m]=[M]^{0.5}[L]^{1.5}[T]^{1} 

ELECTROMAGNETIC UNITS 




Current c. 
The force acting upon a magnetic pole at the centre of a circular arc of wire carrying a currrent, is proportional to the strength of the current, the length of the wire, and the strength of the pole, and inversely proportional to the square of the radius of the arc. 
f μ l c / r^{2} 
That current which, flowing along unit length of wire in the form of a circular arc of unit radius acts with a force of 1 dyne upon a magnetic pole of C.G.S. unit strength placed at the centre. 
C.G.S. electromagnetic unit current. 
[c]=[M]^{0.5}[L]^{0.5}[T]^{2} 
Electric quantity, q. 
The quantity of electricity which passes across any section of a wire is proportional to the current and to the time of passage. 
q c t 
The quantity which in one second crosses any section of a wire in which a C.G.S. unit current is flowing. 
C.G.S. electromagnetic unit of quantity. 
[Q]=[M]^{0.5}[L]^{0.5} 
Electromotive force or difference of potential, E. 
The work done by a quantity of electricity in passing between two points is proportional to the quantity and to the electromotive force or difference of potential between the points. 
w E q 
The E.M.F. between two points, such that the C.G.S. unit quantity of electricity in passing between the points does an erg of work. 
C.G.S. electromagnetic unit of E.M.F. 
[E]=[M]^{0.5}[L]^{1.5}[T]^{2} 
Resistance, r. 
The current passing between two points of a conductor is directly proportional to the electromotive force and inversely proportional to the resistance of the conductor between the points (Definition of Resistance). 
c E/r 
The resistance of a conductor in which the C.G. S. unit E.M.F. produces the C.G.S. unit current. 
C.G.S. electromagnetic unit of resistance. 
[R]=[L][T]^{1}=[V].

Capacity of a conductor, C 
The increase in the potential of a conductor produced by the addition of a given quantity to its charge is inversely proportional to the capacity of the conductor. 
E q/C 
The capacity of a conductor which is charged to 1 C.G.S. unit potential by 1 C.G.S. unit of electricity. 
C.G.S. electromagnetic unit of capacity. 
[C]=[L]^{1}[T]^{2}. 