Introducing time, denoted by *T*, it is easy to see that the dimensions of velocity will be *L/T* or *LT*^{-1}, because the number of units in the velocity of a body is found by *dividing* the units of length passed over by the units of time occupied in passing. The acceleration of a body is measured by the increase of velocity in relation to the time, that is, we must divide the units of velocity gained by the units of time occupied in gaining it; hence its dimensions will be *LT*^{-2}. Momentum is the product of mass and velocity, so that its dimensions are *MLT*^{-1}. The effect of a force is measured by the acceleration produced in a unit of mass in a unit of time; hence the dimensions of force are *MLT*^{-2}. Work done is proportional to the force acting and to the space through which it acts; so that it has the dimensions of force with that of length added, giving *ML*^{2}*T*^{-2}. It should be particularly noticed that angular magnitude has no dimensions at all, being measured by the ratio of the arc to the radius (p. 305). Thus we have the dimensions *LL*^{-1} or *L*^{0}. This agrees with the statement previously made, that no arbitrary unit of angular magnitude is needed. Similarly, all pure numbers expressing ratios only, such as sines and other trigonometrical functions, logarithms, exponents, &c., are devoid of dimensions. They are absolute numbers necessarily expressed in terms of unity itself, and are quite unaffected by the selection of the arbitrary physical units. Angular magnitude, however, enters into other quantities, such as angular velocity, which has the dimensions 1/*T* or *T*^{-1}, the units of angle being divided by the units of time occupied. The dimensions of angular acceleration are denoted by *T*^{-2}.