Page:Elementary Text-book of Physics (Anthony, 1897).djvu/23

§ 9] angle between two of its positions is measured in degrees on the arc of the circle. For greater accuracy, the readings may be made by the help of a vernier. To facilitate the measurement of an angle subtended at the centre of the circle by two distant points, a telescope with cross-hairs is mounted on the movable arm.

In theoretical discussions the unit of angle often adopted is the radian, that is, the angle subtended by the arc of a cirule equal to its radius. In terms of this unit, a semi-circumference equals π = 3.141592. The radian, measured in degrees, is 57° 17' 44.8."

8. Dimensions of Units.— Any derived unit may be represented by the product of certain powers of the symbols representing the fundamental units of length, mass, and time.

Any equation showing what powers of the fundamental units enter into the expression for the derived unit is called its dimensional equation. In a dimensional equation time is represented by $$T$$, length by $$L$$, and mass by $$M$$. To indicate the dimensions of any quantity, the symbol representing that quantity is enclosed in brackets.

For example, the unit of area varies as the square of the unit of length; hence its dimensional equation is $$[area] = L^2$$. In like manner, the dimensional equation for volume is $$[vol.] = L^3$$.

9. Systems of Units.— The system of units adopted in this book, and generally employed in scientific work, based upon the centimetre, gram, and second, as fundamental units, is called the centimetre-gram-second system or the C. G. S. system. A system based upon the foot, grain, and second was formerly much used in England. One based upon the millimetre, milligram, and second is still sometimes used in Germany.