Page:Elementary Text-book of Physics (Anthony, 1897).djvu/87

 bodies, which have a centre of gravity even when the forces are not parallel, are called centrobaric bodies.

60. Measurement of the Force of Gravity.—When two bodies attract each other, their accelerations relative to their fixed centre of mass are inversely as their masses. In the case of the attraction between the earth and a body near its surface, the mass of the earth is so great that its acceleration may be neglected and the acceleration of the body alone need be considered. Since the force acting upon it varies with its mass, and since its gain in momentum also varies with its mass, it follows that its acceleration will be the same, watever its mass may be. We may, therefore, obtain a direct measure of the earth's attraction, or of the force of gravity, by allowing a body to fall freely, and determining its acceleration. It is found that a body so falling at latitude 40° will describe in one second about 16.08 feet, or 490 centimetres. Its acceleration is therefore 32.16 in feet and seconds or 980 in centimetres and seconds. We denote this acceleration by the symbol $$g$$.

The force acting on the body, or the weight of the body, is seen at once to be $$mg$$, where $$m$$ is the mass of the body.

On account of the difficulties in the employment of this method, various others are used to obtain the value of $$g$$ indirectly. For example, we may allow bodies to slide or roll down a smooth inclined plane, and observe their motion. The force effective in producing motion on the plane is $$g \sin{\phi}$$, where $$\phi$$ is the angle of the plane with the horizontal; the space traversed in the time $$t$$ is $$s = \tfrac{1}{2}gt^2 \sin{\phi}$$ By observing $$s$$ and $$t$$, the value of $$g$$ may be obtained. The motion is so much less rapid than that of a freely falling body that tolerably accurate observations can be made. Irregularities due to friction upon the plane and the resistance of the air, however, greatly vitiate any calculations based upon these observations. This method was used by Galileo in his investigation of the laws of falling bodies.

The most exact method for determining the value of $$g$$ is based upon observations of the oscillation of a pendulum.

A pendulum may be defined as a heavy mass, or bob, suspended