176 GRAVITY tions, we shall have to consider more in detail the perturbative action of gravity. In the present place, therefore, we limit ourselves to the consideration of terrestrial gravity in its effects on bodies upon or close to the surface of the earth. There are two ways in which the action of gravity at any station can bo measured. We can examine its effect in caus- ing bodies to have weight ; this is the statical action of gravity. Or we can consider its effect upon bodies let fall to the earth ; the ve- locity acquired in a given time affords the means of estimating this, the dynamical action of gravity. For many reasons the latter is the more convenient method of measuring it. The balance, the readiest and most trustworthy method of weighing bodies, obviously fails us when the measurement of the effect of gravity is in question, since the weight and the body weighed are equally under its influence. Nor can the spring balance be trusted for compar- ing the action of gravity at different stations, even though the utmost precaution has been exercised in freeing the instrument from the disturbing influences of differences or changes of temperature. No difficulties of this sort attend the dynamical method of measuring gravity; because bodies of different specific gravity, or the same body in different condi- tions of temperature, will fall (invacuo) through the same space in the same time under the in- fluence of gravity. The resistance of the air may indeed be neglected where the difference of specific gravity is very small, as in the case of the same mass of metal at different tempera- tures. The method of measurement here in- dicated is however comparatively rough. It was that used by Galileo to determine the time of fall of bodies under the influence of gravity, and by means of the mechanical ar- rangement called Atwood's machine it can be applied to obtain a fair approximation to the velocity acquired in a given time. But for all delicate researches the pendulum is employed. It is known that when a pendulum swings in a short arc its rate of swing is appreciably constant (though the small arc should vary), and depends on the length and figure of the pendulum and the action of gravity. Contri- vances have been invented by which the true rate of swing at any place, for a pendulum of known figure, can be most accurately ascer- tained. This being effected, it becomes possi- ble to compare the action of gravity at differ- ent terrestrial stations. Gravity varies on the earth's surface owing to two principal causes. In the first place, the earth is rotating, and every point on its surface therefore has a tendency (constantly overcome by gravity) to move in a straight line tangent to the earth's surface. This tendency is commonly called the centrif- ugal force due to the earth's rotation ; an ob- jectionable mode of expression, because no force properly so called is in question. The tendency is mere inertia. If the tendency were the same at all stations, gravity would be uniformly affected, and no difference would accrue; but the tendency is greatest at the equator, where the motion is most rapid, and diminishes thence to the poles, where it is zero. The action of gravity in producing weight or in causing the fall of a body is obviously di- minished by this tendency; and being most diminished at the equator, gravity is there least on this account, and gradually increases to- ward the poles. It is estimated that, so far as this cause alone is concerned, gravity at the equator should be less than at the poles by ^ part. But secondly, owing to the same cause (the rotation of the earth), the terrestrial globe is not a perfect sphere, but is compressed at the poles. Hence a body placed at a pole of the earth is nearer to the centre of gravity than a body placed at the equator ; and though this cause alone would not suffice to render the action of gravity greater on the body at the pole, since at the bottom of a mine gravity may be and usually is less than at the mouth (see EAETH), yet under the actual circum- stances a body at the pole is on the whole brought under the more effective action of gravity. A complete mathematical comparison of the attractions under the two conditions shows that gravity at the equator, so far as the cause we are now considering is concerned, is less than gravity at the poles by about -^fa. Combining the two effects, we obtain for the total decrease of gravity at the equator: y^+^zs-j^y. In other words, if gravity at the poles be represented by 195, gravity at the equator will be represented by 194. Minor causes exist, which however need not here be taken into consideration. We may simply mention that they arise from the non-homo- geneity of the earth's substance (near the place of observation), as the existence of can- ties, of great masses of unusual density, and so on. The following table shows the results ob- tained by Capt. Kater in different parts of the British isles : PLACE OF OBSERVATION. Latitude. Longitude. Vibrations in a mean golar day. Leu-thofthe pendulum vibrating lecondg. TJnst 60 45' 28-01" 86096-90 89-17146 Portsoy Leith Fort Clifton Arbury Hill . . . London Shanklin Farm . 57 40 55 53 58 27 52 12 51 81 50 87 58-65 40-80 43-12 55-32 8-40 23-94 86,086-05 86,079-40 86,068-90 86,065-05 86,061-52 86,058-07 39-16159 89-15554 89-14600 89-14250 89-13929 89-18614 Deducing from these values the velocity ac- quired by a body in falling, Capt. Kater found that a body falling at Leith Fort would acquire in one second a velocity of 32-207 feet per second ; and that the variation in this velocity for one degree of difference of latitude is at Leith only -0000832 of its own amount. The following table gives the length of the seconds pendulum at different places, and the value of the accelerating force of gravity according to Sir George Airy :
