Gravity , or Gravitation (Lat. gravitas, weight), in physics, the tendency of bodies toward each other or toward a centre of attraction. In the article Astronomy we have considered the history of the discovery of the great law of gravitation, and have sketched the application of the law to elucidate a variety of problems of interest connected with the motions of the celestial bodies; in the article Earth we have considered the application of this law to determine the mass and figure of the earth; and in dealing with the lunar motions, 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 be measured. We can examine its effect in causing 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 velocity 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 comparing 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 conditions of temperature, will fall (in vacuo) through the same space in the same time under the influence 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 temperatures. The method of measurement here indicated 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 arrangement 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. Contrivances have been invented by which the true rate of swing at any place, for a pendulum of known figure, can be most accurately ascertained. This being effected, it becomes possible to compare the action of gravity at different 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 centrifugal force due to the earth's rotation; an objectionable 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 diminished by this tendency; and being most diminished at the equator, gravity is there least on this account, and gradually increases toward 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 1/289 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 Earth), yet under the actual circumstances 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 1/599. Combining the two effects, we obtain for the total decrease of gravity at the equator: 1/599+1/289=1/195. 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-homogeneity of the earth's substance (near the place of observation), as the existence of cavities, of great masses of unusual density, and so on. The following table shows the results obtained by Capt. Kater in different parts of the British isles:

PLACE OF

OBSERVATION.

Latitude.

Longitude.

Vibrations in a mean solar day.

Length of the pendulum vibrating seconds.

Frist..........

60° 45'

28.01"

86,096.90

39.17146

Portsoy.......

57 40

58.65

86,086;05

39.16159

Leith Fort.....

55 58

40.80

86.079.40

39.15554

Clifton........

53 27

43.12

86.068.90

39.14600

Arbury Hill ...

52 12

55.32

86,065.05

39.14250

London .......

51 31

8.40

86.061.52

39.13929

ShanklinFarm.

50 37

23.94

86,058.07

39.13614

Deducing from these values the velocity acquired 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:

OBSERVER.

Place.

Latitude.

Length of pendulum vibrating seconds, in inches.

Velocity in feet acquired in one secend by a body falling from rest.

Sabine...................................

Spitzbergen............

N. 79° 50'

39.21469

32.2528

Sabine.......................................

Hammerfest..

70 40

39.19475

32.2363

Svanberg ...................................

Stockhoim.......

59 21

39.16541

32.2122

Bessel.......................................

Konigsberg............

54 42

39.15072

32.2002

Sabine.......................................

Greenwich.............

51 29

39.13988

32.1912

Borda, Biot, and Sabine.......................

Paris..................

48 50

39.12851

32.1819

Biot....................... ............

Bordeaux..............

44 50

39.11296

32.1691

Sabine.......................................

New York.............

40 43

39.10120

32.1594

Freycinet.......

Sandwich islands.......

20 52

39.04690

32.1148

Sabine.......................................

Trinidad...............

10 39

39.01888

32.0913

Freycinet........

Rawak................

S. 0 2

39.01433

32.0880

Sabine and Duperrey.......

Ascension .............

7 55

39.02363

32.0956

Freycinet and Duperrey......................

Mauritius...............

20 10

39.04684

32.1151

Brisbane and Rumker........................

Paramatta.............

33 49

39.07432

32.1375

Freycinet and Duperrey......................

Falkland islands.......

51 35

39.13781

32.1895

From these values the following very simple and convenient formula has been deduced : If L denote the length of a seconds pendulum at any latitude Gravity 0800125 and 39.017 inches be the length of a seconds pendulum at the equator, then L=39.017 +0.200 sin 2 Gravity 0800126