INTRODUCTION TO ASTRONOMY. xliii 



It would be natural to suppose that the prominence at the equator and 

 depression at the poles would render the attraction of gravity stronger at 

 the former, so that a body would weigh heavier at the equator than at the 

 poles. Tin's, however, is erroneous. The manner in which the force of 

 gravity varies at different spots on the surface of the earth depends on 

 considerations too complicated to be here explained ; but the general 

 result is that, although the difference in different situations is very small, 

 the nearer any part of the surface is to the centre of attraction, the more 

 strongly it is attracted. We refer, however, only to any situation on the 

 surface of the earth. Were you to penetrate into the interior, the attrac- 

 tion of the parts above you would counteract that of the parts beneath 

 you, and consequently diminish the power of gravity in proportion as you 

 approached the centre ; and if you reached that point, being equally 

 attracted by the parts all around you, gravity would cease, and you would 

 be without weight. Bodies therefore gravitate less, and consequently 

 weigh less, at the equator than at the poles, while their centrifugal force 

 is much greater ; and as this force tends to drive bodies from the centre, 

 it is necessarily opposed to, and must decrease the power of gravity. 

 There are then two causes which render bodies lighter in weight at the 

 equator than at the poles : the diminution of gravitation, and the increase 

 of the centrifugal force. Men of science have travelled both to the equator 

 and to Lapland, with a view of ascertaining this fact. The severity of the 

 climate and the obstruction of ice has hitherto rendered every attempt to 

 reach the pole abortive ; but the difference of weight of a body at the 

 equator and in Lapland is very considerable. 



This difference cannot be discovered by simply weighing bodies; for if 

 the body under trial at the equator decreased in weight, the weight which 

 was opposed to it in the opposite scale must diminish in the same propor- 

 tion. For instance, if a pound of sugar did not weigh so heavy at the 

 equator as at the poles, the leaden pound which served to weigh it would 

 not be so heavy either ; therefore they would still balance each other. A 

 pendulum is the instrument used for the purpose of discovering the varia- 

 tions of gravity in different situations on the surface of the earth. A pen- 

 dulum consists of a line, or rod, to one end of which a weight is attached, 

 and it is suspended by the other to a fixed point, about which it is made 

 to vibrate. Without being put in motion, a pendulum, like a plumb-line, 

 hangs perpendicular to the general surface of the earth, by which it is 

 attracted ; but if you raise a pendulum on one side, gravity will bring it 

 back to its perpendicular position. It will, however, not remain sta- 

 tionary there, for the velocity it has received during its descent will impel 

 it onwards, and it will rise on the opposite side to an equal height: from 

 thence it is brought back by gravity, and again driven by the impulse of 

 its velocity. Were the motion of a pendulum not opposed by the resist- 

 ance of the air in which it vibrates, and by the friction of the part by which 

 it is suspended, it would be perpetual ; and were the force of gravity 

 which produces these vibrations always the same, they would be perfectly 

 regular, being of equal distances and performed in equal times. This is 

 the natural result of the uniformity of the power which produces these 

 vibrations: the force of gravity being always the same, the velocity of the 

 pendulum must consequently be uniform. But if the force of gravity is 

 less at the equator than at the poles, the vibrations of the pendulum will 

 be slower. 



It was thus that the difference of gravity was discovered, and the true 

 figure of the earth ascertained ; for after having _made due allowance for 



