122 



POPULAR SCIENTIFIC LECTURES. 



we have penetrated into the interconnections 

 of natural phenomena. And that the general 

 laws, which we have found, also hold for the 

 most distant vistas of spaco, has acquired 

 wtrong actual confirmation during the past 

 half-century. 



In the front rank of all, then, is the law of 

 gravitation. The celestial bodies, as you all 

 know, float and move in infinite space. 

 Compared with the enormous distances be- 

 tween them, each of TIS is but as a r--un of 

 dust. The nearest fixed stars, vie^ oJ even 

 under the most powerful magnification, have 

 no visible diameter ; and we may be sura 

 that even our sun, looked at from the near- 

 est fixed stars, would only appear as a single 

 luminous point ; seeing that the masses of 

 l lios stars, in so far as they have been de- 

 termined, have not been found to be 

 materially different from that of the sun. 

 But, notwithstanding these enormous dis- 

 t-inof-s, there is an invisible tie between them 

 which connects them together, and brings 

 them in mutual interdependence. This is 

 the force of gravitation, with which all heavy 

 masses attract each other. We know this 

 force as gravity, when it is operative between 

 an earthly body and the mass of our earth. 

 The force which causes a body to fall to the 

 ground is none other than that which con- 

 tinually compels the moon to accompany the 

 earth in its path round the sun, and which 

 keeps the earth itself from fleeing off into 

 space, away from the sun. 



Yon may realize, by means of a simple 

 mechanical model, the course of planetary 

 motion. Fasten to the branch of * tree, at n 

 Hufficient height, or to a rigid bar, fixed hori- 

 jsontally in the wall, a sili cord, and at its end 

 a small heavy body for instance, a lead ball. 

 If you allow this to hang at rest, it stretches 

 the thread. This is the position of equilibri- 

 um of the ball. To indicate this, and keep 

 it visible, put in the place of the ball any 

 other solid body for instance, a large terres- 

 trial globe on a stand. For this purpose the 

 ball must bo pushed aside, but it presKea 

 against tho globe, and, if taken away, it still 

 tends to come back to it, because gravity im- 

 pels it toward its position of equilibrium, 

 which i.s in the centre of the sphere. And 

 upon whatever wide it is drawn, the same 

 thing always happens. This force, which 

 drives the ball toward the globe, represents 

 in our model the attraction which the earth 

 ?xerts on the moon, or the sun on the plan- 

 ets. After you have convinced yourselves of 

 the accuracy of these facts, try to give the 

 Ixall, when it is a little away from the globe, 

 a slight throw in a lateral direction. If you 

 have accurately hit the strength of the throw, 

 the small ball will move round the large one 

 in a circular path, and may retain thin motion 

 for S3iu3 time ; just as the moon persists in 

 its coursa round the earth, or the planets 

 about the sun. Now, in our model, the cir- 

 cles described by the lead ball will bo con- 

 tinually narrower, because the opposing 

 forces, tho resistance of the air, the rigidity 

 of the thread, friction, cannot be eliminated, 



in this case, as they are excluded in the plan- 

 etary system. 



If the path about tho attracting centre is 

 exactly circular, tho attracting force always 

 acts on the planets, or on the lead sphere, 

 with equal strength. In this case, it is im- 

 material according to what law the fore* 

 would increase or diminish at other distance* 

 from the centre in which the moving body 

 does not come. If the original impulse ha* 

 not been of the right strength in both case*, 

 the paths will not be circular but elliptical, 

 of the form of the curved line in Fig. 3. 

 But these ellipses lie in both cases differently 

 as regards the atiractiug centre, lu our 

 model, the attracting force is stronger, 

 the farther the lead sphere is removed 

 from its position of equilibrium. Under 

 these circumstances, the ellipse of the 

 path has such a position in reference to 

 the attracting centre, that this, is in th 

 centre, c, 01 the ellipse. For planets, 

 on the contrary, tho attracting force is feebler 

 the farther it is removed from the attracting 

 body, and this is tho reason that an ellipsa 

 in described, one of whose foci lies in th 

 contra of attraction. The two foci, a and 

 b, aro two points which lio symmetrically 

 toward tho ends of tho ellipse, and are 

 characterized by tho property that the sum 

 of their distances, am -f- bin, is the same t'rou* 

 any given points. 



Kepler had found that the paths of th 

 planets are ellipses of thin kind ; and since, 

 as tho above example shows, tho form ami 

 position of th orbit depend on tho law a"- 

 cording to which the magnitude of the at- 

 tracting force alters, Newton could deduce 

 from the form of tho planetary oibits th* 

 well-known law of tho force of gravitation, 

 which attracts the planets to the sun, accord- 

 ing to which this forc-j decreases with in- 

 crease of distance as the square of that dis- 

 tance. Terrestrial giavity must obey tliin 

 law, and NoM'ton had tho wonderful self- 

 denial to refrain from publishing his impor- 

 tant discovery until it had acquired a direct 

 eonnrmation ; this followed from the obser- 



