124 LECTURES TO SCIENCE TEACHERS. 



will endeavour to explain in a few words. Suppose this circle 

 to represent the earth, which for simplicity's sake I will 

 suppose to be of uniform density throughout. Newton 

 divided the earth into concentric shells, and he proved that 

 the total gravitation of each shell would ba equal to the 

 mass of the shell concentrated in the geometrical centre of 

 the earth. The sum of all the shells would therefore give the 

 total gravitation of the earth. That being so, it is easy to 

 conceive that in going away from the surface of the earth, 

 ascending over it or descending below it, would materially 

 affect the result of the total gravitation ; but it does not 

 follow from this mode of viewing the question that moving 

 along the surface of the earth there would be any variation. 

 The centre of the earth would remain at the same distance, 

 and this being what is called the centre of gravity of the 

 earth, the total gravitation would, it might appear, remain 

 the same. Newton proved that the total gravitation of the 

 earth must vary as you approach from the equator towards 

 the poles. He proved mathematically and indicated the 

 means of ascertaining practically that the poles must be 

 depressed, and this depression would bring the poles nearer 

 to the centre, and therefore at the poles there would be a 

 greater total gravitation. But there is another reason 

 which Newton also pointed out why gravitation should be 

 less towards the equator than towards the pole, and that 

 is the centrifugal force generated by the rotation of the 

 earth. Both these causes the depression of the poles and 

 the rotation of the earth tend to diminish gravitation 

 towards the equator, and the ratio of increase of the total 

 gravitation towards the poles proceeds in the ratio expressed 

 by the square of the sine of the latitude ; therefore in 

 looking at the state of science with regard to gravitation 

 I did not find much help towards the solution of my 

 problem, and I found it necessary to try another mode of 

 viewing the same. There can be no doubt about this, that 

 the total gravitation of the earth is composed of the gravi- 

 tation of each portion of it. 



Then, in order to calculate the amount of variation that 

 will be produced in the total attraction of the earth, by a 

 given depth of water below the attracted point P, a line is 

 drawn from that point to the centre of the earth, and the 

 same is divided into an unlimited number of indefinitely 



