the Solid Crust of the Earth. 281 



force equal to one millionth of a grain weight. No doubt its 

 neighbour, by friction and viscosity, might be induced to move 

 on with it. But suppose one were acted on by a force of one 

 whole grain plus one millionth of a grain, and the other by one 

 grain in the opposite direction. If the particles were rigidly 

 connected the pair would move on as before, as the difference of 

 forces is the same. But if they are fluid particles, however vis- 

 cous, they would part company. Now this represents the con- 

 dition to which the particles of the earth's mass are perpetually 

 being subjected, as I propose now to show. 



2. Let S be the mass of the sun, c its distance from the earth's 

 centre ; let the axis of x be drawn through the sun from that 

 centre as origin, the plane of xy being the ecliptic. 



The attraction of the sun on any particle of the earth's mass 

 is S -5- (distance) 2 towards the sun. The disturbing force of the 

 sun on this particle relatively to the earth's centre is the resultant 

 of this force and a force S -f- c 2 acting on the particle parallel to 

 the axis of x, away from the sun. When these two forces are 

 resolved parallel to the axes of coordinates, very small quantities 

 of the second order being neglected, and S^-c 3 put = fi, and 

 forces tending from the earth's centre reckoned positive, the three 

 disturbing forces on the particle parallel to the axes are 



2/j, . x, —p .y, -fi. z. 



3. I will take the first of these first, viz. 2/uux parallel to x. 

 On the sun-side of the plane yz it is always positive ; on the op- 

 posite side it is always negative. The aggregate of the forces on 

 all the particles on the one side will produce a resultant force 

 drawing the earth's mass towards the sun^ and the resultant on 

 the opposite side will be an equal force drawing it in an oppo- 

 site direction. These two equal and opposite forces would act 

 at the same point in the plane yz (viz. the earth's centre) if the 

 earth's mass were symmetrically arranged about its centre. Owing 

 to the slight deviation from that arrangement, the first resultant 

 force will act at a point extremely near the centre, but not at the 

 centre ; and the'other force parallel to it at an equal distance on 

 the opposite side ; so that the two forces will produce a mecha- 

 nical " couple," with a very short " arm," the moment of which 

 will be a very small quantity, although the two forces are not so 

 small. I at present assume the earth's particles to be all rigidly 

 connected together. The couple will tend to make the earth 

 revolve round a diameter at right angles to the plane of the 

 couple and lying in the plane yz. 



The effect of the sun's action will therefore be to put the 

 earth's mass in a state of tension in the direction of the line 

 joining the earth and sun, tending every instant to separate the 



