September, 1910. 



KNOWLEDGE. 



339 



the particles that are near her harder than those 

 which are further from her, and somewhat in the 

 proportions given in 15. 



Now the effect in both cases, as far as urging the 

 Earth as a whole is concerned, will be precisel\" the 

 same for both sets. The great difference lies in the 

 fact that under the first set there is no strain at all. 

 while there must be strain in the second case. It 

 will be impossible from mere common sense and 

 experience to sav what sort of change of shape will 

 take place in case B, but there must be 

 some strain, and we shall presently shew 

 what its nature is. 



Of the two diagrams A and B we mav 

 sa\- briefly: A will shift the Earth as a 

 whole without distortion. B will shift it 

 in the same way, but with distortion. 

 A, therefore, represents for us all that is 

 in B. If we can subtract all that there is in A from 

 what there is in B, we shall have onl}' the distortion 



9? 



^ 



/oct 



Figure 



;le\-ant 



same ; .A-B represents a section through the earth, all 

 points of which are equi-distant from the Moon. 



In Figure 4 we have before us the simplest form 

 of the tide-generating forces produced by the 

 Moon's attraction, but the diagram is not really 

 complete, our intention being onh- to give a rough 

 idea of how the tides are produced. We can see 

 that the general effect is to urge every particle on the 

 near side of the Earth towards the point A, and 

 ever\- particle on the far side towards the point B, 

 and thus we account for the two tides. 

 Both form part of one single process, 

 and a teacher should therefore be care- 

 ful not to give any explanation for tide 

 at A which will not also explain the tide 

 at B. The student who confesses that 

 the tide on the far side is a mystery to 





■> 



on 

 not 



rightly 



understand the tide 



But how can one subtract one picture from another? 

 It is not difficult. Let us take the particle marked 

 P. In .\ it has a force of 100 on it ; in B it has 

 102. Subtracting A from B we shall have just a 

 force of ^w'o acting on P to the left. , 



It is that txco that makes for distor- 

 tion. That is at any rate easw 

 now take the particle O. 

 we have to subtract 100 

 98. We do it by recourse 

 expedient. In 

 two particles. 

 force 98 to the 

 by two forces. 

 2 to the right. 



But 

 Here 

 from 

 to a 



Figure 



, e 

 verv simple 

 3 we see 

 One is urged by a 

 left, and the other 

 100 to the left and 

 Surely both particles \\'\\\ behave 

 in exactly the same wa_\'. and so in 

 the case of Q we mav replace 98 



h\ 



100 to the left and 2 to the right. 



Then if we subtract 100 to the left, 

 we have left 2 ii) the ri'^ht. This then is the distort- 

 ing force on U. 



Carrying out the work on all the other particles in 

 the same way, we obtain the diagram of forces in 

 Figure 4. These are the tide-generating forces 

 produced by the Moon's attraction. 



It should be noted that onl_\- nine particles are 

 marked, and are taken as representing all the others. 

 The intensity of the Moon's attraction marked in 

 A (Figure 2) depends only on the distance that the 

 particle in question is from the Moon ; it does not 

 matter whether it is on the surface of the Earth or 

 in the interior. The force of gravity cannot be 

 screened off, every particle of the Earth feels it, 

 whether on the near side or far side, on the inside or 

 the outside. It is easy to forget that every drop of 

 water, even to the bottom of the ocean, feels the tide- 

 generating forces, and it is still easier to forget that 

 every particle deep in the body of the Earth feels 

 them too. The intensity of the force in Figure 2 

 for every particle on the dotted line A-B will be the 



him. can certainly 

 on the near side. 



It is also remarkable how small the forces are that 

 make the tides. Onlv -3",j is at most available for 

 the purpose. The tides are an e.xcellent illustration 

 of the fact that phenomena are often the result of 

 forces which nearlv balance or which interfere with 

 one another, and we see only the effect of the residual 

 or outstanding difference. If we had 

 space enough to carry out the next 

 step we should see that even the 

 forces on Figure 4 must be cut 

 down considerably. It must suffice 

 now if we point out that the Force 3 

 at A merelv tends to lift or lighten 

 the water there ; the intensity of 

 the force is one eight-millionth of 

 the weight of the water, so we can 

 onlv say that it tends to lift, but it 

 clearlv does not tend to shift that 

 water, and so has no effect whatever 

 in producing a tide. Had there 

 been a force acting to the left on the 

 diagram at C it would have been ver\- 

 efficient in shifting the water, but just there, as we 

 see in Figure 4, the tide-raising force is zero. 

 Accordingly the forces that are chiefly accountable 

 for the heaping of the water at A and B are forces 

 like that acting at P and even those are wasting a 

 good deal of their energy in trying to lift the water. 

 The linal consequence is that the greatest tide- 

 generating force anywhere on Earth is only one 

 twelve-millionth of the weight of the particle which 

 it tends to shift. It is ven,- remarkable that a tidal 

 wave should ever be formed at all, and not surprising 

 that the solid crust gives no noticeable evidence of 

 strain under these forces. 



The foregoing paragraphs give so brief an account 

 of a reallv difficult subject that it can only be hoped 

 that thev will leave a general idea of the process 

 of tide-raising ; but they will hardh- fail to leave the 

 impression that the forces at work could not have 

 been guessed at by common sense method, and that 

 it is a very incomplete, if not misleading, description 

 to sav baldlv that " the tides are caused bv the 



