338 



KNOWLEDGE. 



September, 1910. 



exaggerates the depth of the water and the rise of 

 the tide ; one foot increase at A and B and six inch 

 decrease in depth round " the waist " CD., is about 

 the observed range of the tide. \\'e are looking at 

 the Pole and so the outer circle is the Equator ; an 

 inhabitant living on the Equator will be carried 

 round as the arrow shews and find himself in high 

 water followed by low water twice each day. Thus 

 the diagram fits well with the experiences of the 

 inhabitant on earth. Does it, however represent 

 (exaggerations apart) what we should see if we were 

 awa\" outside the earth, as supposed by the diagram ? 

 Speaking very roughly it does. Strange as it may 

 seem, there are alwa\s two tides, one on the side 



we know that an iron bar will not bend, and we 

 call it rigid : but it is all realh' a question of more or 

 less ; even the bedrock that we use as a proverb for 

 steadfastness does yield. Put it under sufficient 

 stress and it will be strained. Stress and strain are 

 technical words that are, unfortunately, used looselv 

 in common conversation. A stress is a force, a 

 strain is a resulting deformation, and we may 

 convenienth' divide what follows into the two 

 chapters : The stresses at work, and the strains that 

 thev produce. 



We shall have in mind in our discussion a verv soft 

 indiarubber ball or limp air-balloon, and we shall clear 

 the ground by making two preliminarv statements. 



Pi. 



Figure 2. 



near the Moon and one on the far side. It ma\- be 

 frankly admitted that the tide on the other side is 

 a very puzzling thing, but for the moment we ma\" 

 content ourselves with stating that it is there, and 

 leaving the explanation alone. 



Once again, then, what is a tide ? Speaking from 

 the wicier point of view of a celestial giant survey- 

 ing the Earth from some point of vantage in space, 

 we will now say that it is a deformation of the 

 surface of the ocean. We are not concerned 

 whether the water flow or not, but only with the 

 change of shape of the surface. The figure, as it is 

 called, of the Earth ceases to be round, or spherical, 

 and becomes egg-shaped. We will think of an 

 indiarubber ball crushed inwards round the circle 

 CD (Figure I), and drawn outwards at A and B. 

 The forces that squeeze and draw the Earth are 

 called tide-generating forces, and the question at 

 once arises : To what are they due ? 



Newton taught us that the tides are due to the 

 attraction of the Moon, but at least two thousand 

 years ago they that went down to the sea in ships 

 on the coasts of the Atlantic knew that the tides 

 were connected with the Moon. What Newton did 

 was to include the tides in his one comprehensive and 

 coherent theory of gravitation. He and his succes- 

 sors, however, thought only of the water as being 

 influenced ; they considered the land as rigid. We 

 know how a cane will bend, and we call it elastic : 



(1) It will (inl\- be strained when different parts 

 of it come under different degrees of stress. If you 

 have to lift a ver\- limp or fiims\' thing you certainly 

 must not hold it bv one point if its shape is to be 

 maintained; you will support it at as large a number 

 of psints as possible. That is how the water supports 

 a ship: if the ship strikes a rock and rests on it and the 

 tide falls, the ship's back will probably be broken by 

 the stress of its own weight. To avoid all strain you 

 should, theoretically, support every point with equal 

 force. Our first statement, then, is that an object 

 is under no strain if all its particles are acted on b\' 

 equal forces. 



(2) In such a case it matters not in the least how- 

 great the forces are. If they are great the object as 

 a icliole will be urged on more rapidly, but this has 

 no effect at all on the shape of the object. 



When we sav equal forces we include the idea of 

 parallel forces, for it is clear that if the forces are 

 not parallel they will exert some crushing or tearing 

 influence, from which strain will result. 



We shall apply these two propositions later on, 

 but our investigation of tide-generating forces must 

 begin by a comparison of the two diagrams, A and B 

 shewn in Figure 2. A represents an Earth of which 

 all the particles are being urged by equal forces of 

 intensity, 100. In B the forces vary from 103 to 

 97, but the average is clearly still 100. This is 

 not far from the actual truth : for the Moon pulls 



