Chapter VIII 



The Tide-generating Forces 



1. Fundamentals for Determining Tidal Forces 



The foundation on which any explanation of the tidal phenomena must be 

 based is the system of tide-producing forces which is exerted by the moon 

 and the sun on the earth. It is necessary to make a sharp distinction between 

 the system of forces producing the tidal phenomena on the earth — not 

 only in the oceans, but also in the atmosphere and in the solid earth — and 

 the effects of this system of forces on the mobile masses in these three 

 layers of the earth. This distinction is of importance for the following 

 reasons. The nature of the tide-producing forces is well known. It was 

 even possible to verify the existence of these forces in laboratory experiments. 

 However, the effects of the tide-producing forces on the oceans, the solid 

 earth and the atmosphere, i.e. the formation of the tides, are not clear in 

 all points, although during the past decades an essential progress has been 

 made (Defant, 1942; see also Proudman, 1927; Thorade, 1928). The 

 problem of the tide-producing force of a celestial body — sun or moon — is 

 linked, according to Newton, to the forces of attraction existing between 

 the masses of two bodies. These forces are proportional to the masses of the 

 two bodies and inversely proportional to the square of the distance between 

 them. The forces of attraction regulate in the astronomical system of the 

 sun, the planets and their satellites the annual and monthly motion of the 

 centre body and the secondary body around the common centre of gravity. 

 Considering the system earth-moon, these forces also govern the monthly 

 movement around its centre of gravity. 



The mass of the earth is approximately 81 times that of the moon; there- 

 fore, the centre of gravity lies about 81 times closer to the centre of the earth 

 than to the centre of the moon. The distance between the centre of the earth 

 and the centre of the moon corresponds to 60 earth radii, and the common 

 centre of gravity lies still inside the earth, viz. at a distance of approximately 

 three-fourths of the earth's radius, 4600 km from the centre of the earth. 

 The monthly orbit of the earth around this point is, therefore, very small 

 compared to that of the moon. If the system earth-moon were only sub- 

 jected to the forces of attraction, then these would constantly endeavour to 

 reduce the distance earth-moon. The monthly motion of the two bodies around 



