116 A TEXTBOOK OF OCEANOGRAPHY 



last quarter. In this case the tide-ellipsoid produced by 

 the moon bas its maximum protubérance coincident with 

 the maximum dépression of the tide-ellipsoid produced by the 

 sun. Consequently, the resulting height of the observed tide 

 is a minimum and we get the period of neap-tide. 



The Strength of the Tide-Producing Forces. 



Let the mass of the earth = i and that of the moon = M. 

 Then M = i/8i45. The attractive force of the moon at the 

 earth's centre is proportional to M/r^, where r is the distance 

 between the centres of the earth and moon. At the point on 

 the earth where the line joining the earth and moon 's centres 

 cuts the surface the attraction of the moon is somewhat greater, 

 being proportional to MI{r-r'Y, where r' is the radius of the 

 earth. 



The différence between thèse two attractive forces is that 

 which gives the " pull" on the water particles at the earth's 

 surface and produces the protubérance at this point. This 

 différence is — 



M MM 



I 



[b-çj- 



But r :r'=i : 60-34 



which is for ail practical purposes 



_ 2Mr' 



The force with which the earth attracts a particle at its surface 

 is_L and the force which produces the tides is the fraction of 



this — 



_ 2Mr' . j^ _ 2Mr^ _ i 

 — ^ ' r'^~ r^ ~ 8945000 



— that is, the tide-producing force of the moon is about one- 

 nine-millionth of the force of gravity. 



