99 



moon occurred at the instant when the luminary crosses the meridian ; 

 but, owing to friction and other causes, the axis of the water-spheroid 

 ia^s 6e/t/nd the moon or sun, so that hmar or solar high water does 

 not occur when the corresponding luminary crosses the meridian, but 

 after a certain interval of time, which, on a rough average, may be 

 taken as three hours. 



We shall find it convenient to imagine the lunar tide as produced 

 by an imaginary moon, which always crosses the meridian three hours 

 after the real moon ; and, similarly, the solar tide as produced by an 

 imaginary sun, which crosses the meridian three hours after the real 

 sun. Thus the axis of the two water spheroids will always be directed 

 towards these imaginary tide-producing bodies, and our previous ex- 

 pl.mations will be brought into accordance with the fact that high 

 water in reaHty occurs about three hours after the moon's transit 

 across the meridian. 



The action of the luminaries being greater as the distance is less, 

 it follows that the spring tides in the winter, when the sun is at his 

 least distance from the earth, will be rather greater than in the 

 summer, and the neap tides rather less. The action of the moon also 

 will be greater the nearer she is to her perigee ; thus the greatest tides 

 that can happen are the spring tides, when the moon is in perigee and 

 the earth in perihelion ; this explains, at least, partly, the enormous 

 tides which occasionally do such great damage. 



The diurnal tides have been really found to exist : thus, at 

 Plymouth, the morning tides in the winter are higher than the 

 evening, and vice versa in the summer. In some places near 

 Behring's Straits this difference between the morning and evening 

 tides is so great that there appears to be only one high water in the day. 



Such in its main outlines is Newton's celebrated theory of the 

 tides, but it would be tedious at present to pursue it into further detail. 



Eleven years after his death the French Academy offered a prize 

 for an essay on the tides, and which in 1740 was adjudged to Daniel 

 Bernouilli, Euler, Maclaurin, and the Jesuit Cavalleri, in whose person 

 Descartes' theory of Vortices received its last honours. The others 

 all adopted Newton's theory ; Bernouilli treated it analytically, and 

 from his results deduced rules for the practical calculation of the 

 tides. 



This theory of Newton and BernouiUi, usually known as the 



