NEWTON S PRINCIPIA. 291 



port of Batsham, in Tunquin, lat 20 5(X N. The tide 

 arrives by two inlets, one from the seas of China, between 

 the continent and the island of Leuconia ; the other from 

 the Indian Sea, between the continent and the island of 

 Borneo. &quot; The tide begins every successive day later by 

 about three quarters of an hour ; so that in fifteen days 

 the time of high water advances from one o clock in the 

 afternoon, for instance, to twelve at night ; after which it 

 does not advance to one in the morning, but falls back 

 thirteen hours to twelve at noon, and so on perpetually. 

 In this way the high water is always in the afternoon 

 during the summer half year (March to October), and in 

 the forenoon during the remaining half. About the time 

 when the tide falls back thirteen hours, the tides are very 

 small and scarcely perceptible ; at the intermediate times 

 they are greatest.&quot; (Phil Trans. 1833, page 224. Whewell.) 

 Let us now follow Newton in his attempt to calculate 

 numerically the forces of the sun and moon to raise the 

 tides. He first refers to his Lunar Theory for a calcula 

 tion of the force of the sun to draw the moon towards the 



earth. When in quadratures this force is G38W . G g, 



where g is the force of gravity at the surface of the earth. 

 When in syzygy the force is double this quantity. But 

 the disturbed bodies are here the particles of water at the 

 surface of the earth, which are nearer the earth than the 

 moon in the ratio of 60 J to 1. These forces must, there 

 fore, be decreased in the same ratio. The force in quadra 

 tures is therefore ^wo g, and that in syzygy double 



this quantity. The first depresses the water in quadra 

 ture, the second raises that in syzygy. Hence the two 

 produce the same effect, and the whole force to raise tne 

 sea will be the sum of the two, that is, tfrice the torce in 

 quadrature. 



u 2 



