399 

 The values of these several ratios are as follows : 



M 1 _ 1 p_ 47r /s 

 E &quot; 74 c ~ 60 *** ~3~ pa 



whence the coefficient is nearly 

 1 1 



7 feet. 



By observation p = 1 p nearly, and in this case the height of 

 the tide is small. But if p f be much greater, this expres 

 sion soon becomes considerable, and if the density of the 

 sea had been much greater than that of the earth, the 

 tides would have been very high. 



We see also that the height of the tides caused by dif 

 ferent luminaries varies as their masses, and inversely as 

 the cubes of their distances. 



The coefficient being called h, the greatest elevation of 

 the tide will manifestly be 2A, and the greatest depression 

 below the spherical surface will be h. The elevation is 

 therefore double the depression. But it must be remem 

 bered that this spherical surface is not the mean surface of 

 the ocean at the place in question, but the surface as it 

 would be if undisturbed by any luminary. 



There will be a similar expression for the tide caused by 

 the sun, and the two together may be expressed by the 

 formula 



sin 2x 



f cos 2 A ( A (^cos 2 cos2(7-y)+A / (j^ 



where Z, A, are the longitude and latitude of the place, y, S, 

 the right ascensions and declinations of the moon, c , c, her 



