XIIL INTERFERENCE OF WAVES. . 93 



either. But if one wave precede the other by exactly 

 half an undulation, the elevation of the one will coincide 

 with the hollow of the other, and the hollow of the one 

 with the elevation of the other ; and the waves will so 

 entirely obliterate one another, that the surface of the 

 water will remain smooth and level. Hence if the length 

 of each wave be represented by 1, they will destroy one 

 another at intervals of , , 4, &c., and will combine 

 their effects at the intervals 1, 2, 3, &c. It will be found 

 according to this principle, when still water is disturbed 

 by the fall of two equal stones, that there are certain 

 lines on its surface of a hyperbolic form, where the 

 water is smooth in consequence of the waves oblitera- 

 ting each other ; and that the elevation of the water in 

 the adjacent parts corresponds to both the waves united 

 (N. 156). Now in the spring and neap tides arising 

 from the combination of the simple soli-lunar waves, the 

 spring tide is the joint result of the combination when 

 they coincide in time and place ; and the neap tide hap- 

 pens when they succeed each other by half an interval, 

 so as to leave only the effect of their difference sensible. 

 It is therefore evident that if the solar and lunar tides 

 were of the same height, there would be no difference, 

 consequently no neap tides, and the spring tides would 

 be twice as high as either separately. In the port of 

 Batsha in Tonquin, where the tides arrive by two chan- 

 nels of lengths corresponding to half an interval, there 

 is neither high nor low water, on account of the inter- 

 ference of the waves. 



The initial state of the ocean has no influence on the 

 tides; for whatever its primitive conditions may have 

 been, they must soon have vanished by the friction and 

 mobility of the fluid. One of the most remarkable cir- 

 cumstances in the theory of the tides is the assurance, 

 that in consequence of the density of the sea being only 

 one-fifth of the mean density of the earth, and the earth 

 itself increasing in density toward the center, the sta- 

 bility of the equilibrium of the ocean never can be sub- 

 verted by any physical cause. A general inundation 

 arising from the mere instability of the ocean is there- 

 fore impossible. A variety of circumstances however 

 tend to produce partial variations in the equilibrium of 



