110 INTERFERENCE OF WAVES. [SECT. xm. 



have produced separately : a phenomenon depending upon 

 the interference of the waves or undulations. 



A stone plunged into a pool of still water occasions a 

 series of waves to advance along the surface, though the 

 water itself is not carried forward, but only rises into heights 

 and sinks into hollows, each portion of the surface being 

 elevated and depressed in its turn. Another stone of the 

 same size, thrown into the water near the first, will occasion 

 a similar set of undulations. Then, if an equal and- similar 

 wave from each stone arrive at the same spot at the same 

 time, so that the elevation of the one exactly coincides with 

 the elevation of the other, their united effect will produce a 

 wave twice the size of 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 5, If, f, &c., and will combine their 

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

 ing to this principle, when still water is disturbed by the 

 fall of two equal stones, that there are certain lines on its sur- 

 face of a hyperbolic form, where the water is smooth in con- 

 sequence of the waves obliterating 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 com- 

 bination when they coincide in time and place ; and the neap 

 tide happens when they succeed each other by half an in- 

 terval, so as to leave only the effect of their difference sen- 

 sible. 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 



