1860.] On the Translation of Waves of Water. 273 



theoretically have been about nineteen British miles per hour : and 

 where it equalled fifty feet, the speed should have equalled twenty-six 

 miles per hour : and so on, increasing in direct proportion to the 

 square root of the depth of the river. 



25. It is, however, necessary here to observe that the foregoing 

 remarks are only applicable within certain limits ; and that when the 

 depth of the stream is very small, the continuity of the wave motion 

 is lost ; and the crest of the wave topples over in broken water. The 

 limit of depth within which, wave motion is impossible, is perhaps 

 not very closely ascertained ; but if it be assumed at one-half the 

 height of the advancing wave, it will be sufíiciently cióse for the 

 present purpose. It seems that when a wave reaches shallow water, 

 sufncient partióles do not exist in advance, to maintain the altitude 

 of the anterior slope. — Its form consequently changes gradually 

 from a slope to a perpendicular, until the partióles on the crest still 

 proceeding with the same velocity, find at last no support and topple 

 over by their own momentum in a torrent of foam. The swell upon 

 a coral reef ; the flood bore of the Hooghly • and the heavy surge 

 upon the Madras coast ; are illustrations of this law respecting large 

 waves in shallow water. 



26. It would not have been necessary to dwell upon this fact 

 with relation to the Indus wave of 1858, which certainly was not a 

 broken one ; but, as discredit has been thrown upon the traditions 

 respecting the noise, the foam, and the destruction, &c. of the 

 previous flood of 1841, and the diminution of water previous 

 thereto, together with the greater altitude it attained, because 

 similar phenomena were not present in 1858, I would observe that 

 the very concomitancy of these traditions, leads me to yield a general 

 belief to the whole of them. It is stated that the flood of 1841, 

 culminated at twelve feet higher than that of 1858, and started from 

 a much lower zero. It is, therefore, probable that the positive 

 altitude of the wave was twenty-four feet greater than that of the 

 late flood ; and moreover, that the stream upon which it travelled 

 was twelve feet shallower. It is therefore very probable that the 

 conditional limits within which wave motion is possible, were not 

 present in 1841, though they were in 1858. 



27. I regret that so little practical information can be deduced 



2 o 



