128 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



With water-waves the same as with souud-waves it is to be assumed 

 that, through all deviations, delays, and diminutions that they experi- 

 ence, the time of vibration remains unchanged. This time may there- 

 fore be determined near the shore even though the progressive velocity 

 in shallow water is changed and the form and the length of the waves 

 change. The number, X, of the waves in a minute is expressed by 



,._ GO.a. 



When ((2 increases to naz then A increases to n-A, as shown in my paper 

 of a year ago, and therefore 



jy n • 



n 



A velocity «2=10 metres would give 9.4 waves per minute; on the 

 other hand a velocity «2=5 would give 18.8. 



The counting of the waves without registering instruments is now not 

 to be executed with great accuracy, since on the sea, so far as I have 

 seen it, there are always numerous adjacent waves of rather different 

 periodic times which interfere and give phenomena corresponding to 

 the acoustic beats. During the minimum of motion one can easily make 

 errors in the counting; by repeated countings at the same place we 

 obtain therefore variations of about one-tenth or even more of the 

 desired number. 



The strength of the wind that I observed on the shore did not exceed 

 G.l metres per second. This was on the evening of my arrival in 

 Antibes, April 1, 1890; the wind was from east southeast; I counted 

 between 8.0 and 10 waves per minute. On the next morning, April 2, 

 there were still 10 to 10.5 waves per minute, although the wind had 

 almost entirely gone down. This number of waves would be expli- 

 cable only when a wind about 10 metres per second had blown steadily 

 over the open sea. On the 2d of April the wind rose in the course of 

 the day to a velocity of only 4 metres per second. Yet on the 3d of April 

 also the number of waves was still 9.5 with a very feeble wind ; on the 

 4th of April for the first time an increase was perceptible up to 12.3 

 waves per minute. 



During a series of quiet days the number of steadily diminishing 

 waves gradually increased to 17 or 18. Finally on the 7th of April the 

 wind began again to increase. In the morning I found a velocity of 3.3 

 metres per second, which in the course of the day increased to 5.5 and 

 brought the number of waves down to 11 5. This time, however, the 

 location of the increased wind was demonstrable. In Marseilles during 

 the previous night a sev<^re whirlwind had prevailed and the larger 

 waves excited by it stretched as a sharply defined dark-gray band from 

 the sea horizon hitherward and reached Cape Antibes about midday, 

 long be'ore the stronger wind that had given rise to them and which 

 had morever at the latter place by no means the same force as in Mar- 

 seilles. 



