494 PROFESSOR CHRYSTAL 



established, and the range and wave-length increase no longer, unless the waves run into 

 shallow water. This progressive surface wave motion may persist for a considerable time 

 (in the ocean for days) after the wind has fallen, in the form of swell ; and it may be 

 propagated into regions where there has been no wind. In ordinary circumstances, 

 owing to the continual variation in the strength of the wind, and in the case of lakes 

 probably also to reflections from the shores, at any particular moment not one train of 

 waves is generated, but many of slightly differing wave-length and differing phases. 

 These trains interfere and cause a succession of wave maxima, commonly called " wave 

 groups." 



Several observations of the periods of surface waves and wave groups on Loch Earn 

 were made by counting the waves or wave maxima which passed a given point in a 

 certain time. This is easy in the case of the wave maxima ; not so easy in the case of 

 the single waves, which have a bewildering habit of losing themselves by running into 

 and through each other and through the maxima. Still, the results were fairly con- 

 cordant. The observations were made at the eastern binode and at the Picnic Point 

 during westerly winds of various kinds. The average of the periods for single waves 

 was *035 m , the smallest and greatest values being *024 m and - 045 m . The most usual 

 value of the period for the groups was '5 m to "66 m , the least and greatest values observed 

 being - 33 m and ri7 m . For the single waves ranges of 6 in. to 12 in. were common ; but 

 on one stormy day ranges of 2 ft. to 3 ft. were observed. 



From a set of observations made at my request by Mr James Murray on Loch Tay, 

 the following data were calculated for that lake. T is the period, X the wave-length, 

 and v the velocity of propagation for the single waves ; T g , \, v g , the corresponding 

 magnitudes for the wave groups. The observations were made at Killin, when there 

 was no wind, on swell coming in from the lake and running in water 13 ft. 6 in. to 

 12 ft. deep.* 



For Single Waves. 

 T= •017 m , A = 18 ft. to 25 ft., v= 18 to 25 (ft./sec.) = 12 to 17 (mile/hour). 



For Larger Groups of 4 to 6 Maximum Waves. 

 T g = -5 m to -75 m , A,, = 252 ft. to 283 ft., ^ = 8-4 to 6-3 (ft./sec.) = 5 '7 to 43 (mile/hour). 



For Smaller Groups of 2 to 3 Maximum Waves. 



T„= -OSS'" to •17'", Xg = 42 ft. to 63 ft., v„ = 8'4 to 6-3 (ft./sec.) = 5-7 to 4*3 (mile/hour). 



It is obvious that the single waves could not cause the ordinary and most prominent 

 periods in the embroidery, which run from about , 5 m to 1 *5 m ; but there is no doubt 

 that they cause the thickening or blurring of the limnogram which usually appears 

 when the wind is high. On the other hand, the periods of the wave groups are nearly 

 coincident with some of the more prominent periods of the embroidery. Part of this 



* The velocity of a " long wave " in which would be about 20 (ft./sec.). 



