February 3, 1898] 



NATURE 



321 



other considerations, lead us to give the preference to 

 this form. The advantage is not, however, great, and 

 disappears when we have to distinguish cases where we 

 must substitute n^ for «*. The reason why I prefer Ryd- 

 berg's form at present lies in the fact that it adapts itself 

 better to bring out the regularities as well as the irregu- 

 larities of distribution of the lines independently of any 

 special form of equation. To show this we may write 

 Rydberg's equation in the form 



« + M _ I 



Vb Va - n" 



The convergence frequency, A, may be determined by 

 some graphical process if a-sufficient number of lines have 

 been observed, and the law of formation of a spectro- 

 scopic series may therefore be expressed as follows : 



The inverse square roots of ihc difference between the 

 convergence frequency and the frequency of successive lines 

 are very approximately in arithmetical progression. If 

 we wish to determine how far any series conforms to this 

 law, we may in the first place calculate the right-hand 

 side of the above expression with some approximate value 

 of A. Systematic deviations from arithmetical pro- 

 gression may then be corrected by a small change, 8A 



producmg a difference —j ~ ■ ' in the numbers. But 



v(A-N}3 

 it will nearly always be found that there are some out- 

 standing deviations which cannot be corrected for in this 

 way. The value of B is found at once from the arith- 

 metical progression successive numbers differing by 



—fz^. I have found this method of testing the series aad 

 \'B 



calculating the constants very useful, and hope on some 

 other occasion to return to it. 



Arthur Schuster. 



UNDULATIONS IN LAKES AND INLAND 

 SEAS DUE TO WIND AND ATMOSPHERIC 

 PRESSURE. 



T T is generally known that considerable variation takes 

 •*■ place in the level of the surface of the water in lakes 

 and inland seas owing to the effect of the wind in gales 

 and during stormy weather. The minor undulations 

 which occur at more regular intervals have not attracted 

 the same observation, and the cause of these is still a 

 matter of some uncertainty. In the large lakes in 

 America, fishermen and boatmen have learnt to regard 

 these undulations as storm warnings ; and on the coasts 

 of Europe, the rollers which break on the shore in calm 

 weather are looked upon as indicative of a coming storm. 

 Thus, in the Bay of Biscay frequently during the autumn 

 and winter in calm weather a heavy sea gets up and rolls 

 in on to the coast four-and-twenty hours before the gale 

 which causes it arrives, and of which it is the prelude. 

 In this case the wave action, generated on the other side 

 of the Atlantic by the wind, travels at much greater rate 

 than that of wind, and thus gives timely warning of the 

 coming storm. So also on the opposite side of the 

 Atlantic, on the coast between North Carolina and Cape 

 Hatteras, the currents, which are there largely governed 

 by the wind, begin to run strongly several hours in 

 advance of the wind which causes them. In summer a 

 change of the current from north-east to south-west 

 is always taken as a true indication of an approaching 

 north-east wind. 



The effect of gales on tideless seas and lakes is so marked 

 as to cause frequently considerable inconvenience and 

 anxiety to mariners. Thus, in the Caspian Sea a gale will 

 raise the water on one side 6 feet and depress it on the other 

 as much, making a total difference of level of 12 feet.^ 



1 "Tidal Rivers," chap. v. (Longmans, Green, and Co.). 



NO. 1475. VOL. 57] 



In the Baltic easterly gales will alter the level upwards 

 of 8 feet. In Lake Erie ' depressions and elevations 

 of from 2 to 4 feet are common, while occasionally heavy 

 gales have produced a difference of level of upwards of 

 1 5 feet. Almost invariably about the time of the spring 

 equinox strong gales occur from the east, raising the water 

 from 4 to 6 feet at the west end of the lake, and de- 

 pressing it to a similar extent at the east end, making 

 a total difference of from 8 to 12 feet. About the time of 

 the autumn equinox gales from the west lower the water 

 7 to 8 feet at the west side, and raise it 5 to 8 feet at the 

 east end, making a difference from the normal level of 

 from 12 to 16 feet. An illustration is given by Mr. Blunt,, 

 the engineer, who reported on the subject for the United 

 States Commission as to the way in which the navigation 

 of the lakes and of the rivers connected with them is 

 affected by storms acting on the surface of the water. A 

 steamer which had to make a trip down the river found 

 the water at the pier from which she started, five miles 

 from the mouth, had receded to ^\ feet below the normal 

 level. In the river, flats were showing where a few days 

 before they had found 8 feet of water. In the middle 

 of the bay a large dredger was aground where there 

 ought to have been 17 feet of water. 



In addition to these larger oscillations, there are also 

 minor undulations which occur at varying intervals, the 

 largest period for a complete oscillation not exceeding 

 half an hour, and the alteration in the level of the water 

 not more than from three to four inches. The phenomena 

 had been noted by Duillier on the Swiss Lakes in the 

 middle of the last century, the name locally given to them 

 being Seiches. In 1804 Vaucher also investigated the 



UNDULATIONS AT MOUTH OF MUMBER RIVER. 



Fig. I. 



matter and published an account of his researches, his 

 experience being that they were common to all the lakes ; 

 that they recurred at all seasons of the year, but most 

 frequently in spring and autumn, the greatest oscillation, 

 however, occurring in the summer ; and that the intervals 

 between the oscillations did not exceed twenty to twenty- 

 five minutes, and more frequently less. 



A few years since the writer had occasion to investigate 

 the oscillations which took place in one of the Norfolk 

 Broads, and which were taken as showing that the water 

 was tidal. It was found that variations of from half an 

 inch to two and three inches in the level of the water 

 took place periodically, and at times when the atmosphere 

 was calm. Observations spread over a considerable time 

 proved that these undulations were not coincident with 

 the rise and fall of the tides, and that they had no direct 

 connection with the ebb and flow in the river with which 

 this Broad was connected. 



The character of the undulations on Lake Superior has 

 been investigated by Mr. Napier Denison, and the results 

 communicated to the Canadian Institute in February 

 1897, in a paper entitled "The great lakes as a sensitive 

 barometer." For the purpose of tracing these curves 

 Mr. Denison had two self-recording gauges constructed, 

 one being fixed at the mouth of the river Humber, and 

 the other at the Burlington Canal. The results of one 

 day's reading at the mouth of the Humber are shown in 

 Fig. I, which is sufficient generally to illustrate the result 

 of the readings obtained, and as showing the rapid undu- 

 lations upon the lakes during light winds and fine weather 

 preceding a severe storm. (The divisions in the above 



J Report of Deep Waterways Commission, U.S.A. (Washington, 1897). 



