5§4 



NA TURE 



[April 23, 1903 



have been made. Further on the criticism reads, " I fail 

 to see any adequate consideration of the variability of depth, 

 of the absence of synchronism in the disturbing force in the 

 direction of the canal." This "absence of synchronism " 

 is precisely what the criticised equation 308 (or 311) enables 

 us to take account of. 



It seems to me that enough has been given in §§ 38, 42, 

 45. 55. an d °3 to show that the variability in depth has not 

 been permanently lost sight of, and also enough to convince 

 one that " areas " as nearly uniform in depth as are many 

 portions of the ocean can, as a first approximation, be 

 treated as bodies having strictly uniform depths. 



(2) Of course there are instances where the deflecting 

 force due to the earth's rotation becomes important ; for 

 example, most moderately narrow arms of the sea in which 

 the current is swift — such as the English Channel, Irish 

 Channel, and Gulf of Georgia. But if in any of these a 

 large stationary wave actually exists, it is hard to see how 

 the times of its high and low waters near the loops can be 

 seriously affected by this force, and these are the only 

 times which chapters vi. and vii. undertake to determine. 

 Near the nodes, when the current is swift, the deflecting 

 force may, in a canal the width of which is but a moderately 

 small fraction of a half wave-length, cause high water at 

 one end of the nodal line, and at the same time low water 

 at the other. This is true because the narrowness of the 

 body permits its transverse slope to respond at once to the 

 transverse forces. A progressive wave can be so superposed 

 as to diminish or even destroy the range at one end of the 

 nodal line while increasing the range at the other end. 



Considering now a broader " area," with one or both of 

 its lateral boundaries wanting, it is hard to see how the 

 transverse motion occasioned by the earth's rotation can 

 seriously interfere with the character of the stationary 

 wave, and especially the time of elongation of the particles ; 

 for its effect cannot accumulate and so tend to produce a 

 transverse stationary oscillation. If. on the other hand, 

 a square or rectangular " area " about half a wave-length 

 wide have solid lateral boundaries, it would seem that the 

 deflecting force might, except in the equatorial regions, 

 so alter the mode of oscillation that it could not be ignored 

 even in the first approximation. So far as I know, there 

 is no near approach to this case in any of the " areas " 

 which probably exist (see Fig. 23 of my paper). 



Hence, while it is true that the free oscillations in a 

 rotating rectangular sheet of water is an unsolved problem, 

 we see that the critic's remark, " It seems to follow that 

 either Lord Kelvin or Mr. Harris is wrong," if in any sense 

 true, really has very little to do with the case. In a word, 

 taking an oscillating body as a whole, it seems to me that 

 the oscillation, in accordance with a simple mode, can 

 generally be regarded as the fundamental and important 

 thing, and the effect of the earth's rotation a modifying or 

 induced phenomenon. 



(3) Now in regard to the improbability " that any large 

 portion of our curiously shaped oceans should possess even 

 approximately the critical free period," several things can 

 be said. In the first place, we are not restricted to single 

 half wave-lengths; the rectangular "areas" may run in 

 any direction ; the " areas " may be approximately trape- 

 zoidal, triangular, or of other forms, their free period may 

 differ perhaps 10 per cent, or more from the period of the 

 forces, and still have their tides greatly augmented by their 

 approach to critical lengths. There are, indeed, portions of 

 the ocean which cannot be covered by any areas the periods 

 of which would be satisfactory, and in which it would be 

 possible for the tidal forces to incite a considerable tide. 

 Upon referring to the map, Fig. 23, it will be seen that one 

 such region exists west of Australia, another south of New 

 Zealand, another east of southern South America, the 

 Arctic Ocean constitutes another. Upon referring to the 

 map of the diurnal tides, Fig. 24, it will be seen that the 

 South Atlantic, the South Pacific, and all of the Arctic 

 Ocean are not regions where we can reasonably expect to 

 find large diurnal tides. 



Referring again to Fig. 23, and noting that the ocean is 

 for the most part actually parceled out into areas of consider- 

 able width the free periods of which can hardlv differ greatly 

 from twelve lunar hours, and are, moreover, so situated 

 that the forces do not approximately destroy one another, 

 in be seen by applying the rule quoted in the criticism, 



NO. I /47, VOL. 67] 



it may, perhaps, be justifiable to ask how it happens that 

 the times of high and low water at the loops, as deter- 

 mined by this rule, do approximately agree with observed 

 times, unless there is some considerable truth in this 

 "partial explanation of the. tides." 



Recently I have been working out in considerable detail 

 the tides in the equatorial belt of the Indian Ocean, where 

 it is fair to assume that the effect of the deflecting force 

 must be small. The work goes to show that the theory set 

 forth in the criticised paper is substantially correct. I 

 therefore venture to refer Prof. Darwin to this discussion, 

 which will appear in the March number of the Monthly 

 Weather Review. 



To avoid needless misunderstanding, it may be added here 

 that I am well aware of the incompleteness of the treatment 

 given in my paper. For instance, mathematicians have nol 

 up to this time been able to treat the simple problem of a 

 rectangular " area " the rigid boundary of which consists of 

 only two opposing end walls, although much has been done 

 upon analogous problems relating to the open organ pipe. 

 Even an approximate absolute value of the range of tide 

 (excepting in small deep bodies) has not been attempted in 

 this paper, because its determination would involve the 

 numerical value of frictional resistance, which can be kept 

 in abeyance when we seek only the times of tides in systems 

 which have as free periods very nearly the tidal period. 

 Many deductions and refinements were purposely omitted 

 from my paper — the chief aim being simplicity. I hope 

 eventually to be able to consider more fully matters like 

 these in connection with detailed studies of the tides in 

 various seas. R. A. Harris. 



Washington, D.C., March 28. 



March Dust from the Soufriere. 



Sir W. Thiselton-Dver has kindly forwarded to me a 

 packet of volcanic dust sent to him by Dr. D. Morris, which 

 fell in Barbados last month after an eruption of the 

 Soufriere of St. Vincent, a brief description of which may 

 be of interest. The sample, Dr. Morris states, was col- 

 lected at Chelston, Bridgetown, on sheets laid out upon 

 the lawn, the material being brought in and weighed every 

 hour, and the fall continuing from 11 a.m. to 5 p.m. on 

 the day of the eruption. It is free from all extraneous 

 matter, and may be regarded as typical of the ash which 

 fell on Barbados. The weight of this is estimated at about 

 6000 pounds (avoir.) per acre. At an average rate of three 

 tons per acre, this would be equivalent to about 300,000 

 tons for the whole island. 



The dust is of a dull dark brown colour, showing on close 

 examination a minute speckling with a lighter tint. If 

 poured on a piece of white paper and removed in the same 

 way, a distinct warm-brown tint remains, produced by the 

 verv finest part of the powder, which is not easily removed. 

 In Dr. Flett's excellent account of the dust which fell in 

 Barbados after the eruption of May 7 (Quart. Jour. Geol. 

 Soc, Iviii., 1902, p. 368), it is stated that this was at first 

 brown, then slightly redder, and at last a whitish-grey im- 

 palpable powder. A bulk sample of that fall is distinctly 

 greyer than the recent one, and a small one of the fall of 

 1812, in my possession, is a rather pale grey with a slight 

 brown tinge. The new sample under the microscope differs 

 only in detail from that described by Dr. Flett. The frag- 

 ments, as a rule, do not exceed 001 inch, and are thus very 

 slightly smaller than some in the May eruption ; from 0-06 

 to o 08 is a rather common size, and there is a fair amount 

 of exceedingly minute dust. The principal minerals are the 

 same, plagioclastic felspar, hypersthene, and a green 

 augite, but in the first steam cavities are now more 

 abundant than glass enclosures, and I think brown glass 

 is more often adherent, but to make certain of this 

 point requires a fuTler examination than I can give for the 

 next few days. T. G. Bonney. 



The Lyrid Meteors. 

 The Lyrid meteors excite an interest that might be re- 

 garded as quite disproportionate to their numerical import- 

 ance. They are a very rare shower, and even when con- 

 sidered by experienced observers as unusually abundant, they 

 seldom appear at a higher rate than about twenty per hour. 



