May 9, 1872 



NATURE 



27 



outside these streams, or in their possible, but not actual, 

 extension. 



Having stated that he was prepared to give, in another 

 paper on the origin of the disease which he was prepar- 

 ing, an ample explanation of some well-known points about 

 cholera ; such as its partial connection with the east wind, 

 its following the course of large rivers, its greater preva- 

 lence on tertiary strata, alluvial tracts, and the deltas of 

 rivers, and its comparative rarity on secondary and pri- 

 mary strata, the author proceeded : " It was not my in- 

 tention at the present time to enter into the question of 

 the origin of the disease; but having read a few days ago 

 that Dr. Buchanan in this very hall congratulated the 

 meeting on being able to number among the things of the 

 ^ast the time when the propagation of cholera was sup- 

 posed to be due to all manner of cosmic and atmospheric 

 influences, and on having ' reached a solid basis of fact 

 and knowledge upon which further observation might be 

 built with security,' I am tempted to declare that I for 

 one maintain that this despised theory, which Dr. Bu- 

 chanan fancies is buried and put out of sight, is the correct 

 one. I maintain that cosmic influence lies at the origin 

 of cholera — that cholera is intimately connected with 

 auroral displays and with solar disturbances. I believe 

 (/that I am able to show that a remarkable connection 

 exists between the maxima and the minima of cholera 

 epidemics and of solar spots ; and in directing your atten- 

 tion to this map, on which I have represented graphically 

 the amount of cholera and the number of sun-spots for the 

 last fifty years, I wish to show that there is here also ' a 

 solid basis of fact and knowledge upon which further ob- 

 servation might be builtwith security.' You are all probably 

 aware that the great astronomer Schwabe discovered that 

 the sun-spots have what is called a ten-year period ; that 

 is, there is a minimum of spots every ten years. It was 

 also discovered that the diurnal variation in the amount 

 of declinationof the magnetic needle has a ten- year period. 

 The same was proved in regard to eavth currents, and 

 also aurone. The maxima and minima of the four were 

 found to be contemporaneous. This was a great result ; 

 but Professor Wolf, on tabulating all the sun-spots from 

 :he year i6i i, discovered that the period was not ten 

 years, but irii years. This period is no v the accepted 



,_ ' one for the sun-spots, and it has been established for the 

 magnetic declination, and by Wolf for the aurora;. Now, 

 it is a curious fact that the last year of every century, as 

 iSoo, has a minimum of sun-spots, so that the minima 

 are iSoo, iSirii, i822'22, i833'33, &c. The maxima do 

 not lie midway between the minima, but anticipate it by 

 falling on the year 477 after a minimum ; for example, 

 iSoo was a m.inimum year, then 180477 "'as a maximum 



[, year. Now, cholera epidemics have, I believe, a period 

 equal to a period and a half of sun-spots. Reckoning 

 then from 1800, we get as a period and a half the date 

 ]Si6'6'i, which was shortly before the great Indian out- 

 break ; another period and a half gives i833'33, a year in 

 which there was a maximum of cholera; another, iS49'9g, 

 that is, 1 850, a year having a maximum of cholera ; another, 

 i866'66, a year having a maximum of cholera ; another, 

 • 1 883*33, 'IS the year in which there will be a cholera 

 maximum. It follows from what has been already said 

 that I 783'33 would be a year in which cholera was at a 

 maximum. Now it is a fact that in April 1783 there was 

 a great outbreak of the disease at Hurdwar. 



" I would call attention to the parallelism of increase and 

 decrease of these curves. I am not, however, prepared to 

 say that sun-spots originate cholera ; for they may both 

 be the effects of some other cause, which may indeed be 



^^ the action of the other planets upon the earth and upon 

 the sun. If tliat be the case — and 1 see no reason why it 

 should not— wc may then have an explanation of the 

 minor periods and of the large period of 56 years, which 

 Wolf believes he has detected,and also of the minorperiods 

 observed in cholera-epidemics. 



" My own opinion, derived from an investigation of the 

 subject, is that each planet, in coming to and in going from 

 perihelion — more especially about the tima of the 

 equinoxes — produces a violent action upon the sun, and 

 has a violent sympathetic action produced within itself — 

 internally manifested by earthquakes, and externally by 

 auroral displays and volcanic eruptions, such as that of 

 Vesuvius at the present moment ; in fact, just such an 

 action as develops the tail of a comet when it is coming 

 to and going from perihelion ; and when two or more 

 planets happen to be coming to or going from perihelion 

 at the same time, and are in, or nearly in, the same line 

 with the sun — being of course nearly in the same plane — 

 the combined violent action produces a maximum of sun- 

 spots, and in connection with it a maximum of choIera\ 

 on the earth. The number of deaths from cholera in any 

 year— for example, the deaths in Calcutta during the six 

 years 1865-70 — increased as the earth passed from peri- 

 helion, especially after JVIarch 21, came to a minimum 

 when it was in aphelion, and increased again when it 

 passed to perihelion, and notably after equinoctial day ; 

 thus affording a fair test of mv theory." 



ON THE DEPTHS OF WATER IN WHICH 

 WAVES BREAK 



OBSERVATIONS MADE AT SC.4RB0R0UGH IN 1870 



A .S the force which different sea-works have to resist 

 -^^~^ varies with the height of the waves that reach the 

 coast line, any data which will enable the marine engineer 

 to predict this height when designing such works must 

 obviously be of importance. In the Edinburgh Pliiloso- 

 pliitdl Journal for July 1S52, I stated, as the result of 

 experiments made in 1850 on a small fresh-water loch, 

 and afterwards on larger sheets of water, that the height 

 of the waves increased most nearly in the " ratio of the 

 sqttaic root of their distances from the windward shore'' 

 or, in other words, the crest of the wave as it increases in 

 height describes a parabolic curve. So that, if h = height 

 of wave, d = distance, and a is a coefficient varying with 

 the strength of the wind, h = a ^/ d. For most practical 

 purposes of the engineer, the coefficient a may for heavy 

 gales be taken at one and a half ; so that the formula 

 becomes — 



//= 1-5 ^ d, 

 where // represents the height of the wave in feet, and 

 d = length of exposure in miles.* As elsewhere stated, f 

 this formula becomes for short distances — say for under 

 ten miles — 



/; = 1-5 ,/ ^-f (2-s -</,/). 



The height of the wave, however, which reaches any 

 particular work, is not necessarily that which is due to 

 the line of exposure ; for the shallowing of the water near 

 the shore may cause the heaviest waves to break, either 

 partially or wholly, before they reach the work. Mr. 

 Leslie found that at Arbroath Harbour the works were 

 not so severely tried by the very heaviest class of waves 

 as by others of lesser size, which were not tnppe i np by 

 the outlying rocks. The same effect has also been ob- 

 served at the river Aln, where the smaller waves occasion 

 a greater " range " in the harbour than the larger ones 

 which break in passing over the bar, and are thus reduced 

 in height. The larger waves are not, then, always so 

 destructive as the smaller. It becomes, therefore, a ques- 

 tion of some moment to determine the maximum height 

 of wave that is possible in a given depth of water. 



Mr. Scott Russell, whose contributions to what may be 



» Mr. Hciwkesley, in th= "Proceedings of the Institute of Civil Engi- 

 neers," gives a formula which is satisfactory so far as it corroborates th-i law 

 of increase which I had stated in the Edinburgh Philosophical yonntal in 

 1852 ; b It he employs a coefficient which fiives much greater results than 

 my experience warrants. 



t " 'J'he Design and Construction of Harbours," by Thomas Stevenson, 

 F.R.S.E. (Edinburgh, 1864 ; p. 2j). 



