I February 8, 19 12] 



NATURE 



497 



when sixteen communications were made and discussed. 

 Many are of general interest :— Voeil^off (St. Petersburg)] 

 the influence of water on the heat balance of the earth ; 

 \ernadski (St. Petersburg), gaseous interchange in the 

 earth's crust; Tochidlovsiii (Odessa), formation of the 

 elements of fog ; Aganin (Odessa), new hypothesis of forma- 

 tion of thunderstorms ; Dubecki, actinometric observations 

 at the glacier of Berei. In the joint meeting of this 

 section and the Section of Physics four communications 

 were presented. Prince Golitzin (St. Petersburg) gave an 

 account of the actual state of seismologv, and Rosenthal 

 (Warsaw) spoke about the determination of the depth of 

 the origin of earthquakes. 



(5) Considerable interest was taken in the Section of 

 Astrophysics ; in three meetings eleven papers were read. 

 Of these we mention :— Amaftunski (Vilna), theory of sun- 

 spots as resulting from the activity of prominences ; Tikhoff 

 (Pulkovo), on the scintillation of stars; light-filters applied 

 to the study of physical properties of Mars and Saturn ; 

 optical properties of solar prominences ; Donich (St. Peters- 

 burg), astrophysical investigation of complete solar eclipses ; 

 Neuimin, advances of seienium-astrophotometry ; Arzik- 

 hovski (Novocherkassk), spectra of planets obtained by 

 Slipher, and the spectrum of chlorophyll. 



Many papers were also read at meetings of the sections 

 of metallography and technical electrochemistry; aero- 

 dynamics ; biochemistry and biophysics ; agricultural chem- 

 istry ; hygiene ; and didactics, the last-named being devoted 

 to methods of teaching physics and chemistry in colleges 

 (gymnasiums), and kindred matters. 



The exhibitions of physical and chemical apparatus were 

 very successful, and many foreign firms took part in them 

 (viz. A. Hilger, C. Zeiss, Heraeus, Fiiss, and others). In 

 spite of the cold (on some days a temperature of —25° was 

 registered), more than sixty excursions were made to 

 different works and institutions of St. Petersburg and its 

 environs. Almost all museums were open to the members 

 of the congress, and the provincial members made the 

 most of this occasion to acquaint themselves with the 

 ( apital. After the end of our congress many members took 

 part in the Congresses of Applied Geology and Mathe- 

 matics, which were inaugurated in St. Petersburg on 

 January 9. 



RELATION BETWEEN HEIGHT AND LENGTH 



OF THE WAVES FINALLY PRODUCED AT 



SEA BY WINDS OF ANY GIVEN SPEED.' 



Q.BSERVATIONS made by the author, and those cf 



Scoresby, Paris, Abercromby, and others, show that 



when the waves in a storm are fully developed thev tra\«el 



with the same speed as the wind which produces them. 



If there be any excess velocity of wind, such as might be 



>upposfd necessary to prevent the waves from flattening out 



through the effect of friction, it is a quantity so small that 



it falls within the errors of observation. Siniilariv for the 



breakers which reach our coasts after storms in the 



Atlantic, the author has recorded periods which show a 



<leep-water velocity equal to the maxirnum recorded velocitv 



"f the wind during the same spell of weather, the latter 



ing in one case Beaufort's force 11, or 64 statute miles 



I'r hour, and in another case Beaufort's 12, or 77 statute 



miles per hour. He has never recorded breakers with a 



■^peed equal, or nearly equal, to the speed which the wind 



iiomentarily attains in gusts, the speed of the waves not 



Kceeding the average speed of the wind. The observations 



ulicate that if there be any waves which travel faster than 



!)e wind, they do not attain sufficient amplitude to form 



rriakers. 



Since the highest waves finally produced travel with the 



line speed as the wind, their period and length can be at 



luc precisely calculated for any given speed of wind. The 



lorcied heights of fully developetl waves for all weathers, 



iiom " strong breeze ' to " strong gale," 25 to 44 statute 



miles per hour, are proportional to the speed of the wind, 



tlie nuiilipjier being 07. Thus the height of the waves 



finally produced in a strong breeze, such as that of the 



trade winds, i^ 25x07= 17-5 feet, and in the ordinary 



1 Summary of a Cantor lecuire delivered before the Roy.il Society of Arts 

 on January 22 by Dr. Vaughan Cornish. 



NO. 2206, VOL. 88] 



strong gale of the N^irth Atlantic 44x07 = 30-8 feet, 

 ine length of the waves being precisely calculable froir 

 the speed of the wind, their flatness can be calculated bv 

 dividing by the empiric number for height. The ratio of 

 length to height is thus proportional to the velocitv of the 

 wind, the multiplier being 06. 



The author recently obtained measurements of large 

 waves in unusually favourable circumstances, the ship, 

 P. and O. ss. Egypt, being hove-to for nine hours in the 

 Bay of Biscay during the storm of December 21, 191 1. 

 The following' velocities of wind are the means of two- 

 sets of estimates of the Beaufort's number. At 4 a.m., 

 velocity of wind, 485 statute miles per hour; 8 a.m., 46-5; 

 noon, 355. The velocities of the waves were : — 8 a.m., 

 47 statute miles per hour; 10 a.m., 43-5; noon, 39-5. At 

 10 a.m. the prevailing height of wave was 31 feet, very few 

 being lower. There was no "swell," i.e. no waves longer 

 and flatter than these, neither were there any noticeable 

 short waves. This remarkable " sea " was the effect of a 

 very strong wind upon a heavy swell already running in 

 precisely the same direction. The speed of this swell, as 

 observed in the positions occupied by the ship on the 

 preceding day, was 40 statute miles per hour. Its heiglit 

 was usually about 15 feet, individual crests rising occasion- 

 ally to a little more than 20 feet. 



QUANTITATIVE STUDIES IN 

 EPIDEMIOLOGY. 



'T'HK publication of a paper on this subject by Sir Ronald 

 Ross in a recent issue of N'ATtRE ' prompts me to 

 present a note which I had been holding over for a longer 

 article, and have also incorporated in a paper read before 

 the Washington Philosophical Society.' .At the same time, 

 I wish to offer a solution for a certain system of differ- 

 ential equations obtained by Sir Ronald Ross — a solution 

 which presents certain points of interest. 



I. 



We may set ourselves the problem of investigating the 

 relation between the number of the infected population 

 (the focus of infection), the total population, the 

 " infectiousness " of the disease, and its mean duration. 

 We shall here restrict our considerations to the case of a 

 ' disease such as pulmonary phthisis, which it> more or less 

 constantly present (i.e. not epidemic in its occurrence). 

 Brief reflection shows that we can apply to this case a 

 mathematical treatment precisely analogous to that of the 

 growth of a population ; for we may think of the diseased' 

 portion of the population as a separate aggregate, into 

 which new individuals arc recruited by fresh infections, 

 just as now individuals enter an ordinary population by 

 procreation. On the other hand, members are continually 

 eliminated from the aggregate, first by deaths, secondly 

 by recoveries. On the basis of these considerations, 

 formula; can without difficulty be established between th-- 



1 October 5, 1911, p. 466. 



'^ November 11, 1911: "Kvolution in Di»cominuou» Syntem*." Pub- 

 lished in the Journal of the Washington Academy of Sciences, January and 

 February, igia. 



