2.44 



NATURE 



[May i8, 1916 



normal function. By supposing that a constant 

 of the theoretical normal curve, viz., its standard 

 deviation, was itself a variable, and assuming- for 

 the latter a convenient form, he succeeded in 

 obtaining a curve which effectively described cer- 

 tain symmetrical epidemics. 



Brownlee did not, however, obtain any function 

 which satisfactorily accounted for the marked 

 asymmetry which characterises many epidemics. 

 It is an interesting illustration of the way in 

 which apparently disparate problems are inter- 

 connected that his work owes much to the remark- 

 able memoir of Pearson and Blakeman on random 

 migration, a memoir inspired by the problem of 

 mosquito distribution suggested to Prof. Pearson 

 by Sir Ronald Ross. These researches, then, 

 which began in the a posteriori study of statistics 

 and were continued on the a priori assumption 

 of a normal function being at the root of the 

 problem, have carried us some way, but have 

 not so far provided us with a satisfactory mathe- 

 matical law of epidemics. Sir Ronald Ross, 

 whose interest in the subject dates from so long 

 ago as 1899, and whose latest contribution has 

 just been published, followed a different path. 

 Avoiding any presuppositions as to the form 

 which the law should assume, he looked at the 

 problem as one of transfer, viz., of mutual inter- 

 change between groups of affected and unaffected 

 individuals, an interchange complicated by the 

 subjection of each group to certain rates of 

 natality, mortality, emigration, and imrni- 

 gration. Being at first specially concerned with 

 the case of malaria, he formulated the problem 

 in the second edition of his treatise on the pre- 

 vention of malaria (pp. 651-686) in a system of 

 difference equations, the solution of which should 

 provide the required law. A summary of this, 

 work appeared in Nature of October 5, 1911, 

 under the title "Some Quantitative Studies in 

 Epidemiology." In the paper before us,^ these 

 ideas have been extended and clothed in a more 

 convenient mathematical form. 



Sir Ronald Ross's method may. be illustrated 

 by summarising the simplest of his cases. If P 

 be the whole population, x the ratio of affected 

 to all members, v and V measures of the varia- 

 tion due to mortality, natality, immigration, and 

 emigration of non-affected and affected persons 

 respectively, and if the proportion affected in 

 time dt he h . dt . P where h is a constant, then 

 we have the following system of equations : — 

 d?/df = 7'V-{v-Y)xF 

 dxVjdt = /^P( I - a:) + ( V - N - r)xV 

 dxYldt = xdYjdt + Vdxidi. 

 Eliminating dxF/dt and dF/dt, we have :— 

 dxjdt = h -{h + v-N-\r^ + r)x + (v- Y)x^. 

 If now, v = 'V, the equivariant case, the last equa- 

 tion can be written 



dxldf=K{h-x) 

 where K==>% + N + r and L = ^/K. 



Now put jF = L - jc and we have dy/y = - Kd/. 



4 " An Application of the Theory of Probabilities to the Study o^apriori 

 Pathometry." By Lieut. -Col. Sir Ronald Ro.ss. Proc. Roy. Soc, A, T916, 

 xcii., Z04. 



NO. 2429, VOL. 97] 



So that '\l y^ is the value of y at the beginnings 

 y=y^e~^' and x^'L-i^- x^e~^', 

 which gives the proportion of the total population 

 affected at time t, this proportion being x^ when 

 t = o. 



Sir Ronald Ross proceeds to investigate the 

 properties of this curve; he then takes the case 

 of V not equal to V, which is dealt with on similar 

 lines, and ultimately considers the curve arising 

 in the simplest case of departure from the assump- 

 tion that h is constant. The latter results are, 

 no doubt, still somewhat remote from the con- 

 ditions obtaining in practice, but they suffice to 

 illustrate the genesis of an asymmetrical curve, 

 and incidentally show that a form regarded by 

 Brownlee as inconsistent with an hypothesis of 

 constant infectivity and the termination of an 

 epidemic by the exhaustion of susceptible persons 

 may not be so. 



The advantage of Sir Ronald Ross's method, 

 apart from its simplicity and elegance — advan- 

 tages which are, however, no mean matters — 

 lies in its generality, so that it may be possible 

 to include the case hypothesised by Brownlee as 

 a particular example, precisely as Prof. Pearson's 

 system of skew frequency curves included the 

 normal curve as a special case. It is, of course, . ^ 

 too early to speak with confidence. As restric- i 

 tions are relaxed, the analysis will inevitably 1 

 become more intricate, and, having evolved an 

 a priori law, one must devise, usually by the 

 method of moments, a way of applying the law 

 to statistical data. This is work for the future, 

 and all epidemiologists will await with interest 

 the promised second part of Sir Ronald Ross's 

 paper. No sensible man doubts the importance 

 of such investigations as these ; it is high time 

 that epidemiology was extricated from its present 

 humiliating position as the plaything of bacterio- 

 logists and public health officials, or as, at the 

 best, a field for the display of antiquarian research. 

 The work of Sir Ronald Ross, of Dr. Brownlee, 

 and of a few others should at least elevate epi- 

 demiology to the rank of a distinct science. 



M. Greenwood, Jr. 



FROF. EMILE JUNGFLEISCH. 



PROF. EMILE JUNGFLEISCH, who^e death 

 occurred on April 24, at the age of seventy- 

 seven, was born in Paris in 1839. He devoted 

 himself to chemistry and pharmacy, and at an 

 early age joined the Paris Chemical Society. In 

 1863 he was appointed dispenser to the hospital 

 of La Pitie, and in 1869 qualified as pharmacist 

 and member (agrege) of the School of Pharmacy. 

 In the same year he became assistant (prepara- 

 teur) to Berthelot, who had recently been ap- 

 pointed to the new chair of organic chemistry of 

 the School of Pharmacy, and on Berthelot's 

 retirement in 1876 was made his successor. In 

 1890 Prof. Jungfleisch was nominated professor 

 of chemistry of the Conservatoire des Arts et 

 Metiers, and in 1908, again in succession to Ber- 

 thelot, was appointed to the chair of chemistry 



