498 



NAl URE 



[February 8, 19 12 



formulrt-, liow- 



iml; 111 i\'. i!, :iii'l 



,M, i;,,„i ■. ,, ,1.1 



ih. 



|)l IjMll.ll .' HI 111 \\ 



\i Ai li' il I (|ui!il'riuin. 



\\ . iii.i\ lliiii priM I <(1 a^ follow - : 

 I.. 1 \ !»• Ill" lol.-il iKimlM-r of lli>- 1' 



nuinlii I .iri1i(l((l Willi lln- dis'Tisc 

 I.il S N.v !>.■ ih.- lol.-il iiuiiilur i 



fill!.. .Itlll lit S, \ K l.i ill.' lUIMlli 



oi liinr dill' lo 111' (li~. .1^' I .iridic]. 1 1 (1. 



ln|)ul:ili 



.r ol I 



-. ])ir unit III 

 ■.illi^ |M I unil 



N 



I" 1 



X, 



be the total number of in(li\ kUi.iN 



rliiiiiii.ilid ffom 111!' agc;i'i-.t;nt'^ of riisr-nsirrl prrsnir^ P'r unit 

 of linir fioin all cali-.i-, iiichlilini; di'allis l)\- ih.- <ll-..:i~.- 

 uniliT rniisidrralioii, li\ oi lur di^'-a^i'^, and aUo r'-covn i'-. 



W'hrii a slatioiiar\ roiidiiion i-- n-acliid, ir, mii--t 1)'' 'tjiial 

 (o ilii' rii'i|)ro(al of tli' iiuan duration L ol iln- diM-a--i-. 



In llii- ca'-c we ha\i', llnii, 



\,M = N, 



(i> 



Furtlierinori', if -y i-; a factor indicating tliat fraction of 

 the total di aili- wliirh i^ due to the disease considered, 

 then 



NiX, = N,^=7N. (2) 



Hence 



or, solving for L, 



N T 



1.= 



N, T 



N 7^ 



(3) 



(4) 



dt 

 d^ 

 dt 



=.kz{J>' -%') + q'z' 



(s) 



(6) 



By the wa}' of a numerical example, I will substitute in 

 the formula thus obtained some data slathered from the 

 statistics of New York City. The supposition of a 

 stationary population and equilibrium condition of the 

 disease is quite unwarranted here, but in the absence of 

 more suitable material, and in view of tlv^ i^i' :it un- 

 certainty of the figures obtainable, we shall hav to rest 

 ■content with this very crude illustration. 



In 1909 the population of New York numbered about 45 

 millions. The total number of consumptives at the time 



N 

 has been estimated at about 45,000. Hence — i = 0'oi. The 

 * N 



death-rate per head per annum from all causes was 0016; 

 that from tuberculosis alone, 0002. Hence 



5 = o-oi6 

 75 = 0-002 

 7 = 0-125. 



The coefficient t represents a measure of the " deadli- 

 ness " of the disease — i.e. it expresses what fraction of the 

 persons once struck with the disease ultimately die there- 

 from. It is difficult to obtain any kind of estimate of the 

 value of T. We will assume that t=o-8. 



We then have by (4) 



J _0'oi xo'8_ 



L. 4. 



O'0O2 



In view of the crudity of the data on which it is based, 

 this calculation must be regarded purel\ ;is an illustration 

 of the principles involved, and not in any si-nse as an 

 attempt to determine L, although the endeavour has been 

 made to preserve at least the right order of magnitude in 

 the example given. 



II. 



In dealing with metaxenous diseases. Sir Ronald Ross 

 obtains the equations 



'^' = k'z'(p-z) + <jz 



NO. 2206, VOL. 881 



He points oiu that 



di~ dt 



when 



' LL't,' l„ 



i : i> introduce new variablns 



IU|.K|.^ 



dt 



dt 



a/. 



(8) 



(9) 

 10) 



whore the coitTai. iii ~ u, <i , '•. : ■• tunctioiis of 



k. k'. p, p'. ./, ./ . 11 thi-^i' laii' ^tant, the solu- 



'■ ' III), (I.;) < -•in inun '■ •■•". down in 

 im, nami'ly, 



and a ><imilai <• rii- for '/.' . '\'h< 



can In- cvahialid l>\ -uli-lilur 

 original cqualion^ and i-qiialin^ ii;- 1 i» 11,1 !• p.i - 

 lof^ou-~ liiin-- of till- rif^hl-hand and l>ft-lian<l u, 

 particular, we thus obtain 



// = - i \{a + />')+ \'{a-d'f + 4a'f 



il - \ 'Ja--^ b') - J {a - />')' + 4a V;; . 



'i lii^ I'r^ul; ilirow- an interestinil litjht on tt;- 

 of ill'- path ti\ wliiih thf fin.! 

 rcaclii (1 ; ihi- proc >> i> o^iillali)r\ 



(a - />')- + 4a't'>-:o 

 The solution {13) is th^n preferably wriin n in iriimno- 

 metric form, 



Z = <'~'^(P|Cos;//-J-Q,sin;//)-f <"-""(PjCos2///- i^._...... .;... . ... . 



<■"'""'( 1'., c.i- 3/,'.' i^).;sin j/;/ + R3 COSMZ+Sssin «/)•+ ... (16) 



with a similar s 1 ir^ for Z'. It will be observed that for 

 large values of / hoih Z and Z follow the law of damped 

 harmonic oscillation, with a common period, and a phase 

 difference depending on the value of the constants 

 n, a', h, h'. 



In conclusion it may be remarked that Sir Ronald Ross"- 

 equations (5) and (6) can still b>' ^^olved by the metho<i 

 here set forth if the coefilcients k. />', />. />', q, q' of thos-- 

 equations are not constants, but functions of 5 and z'. 

 The right-hand members of equations iii) and (12) are then 

 obtained as Taylor's series for two variables, and thus 

 extend to an infinite number of tcrnT;. Th:~ dofsnot in 

 any way alTcir the form of the sohn • -Ahich 



n-niain \;ilid al>o in these circumstaiii 



NATIONAL SYSTEMS OF K PI CATlo.X . 



'1"*HE Internatioml Couni ii ■: W r n i.t- ;~- . 



special pamphlet .11; 

 Education," which oiii^lit i.- 



and to the large body of voli;r,i,ii> -v\o:iv-is wlio iiuercit 

 themselves in educational proi^n >-. Ih-- i)aniphl>t com- 

 prises short accounts of the 1' adinj; features of educiation 

 in the various countries or Stales represented within the 

 International Council of Women — L'nitid States, Canada. 

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 Netherlands New South Wales, \ictoria and Queensland 

 in .'\ustralia, Tasmania, .\ew Z'-aland. France, Switzer- 

 land, Austria, Ilunt^arv, \orwa\', Belgium, Greece, Russia. 

 Finland, Italy, Servia, and Bulgaria. 



These accounts have been contributed by the members of 



1 First Report of the Education Committee of the Internat'onal Council 

 of Women, compiled by Mrs. Oailvie Gordon, Convener. Pp. 94. (.-Vber- 

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