936 



NA TURE 



[Dkcember 29, 1923 



WM absent from the island of Reunion, wtiere A . costalis 



waa present. I understand that Mr. ^! '' "r 



foand A. funestus in numbcrH during tht- : 



summer when we were in the island ; but, ii 

 to all this, it is most remarkable that Mr. 1)1 

 who was appointed in cliargc of the ai 

 measures after we left, had not detected thi^ 

 during all these years. The most likely 

 appears to me to be that A. funestus has Ixien im- 

 ported quite recently. I woncier whether it has also 

 appeared in Reunion. 



In my report I discussed the question whether 

 malaria had been introduced into Mauritius and 

 Reunion in 1866-7 (^s was the cjise) by the intro- 

 duction of large numbers of coolies from India, or 

 by the introduction of A . costalis, and I preferred the 

 latter theorj'. Against the coolie theory there was 

 the fact that Indians had been pouring into both 

 islands long before those years. 1 thought it more 

 likely that A . costalis had been brought in some time 

 previous to 1866, possibly by some ship. If therefore 

 A. funestus has been a new introduction, this hypo- 

 thesis of mine will be further supported. The entire 

 absence of both species from Rodrigues is another 

 confirmation. The most likely picture appears to 

 me to be that all three islands were Anopheles-free 

 up to 1865 or so, but that two of the islands have 

 become infected since by shipping from Madagascar. 

 I understand that both species are absent from India, 

 but have not been following the recent literature. 



It is very disappointing that all the antimalaria 

 measures advised by me have been allowed to fall 

 into abeyance in Mauritius, and I have long been 

 convinced that anti-mosquito work will not be properly 

 carried out in British dominions until stronger dis- 

 cipline is enforced. Ronald Ross. 



Methods of Chemical Reactions. 



The general scheme of a chemical transformation 

 can be reproduced by the equation : 





-}-;»r2AdB,C, 

 +>'2A,B,C, 



+;«r8A,BAC, . . . + 



+>'gA,B„C, 



+ . 



A, B, C represent chemical elements or groups of 

 elements, which are transferred as whole complexes 

 from one side to the other of the chemical equation 

 {i.e. NH4, SO^, NO2, etc.). We shall call these groups 

 of elements for short the elementids of a chemical 

 equation ; the chemical elements are thus the simplest 

 elementids. It is evident that in determining the 

 number of elementids of a chemical equation the 

 minimum rule must be observed — that is, the elements 

 must be brought together into groups, so that the 

 number of these groups (elementids) shall be the 

 smallest possible. The composition of these groups 

 must fulfil one condition : that their number taken 

 as a whole and for each formula individually should 

 be the same on the right and on the left side of the 

 chemical equation. In most cases the problem of 

 determining the elementids is simplified by the fact 

 that the number of elementids is the same as the 

 number of elements. 



a, b, c, d, etc., as usual in chemical equations, are 

 numbers showing how many times a given element 

 (or elementid) occurs in the composition of a chemical 

 compound. Equation ( i ) contains molecules composed 

 of all elements of a given chemical transformation ; 

 of course, the absence of some elements in the com- 



Eosition of a particular chemical molecule is expressed 

 y making the corresponding multiplier {i.e.. a or b 

 or c, etc.) equal to zero. 



^i. •*2. ^». also yi, Vj, y,, etc., are the numerical 



NO. 2826, VOL. I I 2] 



coefficients to be determined by chemists using: 



chemical equations. i 



To determine these coefficients algebraically, aOv^ 



rr.r.iin^ to the rule requiring an equal number <if^| 



its on both sides of a chemical equation, 



rite : 



Xib+x^ +xji + 

 XiC +xlf + x,l + 



=yi» +y^ +y9» ? 

 =yiP +yt^ +>'•» + 



In calculating the numerical values of the co 

 efficients ;r„ y,, x^, y,. etc., as required by stoichio- 

 metry, the following rules must be observed : first, 

 all the coefticients must be whole and positive 

 numbers ; the coefficients must not have a common 

 divisor. This last condition is satisfied by giving 

 the smallest possible whole number to the coefncient 

 of the molecule occurring the least number of times 

 in a chemical reaction. 



It follows from the series of e(]uations that the 

 number of elementids of a chemical equation corre- 

 sp>onds to the number of separate equations serving 

 to determine the necessary coefficients ; and the 

 number of heterogeneous molecules (separate sub- 

 stances) taking part in a chemical reaction corresponds 

 to the number of unknown quantities. Hence : 



In the simplest case the nutnber of separate sub- 

 stances taking part in a chemical reaction will be 

 greater by one unit than the number of elementids. 



To illustrate this we shall give several chemical 

 equations : 



(a) Two elements and three substances : An example 

 of the simplest reaction is the formation of water 

 (two elements, H and O, and three substanc< 

 Oj, and HjO). 



(ft) Three elements or elementids and four subslatu^s : 



(i) 2CgH402+Zn =Zn(C,H,Oj),+H, ; tb^ tlir^ 

 elementids are Zn, H, and CjH,Oj. 



(c) Four elements and five substances : 



4S -f6NaOH =2Na,S -hNa,S,0, + 3HjO. 



{d) Five elements and six .substances : 



2Sr(NO,)j -f6NH«Cl =2SrClj -l-sN, -HCl, - I J i 1 ,u. 



{e) Six elements and seven substances : 



KgCraO, -1-6HI +4HjSO« = KjSO« -l-Cr,(SO,), 



-h7H,0-|-3l^ 



More complex chemical equations containing more 

 than six elementids are comparatively rarely met with 

 in chemistry. 



We shall now investigate an example in which 

 seven elements and eight substances take part in a 

 reaction : 



;r,K,Co(CN), -f;r,HjSO, =:v,CoS04 +y,K,SO« 



+ V3(NH4)jSO, +>'.CO -f-v.CO, +ytSO,. 



By solving the algebraical equations corresponding 

 to this chemical reaction we get the following : 



2K,Co(CN), +24HJSO4 =2CoS04 +3K,S04 



+6(NH4),S04 -1- 1 iCO -l-CO, + 13SO,. 



This reaction is so complex, that even Prof. 

 Treadwell, who did not know of the algebraical 

 method of finding the coefficients, wTote the equation 

 wrongly from the strictly stoichiometrical point of 

 view-. His rendering of it was as follows : * 



2K,Co(CN), + i2HjS04 + i2H,0=2CoS04+3K,S04 



+ 1 iCO -hCO, -t-6(NH4) JSO4 -hSO,. 



' Treadwell, " .Analytical Chemistry," voL iL 



