492 SCIENCE PROGRESS - 



people and 3,000 Anophelines, p — 1,250, m — o"6, a = 2"4; 

 and we calculate roughly that the number of infecting Anophe- 

 lines and also of inoculations will be about 9'4." (It is not 

 clear, however, to what length of time this applies, whether 

 week, month or year.) 



It is pointed out further, however, that a mosquito which 

 is infective may bite a person who is already infected, so that 

 the expression b^saimp does not denote the new infections. If 

 mp denotes the number of persons already infected, p — mp 

 denotes the number of healthy persons. Then the number of 

 mosquitoes which succeed in biting healthy persons is shown 

 to be b'sai{\ — ni)mp ; and if each of these mosquitoes bites a 

 different person, the expression will denote the addition to the 

 number of cases of malaria in any locality during a given 

 period. 



It is extremely doubtful, however, if the biting factor can 

 be expressed so simply as is suggested by Ross. It is known 

 that the malarial parasite requires a certain length of time to 

 develop in the mosquito; on p. 52 this period is stated to be 

 ** more than a week." During this period the mosquito pro- 

 bably feeds one or more times without being in a position to 

 produce an infection; on p. 55 we are told that Anophelines 

 feed " every few days." If, for example, we put the develop- 

 mental period of the parasite at eight days, and suppose that 

 the mosquito feeds every three days, it is clear that it will not 

 be able to produce an infection before its fourth feed, counting 

 as the first that at which it took up the parasite. It is not 

 necessary to suppose, however, that all these four meals must 

 consist of human blood ; it is only essential, in all probability, 

 that the first and fourth feeds of the mosquito should be at 

 the expense of human beings, in order to produce an infection 

 of malaria. 



Following Ross's method, let b, as before, express the pro- 

 portion of Anophelines, say \, which succeed in biting human 

 beings, and b^ the proportion, say ^, which succeed in biting 

 any vertebrate during a given time ; then the biting factor must 

 be expressed by bb^-, = -f/ir, or •sV approximately ; in any case 

 it is less than yV (^^), since b^, whatever value be given to it, 

 must be less than unity. But this again is far from expressing 

 accurately the complexity of the actual state of affairs, since 

 it is highly probable, from what is known of the transmission 



