124 Mr. Gwyther on the 



En Angleterre, on adopte assez communement la derniere 

 proportion : dans d'autres pays il ne parait pas que la mor- 

 talite de cette maladie soit si grande. 



" Quant a la proportion qu'il y a de la mortalite de la 

 petite verole a la mortalite entiere du genre humain, on a 

 suppose communement en Angleterre comme i a 14 : il ya 

 la-dessus des listes rapportees par M. Susmilch, qui mar- 

 quent qu'a Londres il est mort de la petite verole 19,745 

 sur 260,875, ce qui donne la proportion i a 13V5; a Vienne, 

 cette maladie a enleve 1,083 sur 13,521, c'est i sur I2j^; a 

 Berlin, 586 sur 6771, c'est i sur ti^; a Breslau, 431 sur 

 4,579, c'est I sur 10^. Mais ces dernieres proportions n'ont 

 ete prises que pour deux et trois ans pendant lesquels il 

 peut y avoir eu une epidemic un peu forte." 



I am unable to state what is now regarded as the 

 average ratio of deaths to cases, but during the last ten 

 years the ratio of deaths from small-pox to the total deaths 

 has been about i to 286, and during the epidemic "un peu 

 forte" of 1 87 1 -2 the ratio was about i to 23^. 



It is necessary to note this change to understand at all 

 how it was possible that his mathematical results which I 

 am about to notice could have seemed to represent in any 

 respect the rate of mortality at the time. It must be borne 

 in mind that the mortality tables which they had were very 

 defective ; but the objections to the paper seem to have 

 been founded on minor points, and not on any doubt of its 

 general representation of the facts of the case, while at the 

 present time the divergence of his results from actual expe- 

 rience would be patent to everyone. The investigations of 

 which I speak are two, which I shall give in only slightly 

 modified form : — 



I. To find the ratio between the number of those at an 

 age X who have not yet had small-pox, and the total num- 

 ber of survivors at that age. 



Let the age be expressed by x, the number of survivors 



