In order to bring this matter to the test of calculation, in order also to institute a comparison of the mortality of Small Pox as influenced by Vaccination, as well as by Inoculation from itself, I have selected from the bills of mortality four periods, each of fifteen years, for the purpose of exhibiting the mortality of Small Pox in each of these series in regard to each other. These are thrown into the form of Tables, and annexed to this article. The first series, is the fifteen years immediately preceding the introduction of Inoculation; that is, from 1706 to 1720, both included. Previous to this period, no account that could be depended upon regarding the Small Pox, could be derived from the bills of mortality; for down to the beginning of last century such was their imperfect construction, that Small Pox, Measles, and Flux were blended under one head. Exception may be taken against the accuracy of these bills, even in this improved state, particularly with regard to the discrimination of diseases. This objection, however, is certainly less applicable to Small Pox than any other disorder, its character being so striking as not to be mistaken by the most ignorant and careless observer. The second series is taken at the middle of the last century, when Inoculation had made considerable progress; that is, from 1745 to 1759, both included. In comparing this with the preceding series, with regard to absolute numbers, it ought to be taken into account, that eleven parishes were added to the bills of mortality, between the years 1726 and 1745, both included: so that the progressive improvement of general salubrity ought to be estimated still higher than what is indicated by the diminished mortality, as it stands in the Tables. The third series comprises the fifteen years previous to the introduction of Vaccination, when Inoculation had made still greater progress; that is, from 1785 to 1798, both included. The fourth series comprises the time in which the vaccine Inoculation has been so far diffused as to produce a notable effect on the mortality of Small Pox; that is, from 1804 to 1818, both included. The result of these computations stands as follows:— _Ratio of the Mortality of Small Pox to the total Mortality._ From 1706 to 1720, one in 12.7; that is, 78 in 1000. From 1745 to 1759, one in 11.2; that is, 89 in 1000. From 1785 to 1798, one in 10.6; that is, 94 in 1000. From 1804 to 1818, one in 18.9; that is, 53 in 1000. Fractions are not noticed in the last column of numbers.