60 NOTES ON THE ARITHMOMETER, ETC. 



tion. These tables show the value at the end of any number 

 of years of an endowment assurance for <£100, payable at 

 different ages and under different rates of interest, according 

 to the " Institute of Actuaries H.M. Tables of Mortality." In 

 constructing these tables Mr. Carment utilised a modification 

 of Gray's continuous method, and, speaking briefly, the work 

 consisted in placing upon the machine a constant (the recip- 

 rocal of a certain function) and multiplying this by the suc- 

 cessive differences of another function, the results being, of 

 course, taken down after each operation. The process of the 

 work is lucidly explained by Mr. Carment in the preface to 

 his tables. It must be noted that the multiplication referred 

 to is performed continuously, and that each step is performed 

 without erasing the result attained by the preceding operation. 

 The correctness of each column of results is proved by a very 

 simple calculation. The whole of the tables were calculated 

 by means of the arithmometer, with the exception of a small 

 portion at the end, which, owing to the partial breakdown of 

 the author's machine, were done by another process ; the 

 book is an interesting example of the work that can be per- 

 formed by the calculating machine. 



I have frequently had occasion to use the arithmometer in 

 the computation of different results, and have found it a most 

 correct and expeditious means of performing work that might, 

 under ordinary circumstances require a tedious mental appli- 

 cation. The arithmometer now exhibited by Mr. Johnston is, 

 as he has stated, of the latest pattern, and combines the 

 original model with a stability and perfection of construction 

 that should reduce to a minimum the possibility of errors 

 arising from imperfect or impaired machinery. 



