59 



A NOTE ON THE ARITHMOMETER AS AN AID TO 

 ACTUARIAL WORK. 

 By F. J. Jacobs, A. I. A. 



The arithmometer is peculiarly adapted for working out the 

 chief details of a classified valuation of a life assurance office. 

 The process is a simple one, being merely a series of multipli- 

 cations, and the work cau be carried out very rapidly by an 

 ordinary computer. The results worked out and set down by 

 one computer can be checked and verified by a second com- 

 puter usiug a different machine, while any errors in the 

 original work may be investigated by a third worker, using a 

 third machine. By this means complete accuracy is ensured, 

 and the use of the different machines avoids any possibility of 

 error should either of them happen to fall out of order and 

 become liable to repeat its own mistakes. 



Several able expositions of the uses of the arithmometer 

 have been published, and amongst them may be cited papers 

 by Major-General Hanuyngton and Mr. Peter Gray in the 

 16th and 17th volumes respectively of the Journal of the In- 

 stitute of Actuaries. At the beginning of his paper Mr. Gray 

 remarks : — " It is usual to describe the arithmometer as a 

 machine which enables a person, however unskilled himself, 

 to perform the operations of multiplication and division with 

 facility, rapidity, and unfailing accuracy. This, as a descrip- 

 tion, is correct as far as it goes, but as an enumeration of the 

 properties of the machine it is inadequate and defective. It 

 entirely omits that property which forms its special adapta- 

 tion to our purpose, and in default of which its utility would 

 be comparatively limited. Besides the facilitation of the 

 operations named the machine will also in forming the product 

 of two given numbers either add that product to or subtract 

 it from another given number according to the pleasure of the 

 operator." Mr. Gray then proceeds to give illustrations of 

 the adaptability of the machine for the construction of tables, 

 and amongst the acturial problems he investigates are : — 



1. To form a table of assurances from a corresponding 



table of annuities. 



2. To construct a table of policy values from a given 



table of annuities. 



3. To construct commutation columns from any given 



mortality table. 

 Amongst modern tables constructed by the calculating 

 machine must be mentioned those computed by Mr. David 

 Carment, F.I. A. A copy of the work is submitted for inspec- 



