IV 
PREFACE. 
designation of Columns D, N, M, S, and R, for single lives, and 
Columns D and N for two joint lives for the Carlisle rate of mortality. 
Similar tables are given for single and joint lives by the Northampton 
rate of mortality at 3 per cent interest. 
It affords the Author great pleasure to acknowledge here the liberality 
of Messrs. Davies and Milne in giving permission to use their respective 
works to assist in the objects of this publication. From Mr. Milne’s 
work have been taken the values of Annuities by the Carlisle table for 
single lives, and at 5 and 6 per cent for joint lives. Mr. Davies’s work 
has furnished the rates of premiums for two lives by the Northampton, 
the values of policies by the same mortality, &c. 
The values for two joint lives by the Carlisle 3 per cent were kindly 
furnished by Mr. Ansell, Actuary to the Atlas Office, and for two joint 
lives by the Northampton 3 per cent by Mr. Ingall, Actuary to the 
Imperial. For the D and N columns by the Northampton 3 per cent, 
the author has to express his thanks to Mr. Keys, Secretary to the 
Guardian Assurance Office. 
It may be here remarked, that all the tables which have been con 
structed for this work have been done independently by two separate 
computers, and the results afterwards carefully compared. The tables 
for joint lives by the Carlisle rate of mortality at 3^, 4j, 5, and 6, per 
cent have the values interpolated for those ages where the difference is not 
some multiple of 5. The difficulty of guarding against every source of 
error in such a multiplicity of operations has always been felt by the 
author, but he trusts that the care which has been bestowed on the 
tables has been such as to render them entitled to confidence. 
For valuable assistance in the construction of the various tables com 
puted expressly for this work, the Author is indebted to his brother, 
Mr. Jenkin Jones, Actuary to the National Mercantile Assurance Office, 
and to Mr. David Jones, at present engaged in the service of the Poor 
Law Commission. 
Those who are not intimately acquainted with Algebra will find it 
convenient to possess the Treatise on Arithmetic and Algebra published 
by the Society, and frequently referred to in the present work.