1013 



TABLE. 



TABLE. 



3.1 ; 



extension of his original plan. The only tables in existence for every 

 combination of two lives had been published by Mr. McKean, in 1837, 

 giving on one large sheet the rates 3, 4, 5, 6 per cent., by interpolation 

 from the Carlisle tables. Mr. Jones (whose work was completed in 1843) 

 gave every combination for 3, 3 J, 4, 4J, 5, 6 per. cent., both in the annui- 

 ties, and in Barrett's subsidiary tables ; that is, twelve tables for all 

 combinations, instead of four tables * for combinations differing by 

 multiples of five years of age : and this far from all. A short account 

 of some of the tables since published will show that the example has 

 been vigorously followed ; both as to the completion of things which 

 had been but partially done, and as to the origination of new under- 

 takings. 



In saying that the Useful Knowledge Society first showed the way, in 

 actual print, to the construction of more extensive tables, we should 

 commit great injustice to a most daring and persevering calculator, if 

 we omitted to notice that Mr. Edward Sang could have received no 

 hint from their proceedings. His ' Assurance and Annuity Tables,' 

 Edinburgh, 1841, large folio, give, for one life and 3 per cent., almost 

 every deduction from the Carlisle tables which an actuary could have 

 supposed possible to be wanted. And Mr. Sang worked with his 

 hands t as well as with his head. Over and above a table of five- 

 decimal logarithms and antilogarithms, every result in the book has its 

 logarithm attached to it. And with this we have the present values 

 of every annuity and assurance, temporary or deferred, which can be 

 on one life, at any age, and for any duration or deferment : 

 together with a mass of values and premiums for other cases which we 

 shall not attempt to specify. In 1859, Mr. Sang published a second 

 volume, containing, also for 3 per cent., a body of results on two 

 lives which meet all the actuaries' cases ; also with logarithms attached. 

 _The offices, and many of the actuaries, were at first inclined to look 

 very coldly upon these magnificent efforts ; but, so far as we have 

 observed, we think there is now a disposition to acknowledge their 

 utility : their merit was never denied. 



Mr. Jones and Mr. Sang, independently of each other, showed that 

 there was no occasion to be frightened at the notion of calculating and 

 i 'I all the cases of a problem of two lives, or of one life for terms 

 of yean : at the time when they began their labours, a routine had 

 been established by the consent of several distinguished writers, which 

 consent caused ordinary calculators to look upon anything beyond the 

 routine a next to impracticable. In 1848, Mr. T. Wigglesworth, in 

 ' Carlisle Probability-Tables of the Logarithms . . . .' London, 8vo., gave 

 the logarithm of the chance of surviving every number of years, at 

 every age, from the Carlisle tables. In 1850, Mr. W. Orchard, in 

 ' .Single and Annual Assurance Premiums,' London, 8vo., gave tables 

 for converting the value of an annuity into the single or the annual 

 premium for a corresponding assurance ; the necessity for which often 

 arrives in masses of instances together. The rates are 2J, 3, 3^, 4, 4, 

 .tnd 7 per cent. 



In 1850, Mr. H. E. Filipowski, in an appendix to hh work on anti- 

 logarithms, London, 8vo., gave Carlisle annuities at 3 per cent., for 

 three joint lives, for all combinations of quinquennial ages. This is the 

 first table of three lives : nothing more than specimens had been pre- 

 viously published. 



la 1851, Messrs. P. Gray, H. A. Smith, and W. Orchard, in ' Assu- 

 rance and Annuity Tables,' London, 8vo., gave, for the Carlisle 

 tables, at 3 per cent., the premium and the annual premium for 

 every case of survivorship assurance on two lives. In 1850, Mr. W. T. 

 Thomson, of the (Scotch) Standard Life Assurance Company, pub- 

 lished, in fif teen t sheets, meant to be joined in one, what we may 

 describe as, for the Carlisle tables at 3 per cent., a collection of 

 Barrett's tables, one for each age in the tables : or the number 

 living at every age of life discounted to every lower age. This table 

 might have had its use, if Mr. Thomson himself had not superseded 

 it, in 1858, by his bmk, entitled ' Actuarial Tables, Carlisle Three per 



to the undertaking, would not hare ventured to propose such an unheard-of 

 extent of Ub;e; and this extent was proponed to him, and not by him, during 

 the actual progress of the work. It was Mr. Jones who flrst proposed a large 

 extension ot existing means, and the Society asked for more. 



In our first article appear* tbe following : " The work of Mr. Jones on 



Mr fcuig arranged the types in the hoxc, before using them, with all the 

 cai'c of composition, und set them up in the boxes all in one way. He then set 

 the types for printing from with his own hand*. The second volume wns 

 treated in the same way by his computers. A computer can set up the types 

 from the original calculations; and thus the labour and risk of re-writing are 

 avoided. The time of setting up was ultimately reduced to not much more 

 than what would have been required for re-writing the manuscript ; the com- 

 uter after very little practice, were able to outstrip the speed of ordinary 

 -itor*. The only predecessor of Mr. Sang in this matter that we know 

 if is Mnstlinnr, who, in 159(i, while superintending some printing for Kepler, 

 writes that thc'ubles have been very badly described (a to structure), and adds, 

 lliitcnullut tyjxitlietarum operi mama admotere poteit : Jpse rogor typulhrttim 



t"ibi form U impracticable. The fifteen sheets joined together make a table 

 of 9l feet by 4? feet. This is too much, even for the wall of an office. We 

 examined the table by nailing the sheets against the front of a bookcase, and 

 atlas a step-ladder, as Gulliver did when pursuing his studies at Brobdmgmg. 



cent.,' Edinburgh, 8vo., giving the ultimate elements of the old form 

 of calculation : that is, the present value and logarithm of every year 

 of annuity, and the logarithm of the risk of death iff each year, from 

 and after every age. These values are put together in successive sums 

 so that the present value of every deferred annuity, and of every 

 deferred and temporary assurance, is gained directly from the table. 

 A complete table of probabilities of living, logarithms and primitives 

 both, is also given; with some other tables. In 1858, Mr. David 

 Chisholm, in ' Commutation* Tables for Joint Annuities and Survivor- 

 ship Assurances, based on the Carlisle tables at 3, 34, 4, 5, and 6 per cent.,' 

 London, 2 vols., 8vo., introduced, in addition to Barrett's tables for 

 two joint lives, the form for survivorship assurances, by which sucli as- 

 surances for terms of years, or when deferred, are immediately 

 calculated. There are other efforts with which we are not acquainted : 

 from those which we have cited, the reader may see the very great 

 progress which the actuary's tables have made in the last twenty 

 years. 



AYe shall mention a literary curiosity of the subject, the spurious 

 edition of Francis Baily's celebrated work t on Life Assurance : the 

 only instance in modern times, we believe, in which a heavy work of 

 algebra and tables has been counterfeited. The genuine work, though 

 never out of reputation, was soon out of print : and such copies as were 

 sold by auction fetched enormous prices. About the year 1850, copies 

 of the work, in appearance, were ottered at the assurance offices at less 

 than a quarter of the old auction prices : which were discovered on 

 examination to be spurious. The type, paper, &c., of the genuine 

 work had been imitated almost to the smallest points ; but the careful 

 supervision which Baily always gave to details, and the excellent per- 

 formance of his printer, could not be imitated. Those who do not 

 know the original edition will immediately detect the spurious edition 

 by an inverted 8 being always used for the letter p. Shabby as the 

 undertaking was, it invaded no copyright : and as no one now much 

 wants Baily's work for the tables, so that it matters less whether these 

 be accurately reprinted or not, it must be granted that the still valuable 

 part of Baily's work has been made more accessible, and therefore 

 more useful. We are of opinion that an edition of the work, with no 

 more than specimens of the tables, and notes, critical, historical, and 

 prospective, would command circulation. 



The railroads have created a demand for tables of the cubic yards in 

 cuttings, embankments, &c. Of these we select three, of extreme and 

 mean sizes. First, ' A general sheet-table, &c.,' on one side of one 

 sheet, by F. Bashforth, M.A., very efficient for its size. Secondly, 

 ' Tables for .... earthwork of Railways,' 1847, by C. K. Sibley and 

 W. Rutherford ; a collection of sheets, with flexible cover, small folio. 

 Thirdly, the second edition, ' Tables for facilitating the calculation of 

 earthwork,' by Sir John Macneill, Dublin, 1846, an 8vo. volume of 

 368 pages. We describe what we have by us, not knowing what edi- 

 tions may now be current, or what other works there may be. 



The practice of stereotyping tables is one which should be strongly 

 enforced, if it were not that publishers seem now to be aware of its 

 importance. A second edition derives no authority from the goodness 

 of the first, because the printer, who is, as already observed, as im- 

 portant a person as the author in the matter of tables, has again 

 stepped between the latter and the public. In reading the proofs of 

 important tables, it is desirable that three persons should be employed, 

 one to read from the manuscript, the others to watch two separate 

 proofs, without communication with each other, as done in the Nautical 

 Almanac office. The strictest investigation should take place in the 

 proof which is taken from the stereotype, ordinary pains being taken 

 with the previous proofs. Persons who have to correct the proofs of 

 tables alone should bring the manuscript as near as possible to the 

 proof by folding it conveniently : even if the folds were altered after 

 every two or three lines, so as always to have both manuscript and 

 proof under the eye in one position, it would not give more trouble 

 than would be well repaid. Double figures should be particularly 

 attended to ; no mistake is so likely to be made, either by the com- 

 positor or the reader, as 744 for 774, and the like. This, and mis- 

 placing the order of the figures, as 012 for 102, are the things which it 

 is most difficult to avoid. Again, of the two tilings under examination, 

 manuscript and proof, the more difficult one should be looked at first, 

 for the mind is apt to allow knowledge derived from the more easy 

 to give help in interpreting the more difficult. Thus, if the type 

 be liarder to read than the manuscript (a very common thing with 

 thick even-sized numerals), make out the proof first, and then look at 

 the manuscript ; and vice rend. If two readings be given, vary the 

 mode ; the following may for instance be the plan adopted : if the 

 manuscript column contain a, b, c, &c., and the printed column A, B, 

 C, &c., look at a, compare it With A, then at B, compare it with ti, 



* The tables formed on Barrett's method are variously described as Tittn-ett's 

 tables, Dauies's tables (G. Daviej was an improver), D and JV" tables, and CUIH- 

 inut'itioii tables. 



( In 1848-9, something more than a dozen copies of Baily's work came into 

 the hands of Mr. Maynard, mathematical bookseller, slightly imperfect. The 

 missing parts were reprinted (pp. 305-320 and 545-552). These copies were 

 in Daily's hands till his death : and when the book Wiis selling by auction at 

 and over five guineas, his friends applied to him again and again to have the 

 deficiencies made good and the hooks put into circulation ; hut they never could 

 prevail. 



