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Published online by Cambridge University Press: 18 August 2016
The subject of Graduation has recently been brought somewhat prominently before the profession in connection with the exposition of various methods that have been proposed. While the bases of these individual methods have been set forth in a way leaving nothing to be desired, the precise relation of each to the entire problem of the adjustment of probabilities derived from statistics, does not appear to have been so clearly marked out; and therefore, in the following observations, it is proposed to keep prominently in view the conditions under which one method is to be preferred to another.
An intelligent outsider, desirous of becoming acquainted with the actuarial theory of graduation, might, if he overlooked the necessarily limited application of particular systems, derive from his researches an impression of disagreement among the various authorities, which would have a rather bewildering effect.
page 315 note * Since this was written Mr. Sutton has submitted to the Institute a Table showing that the HM graduation retains the same close agreement with the raw observations as is here found to be so marked a feature of the HMF graduation.
page 315 note † I may perhaps be allowed to suggest, however, that Mr. Woolhouse's method of adjusting the numbers living at the first seven ages in the table, to which his formula cannot be applied, should be reconsidered. In the HMF observations, as will be observed, that method has led to the somewhat anomalous circumstance of the rate of mortality decreasing after age 10, and being less at age 16 than at the former age.
page 318 note * Mr. McCay, through some mistake, states this ratio as 4:5.
page 318 note † Mr. McCay says 6: he adds that none of these are one-tenth of the annual deaths at the corresponding ages; but such does not appear to be the case.
page 321 note * “On the Investigation of the Orbits of revolving Double Stars”, by Sir J. F. W. Herschel; Memoirs of the Royal Astronomical Society, vol. v, p. 171. This paper was read before the Society in 1832, and so far as can be judged by internal evidence, the author devised independently what has been called a graphical graduation. Such an opinion is supported by a passage in Whewell's History of the Inductive Sciences, third edition, vol ii, p. 204, where he, referring to the laws of double stars, mentions Sir J. Herschel as “inventing a method which depended upon the whole body of observations, and not upon selected ones only." It is quite likely, however, that an analogous process may have been used by previous investigators in other fields. At the beginning of his paper Herschel states that, with permission of the Council, he had suppressed a "brief and imperfect account of the principle of this method" contained in a former communication to the Society.
page 322 note * Encyclopaedia Britannica, ninth edition, article— “Herschel, Sir J , F. W.”