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On the Forms under which Barrett's Method is presented, and on Changes of Words and Symbols

Published online by Cambridge University Press:  18 August 2016

A. De Morgan
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Extract

The mode of using Barrett's method has now something of farrago about it: a little discussion may be useful, were it only to awaken attention to the confusion arising from changes made without adherence to the recognised laws of perspicuity.

The farrago to which I have alluded arises out of a struggle between the annuity, as commonly understood, and what I shall continue to call the annuity due. According to the technical meaning of the word annuity, the payment begins to grow at the moment of the grant: thus, a yearly annuity for 12 years, deferred 20 years, begins action at the end of 20 years, and grows the first payment in the 21st year. I shall vary the phrase used in my “Essay on Probabilities” (Cab. Cycl.) by allowing the words “annuity due for x years” to signify an annuity of x payments, the first immediately. Thus an annuity for 12 years, now granted, will in a year become an annuity due, also for 12 years.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 10 , Issue 6 , January 1863 , pp. 301 - 312
Copyright
Copyright © Institute and Faculty of Actuaries 1863

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References

page 303 note * The record of stories which have taken rise in resemblance of surnames would be a curious book. When looking after the history of Barrett, I had to inquire into a rumour of his having been assisted in his calculations by Griffith Davies. I n this there was no truth whatever; but Mr. Davies remembered teaching Mr. Berry, who was in the Hope Office with Barrett, and whom he did assist in official calculations after Barrett had left.

page 304 note * Morgan, William, in his Rise and Progressof the Equitable Society, 1828,Google Scholar made some remarks on Mr. Babbage's account of the Equitable Society. Baily, Francis criticised these remarks in the Times, June 26, 1828;Google Scholar and Morgan replied July 1, 1328. These letters ought to be preserved, and I hare accordingly transmitted my copies to the Editor of this Journal, for publication.

page 305 note * We are reminded of the Greek philosopher, who maintained that life and death are all one. “Why then do you not kill yourself?” asked an opponent “Because it is all one,” replied the sage.”

page 307 note * The first notorious place i n which I find it is in the authorised version of the Bible; tut it also appears in the older Protestant versions. Omitting Isaiah xxvi. 14, which those who compare the Septuagint with the English will suspect of having a difficulty in the Hebrew, it is seen in Matth, xxii. 25, Luke ix. 31, 2 Pet. i. 15. In the first passage ό πρωτος γαμηας έτελευτησε is translated “the first, when he had married a wife, deceased.” And here the Greek is really came to an end, ceased off; and here Tyndale (1534) and his followers have the neuter verb deceased. But in the other two passages, in which the substantive decease of our version is the translation of έζοδοςdeparture, the previous Protestant versions have departing, while the Rhemish (Roman, 1582) version has decease. It may be suspected that Tyndale meant decessatio, and the Rhemish translator decessus, and that our translators adopted both.

Shakspere has one use of the word: he makes Gower reproach Ancient Pistol with mocking at a memorial of “predeceased valour”: and down goes the word into dictionaries as common English of Shakspere's time. Gower is making rather a stilted speech, and it may be surmised that the dramatist intended to represent him as inventing the word for his own use. If so, this is far from being the only case in which the English peculiar to a comic character ha3 been made the English of the poet's contemporaries.