132 



A Sketch of an Analysis and Notation applicable to the Estimation of 

 the Value of Life Contingencies. By Benjamin Gompertz, Esq. 

 F.R.S. Read June 29, 1820. [Phil. Trans. 1820,;?. 214.] 



Mr. Gompertz begins by establishing a system of notation intended 

 to avoid unnecessary repetitions and circumlocution, and proceeds to 

 apply his abbreviated expressions to a more accurate determination 

 of the value of a number of joint lives, according to any given tables 

 of mortality, than can be obtained by the common approximations. 

 He afterwards investigates the probabilities of the survivorship of 

 two persons of different ages, who were known only to be living at 

 one time and dead at another, which, within certain limits, are sup- 

 posed to be equal : and he inquires into the conditions of mortality 

 that would be requisite in order that this proposition should be accu- 

 rately true. He then applies his method to the problems which have 

 been solved by Mr. Morgan in the Philosophical Transactions, and 

 copied by Mr. Baily in his work on Assurances, relating to some 

 complicated contingencies and survivorships on different suppositions 

 respecting the decrement of life, employing various integrations, 

 summations, and approximations in this elaborate inquiry, but with- 

 out obtaining any results which it is possible to specify in an abstract, 

 as giving a general idea of the nature of his improvements, without 

 entering into forms of expression directed almost as much to the eye 

 as to the understanding. 



On the Measurement of Snoiedon, by the Thermometrical Barometer. 

 By the Rev. F. J. H. Wollaston, B.D. F.R.S. Read June 29, 

 1820. . [Phil. Trans. 1820,^. 295.] 



After adverting to the statements contained in his former paper 

 upon the use of the above-mentioned instrument, and giving certain 

 tables requisite for determining the necessary corrections arising out 

 of the want of uniformity in the variations of the boiling tempera- 

 ture of water at certain elevations, the author details the means 

 which he resorted to for estimating the height of Snowdon by this 

 instrument, and compares his results with the trigonometrical and 

 barometrical measurement of General Roy. 



The height, as obtained by the thermometric barometer, properly 

 corrected from the north end of Carnarvon Quay to the summit, is 

 3546*25 feet. General Roy's trigonometrical measurement gives 

 3555*4 feet, and barometrically 3548*9 feet. During this visit to 

 Carnarvon, the author also took the opportunity of ascertaining, by 

 the same means, the height of Moel Elio, also measured by General 

 Roy. He makes it 2350*55 feet, while General Roy's trigonometri- 

 cal measurement gives 2371 feet, and the barometer 2391*8 feet. 

 This discordance, the author thinks, may be referred to the indetermi- 

 nate form of Moel Elio rendering the point of observation less definite. 



Archdeacon Wollaston concludes this paper with a description of 

 some improvements in the construction of this instrument. 



