xxxvi 



many investigators might have passed a life in the subject without arriving 

 at the fact that the observations existed. 



In a separate work on the heat of vapours and on refraction (1840), 

 the assumption is that the absolute heat of a gas may be represented by 

 A + B X (temperature). A relation between pressure and temperature 

 is then deduced, the constants of which can be determined by joint obser- 

 vations of pressure and temperature. The observations of Arago and 

 Dulong (Mem. Inst. x. 231), and of Ure (Phil. Trans. 1818), are thus 

 satisfied. Employing the observations of Gay-Lussac (Conn, des Temps, 

 1841), he deduces a formula for the calculation of heights by barometrical 

 observation, and then proceeds to the subject of refraction. In this 

 matter, to a great extent, he follows Ivory. The investigation is never- 

 theless new and peculiar, and the conclusions are remarkable. The results 

 of Lubbock's theory and Bessel's Tables are almost identical. Down to 65° 

 of zenith distance the difference is not 0"'01 ; nor from thence to 87° does 

 it ever amount to l"*0 ; at 88° it is 4"'0, It would require a very large 

 number of observations to discriminate between them. It appears there- 

 fore that, from the assumption that the differences of absolute heat in a gas 

 are directly proportional to the difference of temperature, Lubbock has built 

 up a theory agreeing with observation, all his constants, with the exception 

 of one, being determined independently of astronomical observations. His 

 theory also gives a value of the horizontal refraction agreeing closely with 

 the best determinations of that quantity. His atmosphere is a limited one 

 of about twenty- two miles. 



About the year 1830 Mr. Lubbock, jointly with Mr. Drinkwater 

 (Bethune), wrote a tract of thirty-two pages on ' Probability ' in the Library 

 of Useful Knowledge. This most excellent little work ranks as the 

 earliest, and, its size considered, the best of the modern English introduc- 

 tions to the subject. Of late. years it has become almost a rule, in citing 

 this work, to insist on the authorship. A binder put JVIr. De Morgan's 

 name on the outside of a large issue ; and though for more than fifteen 

 years every channel of publicity, from the * Times ' newspaper downwards, 

 has been employed to correct the mistake, entire success has not yet been 

 obtained. This work, though perfectly elementary, has that taste of the 

 higher methods which those who are familiar with them can infuse into 

 common algebra. Mr. Lubbock showed his familiarity with Laplace, 

 before any one in Britain, by two papers in the Cambridge Transactions 

 (vol. iii. part 1), on the calculation of annuities, and on comparison of 

 tables. At the time of publication there was no actuary, except Mr. 

 Benjamin Gompertz, who could have read them : the state of things is 

 now different, and the papers have been reprinted in the Assurance 

 Magazine (vol. ix.). In the same volume is an illustration of the way in 

 which the doctrine of probability applies in every subject. It is a paper 

 contributed by Sir J. Lubbock, on the clearing of the London bankers. 



