vlii PREFACE. 



submitting this question to mathematical investigation, but his 

 own results are not of great practical importance. 



The eighteenth Chapter relates to Trembley. He wrote several 

 memoirs with the main design of establishing by elementary 

 methods results which had been originally obtained by the aid of 

 the higher branches of mathematics ; but he does not seem to 

 have been very successful in carrying out his design. 



The nineteenth Chapter contains an account of miscellaneous 

 investigations between the years 1780 and 1800. It includes- the 

 following names ; Borda, Malfatti, Bicquilley, the writers in the 

 mathematical portion of the Encydopedie Methodique, D'Anieres, 

 Waring, Prevost and Lhuilier, and Young. 



The twentieth Chapter is devoted to Laplace ; this contains a 

 full account of all his writings on the subject of Probability. First 

 his memoirs in chronological order, are analysed, and then the great 

 work in which he embodied all his own investigations and much 

 derived from other writers. 1 hope it will be found that all the 

 parts of Laplace's memoirs and work have been carefully and 

 clearly expounded ; I would venture to refer for examples to 

 Laplace's method of approximation to integrals, to the Problem of 

 Points, to James Bernoulli's theorem, to the problem taken from 

 Buffon, and above all to the famous method of Least Squares. 

 With respect to the last subject I have availed myself of the 

 guidance of Poisson's luminous analysis, and have given a general 

 investigation, applying to the case of more than one unknown 

 element. I hope I have thus accomplished something towards ren- 

 dering the theory of this important method accessible to students. 



In an Appendix I have noticed some writings which came 

 under my attention during the printing of the work too late to be 

 referred to their proper places. 



I have endeavoured to be quite accurate in my statements, 

 and to reproduce the essential elements of the original works 

 which I have analysed. I have however not thought it indispen- 

 sable to preserve the exact notation in which any investigation 

 w^as first presented. It did not appear to me of any importance 

 to retain the specific letters for denoting the known and unknown 

 quantities of an algebraical problem which any writer may have 

 chosen to use. Very often the same problem has been dis- 

 cussed by various writers, and in order to compare their methods 

 with any facility it is necessary to use one set of symbols through- 

 out, although each writer may have preferred his peculiar set. 

 In fact by exercising care in the choice of notation I believe that 

 my exposition of contrasted methods has gained much in brevity 

 and clearness without any sacrifice of real fidelity. 



I have used no symbols which are not common to all mathc- 



