TREMBLEY. 413 



7(31. Trembley's seventh problem is De Moivre's Problem LXiv, 

 and he gives a result equivalent to that on De Moivre's page 207; 

 see Art. 806. But here again after investigating a few terms the 

 main difficulty is left untouched mth the words Perspicua nunc 

 est lex progressionis. Trembley says, Eodem redit solutio Cel. 

 la Grange, licet eaedem formulae non prodeant. This seems to 

 imply that Lagrange's formulae take a dilterent shape. Trembley 

 .probably refers to Lagrange's second solution which is the most 

 completely worked out ; see Art. 583, 



Trembley adds in a Scholium that by the aid of this problem 

 we can solve that which is LXVII. in De Moivre ; finishing with 

 these words, in secunda enim formula fieri debet c =]p — 1, which 

 appear to be quite erroneous. 



762. Trembley's eighth problem is the second in Lagrange's 

 memoir ; see Art. 580 : the chance of one event is p and of an- 

 other q, find the chance that in a given number of trials the first 

 shall happen at least h times and the second at least c times. 

 Trembley puts Lagrange's solution in a more elementary form, so 

 as to avoid the Theory of Finite Differences. 



763. Trembley's ninth problem is the last in Lagrange's me- 

 moir ; see Art. 587. Trembley gives a good solution. 



76-t. The next memoir is entitled De Prohahilttate Causarum 

 ah effectihus oriunda. 



This memoir is published in the Comm. Soc. Reg....GoU. 

 Yol. XIII. The volume is for the years 1795 — 1798 ; the date of 

 publication is 1799. The memoir occupies pages 64 — 119 of the 

 mathematical portion of the volume. 



765. The memoir begins thus : 



Hanc materiam pertractarunt eximii Geometrae, ac potissimum Cel. 

 la Place in Commentariis Academiae Parisinensis. Cum autem in 

 hiijusce generis Problematibus solvendis sublimior et ardua analysis 

 fuerit adliibita, easdem qiiaestiones metliodo elementari ac idoneo usii 

 doctrinae serierum aggredi operae pretium diixi. Qua ratione haec altera 

 pars calculi Probabihum ad theoriam combinationum reduceretur, sicut 

 et primam reduxi in dissertatione ad Kegiam Societateui transmissa. 



