568 



SCIENTIFIC THOUGHT. 



very largely in all statistics, and vitiates them ; and as 

 regards coming events, our minds are in a state of ex- 

 pectation rather than of assurance. But events can be 

 more or less probable, errors can be greater or smaller, 

 cumulative or compensatory, and our expectations may 

 be well- or ill-founded. And so there has arisen the 

 science of Probabilities and of Chances, and the Theory 

 of Error, two subjects intimately interwoven. The 

 former arose in the seventeenth century out of the 

 frivolous or vicious practice of betting and gambling, 1 

 whilst the latter was founded when astronomical observa- 

 tions accumulated, and the question presented itself how 

 to combine them so as to arrive at the most reliable 

 result. The greatest mathematicians and philosophers, 

 such as Pascal, Huygens, and Leibniz, the Bernoullis, De 

 Moivre, Laplace, Gauss and Poisson, have bestowed much 

 thought on the subject, 2 which has nevertheless been very 

 differently judged praised beyond measure by some, and 

 ridiculed by others ; sometimes pronounced to be merely 

 common-sense put in figures, and then again wrapped up 



1 See supra, vol. i. p. 120 sqq. 



2 In addition to the references 

 given in vol. i., the following are of 

 importance. The history of the 

 Theory of Probabilities, as stated 

 above, has been written by Isaac 

 Todhunter. This history brings 

 the subject down to the writings 

 of Laplace, whose two works 

 mentioned in the text still re- 

 main the two standard works 

 on the science. In quite recent 

 times the history has been written 

 and brought up to date by Prof. 

 Emanuel Czuber in his ' Entwick- 

 elung der Wahrscheinlichkeits- 

 Theorie und ihre Anwendungen,' 



contained in the seventh volume 

 of the ' Jahresbericht der Deut- 

 schen Mathematiker Vereinigung' 

 (Leipzig, 1899). The latter work is 

 written on a different principle from 

 that of Todhunter. Whereas Tod- 

 hunter deals in separate chapters 

 with the work of the foremost 

 mathematicians on this subject, 

 Prof. Czuber gives an independent 

 historical and critical analysis of the 

 different developments of the 

 theory and its applications. Quite 

 recently the same author has pub- 

 lished an independent treatise on 

 the subject (Leipzig, 1902). 



