94 M. Poisson's Memoir on the 



great number of speculations, is calculated, from the known 

 losses and gains of another very considerable number of similar 

 operations, that is to say, of which the mean law of probability 

 is supposed the same. 



In other questions depending upon the same theory, where 

 the subject is the greatness of a phenomenon or the measure 

 of any thing which is to be determined by a series of observa- 

 tions, it is supposed implicitly that, among all the values of 

 which this thing is susceptible by its nature, there exists one 

 from which it is equally probable that there will be an equa 

 difference in excess, or defect in each observation ; it is sup- 

 posed, moreover, that this value of the unknown quantity is 

 the same for all the observations, and it is this value, thus 

 defined, that it is sought to discover. That amounts to saying, 

 that the curves of probability relative to all the observations are 

 symmetrical on each side from one of their points, and that 

 this point corresponds to the same abscissa for all these dif- 

 ferent curves. In this hypothesis the centres of gravity of 

 their areas and that of the area of the mean curve will be 

 situated on a common ordinate, the abscissa of which will 

 represent the true value of the unknown quantity. By mul- 

 tiplying the observations, the quantity by which we shall inde- 

 finitely approximate will be constant and independent of their 

 number ; and although their laws of probability may be dif- 

 ferent, their mean result will give a value nearer and nearer 

 to the unknown quantity ; and at the same time, from the 

 whole of the observations collectively, the probability of its 

 degree of approximation may be calculated. But however 

 small may be the error to be apprehended in taking the mean 

 result for the value of the unknown, and however probable may 

 be the limit of this error, it must not be lost sight of that the 

 value of anything drawn from observations is always subordinate 

 to the hypothesis already stated. If any unknown cause render 

 the errors of the instruments or the variable circumstances which 

 influence the phenomena, preponderant one way or the other, 

 or if the thing to be determined varies progressively during the 

 continuance of the observations, this hypothesis will not hold 

 good, and the observations should be rejected as improper for 



