Prof. Boole oyi the Theory of Probabilities. 97 



to 1 ; and this therefore was the probability that some law of 

 nature, some cause was concerned." 'fq^ ^'i hiqin^tsA 



The same doctrine seems to me to be strongly iiiipilied" by 

 Laplace in the Introduction to his great work on Probabilities. 

 Discussing the question of a primitive cause, fixing the direction 

 of rotation of the planets in their orbits, he introduces the object 

 of his inquiry in the words "pour avoir la probabilite avec^ 

 laquelle cette cause est indiquee." And then having determined, 

 on the hypothesis of the absence of such determining cause, the 

 probability against the phrenomenon of rotation in one uniform 

 direction, he says, " Nous devons done croire au moins avec la 

 meme confiance qu\me cause primitive a dirige les mouvements 

 planetaires, surtout si nous considerons que I'inclinaison du plus 

 grand nombre de ces mouvements a Fequateur solaire est fort 

 petite." Laplace does not indeed expressly affirm the principle 

 under consideration, but it appears to me that his language does 

 in some degree give it sanction. 



Mr. De Morgan, in investigating the probability that there is 

 a cause for the observed phsenomenon that the sum of the incli- 

 nations of 10 of the planetary orbits is less than 92°, reasons in 

 the following manner. Having found a calculated probability 

 •00000013, say q, that the sum of the inclinations would be less 

 than 92° on the assumption that all inclinations are equally pos- 

 sible in each orbit, he says, " If there be a reason for the incli- 

 nations being as described, the probability of the event is 1. 

 Consequently it is 1 : -00000012 {i. e.l : q) that there was a 

 necessary cause in the formation of the solar system for the incli- 

 nations being what they are." The probability of the existence 



of such a cause is thus expressed by the fraction 



ooiJibnoo i*m li ^ \ "(aiiicifido'iq 



hQmir^ii iwii'*'' — i . , ... iiyi)d gjjd A 



j^is-fa 9iif il 1+9' I YitiluMoiq ail 



I at on^ time thought that this reasoning involved an eri^orvfei^ 

 nearly equivalent to that which I have adverted to in the previous 

 remarks. But upon examination it appears that Mr. De Morgan^s 

 result is really a limitation of the general formula (1.) obtained by 

 assigning particular values to the constants a and c. For in order 

 to apply that formula to the case considered by Mr. De Morgan, 

 let us assume A to represent the absence of any determining 

 cause of the phsenomenon B, viz. of the phsenomenon that the 

 sum of the planetary inclinations is less than 92°, then will a 

 represent the a priori probability of the absence of a determining 

 cause, and c the probability that on the assumption of its exist- 

 ence the phgenomenon B would result. Mr. De Morgan's rea- 

 soning then involves the hypothesis that a= -^ and that <:==1, 



