LAPLACE. 499 



par la meme integrale etendue a rinfini positif et negatif, exprimera la 

 probabilite que I'ecart de la veiite, est compris entre ces limites. 



A student familiar with the Theorie...des Proh. itself might 

 not find it easy to say what formula Lajolace has in view ; it must 

 be that which is given on page 309 and elsewhere, namely 



dre 4A". 



7 " 



/J TT 



Other examples of the same absurdity will be found on page LL 

 of the introduction, and on page 5 of the first supplement. 



938. A section occupies pages XLix — LXX. entitled Applica' 

 tion du Calcul des Probahilites, d la Pliilosophie naturelle. Tbe 

 principle which is here brought forward is simple ; we will take 

 one example which is discussed in the Theorie . . .des Prob. If a 

 large number of observations be taken of the height of a barometer 

 at nine in the morning and at four in the afternoon, it is found 

 that the average in the former case is higher than in the latter ; 

 are we to ascribe this to chance or to a constant cause ? The 

 theory of probabilities shews that if the number of observations be 

 large enough the existence of a constant cause is very strongly in- 

 dicated. Laplace intimates that in this way he had been induced 

 to undertake some of his researches in Physical Astronomy, be- 

 cause the theory of probabilities shewed irresistibly that there 

 were constant causes in operation. 



Thus the section contains in reality a short summary of La- 

 place's contributions to Physical Astronomy ; and it is a memor- 

 able record of the triumphs of mathematical science and human 

 genius. The list comprises — the explanation of the irregularity 

 in the motion of the moon arising from the sj)heroidal figure of the 

 earth — the secular equation of the moon — the long inequalities of 

 Jupiter and Saturn — the laws connecting the motions of the 

 satellites of Jupiter — the theory of the tides. See Gouraud, 

 page 115 ; he adds to the list — the tem23erature of the earth shewn 

 'to be constant for two thousand years : it does not appear that 

 Laplace himself here notices this result. 



939. Li the second edition of the Theorie ...des Proh. 



32—2 



