DANIEL BERNOULLI. 223 



A French translation of Daniel Bernoulli's memoir occupies 

 pages 95 — 122 of the volume ; the original memoir in Latin occu- 

 pies pages 125 — 144 



395. The portion of the memoir with which we are concerned 

 occurs at the beginning. Daniel Bernoulli wishes to shew that we 

 cannot attribute to hazard the small mutual inclinations of the 

 planetary orbits. He puts the calculation in three forms. 



(1) He finds that the greatest mutual inclination of any two 

 planetary orbits is that of Mercury to the Ecliptic, which is 6° 54'. 

 He imagines a zone of the breadth of 6" 54' on the surface of a 



sphere, which would therefore contain about —z of the whole sur- 

 face of the sphere. There being six planets altogether he takes 

 |i^ for the chance that the inclinations of five of the planes to one 

 plane shall all be less than 6*^ 54'. 



(2) Suppose however that all the planes intersected in a 



common line. The ratio of 6° 54' to 90° is equal to ^q iiearly ; 



1 



and he takes -r—n for the chance that each of the five inclinations 

 13^ 



would be less than 6" 54'. 



(3) Again ; take the Sun s equator as the plane of reference. 

 The greatest inclination of the plane of any orbit to this is 7° 30', 



which is about r=-^ of 90" ; and he takes — r^ as the chance that each 

 12 12*^ 



of the six inclinations would be less than 7" 30'. 



896. It is difficult to see why in the first of the three pre- 



1 . 2 



ceding calculations Daniel Bernoulli took ^^ instead of — ; that is 



why he compared his zone with the surface of a sphere instead of 

 with the surface of a hemisphere. It would seem too that he 

 should rather have considered the poles of the orbits than the 

 planes of the orbits, and have found the chance that all the 

 other poles should lie within a given distance from one of them. 



