204 Mr. F. Y. Edgeworth on 



The outer masses of the belt of greatest condensation are 

 perhaps connected with the inner masses, by the same rela- 

 tions as exist between the outer belt of the system and the 

 chief centre of nebulosity. 



7r 2 (m 1 + m 4 ) = m 2 + m 3 , 



These harmonics give m =4503361m 1 = 2852190m 4 . 



The accordance of the foregoing harmonic values with recent 

 astronomical estimates is shown in the following Table: — 



Harmonic. Astronomical. 



mo-rmi 4503361 4488285 Encke. 



m H-m 2 384962 394094 Hill. 



m +m B 327400 326800 Newcomb. 



«io-r-m 4 2852190 2853500 Hall. 



m -r-m 5 1054*6 1050 Leverrier. 



m +m 6 3491-8 3482 Hall. 



m -rm 7 22497 22600 + 100 Newcomb. 



wo-i-wig 19370 19380+ 70 „ 



XXVII. A priori Probabilities. 

 By F. Y. Edgeworth, Lecturer on Logic at King's College* '. 



I. A PRIORI probabilities not determined by statistics 

 underlie many important calculations both in Physics 

 and Social Science. (1) In the measurement of a physical 

 quantity it is generally assumed that, prior to observation, one 

 value of the qusesitum is as likely as another. Take, for ex- 

 ample, the following! simple problem: — Given a set of obser- 

 vations in a line, x lf x 2 , x 3) diverging according to a given 

 probability-curve from a sought point x, x is found from the 

 equation 



A. p h-^=. € -* 8 {< a: - tr i) 2+ ( a: - ;c 2) 2 +&c.} =: Q 

 dx H v/tt ? 



where p is the a priori probability that the real value of the 

 qua3situm is between x and x + Ax. It is generally assumed 

 that p is constant. But if not, let it equal Ax%(x), where Ad- 

 is an indefinitely small constant. Then the equation 



2h 2 x {(x— x x ) + (x— x 2 ) + &g.}=0 



* Communicated by the Author. 



t See Phil. Mag. 1883, vol. xvi. p. 365. 



