IN THE THEORY OF PROBABILITIES. 425 



The general formula for the determination of B^ is 



but the first terms may be readily found by actual reversion of (3), 

 which gives, if Y„ stand for -^ , 



^' - 18^^ • ^ " T • 



When a = 0, b = \, we have n = — x, v = + oc 



fydx = V(B, + 1^3 + ...) r^e-^'dt, 



whence the formula (2) becomes 



neglecting the terms not previously expressed. 



Tables of the values of 



-7= / e'''dt, or — ^ f e'^^dt, 



were published in the Berlin Astronomisches Jahrbuch for 1834, and are 

 reprinted* at the end of my article on the Theory of Probabilities, in 



* The increasing importance of this Table makes it worth while here to state that it 

 will shortly appear in a comparatively popular Essay on Probabilities on which I am now 

 engaged, and also, as I am informed, in the Article on the subject in the new edition 

 of the Enci/clopaedia Britannica. 



