12 Mr. T. K. Abbott on the Probability of 



superficial expansion of the glass tube, for the number of degrees 

 observed above or below the freezing-point. 



The dilatation of the mercurial column will be = M — G, or 



•00018153 

 -•000017226 



= 000164304 for each degree Centigrade, 

 = •000091280 for each degree Fahrenheit. 



The Tables, French and English, give as the correction, 



•0001614 for 1° Centigrade;= -00008967 fori Fahrenheit; 



but they all take Dulong and Petit' s coefficient for the cubic 

 expansion of mercury, which is lower than that of Eegnault, 

 being only '000180180. 



When the column is thus reduced for the expansion of the 

 mercury, the additional correction for that of the scale has to 

 be applied. 



I am, Gentlemen, 



Yours faithfully, 

 Gavarnie, Hautes Pyrenees, Charles Packe. 



April 22, 1864. 



III. On the Probability of Testimony and Arguments. By T. K. 

 Abbott, M.A., Fellow and Tutor of Trinity College, Dublin*, 



THERE are certain questions respecting the probability of 

 testimony and argument which, although of considerable 

 practical importance, have been either neglected or erroneously 

 treated by writers on the subject. It is the purpose of the pre- 

 sent paper to consider briefly a few of these, keeping in view not 

 so much theoretical generality or completeness, as the corre- 

 spondence of the conditions assumed with those which occur in 

 ordinary experience. 



The case of testimony is represented in the ordinary treatises 

 as follows : — Suppose a witness, A, affirms that a certain event 

 has occurred, the antecedent probability of which was p, and let 

 the witness's credibility be a. Then, it is said, there are only 

 two possible cases. Either he is right, the chance of which is 



and the event has occurred, the chance of which is] 



p ; 



.". the chance of this coincidence is 



op, 



* Communicated by the Author. 



