78 Proceediiigs of Learned Societies. 



nition of the logoraeter is not the most general. Take any two lines 

 •whatsoever passing through the origin, and style them the hases of 

 length and direction. Set off on the first a line representing the 

 logarithm of the length in question, and on the second a line repre- 

 senting the angle it makes with the unit-axis, both on any scale of 

 representation. Then the diagonal of the parallelogram described 

 on the lines just set off is a logometer to the length and direction 

 from which it was derived ; and if under this meaning of the word 

 logometer the preceding definition of A be employed, the equations 



A«A^=A«^^ A^C^=(ACf, (A^)^=A^^ 

 are universally true. 



There is no necessity for the introduction of this more general 

 system, since all its results can be expressed in terms of those of the 

 more simple definition in the second paper. This new definition of 

 the logometer is really nothing more than the process answering to 

 the extension of the theory of logarithms from the system constructed 

 on the Naperean base, to that which is on any base whatsoever. 



" On the Measure of the Force of Testimony in cases of Legal Evi- 

 dence." By John Tozei-, Esq., M.A., Barrister-at-Law, Fellow of 

 GonvlUe and Caius C'ollege. 



The object of this paper is to show that the assumptions made by 

 some English legal authorities on this subject, in opposition to the 

 principles established by scientific processes, are not justified. 



The views more particularly dissented from, as extracted from a 

 work of high legal authority, are thus enunciated : — 



" The notions of those who have supposed that mere moral pro- 

 babilities or relations could ever be represented by numbers or space, 

 and thus be subjected to arithmetical analysis, cannot but be regarded 

 as visionary and chimerical. 



" Whenever the probability is of a definite, and limited nature 

 (whether in the proportion of one hundred to one or of one thousand 

 to one, is immaterial), it cannot be safely made the ground of con- 

 viction ; for to act upon it in any case would be to decide, that for 

 the sake of convicting many criminals the life of one innocent man 

 might be sacrificed. 



" The distinction between evidence of a conclusive tendency which 

 is suflicient for the purpose, and that which is inconclusive, appears 

 to be this : the latter is limited and concluded by some degree or 

 other of finite probability beyond which it cannot go ; the former, 

 though not demonstrative, is attended with a degree of probability 

 of an indefinite and unlimited nature." 



The method pursued is that of investigating algebraic expressions 

 for the probabilities that the allegations made in a case which ac- 

 tually occurred, the trial of a female for murder, are true ; and thence 

 deducing an expression for the probability of the truth of the charge, 

 in passing from the symbolical to the numerical expression, the num- 

 bers employed are not the actual values of the symbols but their 

 limiting values ; the resulting number is therefore a fraction which 

 is not less than the value of the probability of the truth of the prin- 

 cipal allegation, this being what in practice is required. 



