Chase.] 346 [September. 



the simpler root hit, het, our 'bid'); idaro, ' that which becomes 

 collected into a mass,' and English dross; hasUe^ 'landlord' (}ja for 

 o6a, 'master,' si, 'of/ and He, 'land'), and Greek hasileus, 'king!' 

 And the comparer . . . gravely informs us that the calculated 

 chances against the merely accidental character of the last coinci- 

 dence are 'at least a hundred million to one !' More than one un- 

 sound linguist has misled himself and others by calculating, in the 

 strictest accordance with mathematical rules, how many thousand or 

 million chances there are against the same words meaning the same 

 thing in two different and unconnected languages. The calculation 

 is futile, and its result a fallacy. The indications of linguistic re- 

 lationship are not to be reduced to precise mathematical expression." 



E pur si muooc! A wide interest has been awakened by a recent 

 famous will case, in which a disputed signature was referred to 

 one of the most celebrated mathematicians of our day, for his judg- 

 ment as to its authenticity. After a careful examination and calcu- 

 lation of the chances of such a coincidence as is alleged to exist 

 between the signature in question and one which is admitted to be 

 genuine, the referee declares that "this phenomenon could occur once 

 in the number of times expressed by the thirtieth power of five, or, 

 more exactly, it is once in two thousand six hundred and sixty-six 

 millions of millions of millions of times. . . So vast an improbability 

 is practically an impossibility. Such evanescent shadows of prob- 

 ability cannot belong to actual life. They are unimaginably less than 

 the least things which the law cares not for." This calculation is 

 met, not by asserting that " the calculation is futile, and its results 

 a fallacy," but in the only legitimate way, by attempting to show 

 that the coincidence is not of the character which was assumed in 

 the conditions of the calculation. The calculus of probabilities, 

 whether it be applied to language or to any other subject in which 

 definite relations are involved, is as infallible as any other branch of 

 mathematics ; but in all reasoning, the legitimacy of the premises 

 and the logical accuracy of the successive steps which lead to the 

 conclusion may be properly called in question. 



I yield to no one in admiration of the splendid results which have 

 followed the study of linguistic relationships under the guidance of 

 grammatical aifinities.* But, on the other hand, I am unwilling 



* Witness the acknowledgment in the criticized article: "Grammatical anal- 

 ogy, when strongly marked, furnishes nearly demonstrative evidence of a common 

 lineage, and it should, therefore, be the first object of search in all philological 

 comparisons." — Trans. A. P. S., xiii, 36. 



