On the Use of the Noberfs Plate. 27 



familiarity wliich all acquire with any ai^pearance which they have 

 many times reproduced, wiU only serve to mislead, if at the begin- 

 ning spmious lines have been confounded with the true, for then the 

 deceptive spurious appearance will be sought for as eagerly as 

 though it were the true one. 



A realization of this circumstance has led several eminent ob- 

 servers to propose a criterion of resolution which appears at first 

 sight to meet the case, but which I must really think is more diffi- 

 cult and less accurate than the third method. This plan is very 

 well described in the letter of President Barnard quoted in the 

 article to which I have referred.* " When, for instance, I found 

 that the value by micrometer of twenty spaces on the nineteenth 

 band as counted, was exactly equal to the value by the same micro- 

 meter of ten spaces on the ninth band, I could not doubt that the 

 nineteenth band was resolved." This method jDresupposes of course 

 that the lines are ruled at exactly the distances Nobert intended, 

 viz. those of the ninth band 5 oVo^h of a Paris line from centre to 

 centre, and those of the nineteenth loooo ^ti from centre to centre. 

 It also presupposes absolute accuracy in comparing the portion of 

 the two bands selected. 



Now, the supposition that Nobert's estimate of the distances 

 between the rulings is mathematically correct, appears to me 

 highly improbable from many considerations ; but when the attempt 

 is made to demonstrate the precise degree of success attained, many 

 difficulties are encountered. For example, as the ninth band con- 

 tains twenty-seven lines and the nineteenth fifty-seven, if the dis- 

 tance of the lines of the nineteenth band from centre to centre is 

 exactly half that given to those of the ninth, it follows of course 

 that the nineteenth band ought to be broader than the ninth by the 

 space of four of its lines. I have, however, been quite unable to 

 satisfy myself that this is the case ; repeated measurements of the 

 nineteenth band of my plate inclining me to think rather that it is 

 somewhat narrower than the ninth. It is indeed extremely difficult 

 to make such comparison with the requisite precision, so difficult 

 that I do not believe anyone could tell merely by the count and 

 measurement of twenty lines whether he was examining the seven- 

 teenth, the eighteenth, or the nineteenth band. In the most careful 

 and experienced hands, therefore, this plan offers at the best greater 

 difficulties than a simple count across the band, and except in such 

 hands it is only liable to mislead. 



On the other hand, the third method is more positive, for the 

 number of lines in each band being now known, a complete count 

 gives results which cannot reasonably be questioned. But two 

 objections have been made to this plan. First, that an- objective of 



* P. 123. 



