The Examination of Noherfs Nineteenth Band. 195 



spurious. The personal question involved is of no consequence 

 whatever; but the trustworthiness of the method employed is 

 another matter ; and this, I think, is not at all invalidated by the 

 argument of Colonel Woodward. 



This method may be briefly explained thus: — In ruhng his 

 nineteen-band plate, Mr. Nobert has designed to make the spaces 

 between the lines of the ninth band, measured from centre to 

 centre, just 5-oVoth part of a Paris line each; and those of the 

 nineteenth band yowoth each. When I found, by micrometer, 

 that twenty spaces on the nineteenth band, or any other carefully 

 counted number, had the same aggregate value as half as many 

 spaces on the ninth (where the counting is easy), I considered 

 myself justified in concluding that the nineteenth band was truly 

 resolved; and did not think it necessary, in order to prove this, 

 that I should actually count the band clear across. 



Colonel Woodward, however, says that this method will not do, 

 because the spaces have not probably the values nor the relations 

 intended by Nobert, and stated by him to exist. That the absolute 

 values of the divisions are not exactly what was designed is pre- 

 sumable enough ; because it is not possible to construct a scale or 

 anything else in so strict accordance with the intention as to be 

 without error altogether; but in respect to the relations between 

 the spaces of two scales ruled by the same machine, there is hardly 

 room for the same degree of uncertainty. The parts of a ruling- 

 machine by means of which the distances between the lines ruled 

 are regulated, are not microscopic. They are so large that any 

 minute irregularity in them would bear no appreciable ratio to 

 their total magnitude. Moreover, when we consider that the same 

 part of the machine — a ratchet, for instance — bears the divisions 

 by which both the larger and the smaller spaces are regulated, so 

 that — to take the case before us — the very same instrumental 

 measure determines the aggregate value of ten spaces of the ninth 

 band, and of twenty spaces of the nineteenth, we shall see that 

 there can be no sensible error in assuming that the ratio between 

 the mean breadths of these spaces is as two to one. There can be 

 none, at least, except on the supposition of wilful mis-statement by 

 Mr. Nobert — a supposition which his known integrity makes 

 inadmissible, and which is, moreover, abundantly disproved by 

 Colonel Woodward's own photographs and measurements. 



Colonel Woodward, however, thinks that the ninth band is 

 broader than the nineteenth ; whereas, since the former has but 

 twenty- six spaces, while the latter has fifty-six, the nineteenth 

 should have the greater breadth if the spaces are truly to each 

 other in the ratio of two to one. Supposing the total breadths of 

 the bands equal, the numbers just given enable us to state the real 

 ratio to be as two and two-thirteenths to one; or, as Colonel 



VOL. VI. P 



