The Examination of Noherfs Nineteenth Band. 197 



Now for the bearing of this fact of observation upon my test. 

 In looking at the nineteenth band, I saw it as a series of per- 

 fectly regular, well-defined, unifoiTaly distant lines, covering its 

 whole surface, and extending unbroken across the entire field of 

 view of my microscope. The question with me was, Do I see the 

 true hnes, or is this appearance the illusion in which only half the 

 true number are present? In the latter case, I shall find in a 

 given space the same number of lines which I find in the ninth 

 band in the same space ; in the former, I shall find twice as many. 

 Now, if I had 7iot found exactly twice as many (which I did), I 

 should have stiU believed the band to be resolved; for it was 

 impossible to suppose that I saw only half the number of the true 

 lines ; and equally impossible to suppose I saw twice the number 

 of the true fines ; therefore, if I had observed (as I did not) any 

 seeming deviation from the ratio of 2:1, I should have been 

 compelled to account for it on a hypothesis such as Col. Woodward 

 has suggested, viz. that the relations between the spaces in these 

 two bands are not exactly in accordance with the intention of the 

 constructor. 



There is a peculiarity of this plate brought to view by this 

 discussion which has never been noticed, though apparently intro- 

 duced with a purpose. The first band has seven lines, and purports 

 to measure from centre to centre of the bounding lines just i-^ths 

 of a Paris line. The next has ten lines, and similarly measui'es 

 1 smoo ths of a Paris line. The third has thirteen, and measures 

 ^^foths. All these fractions, reduced, give the same value gf o^ths 

 of a Paris line, as the common total breadth of the bands. But 

 the fourth band has fifteen lines only, or fourteen spaces. The 

 spaces Mr, Nobert states to be 2500th parts of a Paris fine ; so 

 that if there had been sixteen instead of fifteen ruhngs in the band, 

 the total breadth would have been ^^^o^lis = ^fo^lis as before. 

 On the other hand, if fourteen spaces occupy ^-g-oths of a Paris line, 

 each space must be greater than s^Voth. Considering that, with 

 a dividing machine, it would be much easier to follow uj) the series 

 TWO 5 TsVoj Woo- 5 25V0 J t^an to substitute, in place of this last 

 term, -j-^qq, as the second supposition would require; and con- 

 sidering that this substitution would be a contradiction of Mr. 

 Nobert's express statement of values marked on every one of the 

 plates, we may fairly conclude that the dropping of a space argues 

 no interruption of the law regulating the values of the divisions, 

 but does argue a reduction of the total breadth of the fourth band. 

 The sixth band contains seventeen lines, or sixteen spaces. If the 

 rulings had been nineteen, and the spaces eighteen, the total 

 breadth of the band would have been ^j^fijths = -rrirths as before. 

 In short, if the aim had been to keep the total breadth of the band 

 always the same, there would have been added always three lines in 



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