24 



THE AMERICAN MONTHLY 



[February, 



of the inch, and the lower four sub- 

 divisions of the centimetre, there be- 

 ing four thousand lines ruled on the 

 whole plate within a space four-tenths 

 of an inch long and wide. The left- 

 hand lines of the whole plate are 

 made to coincide, so that a direct 

 comparison may be made under the 

 microscope, not only of the subdi- 

 visions of the inch with each other, 

 but of the subdivisions of the inch 

 with those of the centimetre. To fa- 

 cilitate this, the fifth and tenth lines 

 of the inch-divisions are made longer 

 and extend into the centimetre band 

 a little way, so that the gain of the 

 inch-divsions is seen in the regu- 

 lar way in which the fifth and tenth 

 lines cut further into the centimetre 

 spaces, gaining one whole division 

 in 623^. 



The first line of the fourth bandof the 

 inch divisions being continued down- 

 ward as above described, is found ap- 

 parently to coincide with the eighth 

 line of the second band of the centime- 

 tre divisions (or the ninth, if the last 

 line of the firsthand is counted as the 

 first line of the second), and- five hun- 

 dred of the subdivisions of the inch 

 are equal to five huncired and eight 

 of those of the centimetres. In other 

 terms i /^ = -jf^-in., or the centime- 

 tre will be .3937008-in. 



Since making the examination of 

 the plate, I am informed by Profes- 

 sor Rogers that the comparative value 

 of the yard and metre which he used in 

 ruling this plate was Kater's, viz. : 39 

 .37079. This is the same as the ratio 

 given by Beale (" How to AVork with 

 the Microscope") as the English statu- 

 tory relation. Prof. Rogers has since 

 ruled other plates with the Chisholm 

 ratio, viz. : 39.37112, and is working 

 upon an independent comparison of 

 the English and French official stand- 

 ards. 



Taking the Kater ratio which the 

 professor used in making the plate, 

 it will be found by computation 

 that if we divide .2-inch by 507.995 

 we shall get the centimetre value 

 .3937046; and if v/e divide the .2- 



inch by the Kater ratio, 3937079 we 

 shall get the number of spaces 507 

 990-I-. It is thus shown that the ap- 

 parent equality upon the plate of 508 

 of the centimetre spaces with 500 of 

 the inch-divisions, cannot be out of 

 the way by one-hundredth of one of 

 the divisions; but as these divisions 

 are -wvsv inch, the maximum differ- 

 ence is one two-hundred and fifty- 

 thousandth of an inch. As the space 

 between the striae of a fine Amphi- 

 pleura pellucida is a hundred-thous- 

 andth of an inch, and the 19th band 

 of Nobert's plates is but little closer, 

 it needs no further proof that the ap- 

 parent coincidence of the lines de- 

 scribed above cannot be distinguished 

 from complete coincidence by any 

 objectives made, and we are unable 

 to prove that Prof. Rogers has not 

 exactly transferred to the plate the 

 ratio between the centimetre and the 

 inch. 



Let us now take a general view of 

 the plate itself. If we begin at one 

 end of the bands in juxtaposition and 

 go carefully through it, we cannot fail 

 to be struck with the great evenness 

 of the gain of the inch-divisions upon 

 those of the centimetre. The more 

 accustomed one is to the comparison 

 of micrometer divisions, the more 

 lively will be his surprise and plea- 

 sure at finding that in all these five 

 hundred spaces thus compared there 

 is no visible mark of inequality. I 

 have never seen any other ruling 

 which would stand even this test of 

 the direct comparison of such bands 

 of stri^ ruled at different times and 

 by a different, though related, scale. 



But, of course, the final and only 

 strict test for the microsc.opist is the 

 actual measurement of the spaces by 

 means of camera, of eye-piece micro- 

 meter, or by photography. By means 

 of the Jackson eye-piece micrometer 

 I have made a comparison of this 

 plate with two stage-micrometers of 

 standard European make. Of these 

 one is known by a series of experi- 

 ments made in the Coast Survey 

 Office, to be made with a screw giv- 



