ZOOLOGY AND BOTANY, MICEOSCOPYj ETC. 135 



3. Lines of a given depth appear finer when closely ruled in bands 

 than they do in single lines. 



4. I add another observation with some hesitation, since I have 

 not been able to prove its truth beyond peradventure. I have often, 

 but not always, found that when single lines, apparently invisible, are 

 placed in close combination in bands, they not only form a visible 

 band, but a band capable of apparent resolution into separate lines. 

 Can any one offer a reason why we can see in combination what we 

 cannot see as separate parts ? Of course I shall be at once reminded 

 by the astronomer that it is much easier to pick up a cluster than to 

 see scattered stars of the same magnitude. But when it is once found, 

 the separate stars composing it are no more easily seen than stars of 

 the same magnitude more widely scattered. I offer this observation 

 in a tentative way, since it has, if true, an important bearing upon 

 the question of the ultimate limit of resolution. Among the accom- 

 panying plates is one that illustrates the statement here made. This 

 plate consists of a series of bands, 12,000 to 24,000 to the inch, each 

 preceded by a heavy finding line. The lines of each successive band 

 are finer than the preceding. The last two bands were ruled with the 

 same pressure of the diamond as the fourth band preceding. The 

 intervals at which they were ruled are 1/80,000 and 1/200,000 in. 

 I do not by any means vouch for the existence of the separate lines, 

 yet the bands are smooth, and there is a distinct difference in the 

 appearance of the two halves of the 80,000 band, the first having been 

 ruled with a forward and the second with a backward motion of the 

 diamond. The corresponding single lines of the fourth band pre- 

 ceding are wholly invisible. This plate seems to show that the 

 visibility of the lines in bands depends somewhat on the narrowness 

 of the interval between the lines, since the lines of the same degree 

 of fineness with an interval of 1/24,000 in. cannot be seen. 



It is obvious that this whole question of resolution needs the 

 most careful consideration and investigation, since it bears an in- 

 timate relation to the limit of visibility of single particles of matter. 

 Mr. Hitchcock, in a recent number of his ' Journal,' has made the 

 claim that resolution has to a certain extent ceased to be a test of 

 the quality of an objective. I suspect that this claim will be found 

 to have some foundation in fact. For the last ten years we have only 

 the assertion of resolution, without doubt honestly made, but yet 

 unaccompanied with the proof. It is time that the proof should 

 accompany the assertion. I insist that simple vision does not afford 

 the required proof. 



Now we must face this question as honest inquirers after truth. 

 There is a limit which theory places to resolution with objectives of 

 given resolving power, not to visibility, as has been frequently stated. 

 Before we can safely assert that observation has gone beyond theory, 

 we must be prepared to offer evidence which can be placed upon 

 record, can be discussed deliberately, can be weighed impartially in 

 the balance with counter evidence, and can still stand unimpeached. 

 Do you say that this is hardly worth the trouble ? I reply that the 

 issue here raised comes to the surface in one form or another at almost 



