096 Transactions of the Society. 



XVI. — A Micrometric Difficulty. 

 By Edward M. Xelson. 



(Read October 19, 1910.) 



Some, in the ordinary course of their microscopical work, may 

 have found, as I have, no little difficulty in counting the correct 

 number of ruled lines, or of diatomic stria?, in a given space. 



For example, a count of 16 may be made; the next count may 

 yield 17 ; subsequent counts may oscillate between 16 and 17 ; so 

 in despair the observer will take the mean and call it 16£, well 

 knowing that actually there must be either 1(5 or 17 — which of 

 the two he cannot tell. 



This trouble does not arise when the interspace appears 

 relatively wide with respect to the breadth of the line, but it is 

 sure to do so the moment the breadth of the interspace appears 

 approximately equal to that of the line. Some difficulty may be 

 experienced in counting Grayson's 20,000 band with a low-angled \, 

 but none with an oil-immersion j 1 ^ ; nevertheless, the phenomenon 

 has been observed with a band as low as 30,000 per in. and an 

 oil-immersion \. It is rather humiliating to think that in this 

 twentieth century there should be any difficulty in counting what 

 may be tolerably large microscopical intervals. 



A great deal more micrometry is performed by counting a few 

 intervals embraced between the lines on a scale in an eye-piece 

 than by the employment of a screw cobweb micrometer; conse- 

 quently, when a count consists of only a few lines, one more or 

 less may make a considerable percentage of difference in the final 

 result. It is not improbable that discrepancies, which some have 

 noted in the striation of diatoms, may be due to this 

 cause, but it does not appear that anyone has given an 

 explanation of the cause of this phenomenon. In brief, 

 it is the black-and-white dot image that is responsible for 

 all the trouble. Thus, let fig. 104 represent 4 lines, or 

 Fig. 104. stria, at black-dot focus, obviously then the lines count 4. 

 When, however, the focus is slightly raised, the lines 

 become a white-dot and the spaces a black-dot image, and the 

 count is but 3. 



Measurements by a screw cobweb micrometer are free from 

 error on this score, for obviously it cannot matter in the least 

 whether the image is at white- or black-dot focus ; but when a 

 count is made between the fixed lines in a micrometer eye-piece, 

 creat care should be exercised. In other words, the fineness of a 



