270 Transactions of the Society. 



sufficiently exact to be made a basis for measurement (see calcula- 

 tion below *). 



It is interesting to note that the breadth of the hairs in these 

 drawings is in the ratio of 65 to 45, and that by equating this 

 ratio to the value given in the table, the true size of the hair agrees 

 with the actual measurement of the apparent size of the hair, viz. 

 •000033 in., by an oil immersion -fa, with a W.A. of *9 + the 

 correction given in the table. 



Thus : -000033 + -000004 = -000037 = ^j^i in -> tllis bein § 

 12 p.c. greater than its apparent size. 



A difference in the apparent size of objects, when viewed on a 

 bright or a dark ground, was recognised many years ago, but neither 

 the absorption nor the diffraction images of the Abbe theory afforded 

 the least clue to an explanation of the phenomenon. But at last 

 the riddle has been unlocked by Mr. Gordon's admirable antipoint 

 theorem, which clears up this, as well as other hitherto unanswered 

 questions, in the interpretation of microscopical images. 



Since this paper was read Mr. Merlin has most kindly measured, 

 with his own apparatus, a hair upon another blow-fly's tongue, 

 both on dark and bright grounds, with the following results : — 



Dark ground, W.A. -858= -0000418 m. 

 Bright „ „ -570 = -0000287 in. 



Equating from these data the size of the antipoint and applying 

 the correction, we find the thickness of the hair to be -0000366 in. 



* Data : — (1) From Mr. Gordon's drawings on bright and dark grounds, with 

 ^-in. objective : W.A. = "45. The measurements are 4i and 6J respectively, by a 

 certain scale which need not be specified. 



(2) Measurement of apparent size of hair, dark on bright ground, with oil immer- 

 sion T \j (W.A. = -9)= -000033 in. 



Let a = actual size of hair. 



6 = apparent size at -45 W.A.J Mcasuml Jaik on bright gromul . 



x = visible antipoint at ■ 9 W.A. 

 2x = „ „ -45 W.A. 



Then a = b + 2x \ 



a = B+ x f 

 x = B- b = -000033 -6 . . . . (i) 



As the drawings measure G£ and 4J, the size of the antipoint is half the difference 

 between them, and therefore on this scale 



and x — J, 



but b = 4£, therefore b = 9a;. 



Putting this value in (i) x — • 000033 - Ox 



x = -0000033, 

 and « = B + x = -000033 + "0000033 = -0000363. 



By table on p. 581 Journal E.M.S. 1903, 



a= -000033+ -000004 = -000037. 

 T he difference being -0000007. 



