THEORY OF MICROSCOPICAL VISION. 25 



markings. Or by stopping off all but g, c, e (or b, d,f), 

 we again have the spectra in the form of equilateral 

 triangles ; but as they are now further apart, the sides 

 of the triangles in the two cases being as \/ 3:1, the 

 hexagons will be smaller and three times as numerous. 

 Their sides will also be arranged at a different angle 

 to those of the first set. The hexagons may be 

 entirely obliterated by admitting only the spectra g, c, 

 or g,f, or &, /, etc., when new lines will appear at right 

 angles, or obliquely inclined, to the median line. By 

 varying the combinations of the spectra, therefore, 

 different figures of varying size and positions are pro- 

 duced, all of which cannot, of course, represent the 

 true structure. Not only, however, may the appear- 

 ance of particular structure be obliterated or created, 

 but it may even be predicted before it has been actually 

 seen under the microscope. If the position and relative 

 intensity of the spectra in any particular case are 

 given, the character of the re- 

 sultant image may be worked 

 out by mathematical calcula- 

 tions solely. A remarkable in- 

 stance of such a prediction is to 

 be found in the case recorded 

 by Mr. Stephenson, where a 

 mathematical student who had 

 never seen 'a diatom, worked 

 out the purely mathematical 

 result of the interference of the p^ 12> 



six spectra & g of fig. 11 (iden- 

 tical with P. angulatum), giving the drawing copied in 

 fig. 12. The special feature was the small markings 

 between the hexagons, which had not before been 

 noticed on P. angulatum. On more closely scruti- 

 nizing a valve, stopping out the central beam and 

 allowing the six spectra only to pass^, the small mark, 

 ings were found actually to exist, though they were 

 so faint that they had escaped observation until the 

 result of the mathematical deduction had shown that 

 they ought to be seen. 



These experiments prove that diffraction plays a 



