the Valves of Pleiiroslgma and other Diatoms, 861 



occupying those spaces, and with it the character of the two re- 

 maining series of lines. In short, the appearance presented by- 

 one of these valves, as seen under a Ross's 5-inch or ^th inch 

 objective and a low eye-piece, differs only in the angles* formed 

 by the diagonal lines from what is seen on a valve of P. angu" 

 latum when examined under a gth or yV^h. In both instances 

 hexagons may be evoked by dint of a laborious effort to detect 

 the precise error of focus essential for the production of this 

 illusory figure ; but it is impossible to witness the contrast be- 

 tween the perfect definition observable whilst the true structure 

 is visible and that presented when the hexagons or " dots " 

 are produced, without perceiving that a fictitious image is im- 

 pressed on the retina in one case, and a true one in the other. 



But the question admits of demonstration in a very remark- 

 able manner. By inserting a delicately-hinged metallic scale 

 between the eye-piece and the tube of the microscope, so as to 

 form a goniometer, I was enabled with accuracy to measure 

 the two angles produced by the intersections of the diagonal 

 lines. These were respectively 83° and 97°. By means of a 

 piece of paper, carefully cut, so as to form a four-sided figure 

 presenting these angles, and gummed to the plane side of the 

 lens of the eye-piece nearest to the objective, I was subsequently 

 able to verify the first observation. The next step was to count 

 how many diagonal lines occupied a given number of divisions 

 of a Ross's screw micrometer ; and then, how many longitudinal 

 and transverse lines occupied the same space. This done, a 

 diagrammatic figure was prepared, the only essential condition 

 in its formation being that the recorded angles should be accu- 

 rately preserved. The two diagonal sets of lines being thus 

 laid down, parallel longitudinal lines were drawn passing through 

 the whole of the angles of 83°, and parallel transverse ones 

 through the whole of those of 97°. It now only remained to 

 count off as many of the diagonal series as were previously ob- 

 served to occupy the predetermined number of divisions of the 

 micrometer, and, employing these as a unit of comparison, to 

 ascertain if the longitudinal and transverse series of lines on the 

 diagram tallied in number with those occupying an equal space 

 on the valve itself. The result, which appears to me conclusively 

 to demonstrate the identity in the series and direction of the 

 lines on the valve itself and the diagram, was as follows f *. — 



* The horizontal angles in P. angulatum are respectively 120° and 60°. 



t It will at once be obvious that the degree of magnifying power em- 

 ployed in this observation is quite immaterial, the relative number of 

 lines, longitudinal and transverse, in any given number of diagonals being 

 all that is requisite. 



Ann. i^ Mag, N, Hist, Ser.3. Vol.xi, 24, 



