III. CENTRIFUGATION 81 



nevertheless converge at A' by reason of the fact that the lenses have been 

 positioned to produce such a result. An analogy holds for the other images. 

 Now suppose, as shown in the second arrangement, that a cylindrical lens 

 with vertical axis is added to the system in such a position that a point light 

 source placed at the position of tlie slit image would be sliarply focused as a 

 vertical line image on the screen. The effect of this lens on each of the original 

 light sheets is to converge it prematurely, so that it again diverges and forms 

 a horizontal line image A ^A 2 A3 on the screen instead of a point image. The 

 vertical positions of the images are not altered by the cylindrical lens. A 

 downward deviation (broken lines) of the sheet at A would not alter the posi- 

 tion of the line image. Suppose now that in the vertical plane containing the 

 slit image a thin diaphragm, provided with a narrow inclined slit, is inter- 

 posed and centered about the optical axis. Then, of the undeviated rays 

 through A, only the central one (heavy unbroken line) is able to pass through 

 the remaining lenses and reach the screen, where it will appear as a point of 

 light A2', as contrasted to the previous horizontal line A^ A, A3. Since the 

 undeviated light sheets through A, B, and C converge in a common image of 

 the light source at the second diaphragm, it follows that B and C will also be 

 represented at the screen, when there is no deviation at the object diaphragm, 

 by light points B'2 and C2, which are situated along a central vertical line pass- 

 ing through Ao. However, if the light sheet from A, for example, is deviated 

 downward (broken lines) suflficiently from its normal course, then only the 

 ray (heavy broken line) at one edge of the light sheet will pass through the 

 remaining lenses, and the light point corresponding to A will appear at Aj. 

 The horizontal distance by which any light point will be displaced from the 

 central line C2 A2 is directly proportional to the downward displacement suf- 

 fered by the corresponding light sheet at the object diaphragm. Light com- 

 ing from 5 or C is likewise affected. The system is thus able to convert a 

 vertical deviation of light into a horizontal displacement of a light point on a 

 screen (or photographic plate) without altering the point's vertical height, 

 which itself corresponds to a certain level (or certain vertically disposed hole 

 in example given) in the object. 



With the elements of the system arranged as described, the light intensity 

 and the resolution at the screen can be increased without affecting the opera- 

 tion of the system by substituting narrow horizontal slits for the holes A, B, 

 and C. In any one light sheet corresponding to one of these slits, more rays 

 will then pass through the inclined slit, diverging from it laterally as they 

 progress toward the camera lens. However, they will be brought to focus 

 again on the screen since the cylindrical lens has been positioned to ac- 

 complish this effect. Now suppose, as illustrated in the third arrangement of 

 Figure 6, that a transparent flat-walled cell containing an immobilized sedi- 

 mentation boundary is substituted for the diaphragm in such a way that the 

 maximum refractive index gradient, i.e., the center of the boundary, is in the 



