Flat-Wavelet Resolution. 587 



and therefore the amount of light, in each of them is 

 infinitesimal. It requires the cooperation of a sheaf * of them 

 to produce an optical punctum p, which the human eye can 

 see. But as is proved in theorem X (see Phil. Mag. Feb. 

 1903, p. 274) a single u£w may be substituted for all the 

 u f w's of such a compact little sheaf, as will contain sufficient 

 light to affect the eve. The image which results from the 

 presence of all the little groups of spurious disks that constitute 

 puncta bright enough to be visible, is the image marked with 

 an .1* in tig. LI, which is the image seen near the back lens 

 of the objective on looking down the tube. To see it properly 

 it is best to put a blank eyepiece into the top of the tube — 

 that is the mounting of an eyepiece, without lenses — whose 

 eyehole (and the eyehole should be small) will serve to keep 

 the pupil of the eye on the axis of the instrument. When 

 accurate experiments are being made it is advisable that the 

 eyehole should not be on the outside of the blank eyepiece, 

 but so far sunk down in it as to bring it to the level of 

 image D. the image of the microscopical object formed by 

 the objective. The image at x as seen through the blank 

 eyepiece may be called the Concentration Image, as every one 

 of its visible puncta is the concentrated light of one of the 

 small sheafs of u f w's, into which the light between image C 

 and the objective may be resolved. 



41 . This concentration image renders the greatest service 

 to the student of microscopical vision. To understand the 

 extent of this service, imagine a " reference hemisphere " 

 with its '•' indicator diagram " (see the annexed figure (fig. 12), 

 and the Phil. Mag. for Feb. 1903, p. 268) constructed with its 

 base upon the plane in which image C lies, and with its optic 

 axis coincident with the axis of the microscope f. Then the 

 concentration image presents to the observer in visible form, 

 upon a plane at the height «r, drawn parallel to the base- 

 plane of the reference hemisphere, that part of the indicator 

 diagram which he has occasion to employ when investigating 

 microscopical problems. This appears upon comparing the 



* By a sheaf of u f w*b is meant a group of them such that if the 

 guide lines of the undulations — lines perpendicular to their wavelets — 

 are drawn through a given point, these guide lines will form an acute 

 solid cone with that point as vertex. 



7 The reader is requested to conceive the reference hemisphere con- 



d of Buch a size thai it- radius — which is also the radius of the 



indicator diagram — shall be that length on the XA scale of figures 18 



.1 14. which expresses the index of refraction of the medium between 



-glass and the front leu- of the objective. This medium is in 



practice either air, water, or oil : of which the indices of refraction ;>re 



1. 1-83, and 1-515. 



2 Q 2 



