236 ON THE THEOKY OF THE MICEOSCOPE. 



pencils being consecutive in order of position, one, two cr more 

 intervening pencils are passed over. Thus a group of two lines 

 only in the object appears as if composed of three or four 

 separated sets. The phantom lines thus created cannot be 

 distinguished by help of any magnification from the normal imaga 

 of actual lintis of double or treble fineness, either in respect to 

 sharpness of definition, or constancy of appearance as may be 

 shewn by a conclusive experiment, in which namely, the falsely 

 doubled image appears side by side with the image of an 

 object actually ruled with lines of double fineness. 



(v.) When two pieces of simple lattice cross each other in 

 the same plane at any selected angle, the systems may, by suit- 

 able regulation of the admitted pencil of light, be rendered visible 

 together, or separately, and further by varying the form of 

 illumination, numerous fresh systems of lines and variously 

 figured fields which do not exist at all as such in the object may 

 be made to appear with equal sharpness of delineation. These 

 new systems of lines always correspond in position and distance 

 from each other with the possible forms in which the points of 

 intersection of the real lines of the object may arrange themselves 

 in equi-distant series. 



Thus, for instance, a rectilineal net or lattice work shews two 

 secondary seta of lines in the direction of the diagonals, the 

 network of the latter appearing smaller than the actual net as 

 1 : Vs. Also four more groups, but shewing more faintly and 

 smaller still in the proportion of 1 : V5, each of which is inclined 

 at an angle of about 27^ to the direction of one of the real 

 networks. "With a network crossing at an angle of 60°, there 

 appears, besides several smaller systems of lines, a third set 

 marked just as strongly as the real net- work of the object, and 

 with equal distance between the lines, inclined also 60 '^ to the 

 others ; and when the three sets are seen together there will be 

 seen perfectly sharpl 7 defined six-sided spaces (fields) of the kind 

 observed on pleurosigma angm., instead of the rhombic fields. 

 It may be added that all the appearances unconformable with the 



