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SCIENCE. 



[N. S. Vol. XII. No. 304. 



The figure shows, moreover, that between 

 A and B there should be virtual focal 

 planes, and these must also be discoverable 

 to the left of A. That such actually occur 

 will be shown below, § 5, by the telescope 

 method. The absence of *S', S", etc., will 

 not appear surprising, since the distance 

 AB is two meters and shadows become dif- 



and S' the second, the focal plane v' will 

 appear. 



In Fig. 6, with the space ratio \, the 

 image C is strong ; the image C was also 

 found ; but with these cases of high incli- 

 nation 6, the images are confused and focal 

 planes are apt to be continuous. Thus an 

 image may be found at S', but not sharply 



fuse. It is rather surprising that images 

 properly produced can be obtained at over 

 30 meters from the projecting grating. 



In Fig. 4 the meshes of B are half as 

 large as A. Table 3 shows at ij that the 

 plane *S comes out strongly and colored. 

 S' was not found nor were the other images 



in position. In general a contracted di- 

 agram is liable to exceptions to be ex- 

 plained below. 



In the preceding cases the original grat- 

 ing space is reproduced, as, for instance, at 

 S in Fig. 6, when, if x = l, x + y= a/b. 

 The figures are symmetrical with respect 



striking. Virtual foci are here also sug- 

 gested. Table 4 indicates that if B be the 

 first grating and S the second (larger) the 

 focal plane r/ is sharply traced. 



In Fig. 5 the grating spaces are as J. 

 Table 3 shows that the planes S and S' are 

 both pronounced (marked j and v). Ac- 

 cording to Table 4, if B is the first grating 



to the strongest focal plane (f in Fig. 6, 

 for instance). The original grating space 

 is reduced in the image or at most equal to 

 it. There is no magnification. 



In the following cases the ratio ajh is not 

 a whole number, and the image may there- 

 fore be magnified to an extent which is the 

 least common multiple of a and 6. ^More- 



