624 



SCIENCE. 



[N. S. Vol. Xir. No. 304. 



They do not account for the accompanying 

 color which is a not infrequent occurrence ; 

 and they predict more focal planes than are 

 easily found. The latter discrepancy might 

 be ascribed to the imperfect gratings (wire 

 gauze), or to lack of intensity taken as 

 proportional to the number of lines which 

 cross at a point in the diagrams. It would 

 merely have been confusing to record other 

 than the strong cases. The diagrams fail 

 altogether to suggest how a thin wire is to 

 cast a shadow of the order of 10-30 meters 

 in length, even in diffuse light. It is in this 

 respect that the explanation will have to 

 be supplemented. In the meantime, how- 

 ever, it seems worth while to test the posi- 

 tion of the virtual foci between AB and 

 beyond B. 



5. For this purpose it is convenient to 

 place the gratings far apart and observe 

 with a telescope as shown in Fig. 2. If 

 / be the focal distance of the objective, and 

 y" the reduced distance of the conjugate 

 focus, corresponding to the virtual focal 

 plane S at a focal distance y' , we may write 

 Ijy' + 1/y" = 1//. "With y' computed in 

 this way, y ^= y' — z, where z is the distance 

 between the objective of the telescope and 

 the grating B; and y, as usual, the distance 

 between this and the image. The distance 

 X may be measured or found by the same 

 method. 



This experiment gives excellent results 

 for the number and relative size of the suc- 

 cessive images between A and B. It is a 

 crude method of finding the distances y, 

 sufficing, however, to pick out their posi- 

 tion in a series. If A be the clapboarding 

 of a distant house and, B an ordinary win- 

 dow screen through which A, distant about 

 300 feet, is observed, the conditions for 

 many virtual foci will be realized. Table 

 5 gives an example of results of this kind. 



The table shows that the limits of y are 

 pretty well given, the visible foci should all 

 lie near B as found. All the focal planes 



observed are predicted by a diagram of in- 

 tersecting pencils of rays of the kind above 

 exhibited, as indicated by the third and 

 fourth columns of the table. Nevertheless, 



TABLE 5. — VIETCJAL FOCI BETWEEN THE GEATINGS. 



a; ^10, 000 CM. 3 = 274 CM. geating 

 SPACES, a = 10.7, 6=22 CM. 



many images are predicted which do not 

 occur ; and whereas the predicted images 

 should be all of nearly a size, practically 

 of the same grating space as B, the images 

 found are all much smaller. They increase 

 to a maximum and then diminish again in 

 the direction BA, with the largest not more 

 than ^ of b. Possibly the presence of two 

 or more focal planes in the telescope at once 

 would account for the discrepancy of size 

 and number, but the planes marked * which 

 should be strong do not appear specially so 

 in the experiment. In general, therefore, 

 the diagrams give a good outline of the 

 phenomena, but fail in the particulars. 

 One may note that the foci found are in a 

 distance ratio of 0, 1, 2, 4, 8, 10, which is 

 liable to be more than a coincidence. 



Another class of virtual foci consists of 

 images not lying between the gratings, but 

 on one side of both when looked at from 

 the other side. This implies the same 

 method of telescopic observation : obvi- 

 ously the cases of Figs. 3-8 can all be 

 found as virtual images by a telescope in 

 front of A, looking from A to B. In such a 



