appearing and then disappearing; a rapid succession of changed appearances is equivalent to a rapid alternation of appearance and disappearance. Why this is so we are unable to say," etc. These authors now take the first step toward explaining the illusion. In their words (_op. cit._, p. 205), "the suggestion is natural that we are dealing with the phenomena of after-images.... If this is the true explanation of the fact that several rods are seen, then we should, with different rotation rates of disc and rod, see as many rods as multiplied by the time of one rotation of the disc would yield a constant, _i.e._, the time of an after image of the kind under consideration." For two subjects, J.J. and G.M., the following tabulation was made. J.J. G.M. Av. time of rot. of disc when 2 images of rod were seen .0812 sec. .0750 sec. " " " " 3 " " " " .0571 " .0505 " " " " " 4 " " " " .0450 " .0357 " " " " " 5 " " " " .0350 " .0293 " " " " " 6 " " " " .0302 " .0262 " "Multiplying the number of rods by the rotation rate we get for J.J. an average time of after image of .1740 sec. (a little over 1/6 sec.) with an average deviation of .0057 (3.2%); for G.M. .1492 (a little over 1/7 sec.) with an average deviation of .0036 (2.6%). An independent test of the time of after-image of J.J. and G.M. by observing when a black dot on a rotating white disc just failed to form a ring resulted in showing in every instance a longer time for the former than for the latter." That this constant product of the number of 'rods' seen by the time of one rotation of the disc equals the duration of after-image of the rod is established, then, only by inference. More indubitable, since directly measured on two subjects, is the statement that that person will see more 'rods' whose after-image persists longer. This result the present writer fully confirms. What relation the 'constant product' bears to the duration of after-image will be spoken of later. But aside from all measurement, a little consideration of the conditions obtaining when the rod is passed _behind_ the disc will convince any observer that the bands are indeed after-images somehow dependent on the rod. We may account it established that _the bands are after-images_.