PHENOMENA OF PHOSPHORESCENCE. 



20" 



The series in the brackets has the value 1 for / = o and as t becomes large 

 approaches the series 



2-3 



1 + 



+ 



+ 



= S 



w-+3 W+3.W+4 



If the decay curve is plotted in the usual way with 7 _i and / as coor- 

 dinates it is clear that the change in slant in passing from small values of / 

 to large values will depend upon S and will be greatest when S is greatest. 

 The maximum deviation from linearity in the form of the decay curve 

 which can result from absorption will therefore be produced when m = o, 

 i. e., when T = o. To determine whether absorption is sufficient to account 

 for the observed type of curve we shall therefore consider this special case 

 for which the effect is greatest. 



For m = o we have 



2 pa /' zdz 2 pa 



(at)- J* "(a-J-^ 2 



/ = 



/3(a/) 2 *'< (a + 2) 2 j8(a/) 



Putting in the limits this becomes 



1 r z 



) 2 l~ a + z 



+ log (a+z) 



] 



al 



1 = 



ipa 

 0(a/) s 



log 



(.+^- 



a J 



at 



a 



.+* 



a 



Writing ft for at/a 



1 = 



2pa 



i[ log(l+ *)__L] 



This 



The curve for and /~*, computed in accordance with this equation, is 

 plotted in Fig. 188, the quantity 2/>a/a 2 /3 being put equal to unity, 

 curve may be looked upon as show- 

 ing the relation between /-* and / 

 for a/ a = 1 . The curve for any dif- 

 ferent value of a/a may then be 

 found by changing the vertical and 

 horizontal scales to correspond to 

 the change in a/a. 



The curve of Fig. 188 is similar 

 in form to the decay curves observed 

 in the case of short excitation. 

 Pierce 1 has also observed curves of 

 nearly this form with zinc sulphide. 

 It is possible, therefore, that the 

 relatively slight deviation from lin- 

 earity in such cases is to be ascribed 

 to absorption. But in the case of the majority of decay curves it is clear 

 that absorption is not to be regarded as an important factor; for no 

 change of scale can bring about any close resemblance between the curve 

 of Fig. 188 and the decay curves usually observed for long and moderately 

 long excitation. 



a e 



Fig. 188. 



C. A. Pierce, Physical Review, xxvi, p. 314 (see Chapter VI, Fig. 77). In our own work with this same 

 substance, " Emanations-pulver," we found a decay curve of the usual type, i. e., with a well-marked "shoul- 

 der" at (=20 sec. (Physical Review, xxvin, p. 50, or Chapter IV, Fig. 59). It is interesting to inquire 

 whether the difference is due to the repeated heating and cooling to which Pierce's material was subjected. 



