476 Prof. W. M. Hicks on 



(3). That part of Handke's measures which lies beyond 

 X=1770 shows clear evidence of connexion as summation 

 lines with D(l) sets, depending not only on different d% 

 sequences (i. e. on different multiple A origins) but on dis- 

 placed d(l) sequents and displaced D (oo ) limits. This is 

 shown by the large number of separations about 10 to 32 

 larger than the normal v and presumably due to the v+cr 

 separations between D n and D 23 . The corresponding in- 

 tensities also are in proper order showing a D u stronger 

 than D 22 with in general D 12 (the weakest not seen). The fol- 

 j lowing are examples arranged on the supposition that there is 

 no displacement on the limit, i.e. v= 248*44. . The supposed 

 D 12 are in [ ] . It should be remembered that the equally 

 probable errors are about 1*5 for the lines and 3 for the 

 differences. 



[565504] (2)58281-9^ [59232-9] [60244-0] [61909-7] 



245 645 1 87 103 94 



(8)565259 (7)58217-4 }>249 (7)59224-2 (3)602337 (3) 61900-3 



(4)56798-8 (7)58530-9; (7)59481-3 (2)60492-4 (1)62158-1 



In the last three sets a separation of 10 corresponds to 

 d\ = *3. The weak line D 12 is therefore very close to the 

 D n and might be overlooked. It should exist in the third 

 set with a strong D 22 ; in the others it might really be too 

 weak to be seen. These small cr separations may be regarded 

 as belonging to actually the same value, and if so their mean 

 will be a real approximation to the true value. This is 9*5. 

 It corresponds to a satellite displacement of 24^ and is in 

 step with that of 23 Sj for D(2). The second is a strong set, 

 gives the normal v, and is at least near a ^ 2 (1) depending on 

 a multiple of A. It may be well therefore to consider it 

 in a little more detail although no certain conclusions can 

 be drawn on account of the large measure uncertainties. If 

 the v is normal, the limit is 31523*48. The D J2 gives d 2 (l) 

 = 26758-4 + ^/ where y l < ±l-7-34i\, and D 12 = 4764*9 -y. 

 No d' — d combinations are found with these as in the cases 

 discussed above under d(\). The d 2 (1) has a denominator 

 = 2'024528-37oy, i.e. a mantissa 1024528-38y. Now 

 140 A = 1022992 -15(^-^0 or 1536 less. The observed 

 may be a sequence displacement on the 140 A, but as there is 

 no combination found with it the displacement probably takes 

 place in the limit (or on both). If the displacement on Si (co ) 

 is xB, it decreases the limit by 4*94.1'. The d 2 (l) sequent as 

 calculated from D 12 is increased by the same amount, and its 



