466 Prof. W. M. Hicks on 



already obtained value. We may therefore regard the f 

 as probably <*02. The d 2 —f gives /( 4) = 4402*56 ±1, 

 that is as in m — 3 it gives f\. The lines 44576 and 53446 

 may be put in evidence because they appear to satisfy 

 a set d x ' — X, d 2 ' + X. d 2 — X would be 98*46 larger and 

 = 44674*46. This with the second as d 2 ' + X gives 

 d 2 = 49060*56, X = 4386*1, or a corresponding set with 

 a large sequent displacement as in/(3). 



m — 5. Only the p —f combinations are observed. They 

 are the same as for D (5), i. e. t /'(5 N > = <f (5), and give 

 / 1 (5) = 3059-20±-4, / 2 (5) = 3057*10 ±1*2. The d' +f is in 

 an observational lacuna and no d' — /'is seen. 



m = 6. The p lt f\ give /, = 2235*50 and 2236*35 with 

 mean limit 31523*85. Nevertheless there may be some 

 doubt as to their belonging to this system since their 

 mantissse as given below are not in step with the others. 

 Also the p-+f line is excessively strcng. If this /(6) is 

 — 2A displacement on the normal it would be more in 

 line. The line under p 2 -f is also probably not the real 

 line. It is 1*5-6 too small and moreover is the exact 

 linked line e. P 2 (l) . 46800 as d 2 '~f gives f(6)=2261'22 

 and 46834 gives /= 2227*44. These look like equal and 

 opposite displacements of 7 8 X in the limit. Their dif- 

 ference is 33*78 and 14Sj shifts 33'58. This would give 

 ^(6) = 2244*33 whose mantissa 992044 is quite in step 

 with the other orders. 



m = 7. d'-f gives /(7) = 1733*70. It is not in step 

 with the normal f. If it is analogous to the second in 

 m = 6, i.e. (7B l )d 2 / —f, then /= 1715*9 and conies into line 

 with the others. 



An attempt may now be made to determine the values 

 of /(I, 2). The run of the mantissse of the higher orders 

 as seen below shows that the denominators of these sequents 

 must be near 1*992 and 2*992. Moreover we have to 

 expect satellites depending on displacements of about 6^8 7 

 which as has been seen is that for /(3). This means for 

 m = 2, f(2) about 12250 and satellite separation 7, and 

 for w=l, /(l) about 27450 and satellite separation 25. 

 The fact that the lower orders of F series are very sus- 

 ceptible to displacement and consequent weakening must 

 also be borne in mind. Several representative sets corre- 

 sponding to the same order m may therefore be expected, 

 and the allocation of a suitable set does not mean that 

 it must be the normal one. 



