42 



SERIES FOR DETERMINING THE VALUES OF b® AND ITS DERIVATIVES. 







LOG COEFFICIENTS OF THE POWERS OF a. 



1 



Powers of 



a 



1 6 T 



, « D J«°> 



a 2 D 2 l<«» 

 lo~ * 



« 3 c 3 j(W 



lO" * * 



a 4 Z) 4 iPj» 



a 5 Z> 5 l<\°> 

 lo™ * i 





L *f 





a a*f 



0g « 2 ^ 



° r 



a° 





1-9.5470280 



+0.5470286 



+1.5012711 



+2.4043611 



+3.2494592 



+4.0276105 



a 2 



- 



-9.2257952 



—0.1777338 



—1.6152145 



—2.7317201 



—37080970 



—4.5716785 



a 4 





-9.0S23713 



—9.5130370 



+0.9691790 



+2.5552876 



+37457183 



+47457183 



a 6 





-8.9861585 



—9.1540663 



+0.1600994 



—1.7346282 



—3.3981864 



—4.6144071 



a 8 





[-8.9123724 



—8.8959819 



-j-9.7123558 



—0.7929022 



+2.4576404 



+4.1467928 



a 10 





1-8.8518916 



—8.6905235 





1-9.3958804 



—0.2327679 





LI. 4283 115 



—3.1112854 



1 a's 





-8.8003147 



—8.5179803 





|-9.1506929 



—9.8154811 





-0.8046083 



—1.9987102 



a 14 





-8.7551650 



—8.3682204 





(-8.9506679 



• —9.4769745 





L0. 3428636 



—1.2949972 



a 16 





-8.7149019 



—8.2352918 





L8. 7818214 



—9.1889289 



+9.9754219 



—07510711 



a 1 " 





-8.6784965 



—8.1153744 





-8.6357467 



—8.9360287 



+9.6710927 



—0.2957320 



a 20 



+8.6452246 



—8.0058554 



+8.5069939 



—87089594 





1-9.4122184 



—9.8950964 



a aa 



+8.6145558 



—7.9048619 



+8.3918341 



—8.5015836 





-9.1875793 



—9.5286211 



a 24 



+8.5860882 

 +8.5595095 



—7.8110000 



+8.2876105 

 +8.1923669 



—8.3096049 





-8.9895282 



—9.1816721 



a 26 



—7.7232009 



—8.1298642 





-8.8125906 



—8.8981216 



Powers of 



a 



log^T 



lnrr * 4 

 0?f 



log ,1 2 



a 3 Z) 3 &<?> 

 log * * 



lo 



° a 3 ft* 



log ",„ * 



a° 



+9.5268252 



+0.5682179 



+1.5682180 



+2.5224605 



-3.4255504 



+4.2706484 



a 2 



+9.2073119 



—0.2054190 



—1.6889414 



—2.8588090 



—3.8971069 



—4.8347436 



a 4 



+9.0653399 



—9.5463043 



+1.0462084 



+2.6871765 



+3.9409679 



+5.0166585 



a 6 



+8.9703643 



—9.1922130 



+0.2382761 



—1.8700532 



—3.5974309 



—4.8900626 



a8 



+8.8976491 



—8.9384579 



-j-9.7904561 



—0.9318112 



+2.6593168 



+4.4254283 



a 10 



+8.8381032 

 +8.7873497 



—8.7368913 





-9.4732818 



—0.3755407 





-1.6307492 



—3.3923716 



a 13 



—8.5678872 





-9.2271350 



—9.9626214 





-1.0060926 



—2.2830750 



a 14 



4-8.7429307 



—8.4213789 





-9.0260938 



—9.6290049 





-0.5418519 



—1.5846506 



a 16 



-J-8.7033201 

 +8.6675010 



—8.2914656 





-8.8502818 



—9.3463657 





-0.1707002 



—1.0489863 



a 18 



—8.1743672 





-8.7093425 



—9.0993890 





-9.8618412 



—0.6057986 



i a 20 



+8.6347593 

 +8.6045716 



—8.0675042 



+8.5798437 

 +8.4640573 



—8.8787761 





-9.5979913 



—0.2223090 





—7.9690301 



—8.6784273 





-9.3682395 



—9.8798852 



a 24 



+8.5765428 



—7.8775729 



+8.3593185 



—8.4941026 





-9.1651830 



—9.5062041 



a 26 



+8.5503661 



—7.7920822 



+8.2636600 



—8.3227280 





-8.9834735 



—9.2733277 





, * ( \ 2) 



, « D. *°$ 



c? Z> 2 6< 12 > 



a 3 Z) 3 6< 12 > 



a 4 D i lf?> 



a 5 z) 5 m 



a 



log _*- 



lo g ,n .* 



l0g ^ 



log * * 



° a 6 f 





log >+,„ *" 



a° 





-9.5083418 



+0.5875231 



+1.6289158 



+2.6289158 



+3.5831583 



+4.4862482 



a 2 





-9.1902787 



—0.2300891 



— 1.7550865 



—2.9722348 



—4.0642824 



—5.0642824 



a 4 





-9.0495455 



—9.5756293 



+1.1152368 



+2.8040272 



+4.1132964 



+5.2527521 



a 6 





r 8.9556411 



—9.2256368 



+0.3085255 



—1.9904750 



—37731624 



—5.1302153 



a 8 





,-8. 8838608 



—8.9755358 



+9.8609192 



—1.0550089 



+2.8372855 



+4.6682848 



a 10 





L8.8251385 



—8.7772635 



+9.5433948 



—0.5016665 



+1.8098247 



—3.0373347 



a 12 





-8.7751153 



—8.6112584 



+9.2966176 



—0.0919487 



+1.1851409 



—2.5302990 



a 14 





-8.7313488 



—8.4675049 



+9.0948396 



—97618367 



+07198127 



— 1.8349419 



a l6 





-8.6923246 



—8.3401421 



+8.9242830 

 +8.7766454 



—9.4830034 



+0.3466786 

 +0.0351507 



—1.3036584 



a 18 





-8.6570350 



—8.2254225 



—9.2401260 



—0.8665692 



a 20 





1-8.6247750 



—8.1207929 



+8.6465207 



—9.0239023 





-97681640 



—0.4912748 



a 22 





-8.5950262 



—8.0244282 



+8.5301901 

 +8.4249892 



—8.8282356 





-9.5350080 



—0.1595579 



a'- 4 





-8.5673995 



—7.9349743 



—8.6488982 





-9.3284478 



—9.8597170 



| a* 



+8.5415923 



—7.8519402 



+8.3289457 



—8.4828361 





-9.1432694 



—9.5843549 



