44 



SERIES FOR DETERMINING THE VALUES OF b\' AND ITS DERIVATIVES. 





LOG COEFFICIENTS OF THE POWERS 



3F a. 



Powers of 



a 



a 4 LP iff 



lo g ^ ' 



, « 5 Z) 4 6<«> 



log - 



a 8 LP 6<\ a » 

 l0g ^ 





1 



c?D 6<\ 2 > 



« 3 D 2 iff 



a° 



+3.8841883 



+4.7872782 



+5.6323763 



+0.9062819 



+1.9854631 



+3.0208558 



a 2 



—4.2443399 



—5.2046788 



—6.0551829 



—0.5520063 



—2.0583348 



—3.2945607 



a* 



+4.1962330 



+5.2754141 



+6.2023168 



—9.9007284 



+1.3G01209 



+3.0585618 



a 6 



—3.7771807 



—5.0615905 



—6.1171159 



—9.5539408 



+0.5055677 



—2.1860606 



a 8 



+2.7735204 



+4.5243260 



+5.7902188 



—9.3070689 



+9.9328078 



—1.2029610 



a 10 





[-1.6836121 



—3.4302486 



—5.1646981 



—9.1120497 



+9.5990642 



—0.6121807 



a la 





-0.9978052 



—2.2721385 





[-3.9960709 



—8.9493226 





L9.2881409 



—0.1741381 



a 14 





-0.4699147 



—1.5837168 





U2.7663615 



—8.8088714 





-9.0227514 



—9.8235499 



a 16 





-0.0312408 



—0.9830938 





Ul. 9535877 



—8.6848364 





(-8.7894428 



—9.5308603 



al8 





1-9.6501229 



—0.5353043 





-1.3033967 



—8.5734708 





-8.5801015 



—9.2796327 



a 20 



+9.3081801 



—0.1620742 





[-0.7274119 



—8.4722208 





[-8.3894100 



—9.0596089 



a 23 



+8.9949767 

 +8.6985355 



—9.8439239 





-0.1919566 



—8.3792624 





-8.2136752 



—8.8638990 



a 24 



—9.5675322 





-9.6145070 



—8.2932417 





-8.0502026 



—8.6877340 





« 4 D 3 6< 12 > 



, a 5 -D 4 6< 12 > 



JDlbW 



« 2 iff 



oPjD.*W> 



a 2 Iff 



a 



** Sr 9 



log * 3 



tog m 3 



tog -r-4- 



lo s a = r * 



^-a4~ 



a" 



+4.0268558 



+4.9810983 



+5.8841883 



+1.7538545 



+2.7538545 



+1.8093718 



a 2 



—4.4111603 



—5.4359432 



—6.3702645 



—1.8179720 



—2.9554998 



—1.8840054 



a 4 



+4.3784473 



+5.5269955 



+6.5431207 





-1.1144544 



+2.6486141 





-1.1891914 



06 



—3.9695033 



—5.3253849 



—6.4715129 





-0.2435490 



—1.6994811 





-0.3256103 



a 8 



+2.9734198 



+4.7965683 



+6.1537157 





1-9.7321501 



—0.6336635 





r 9.8204600 



a 10 





-1.8903509 



—3.7078557 



—5.5344717 





-9.3519389 



—9.9540007 





1-9.4456437 



a ia 





-1.2116515 



—2.5650467 





-4.3711407 





-9.0440696 



—9.4208136 





-9.1424797 



u 





-0.6918574 



—1.7477473 





-2.1485242 





-8.7831029 



—8.9685343 





^8.8856534 



a 16 





-0.2625935 



—1.3651767 





-1.3483653 





-8.5554353 



—8.5667556 





-8.6616562 



a 18 





-9.8923506 



—0.7309881 





-0.7181354 





-8.3528354 



—8.1974184 





-8.4623356 



a 20 



+9.5639199 

 +9.2657845 



—0.4226375 





-0.1834208 



+8.1699061 



—7.8478193 



+8.2823486 



a 22 



—0.0940097 





-9.7072379 



+8.0028837 



—7.5052857 



+8.1179885 



a 24 



+8.9913590 



—9.8066683 





-9.2650538 









Powers of 



yD.iPp 



a 2 &<*?> 



a 3 D &< 12 >" 

 log " * 









a 



a *po 



" a !? 8 











a" 



+2.8507745 



+1.8605244 



+2.9397056 



a 2 



—3.0750739 



—1.9438616 



—3.1819476 









a 4 



+2.7886585 





r 1.2563714 



+2.9116769 









a<5 



—1.8587518 





-0.3990389 



—1.9967340 









a* 



—0.8116862 





-9.8992840 



—0.9639272 









a" 



—0.1509997 



+9.5291729 

 +9.2301490 



—0.3171937 









a' 2 



—9.6377598 



—9.8179724 









a" 



—9.2071979 



-j-8.9769939 



—9.4018570 









a l6 



—8.8301137 



+8.7562746 



—9.0400482 









a 18 



—8.4900709 



+8.5598978 



—8.7166293 









a 20 



—8.1764964 



+8.3825710 



—8.4215217 









„22 



—7.8820120 



+8.2206235 



—8.1483558 









