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12



TABLE 6.
DERIVATIVES AND INTEGRALS/



J


7




x n+i


d arc


d (IX


/*<&


n+i


d t>


= ( u % +v ^) dx


f d *


= logx


^


A*-*V


f*<*




\ 2 /


e


dx n


= wre 71 " 1 dx


fe ax dx


=- e ax








a


d/(w)


-^sr^s-*


fx c** dx


=~(^-i)


de*


-e<fe


/log x dx


= x log xx


de ax


= a e>* dx


/n.*


= u vfv du


d log e x


x


/(a + bx)n d x


_(a+bx) n+l


(n+i)b


dx*


= x x (i+log e z)






d sin re


= cos x dx


f( a 2 +x ^-l dx


= - tan- 1 - =








a a








1 sin- 1 *








a v^^_j_ a 2


d cosx


= -sin x dx


f( a 1_yZ\-\dX


= ^L log a+x






J


2a a x


dtanx


= sec 2 x dx


/(a 2 -re 2 )-* dx


. x , x
= sin" 1 -, or cos -1 -








a a


d cot x


= csc 2 re dx


/x(a 2 x 2 )~*dx


= (<Z 2 X 2 )*


dsec x


= tan re sec re dx


/sin 2 x dx


= i cos xsin x+5 x


d csc re


cot re . scs re dx


/cos 2 re d#


= | sin x cos x+j re


d sin 1 re


= (i re 2 ) -* dx


/sin x cos x dx


= \ sin 2 x


d cos- 1 re


= (i re 2 )"* dx


/(sin x cos x)" 1 dx = log tan x


d tan- 1 re


= (i+re 2 )" 1 dx


/tan x dx


= log cos x


d cot- 1 re


= (i+rc 2 )- 1 ^*


/tan 2 xdx


= tan xx


J sec 1 re


= re" 1 (x- i)-* dx


/cot x dx


= log sin x


d csc- 1 re


= x" 1 (x 2 1)~ * dx


/cot 2 x dx


= cot xx


J sinh re


= cosh x dx


/csc x dx


= log tan ^ x


d cosh re


= sinh x dx


/x sin x dx


= sin xx cos x


d tanh re


= sech 2 x dx


fx cos x dx


= cosx + x sin x


d coth x


= csch 2 x dx


/tanh xdx


= log cosh x


d sech x


= sech x tanh dx


/ coth x dx


= log sinh x


d csch re


= csch x . coth x dx


/sech x dx


= 2 tan- 1 c x =gd u


d sinh" 1 re


= (x 2 + 1) * dx


/csch x dx


= log tanh ~


d cosh" 1 x


= (x 2 I)"* dx


fx sinh x dx


= x cosh x sinh x


d tanh- 1 re


= ( I _ JC 2)-l dx


fx cosh x dx


= x sinh x cosh x


d coth- 1 x


= (j^2)-! </


/sinh 2 x dx


= (sinh xcosh xx)


d sech 1 x


= -x- 1 (i-x 2 )-* dx


/cosh 2 x dx


= i (sinh x cosh x+x)


d csch- 1 re


= -*-'(*<+.)-.


/sinh x cosh xdx


= 1 cosh (2 x)



* See also accompanying table of derivatives. For example : /cos. x dx sin. x + constant.
SMITHSONIAN TABLES.



TABLE 7.
SERIES.



= x n + 2. jn-i y + ^-J *n-2 y + . . .

(-!)... (n-m+i) ^ n _ w
w !

(i x) = i * 4- Mn ~ Ia> " rcfo-i) (M-2).y2 + _ _ + (d






(-fcj! kl
3'~



(-

ip 6^5 4-



f(x+h) = f (x)+hf (x) + k ~ /"(*)+...+ ^ /<> (*) + rayl series.

/ / \ / / \ , x f i \ , x2 * , - ^ n r , n \ Maclaurin's

/ (x) =f(o)+ - )' (o) + - /" (o) + .../ () ( ) + . . . series>



/ i\ i i i i

= hm( i+-) w =i+ - - -f- - - + - 4 - . +...
V ;// i! 2! 3! 4 i T



= i + x + -, H - 1 H - 1 -f- . .



a x = l+x ] ga+ v - -^ +



3!
.r i , i /x i \ " i /x i\ 3

i **=~ + - 2 () + -i(v; +

= O - - M* - O 2 + H* - O 3 -



lg ( T + *) = X $ X 2 4- i A; 3 j .T 4 + . . . .

== l f.ix .-ix\ X * * 5 * 7

~ ~^i (t ~ 3! + ? ~ T"! 4

cos .r = - (e'- r 4- g->) = i- H 1 +... = i_ versin .v



7T T^ T "7 >v5 T *? C A"7

. . i i i ' ^5 **' v5 *^

~ 2 " 6 2*4"5" + 2*4*6'7

tan~ ! x = - cot. 1 # = a: # 3 H .r 5 - a- 7 4- ...

7T I I I



i , x 3 * 5 Jc 7

smh s = ~(e*- e-*) = x + - + - + -,+...



SMITHSONIAN TABLES.



TABLE 7 (continued).

SERIES.



I , X* X* X

cosh x = - (e x + -*) = i H , H : + zi +

2 v 2! 4! 6!


,,'<00)


i 2 17 7


U 2 <io


^^,-.-i + i. *'.-!. a. I.?*'...


(*<!)


23 245 2467




- ^g 2* + 1 ^ - ^ ^ + \ \ I ~ - . . ,


(, 2 >I)


ii 131 i 3 5 i




COSh-! x = log 2X _ - ^ ._ _ . __ ... - - - ^ ....


(* 2 >I)


tanh- 1 A; = x + - .v 3 + - .v 5 + - x 1 + .


(A' 2 <I)


3 5 7




i i 61




cd A: = = x 7 * 3 H -v 5 -~ a; 7 + .
6 24 5040 .


(.v small)


IT i sech 3 .v i 3 sech 5 .v




2 23 245


(.i large)


_ d _, _ . . i 3 i 5 6l AT 4.

r 6 24 5040


(<0


/"(*)=- b + b, cos f- b 2 cos - - + . . .




2 C C




7T V 2 TTX




+ di sin 1- ao cos - - 4-


. . <-<:<.v


r c





TABLE 8.- MATHEMATICAL CONSTANTS,



e = 2.71828


18285


7T =


Numbers.
3.14159 26536


Logarithms,

0.49714 98727


e -i = 0.36787


94412


7T 2 =


9.86960


44011


0.99429


97454


M = logio'r = 0.43429


44819


I

7T


0.31830


98862


9.50285


01273


(M)~ l = log, 10 = 2.30258


50930


Y/ir -


1.77245


38509


0.24857


49363


logio logios = 9-63778


43113


2


0.88622


69255


9-94754


49407


log] 2 = O.3OIO2


99957


I


0.56418


95835


9.75142


50637


Iog e 2 = 0.69314


71806


2


1.12837


91671


0.05245


5 593


logiox = M.log e a*




\i=


1-2533'


41373


0.09805


993 8 5


\ogRX = log e .r. lo


gje


V^ =


0.79788


45608


9.90194


006 1 5


= log e # -j-


log B


7T

4_


0.78539


81634


9.89508


98814


log e TT = i.i 147-


98858


4


0.44311


34627


9.64651


4945


p = - 0.47693


62762


ITT =


4.18879


02048


0.62208


86093


logp = 9.67846


03565


e

V 2 7T


1.08443


755H


0.03520


45477

1



SMITHSONIAN TABLES.



TABLES. 15

VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, OF

NATURAL NUMBERS.



n


loco.*


2


// V"


n


1000.^


*


*


i*


10

ii


[00.000

90.9091


100
121


1000 3.1623
'33 1 3-3'66


65

66


15.3846 4225
15.1515 4356


274625
287496


8.0623
8.1240


12

J 3


83-3333
76.9231


144
169


1728 3.4641
2197 3-6056


67
68


14.9254

14.7059


4489
4624


300763

3 l 443 2


8.1854
8.2462


14


71.4286


I 9 6


2744 3-74I7


69


14.4928


476l


328509


8.3066


15


66.6667


225


3375 i 3-8730


70


14.2857 4900


343000


8. 3 666


16
17


62.5000

58.8235


256
289


4096 4.0000

4913 : 4.1231


7i

72


14.0845
13.8889


5041
5^4


3579"
373248


8.4261
8.4853


18


55^556


324


5832 4.2426


73 13.6986 5329


389017


8.5440


19


52-6316


361


6859 ; 4-3589


74 i3-5!35 5476


405224


8.6023


20


50.0000


4OO


8000 i 4.472I


75 13-3333 5625 ! 421875


8.6603


21 47.6190 441


926l 4.5826


76 13.1579 5776 438976 8.7178


22 45-4545 4^4


10648 4.6904


77 12.9870 5929 i 456533 8.7750


23 43-4783 529
24 41.6667 576


I2I67 47958
13824 4.8990


78 12.8205 6084
79 12.6582 6241


474552 8.8318
493039 8.8882


25 40.0000


625


15625 5-0000


80 12.5000 6400


512000 8.9443


26 38.4615


6 7 6


17576 5.0990


81


12.3457 6561


531441 9.0000


27 37-0370 729


19683 5.1962


82


12.1951 6724


551368 9.0554


28 35.7 i 43 1 784
29 344828 841


21952 5.29I5
24389 5-3852


83
84


12.0482 6889
11.9048 7056


571787
592704


9. 1 1 04
9.1652


30 33-3333 9


27000 54772 I


85


11.7647 7225


614125


9.2195


31 3 2 - 2 5 81 i 96i


29791 5-5678


86


11.6279 7396


636056


9.2736


32 31.2500 1024


32768 ! 5.6569 I


87


11.4943 7569


658503


9-3274


33 3-3 3 Io8 9


35937 i 5-7446


88


11.3636 7744


681472


9.3808


34 29.4118 1156


3934 i 5-83 10


89


11.2360


7921


704969


9.4340


35 28.5714 1225


42875 5.9161


90


ii.ini 8100


729000


9.4868


36 27.7778 ; 1296


46656 6.0000


9i


10.9890


8281 '


753571


9-5394


37 27.0270 1369


50653 6.0828


9 2


10.8696


8464


778688


9-59*7


38


26.3158 1444


54872 6.1644


93


10.7527


8649


804357


9-6437


39 25.6410 1521


59319 6.2450


94


10.6383


8836


830584


9-6954


40


25.0000 1600


64000


6.3246 '


95


10.5263


9025


857375


9.7468


4i


24.3902 ; 1 68 1


68921


6.4031


96


10.4167


92l6


884736


9.7980


4 2


23.8095


1764


74088


6.4807


97


10.3093


9409


912673


9.8489


43


23-2558


1849


7957


6.5574 ;


98


10.2041


9604


941192


9.8995


44


22.7273


1936


85184


6.6332 !


99 10.1010


9801 970299


9-9499


45 22.2222


2025


91125


6.7082


100 1 r o.oooo


I 0000 I 000000


10.0000


46 21.7391 2116


97336


6.7823 i


IOF 9.90099 io2or 1030301


10.0499


47 2 [.2766 2209


103823


6-8557 !


102 9.80392 10404 1061208


10.0995


48 20.8333 ; 2304


110592


6.9282


103 9.70874 10609 1092727


10.1489


49 20.4082 2401


117649


7.0000


104 9-61538 10816 i 1124864


10.1980


50

5 1


20.0000

19.6078


2500
2601


125000
132651


7.0711

7-I4I4 !


105 9.52381
1 06 9-43396


11025 1157625
11236 1 191016


10.2470
10.2956


5 2


19.2308 2704


140608 7.2111


107 9-34579


11449 i ! 225043


10.3441


53


18.8679 2809


148877 7.2801


108 9.25926


11664 l 2597 I 2


10.3923


54


18.5185


2916


157464 1 7-3485


109 9.1743"


Il88l


1295029


10.4403


55


18.1818 3025


166375 7.4162 !


110 : 9.09091


I2IOO


1331000


10.4881


56


17-8571 j 3'3 6


175616


7-4833 !


III g.OOOX)!


I232I 1367631


0-5357


%


17-5439 ! 3249
17.2414 i 3364


185193
195112


7-5498
7.6158


112

"3


8.92857
8.84956


12544 1404928
12769 i 1442897


10.5830
10.6301


59


16.9492


348i


205379


7.6811


114


8.77193


12996 I48I544


10.6771


60

61


16.6667
16.3934


3600
3721


216000
226981


7.7460
7.8102


115 8.69565 13225
116 8.62069 13456


1520875
1560896


10.7238
10.7703


62


16.1290


3844


238328


7.8740


117


8.54701


13689


1601613


10.8167


63
64


i5- 8 730
15.6250


3969
4096


250047
262144


7-9373
8.0000


118
119


8.47458
8.40336


13924
I4l6l


1643032
1685159


10.8628
10.9087



SMITHSONIAN TABLES.



I 6 TABLE 9 (continued).

VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS,
OF NATURAL NUMBERS.



H


1000.^


*


.


V-


n


1 000.1


*


3


V"


120

121


8.33333

8.26446


14400
14641


I728OOO
1/71561


'0.9545
1 1 .0000


175

176


5.71429
5.68182


30625
30976


5359375
545'776


13.2288
13.2665


122


8.19672


14884


1815848


11.0454


177


5.64972


3'3 2 9


5545233


'3-3041


I2 3


8.13008


15129


1860867


11.0905


178


5.61798


31684


5639752


' 3-34 '7


124


8.06452


'5376


1 906624




179


5.58659


32041


5735339


'3-379'


125


8.00000


15625


'953^5


11.1803


180


5-55556


32400


5832000


13.4164


126


7.93651


15876


2OOO376


1 1.2250


181


5-52486


32761


5929741


'3-4536


127


7.87402


16129


2048383


11.2694


182


5-4945'


33 12 4


6028568


13.4907


128
129


7.81250
7-75I94


16384
16641


2146689


'1-3578


183
184


5.46448
5-43478


33489
33856


6128487
6229504


I3-5277
13-5647


130


7.69231


16900


2197000


11.4018


185


5-40541


34225


633 '62 5


13.6015


131


7-63359


17161


2248091


n-4455


1 86


5-37634


34596


6434856


13.6382


132


7-57576
7.51880


17424
17689


2299968
2352637


1 1.4891
11.5326


187
1 88


5-34759


34969
35344


6539203
6644672


13.6748


134


7.46269


'7956


2406104


II-5758


189


5.29101


35721


6751269


'3-7477


135

136
137


7.40741

7-35294
7.29927


18225
18496
18769


2460375
25'5456
2571353


11.6190
11.6619
11.7047


190

191
192


5.26316

5-23560
5-20833


36100
36481
36864


6859000
6967871
7077888


13.7840
13.8203
13-8564


138


7.24638


19044


2628072


11 -7473


!93




37249


7189057


13.8924


139


7.19424


19321


2685619


11.7898


194


5^5464


37636


73 OI 384


13.9284


140


7.14286


19600


2744000


11.8322


195


5.12821


38025


74M875


13.9642


141


7.09220


19881


2803221


11.8743


196


5.10204


38416


7529536


14.0000


142


7.04225


20164


2863288


11.9164


197


5.07614


38809


7645373


14-0357


143


6.99301


20449


2924207


"9583


198


5-0505'


39204


7762392


14.0712


144


6.94444


20736


2985984


I 2.OOOO


199


5-02513


39601


7880599


14.1067


145


6.89655


21025


3048625


I2.O4I6


200


500000


40000


8000000


14.1421


146


6.84932


21316


3112136


I 2.0830


20 1


4.97512


40401


8120601


14.1774


147


6.80272


21609


3'76523


12.1244


202


4.9505


40804


8242408


14.2127


148
149


6.75676
6.71141


21904

22201


3241792
3307949


12.1655
I2.2O66


203
20 4


4.9261 1
4.90196


41209
41616


8365427
8489664


14.2478
14.2829


150


6.66667


22500


3375000


12.2474


205


4.87805


42025


8615125


14.3178


'5i


6.62252


22801


344295'


12.2882


206


4.85437


42436


8741816


14-3527


1 S 2


6.57895


23104


3511808


12.3288


207


4.83092


42849


8869743


'4-3875


'53


6-53595


23409


358 '577


12.3693


208


4.80769


43264


8998912


14.4222


"54


6-4935'


23716


3652264


12.4097


209


4.78469


43681


9129329


14.4568


155


6.45161


24025


3723875


12.4499


210


4.76190


44100


9261000


14.4914


156


6.41026


24336


3796416


12.4900


21 I


4-73934


44521


939393'


14-5258


157


6-36943


24649


3869893


12.5300


212


4.71698


44944


9528128


14.5602


158


6.32911


24964


39443 I2


I2.56 9 8


213


4.69484


45369


9663597


14-5945 '


159


6.28931


25281


4019679


12.6095


2I 4


4.67290


45796


9800344


14.6287


160


6.25000


25600


4096000


12.6491


215


4.65116


46225


9938375


14.6629


161


6.21118


25921


4173281


12.6886


216


4.62963


46656


10077696


14.6969


162


6.17284


26244


4251528


12.7279


217


4.60829


47089


10218313


14.7309


163


6.13497


26569


4330747


12.7671


218


4.58716


47524


10360232


14.7648


164


6.09756


26896


4410944


1 2.8062


219


4.56621


4796i


'0503459


14.7986


165


6.06061


27225


4492125


12.8452


220


4-54545


48400


10648000


14.8324


166


6.02410


2755 6


4574296


12.8841


221


4-52489


48841


10793861


14.8661


167


5.98802


27889


4657463


12.9228


222


4.50450


49284


10941048


14.8997


168


5-95238


28224


4741632


12.9615


223


4.48430


49729


11089567


'4-9332


169


5.91716


28561


4826809


13.0000


224


4.46429


50176


11239424


14.9666


170


5.88235


28900


4913000


13.0384


225


4-44444


50625


11390625


1 5.0000


171


5-84795


29241


50002 i i


13.0767


226


4 42478


51076


i 1543176


'5-0333


172


5.81395


29584


5088448


13.1149


227


4.40529


51529


i 1697083


1 5.0665


173


5-78035


29929


5'777'7


I 3-'5 2 9


228


4.38596


SI984


i 1852352


15.0997


174


5-747I3


30276


5268024


13.1909


229


4.36681


52441


12008989


'5-'3 2 7



SMITHSONIAN TABLES.



TABLE 9 (.continued). I 7

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS, OF

NATURAL NUMBERS.



n


lOOO.jj


*


3


v


n


Iooa i


n*


3


V*


230

231


4-34783
4.32900


52900
5336i


I2I67000
12326391


15.1658
15.1987


285

286


3-50877
3-49650


81225
81796


23149125
23393656


16.8819

16.9115


232


4-3 I0 34


53824


12487168


I 5- 2 3 I 5


287


3-48432


82369


23639903


16.9411


2 33


4.29185


54289


12649337


1 5.2643


288


3.47222


82944


23887872


16.9706


234


4-2735


54756


12812904


15.2971


289


3.46021


83521


24U7569


17.0000


235


4-25532


55225


12977875


1 5-3297


290


3.44828


84100


24389000


17.0294


236


4.23729


55696


I3I442S6


1 5-3623


291


3 43643


84681


24642171


17.0587


237


4.21941


56169


13312053


15.3948


292


3.42466


85264


24897088


17.0880


238


4.20168


56644


13481272


15.4272


293


3-41297


85849


25153757


17.1172


239


4.18410


57121


13651919


I5-4596


294


3.40136


86436


25412184


17.1464


240


416667


576oo


13824000


I5-49I9


295


3.38983


87025


25672375


17.1756


241


4.14938


58081


1 3997 5 2 i


15.5242


296


3.37838


87616


25934336


17.2047


242


4-13223


58564


14172488


'5-5563


297


3.36700


88209


26198073


17.2337


243


4-11523


59049


14348907


15-58^5


298


3-35570


88804


26463592


17.2627


244


4.09836


59536


14526784 .


15.6205


299


3-34448


89401


26730899


17.2916


245


4.08163


60025


14706125


1 5-6525


300


3-33333


90000


27000000


17.3205


246


4.06504


60516


14886936


15.6844


3 r


3.32226


90601


27270901


17.3494


247


4.04858


61009


i 5069223


15.7162


302


3.31126


91204


275436o8


17-3781


248


4.03226


61504


15252992


15.7480


33


3-30033


91809


27818127


17.4069


249


4.01606


62001


15438249


15-7797


34


3.28947


92416


28094464


17-4356


250

2 5 r
252


4.00000
3.98406
3.96825


62500
63001
635 4


15625000
15813251
16003008


15.8114
15.8430

15-8745


305

306
37


3.27869
3.26797
3-25733


93025
93636
94249


28372625
28652616
28934443


17.4642
17.4929
17.5214


253


3-95 2 57


64009


16194277


15.9060


308


3-24675


94864


29218112


17-5499


254


3-93701


64516


16387064


1 5-9374


309


3-23625


95481


29503629


17-5784


255


3-92I57


65025


16581375


15.9687


310


3-22581


96100


29791000


17.6068


256


3.90625


65536


16777216


1 6.0000


3"


3-21543


96721


30080231


17.6352


257


3.89105


66049


16974593


16.0312


312


3-20513


97344


30371328


17-6635


258


3-87597


66564


I7I735 12


16.0624


3'3


3.19489


97969


30664297


17.6918


259


3.86100


67081


17373979


16.0935


3'4


3.18471


98596


30959144


17.7200






















260


3-84615


67600


17576000


16.1245


315


3.17460


99225


31255875


17.7482


261


3-83H2


68121


i777958i


'6-1555


3i6


3.16456


99856


3 1 554496


17.7764


262


3.81679


68644


17984728


16.1864


3*7


3-*5457


100489


3 l8 55 OI 3


17.8045


263


3.80228


69169


18191447


16.2173


3i8


3- 14465


101124


32157432


17.8326


264


378788


69696


18399744


16.2481


3*9


3.13480


101761


32461759


17.8606


265


3-77358


70225


18609625


16.2788


320


3.12500


102400


32768000


17.8885


266


3-75940


70756


18821096


16.3095


3 21


3- IT 5 6


103041


33076161


17.9165


267


3-74532


71289


19034163


16.3401


322


3 I0 559


103684


33386248


17.9444


268


373'34


71824


19248832


163707


323


3-09598


104329


33698267


17.9722


269


3-7*747


72361


19465109


16.4012


324


3.08642


104976


34012224


18.0000


270


370370


72900


19683000


16.4317


325


3.07692


105625


34328125


18.0278


271


3.69004


73441


1990251 i


16.4621


326


3.06748


106276


34645976


18.0555


272


3 67647


73984


20123648


16.4924


327


3.05810


106929


34965783


18.0831


273


3.66300


74529


20346417


16.5227


328


3.04878


107584


35 28 755 2


18.1108


274


3.64964


75076


20570824


16.5529


329


3-0395 i


108241


35611289


18.1384


275


3.63636


75625


20796875


16.5831


330


3.03030


108900


3^937000


18.1659


276


3.62319


76176


21024576


16.6132


33 1


3.02115


109561


36264601


18.1934


277


3.6101 1


76729


21253933


16.6433


332


3.01205


110224


36594368


18.2209


278


3-59712


77284


21484952


16.6733


333


3.00300


110889


36926037


18.2483


279


3-58423


77841


21717639


16.7033


334


2.99401


"'556


37259704


18.2757


280


3-57M3


78400


219152000


16.7132


335


2.98507


112225


37595375


18.3030


281


3-55872


78961


22188041


16.7631


336


2.97619


i i 2896


37933056


18.3303


282


3.54610


79524


22425768


16.7929


337


2.96736


"3569


38272753


,8.3576


283


3-53357


80089


22665187


16.8226


338


2.95858


114244


38614472


18.3848


284


3.52H3


80656


22906304


16.8523


339


2.94985


114921 i


38958219


18.4120



SMITHSONIAN TABLES.



18



TABLE 9 (contin



VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS
OF NATURAL NUMBERS.



n


1000.1


n*





tf*


n


10004


+


*


V"


340


2.94118


115600


39304000


18.4391


395


2.53*65


156025.


61629875


19.8746


341


2.93255


116281


39651821


18.4662


396


2-52525


156816


62099136


19.8997


342


2.92398


116964


40001688


18.4932


397


2.51889


157609


62570773


19.9249


343




117649


40353607


18.5203


398


2.51256


i 58404


63044792


19.9499


344


2.90698


118336


40707584


18.5472


399


2.50627


159201


63521199


19.9750


345


2.89855


119025


41063625


18.5742


400


2.50000


160000


64000000


20.0000


346


2.89017


119716


41421736


18.6011


401


2-49377


160801


64481201


2O.O25O


347


2.88184


120409


41781923


18.6279


402


2.48756


161604


64964808


20.0499


348


2.87356


121104


42144192


18.6548


403


2.48139


162409


65450827


20.0749


349


2.86533


121801


42508549


18.6815


404


2.47525


163216


65939264


20.0998


350


2.85714


122500


42875000


18.7083


405


2.46914


164025


66430125


20.1246


35 1


2.84900


123201


4324355 1


*8-735o


406


2-46305


164836


66923416


20.1494


35 2
353


2.84091
2.83286


123904
124609


43614208
43986977


18.7617

18.7883


407
408


2.45700
2.45098


165649
166464


674>9*43
679*73*2


20.1742
20.1990


354


2.82486


125316


44361864


18.8149 |


409


2-44499


167281


68417929


20.2237


355


2.81690


126025


44738875


18.8414


410


2.43902


168100


68921000


20.2485


356


2.80899


126736


451 18016


18.8680


411




168921


69426531


20.2731


357


2.80112


127449


45499293


18.8944


412


2.42718


169744


69934528


20.2978


358


2.79330


128164


45882712


18.9209


4*3


2.42131


170569


70444997


20.3224


359


2.78552


128881


46268279


18.9473


4*4


2.41546


171396


70957944


20.3470


360


2.77778


129600


46656000


iS-9737


415


2.40964


172225


7*473375


20.37*5


361


2.77008


130321


4704588 r


1 9.0000


416


2.40385


173056


71991296


20.3961


362


2.76243


131044


47437928


19.0263


4*7


2.39808


173889


7251*713


20.4206


363


2.75482


131769


47832147


19.0526


418


2.39234


174724


73034632


20.4450


364


2.74725


132496


48228544


19.0788


419


2.38663




73560059


20.4695


365


2-73973


133225


48627125


19.1050


420


2.38095


176400


74088000


20-4939


366
367


2.73224
2.72480


1 33956
134689


49027896
49430863


19.1311
19.1572


421
422


2.37530
2.36967


177241
178084


74618461
7515*448


20.5183
20.5426


368


2.71739


1 35424


49836032


I 9'* 8 33


423


2.36407


178929


75686967


20.5670


369


2.71003


I36l6l


50243409


19.2094


424


2.35849


179776


76225024


20.5913


370

37 *


2.70270
2.69542


136900
1 3764 *


50653000
51064811


I9-2354
19.2614


425

426


2.35294

2.34742


180625
181476


76765625

77308776


20.6155
20.6398


372


2.68817


138384


51478848


19.2873


427


2.34192


182329




20.6640


373


2.68097


I39I29




19.3132


428


2-33645


183184


78402752


20.6882


374


2.67380


139876


523*3624


19-339*


429


2.33100


184041


789535%


20.7123


375


2.66667


140625


52734375


19.3649


430


2.32558


184900


79507000


20.7364


376
377
378


2.65957
2.65252
2.64550


MI376
I42I29
142884


53*57376
53582633
54010152


19.3907
19.4165
19.4422


43*
432
433


2.32019
2.31481
2.30947



Online LibrarySmithsonian InstitutionSmithsonian physical tables → online text (page 6 of 72)