Tables of Orthogonal Polynomial Values Extended to N: 104

April, 9 Research Bulletin 97 Tables f Orthgnal Plynmial Values Extended t N: 0 By R. L. ANDERSON AND E. E. HOUSEMAN AGRICULTURAL EXPERI MENT STATION IOWA STATE COLLEGE OF AGRICULTURE AND MECHANIC ARTS STATISTICAL SECTION AGRICULTURAL MARKETING SERVICE UNITED STATES DEPARTMENT OF AGRICULTURE Cperating AMES, IOWA

CONTENTS Page Methds f calculatin and use 69 Intrductin 69 A cmparisn f available methds f calculatin. 696 The methd. 697 The fitting f plynmials by the e methd 00 Tabulatin f the e values 'li08 References cited '009 Tables 90

Tables f Orthgnal Plynmial Values Extended t n = 0 By R. L. ANDERS ON an~ E. E. HOUSEMAN METHODS OF CALCULATION AND USE INTRODUCTION Interest in rthgnal plynmials has been stimulated ill recent years, especially amng bilgists, by Fisher's use f them in evaluating a regressin integral 7), applicatin and extensin f which have fllwed each ther in rapid successin ) 9). Aside frm this specialized use, rthgnal plynmials are valuable in the study f time series bth in ecnmics and in agrnmy where ne may wish t study the effect f envirnmental cnditins n the yields f crps. If there has been a gradual depletin r imprvement in the level f fertility ver a perid f years, it shuld be evaluated and deviatins frm trend used in t.he study f envirnmental effects. Any reductin f the labr f calculatin ilvlved in such investigatins seems wrthy f sme effrt. If the independent variable is equally spaced, such as in time r space, the cnvenient methd f curve fitting by rthgnal plylmials can be used. The advantage ver the usual regressin methds f fitting nnrthgnal plynmials arises frm the fact that rthgnal plynmials are s cnstructed that any term f the plynmial is independent f any ther term. This prperty f independence permits ne t cmpute each regressin cefficient independently f the thers and als facilitates testing the significance f each cefficient. In additin the cmputing time fr curve fitting by means f rth I Prject f the Iwa Agricultural Experiment Statin., The authrs wish t acknwledge the material aid furnished by the Iwa State Research Cuncil making pssible the cmpletin f the cmputatins. They are indebted t Prfellsr G. w. Snedecr fr valuable criticism f the presentatin f the text. They wish t thank Prfessr R. A. Fisher.and Dr. F. Yates fr permitting the inclusin f the e values up t n=.

696 gnal plynmials is less, especially if a plynmial f degree greater than the secnd is fitted: The labr f fitting rthgnal plynmials t a lng series f data may be reduced thrugh the use f the frms intrduced by Yates. Designated' as e, and presented in a series f lectures at Iwa State Cllege in 97, t~ey have since been published by Fisher and Yates 8). The utility f this methd depends upn the availability f tables f e values f the same length as the series t be fitted. Since the existing tables are nly applicable t series f bservatins r less, it seemed wrthwhile t extend them in this bulletin t twice that number. With the generus permissin f the authrs and publishers f the riginal tables, we are able t present the cmplete set f e values up t and including thse fr n = 0. The 'bjectives f this bulletin are:. T present the tables f rthgnal plynmial values,. t illustrate the usel f the tables in fitting plynmials,. t give an elementary descriptin f the e methd,. t make a brief cmparisn f methds f fitting rthgnal plynmials and. t make a nte f hw the tables were extended and checked. A COMPARISON OF AVAILABLE METHODS OF CALCULATION The summatin methd, develped by Fisher 6), als presented by Snedecr ), is anther cnvenient methd f fitting rthgnal plynmials. In practice the e methd and the summatin methd are mst cmmnly used. Fisher and Yates 8) have made the statement that the e methd is decidedly mre expeditius than the summatin methd if nly a calculating machine nt a printing adding machine) is available, especially when the number f bservatins is small. Befre undertaking the task f extending the tables it was thught advisable t cmpare the tw methds rather extensively with respect t time f cmputing and accuracy when bth a calculatr and a printing adding machine are at hand, since the summatin methd invlves a cnsiderable amunt f cntinuus additin. We have cncluded frm varius cmparisns that:. If bth printing adding and calculating machines are available, the summatin methd requires almst 0 percent mre time n the average. This time is almst dubled when n adding

machine is available.. There is a tendency fr the relative efficiency f the e methd t be reduced slightly as the number f bservatins is increased.. The relative efficiency f the e methd is greater fr high degree plynmials.. If the investigatr is uncertain as t the degree f equatin suitable fr the regressin, he can save time in the use f the e methd, since new plynmial values are easily btained by adding t r subtracting frm) the ld values, while the summatin meth)d, which uses a prcess f differencing t btain the estimated values, necessitates recmputatin f the initial differences.. If n tests f significance f the reductin in sum f squares by succeeding terms f the plynmial is required, there may be little difference in the cmputing time f the tw methds. 6. Since there are fewer frmulas invlved in the e methd, it is learned much mre quickly by the cmputer.. If anyne intends training a cmputer t handle plynmials exclusively, we recmmend cnsideratin f a methd described by Aitken ). We fund the time f cmputatin culd be reduced belw that required fr the e methd, but the methd is t invlved fr rdina7 cmputing wrk. THE METHOD, At this pint a brief, simple descriptin f the e methd)s included. R. A. Fisher has presented a mre general discussin 6). Fr a mathematical presentatin, an article by F. E. Allan ) is cmmended. It can be prved that an rdinary plynmial [IJ always can be expressed in terms f rthgnal plynmials fr any specified set f values f x. Fr example, where x =,,..., 7, can be rewritten in the frm, 'i. e. plynmials which are independent nncrrelated).

li98 where the quantities in parenthesis are rthgnal plynmials. By definitin, tw plynmials, P and P', where x takes n a specified set f values, are said t be rthgnal if ~PP' = 0 As shwn belw the plynmials P l = + x), P = 8x + X), and P = 6 + 6,x ",:,;;' + ~ x ) satisfy the definitin f rthgnality:., P, p, p, PIP, PIP, p, P. 0 0 0 0 0 0 0 0 6 0 0 0 7 Ttal 0 0 0 0 0 0 Fisher and Yates have designated plynmials such as Pl, P and P by the symbl e; ~: being a plynmial in x f the first degree, ~; a plynmial in x f the secnd degree, etc. Thus using their I!.tatin, equatin [] can be written in the general rthgnal frm, [] where the A "s are cnstants. Fr the imprtant case where x takes n the values,,,..., n, the relatinships between the e's and x up t the fifth degree are ~~=Al xx) ~~= A [ XX) n:~ ] ~~=A[ XX)LXX) ~~7] ~~= A[ XX)LXX) ~n;~ ) + n!~6 n 9)] /:"=' [ _) ) n 7»)+ ) n L 0n +07] ';; " x X X x 8 x x 008 where x is the mean value f x, and the A'S, which depend n n,.. In case x is a cntinuus variable the summatin is replac by integratin.

)99 are s chsen that the values f the ~"s crrespnding t the n values f x are integers reduced t lwest terms Since the ~"s are s cnstructed that ~~: ~; = 0 fr i ~ j, the terms f equatin [] are independent. The independence f the terms in [] ffers the previusly mentined advantages f this methd f curve fitting. Frm the abve table f values f the rthgnal plynmials PI, P and P a we see that the last half f the values f P are the same as the first half except that they appear in reverse rder. The same is true fr the values f PI and P a, but in additin t being in reverse rder the signs are als changed. The ~"s als have the same prperty; i. e., the sequences f values f and are symmetrical abut their middle terms.,,, The values f ~I' ~a' ~ are als symmetrical except that the values in the first half f the sequences are the negatives f thse in the latter half. See the tables f e values fr n < 9.) Since this prperty hlds fr all values f n, nly the lwer half f the e values when n is even and the lwer nt when n is dd are given in the tables, except fr n less than 9. In the fitting f plynmials f the frm [] the cnstants t be evaluated are the regressin cefficients, A~. They are I I I t I I chsen s that the quantity ~y A A ~... A k ~k), I I which is the sum f squares f the deviatins frm the regressin curve, is a minimum: After the A "s have been determined, ne can substitute fr the ~"s equivalent expressins in terms f x as given abve and thus change the regressin equatin frm the frm [] t the f '" =,,,, the crrespnding values f ~~=Aa[ xx)lx_x) n~~)j=a a [ x_x)a_:~x_x) ] Aa 9Aa 9A A arelo, 0' 0' 0' Hence A is taken equal t 0 s that t' = t;; ",.

."00 frm []. Hwever, that is seldm necessary, since the estimated values f y crrespnding t the n equally spaced values f x can be cmputed, as shwn in the next sectin, by substituting the values f the ~"s in the regressin equatin f the rthgnal frm []. The sum f squares f deviatins frm regressin is given by the expressin ~ya~~y) A~~y~~) A~~y~~)... A~~y~~) The first telm, ~y, is the sum f squares f the riginal bservatins, and the secnd is the usual crrectin term fr the mean. The sum f the remaining terms cnstitutes the regressin sum f squares, the third term being the linear regressin sum f squa~es, the furth represents the reductin in the sum f squares f deviatins frm linear regressin btained by fitting a secnd degree plynmial, etc. THE FITTING OF POLYNOMIALS BY THE METHOD T illustrate the e methd f fitting rthgnal plynmials, we have chsen a series f 6 annual sugar prices 0), 87 96. Frm the scatter diagram f the prices, fig., it appears that a third degree plynmial will fit the data nearly as well as well as a plynmial f higher degree. Thus in actual practice ne might be cntent t fit a plynmial f the third degree. Hwever, fr purpses f illustratin a furth degree curve is fitted in additin t a third degree curve. The directins fr cmputatin are presented in detail fr cnvenience f the cmputer. Part f the discussin is nt very pertinent s far as time series are cncerned, but may be helpful when ther kinds f data are used. The prices are in terms f mills cded by subtracting 0 mills frm each price; the cded figures are presented in table tgether with the e values fr n = 6, cpied frm page 60. The first clumn cntains the last half f the prices f them), beginning at the tp with the price fr 906 and ending with that fr 96. In the secnd clumn is the first half f the prices written in reverse rder; i. e., starting at the tp with the price fr 90 and ending with that fr 87. Thus ne can read the series in rder frm 87 t 96 by starting at the bttm f clumn, reading upward t the tp f the

TABLE. "0 CODED ANNUAL SUGAR PRICES, 8796, AND VALUES FOR N = 6. Price d I ~ ~ I 8 8 60 96 + 96 6 8 9 87 + 979 0 6 6 + 7 7 + 079 8 + 7 68 + 06 0 0 0 0 9 0 8 + 676 6 0 00 + 07 0 9 9 + 9 7 + 689. 0 7 00 + 090 7 + 7 8 + 6 + 9 9 + 79 9 + 7 0 6 + 7 8 + 6 9 70 76 8 8 6 + 0 8 70 696 0 + 7 7 69 77 0 7 6 80 + 68 9 769 9069 0 0 76 8 9 6 7 67 76 0 7 + 7 7 6 0 + 7 + 988 6 6 9 + 0 7 0 9 9 + 0 066 6 8 8 6 0 +7 87 6 60 0 + 9 7 0 6 7 +6 88 096 6 7 6 9 +0 + 96 86 6 60 +6 '+ 69 989 0 8 8 8 +9 + 8 +8 +60 + 670 7 7 7 7 +6 + + 0M 6 68 6 9 +7 +89 + 70 7 67 7 60 6 +0 +99 +07 Sum 80 6 70 clumn and then dwn clumn. If the number f prices had been dd, half f the median price wuld have been written at the tp f each clumn; i. e., if there were 6 prices and the thirtysecnd price was, the first item in each clumn wuld be 6. In clumn the numbers, s, are frmed by adding the crrespnding pairs f numbers in clumns and, + = 8 etc., while the numbers,, in clumn are frmed by subtracting the numbers in the secnd clumn frm thse in the first, = 8, etc. As a check, the sum f the third clumn, ~s, shuld equal the sum f the first tw clumns, and the sum f the furth clumn, ~d, shuld equal their difference; i.e., ~s=6=80+ and ~d= 70=80. The next step is the cmputatin f the regressin cefficlents. A' A' A" h. 0' "'" In t e equation,

,"0 y= A~+A~~~+A~~~+A~~~+A~~~ The first, A I, is the mean, g, f the price series, A'=~s =,6 =8 N 6. The secnd cefficient A~ is simply related t the linear regressin cefficient, b, in the best fitting straight line Y = g + bx x). In fact A I is equal t b when n is dd, and A I equals 6 b/ when n is even. Here, A' ~dw 8))+))+... +60)6) ~U~) 79,, 086 =79, =0., the sum f squares f ~/, ~~/), being taken frm the ft f I the clumn f ~/s fr n = 6. The remaining A "s are: A' ~s~~) ~ ~~) 7,77 = 70 7= 0.077,, A' = ~dw ~ ~~) 8)60)+)9)+... +7)0),70,7 _ 8) 96)+) 87)+... +60),99) 9,8,,080,7 0007760 =98= ',,, A ' = ~sw = 8),96)+... +7) 0,7) ~U~) 0,69,68,0 = 7,99,0 000007 0,69,68,0 =. the quantities, ~)\ ~~/), and ~~/) als being taken frm the tables at the ft f the crrespnding clumns f ~"s. 6 ~~= xx) frddn. ~~=xx) frevenn.

~0 If ne is fitting a plynmial f the third degree r less it may nt be wrth while t split the series int tw parts and cmpute sums and differences as in clumns and, table l. Instead cnsidering a secnd degree plynmial) the prices and e values can be arranged as fllws: Year Price 87 876 67 6 6 9 0 7 877 7 7 6 ~I I ~ 90 ' 60 906 60 9 i 7 6 9 9 7 96 7 6 0 Thus AI = 6 = 8 6. A' = A' = 67) 6)+6) 9)+... +7) 6) =0 79,.. 67) 0)+6) 7)+... +7) 0) 0.077,70,7 We are nw at a pint where the tests f significance, table, TABLE. TESTS OF SIGNIFICANCE. Surce f variatin D egrees f freedm Sum f squares Mean square Ttal, l:y' Crrectin fr mean Deviatins frm mean Linear regressin Deviatins frm linear regressin Secnd degree term Deviatins frm quadratic regressin Third degree term Deviatins frm third degree regressin Furth degree term Deviatins frm furth degree regressin **Highly significant. *Significant. 6 08 8788 6 0 8 60 0069 68 9 90 886 8 7 7 7 698 8 ** 68** 69 886** 9 7*

'0 f the varius regressin cefficients can cnveniently be made. The ttal uncrrected sum f squares f the prices, ':,y = ) + 8) +... + 7) = 08, and the crrespnding degrees f freedm, 6, are entered at the tp f the table. The crrectin term fr the mean, A I ':,s) =.8) 6) = 8,788, which takes ne degree f freedm, is subtracted frm the ttal sum f squares leaving,0 as the sum f squares f deviatins frm the mean. The sum f squares attributable t linear regressin, A' ':,d ~/) = 0.) 0,86) = 8, is subtracted frm,0 t give the sum f squares f deviatins frm linear regressin, 0,069. The value f F, 8 / =., shws that a highly significant prtin f the sum f squares,,0, is accunted fr by linear regressin. Of curse the significance f the linear regressin des nt necessarily mean that a straight line regressin gives a gd fit r that the regressin is linear. It means that the linear regressin line fits the data better than a hrizntal straight line drawn I I thrugh y. The sum f squares, A ':,s ~) = 0.077)7,77) = 68, assciated with the secnd degree term is the amunt which the residual sum f squares, 0,069, is reduced by fitting a quadratic equatin. The secnd degree term is highly significant since the value f F is 68/69 =.. Similarly the third and furth degree terms with the sums f squares A'':,d) = 0.007760)087) = 886 and AI':,S~/) = 0.00007)799,0) =7 are highly significant and significant, ref?pectively. Even thugh the furth degree term' is signi cant, it is nt very imprtant since the standard errr f estimate, V 9 =., wuld nly be reduced t V =.0 by fitting a furth degree curve instead f a third degree curve. The first, secnd and third degree terms all give ma"'ked decreases in the residual sums f squares. It may als be wrth pinting ut:. That the significance f any term higher than the first indicates nnlinear ppulatin regressin.. If the third degree term, fr example, is nt significant, nnsignificance f higher rder terms is nt guaranteed. Varius pssibilities can best be judged frm the scatter diagram. Fr the third degree curve the estimated values f Y, that is, the rdinates f the regressin curve, can be fund by substituting the values f the ~"s in the regressin equatin, [] Y =.0.~~+O.077 ~~O.007760 ~~

~ 0 Thus in the first clumn f table we have the prduct f TABLE. CALCULATION OF THE ESTIMATED VALUES FOR THE THIRD AND FOURTH DEGREE POLYNOMIALS. 6 7 8 I I A /: " A' A' Estimated values fr rd degree plynmial A' t I Estimated values fr <; th degree plynmial 0. 0.77.8.79.0 9.6 9. 8.99 8.8 8.9 0.7..69. 6.7.9.9.0 6.0 7. II. 9.0 0. 9. 8.8....9.7 9. 0.6.8.. 8. 7.7 7.0 6. 6..8..8..8 8.0 7.96 7.6 7.0 6.9 7.77 8.98 0.09.08.9 8. 9. 0...0 8. 7.9 7.7 7.7 7.9..0.. 0..9 7. 8.7 0.. 6.0.9 6. 6.6 7..6.87 6.9 6.90 7. 6.0.8.70.9..66..8.76.7.8..0..7 8. 8.8 9.7 0.7. 0.0 0...6..8.0. 6. 6.8 8. 9. 0.8.. 7.9 8. 8.9 9. 9.96.9.7 0.0 0.6. 7.7.98..0 9.89.8.7..9..7.6 7.9 0...6.0..7.8 7. 7.7 7.8 7.6 7.0 6. 8.6.. 7. 0.7 0.98.9.00..86.07. 6.6 8.0 8.7 6..07.6...0 9. 7.6. 6.6 0.. 8.7.6.9.7..0. 6..7.0 0.6 7.8 0..0 7.8.7.9.0..0.60.07.8 9. 0.9.8.09.7 7.7.88 8.6.8 7.0. 7.9. 0. 7..6.. 8.9.7 60.9 67.6 7.8 8.. 0...0. 7.6. 0. 6.0.6.. 0..9 9.7 6.6 69.7 7.9 I I A = 0. and the values f ~, which were fund by put ting 0. in the calculatr and multiplying successively by I the values f ~: 0.)) 0. 0.)) 0.77 0.)6) =.8 Similarly, the entries in clumn were btained by placing A I = 0.077 in the calculatr and multiplying successively by th~ values f, and likewise fr clumns and 6. Estimated

'i06 values fr the third degree plynmial appear in clumns and in the same rder as the crrespnding prices in clumns and, table. Each entry in clumn is A I =. plus the sum f the crrespnding numbers in the first three clumns:. 0. 9.6 + 0.7 =.9. 0.77 9. +. =.9..8 + 7.7 7.9 =. In clumn each entry is. plus the sum f the crrespnding numbers in the first clumns with the signs f the numbers in clumns and changed:. + 0. 9.6 0.7 =.9. +.8 + 7.7 + 7.9 = 8. The regressin equatin f the furth degree is Y=.0. {+0.077 ~:0.007760 0.00007. ~ which differs frm equatin [] nly by the additin f the furth degree term. Since the rdinates fr the third degree curve have already been cmputed, the simplest way t find the rdinates fr the furth degree curve is t add the values f the term 0.00007 t the rdinates f the third degree I I curve. Thus in clumn 6 we have the values f A ~. In clumn 7 the entries are.9. = 9., etc., and in clumn 8,.9. = 8., etc., these nu'mbers being the rdinates fr the furth degree curve. If the subscript n had been dd, the numbers in clumn 6 wuld have been subtracted itlstead f added) frm thse in clumn t btain the entires in clumn 8, the reasn being the reversal f signs h the secnd half f the dd ~"s. Frm fig. we see that there is little difference between the third and furth degree curves, which was t be expecterl. Interplatins made frm the graph are accurate enugh fr mst practical purpses; hwever, since cases may arise where

~07 0 0 Price s were cded by subtracting 0 mills frm eaen price 80 \.., c ~ " 0 ~.,.!'! '" ci: 0.., Q) ; 0 ~ 0 87 \ 0, 0 0,, 0 0 th Degree ' \~ 0 0 0 0 V:;=: \ 0 "'~ 0 ~.,\ " rdd.r.~ 0,. 0 ~_:_,:;. 0 0 0 0 0 0 0 0 "", 00 Qf 0 0 0 0 0 0, \ 88 87 90 9 9 9 FiQure. Cded Sugar Prices, 8796 G. Watsn it is necessary r desirable t have t he regressin equatin in terms f x instead f e, we shall illustrate hw t change the abve third degree regressin equatin, [], int an equatin in terms f x. This is dne by substituting in [] the relatinships between x and the ~"s given in the previus sectin: Y =.0.AJ xx) +0.077A [ xx) n~ ] 0.007760 A [ xx) _ xx) en;~7)] Since n = 6, x =., and Al =, A = /, A = /, the A'S being taken frm t he ft f the clumns f the crrespndhg ~"s, we have Y=.0.) x.) +0.0777')[ x.)l0.] 0.007760 / ) [ x.) _ x.) 76.) ], which upn simplificatin becmes

08 l] Y =.8+0.9799 x.) +0.086 x.) 0.0087 x.) Equatin [] culd be further simplified if desired by expanding the quantities in parenthesis. TABULATION OF THE f VALUES Tw methds f calculating the e values have been emplyed in rder t check the results. In the first methd the recursin frmula, was used, where r is the degree f the plynmial, in rder t find ~ values. The e values were then derived frm the ~ values using the relatinship e = A ~ where A is s chsen that the e values are integers reduced t lwest terms. The secnd methd utilized a prcess f differencing suggested by Aitken ). By using a printing adding machine with a subttal key the differencing can be carried ut easily fr plynmial values up t the fifth degree, but it is dubtful if this methd wuld be feasible fr higher degrees since the number f differences is equal t the degree f the plynmial calculated. Aitken used scalled T values which are related t the e values as fllws: e~t A', where A is the factr mentined abve fr changing the ~ values int e values. The quantity A' is the same fr each degree regardless f the size f n; its values fr the first five degrees are,, 0/, / and /0, respectively. Aitken als gave a frmula fr cmputing the sum f squares f the T values, which we have mdified t give the sum f squares f the e values. The mdified frmula, which is ~e= nr) nr+)... n+r) n+r) ~) " r r + ) r!) A; was used in cmputing the sum f squares f the e values.

'W09 REFERENCES CITED ) Aitken, A. C. On the graduatin f data by the rthgnal plynminals f least squares. Prc. Ry. Sc. Edinburgh, : 78. 9. ) Allan, F. E. The general frm f the rthgnal plynminals fr simple' series with prfs f their simple prpel'ties. Prc. Ry. Sc. Edinburgh, 0: 00. 9. ) Brandt, A. E. Tests f significance in reversal r switchback trials. Iwa Agr. Exp. Sta., Res. Bul.. 98. ) Davis, F. E. and Pallesen, J. E. Effect f the amunt and distributin f rainfall and evapratin during the grwing seasn n yields f crn and spring wheat. Jur. Agric. Res., 0:. 90. ) Fisher, R. A. An examinatin f yields f dressed grain frm Bradbalk. Jur. Agric. Sci., : 07. 9. 6) Fisher, R. A. Statistical methds fr research wrkers. Seventh Editin. Oliver and Byd, Edinburgh. 97. 7) Fisher, R. A. The in'fluence f rainfall n the yield f wheat at Rthamsted. Phil. Trans. Ry. Sc. Lndn, Series B., : 89. 9. 8) Fisher, R. A. and Yates, F. Statistical tables fr bi,lgical, agricultural and medical research. Oliver and Byd, Edinburgh. 98. 9) Hpkins, J. W. Weather and wheat in western Canada. I. Influence f rainfall and temperature during the grwing seasn n plt yields. Canadian Jur. Res. : 06. 9. 0) Schultz, Henry. Thery and measurement f demand. p. 67 677. University f Chicag Press. 98. ) Snedecr, G. W. Statistical methds. Cllegiate Press, Ames, Iwa. 90. ) Wishart, J. Grwthrate determinatin in nutritin studies with the bacn pig and their analysis. Bimetrika, 0: 68. 98.

TABLES OF e VALUES* n= n= n= n= I ~ ~ + + + + + + + + + 0 0 +6 + 0 + + + + + + + + + + + + + + + 6 0 0 0 0 70 70 8 0 / /6 / / n=8 n=9 n= I I I I ~ ~ ~ ~ ~ 7 +7 7 + 7 7 + + + +7 7 + +9 0 0 0 +8 0 + + +9 + + 7 9 +9 +9 + + 7 +7 + 8 + + + + + +7 7 +7 + +7 +7 +7 +7 +7 + +8 + + + +9 +6 + 68 68 6 66 8 60 77 990 00 68 0 8 / 7/ 7/0 /6 7/ /0 / *This prtin f the table is taken by cnsent frm "Statistical Tables" by l{. A. Fisher and F. Ya

~I TABLES OF e VALUES*Cntinued) n= n= I I I ~ ~ ~ ~I ~I ~I I ~ 0 0 +8 0 + 7 +8 +0 + +6 +0 + 9 9 + + + 0 7 + +6 + 7 +9 + 8 + +7 + + + 6 96 8 +9 + 7 7 + + 0 66 + + + + + +6 + + +99 + 7 0 8 8008 9 8 00 7 68068 688 / 7/ /0 /6 7 / 7/0 ~I I ~ n= n=6 ~I I ~ ~I ~I ~I ~I 0 6 0 + 76 0 + 6 +89 + + 7 + 6 + 67 + 9 79 +9 + + 9 + +000 + 6 + + + 9 6 9 + 7 +7 9 0 0 + 77 + 8 8 70 +9 67 0 + +9 869 979 + +9 +6 + + 9 + + + 9 9 +7 +9 +9 +00 +00 + + + +7 + 80 78 9780 66660 0880 60 7 007760 7088 0 /6 / /0 0/ 7/ /0 *Thi. prtin 0 the table is taken by cnsent frm "Statistical Tables" by R. A. Fisber and F. Yates

TABLES OF e VALUES*Cntinued) n=8 n=9 I ~ t ' a 6 " + 0 8 + +0 0 0 0 +96 0 + 7 + +8 + 9 + + + + +7 + 6 8 +7 + 7 +7 +88 + + + 79 +9 0 6 +6 + 6 68 + + + 9 + 0 + + + 7 87 +6 +6 89 8 + + +0 676 +7 +9 8 88 98 +7 +68 +68 +68 +88 +8 + + 68 68 68 +9, + +0 +6 +0 98 6 69 70 80 898 6 8 66 88 / / / /0 /6 7/ /0 n= n=. 6 6 0 0 0 +9 0 + 0 + 70 + 9 + 07 +0 +0 + 9 + 8 +07 + 98 0 +8 + + 7 + 6 +0 + 8 +0 +89 +7 70 + 70 + + 6 66 0 + +9 0 78 8 + + 70 06 +06 + 77 6 + 6 +6 9 6 788 + + 6 77 66 +7 + 7 98 680 68 + +8 0 80 9 +.8 + 8 0 68 +7 +6 0 70 9 +9 + + 0 98 +9 + + 7 + 7 96 +0 +90 +8 +969 +876 + + + +97 +6 770 60 68700 960 06 089.;700 708 87870 /6 7/ /0 / / 7/ 7/ *This prtin f the table is taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yate

TABLES OF e VALUES* Cntinued) n= n= I ~ + + + 7 0 0 + 88 0 + 7 9 + +00 + 77 + 80 + 7 + 66 + 8 +89 + 8 9 + 6 + 00 + 7 07 86 +. +7 + + 9 + 6 +9 8 987 7 +7 + 6 8 + 78 + 66 + 0 87 + + 7 8 67 + 0 + 7 99 7 69 +6 6 87 97 + 6 + + 7 6 07 + 7 9 87 9 +7 +7 9 7 +8 + 96 98 88 +9 +7 + 97 7 +9 +9 9 897 7 + +87 + 87 + 6 +0 +8 + 7 78 + + +77 + +807 + +69 + + + +9 +06 +8 +0 600 7760600 779890 00 8000 780900 9680 9680 80 070 0/ /. /0 /6 / /0 "This prtin f the tahle is taken hy cnsent frm " Statistical Tables" by R. A. Fisher and F. Ya t

TABLES OF e VALUES*Cntinued) n=7 n=8 6 6 0 8. 0 +68 0 + 6 9 + 96 + 60 + 79 8 +8 + 960 + 6 + 80 + 6 + 70 +8 + 70 + 9 8 + 6 + 670 + 0 + 870 + 979 +7 + 9 + 79 + 6 + 8 +008 + 9 9 + 8 + 7887 + 07 70 6 + 880 + 9 9 + 67 +6 7 7 867 + 78 + 90 + 78 +7 70 00 + 6 + 9 0 870 +8 + 0 60 770 88 +7 + 7 00 8 +9 + 6 87 97 +9 + 7 07 7866 +0 +8 87 + + 9 879 98 + +8 + 78 0879 + + 67 + 9 89 + +0 + 70 + 690 0 + + 9 + + 9 + + +0 +990 +6 +7 +7 +8 +7 + 68 0790 060 7?08 0660 7700 70 680 900 9660 /6 7/ /0 / 7/ 7/0 "Thi. prtin f the table is taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yates, p

TABLES OF e VALUES*Cntinued) n=0 n=. 6 6 + +76 + 768 +0 80 0 +08 0 + 09 +7 + 08 + 79 9 +9 + + 0 + 9 + 77 + 76 + + 6 +7 9 7 + 6096 + 908 + 7 7 +6 + 6 +9 8 88 + 76 + 9768 + 6 6 +6 + 66 + 67 97 79 + 8679 + 9 + + 67 + 9 00 99 + 69 +6 9 99 + 8 + 8 980 97 + 8 +7 9 + +7 88 70 76 +8 6 + 88 +9 + 70 9 68 +9 + 7 9 07 + + 7 79 0 +0 + 0 6 67 96 + + 86 6 00 960 + + 09 9 7 + + + 0 7 960 + + 6 + 7RO +7 +6 +lo7 + 77 8.'; + + 89 + 7 99...) +9 +0 +87 +7 +696 + +6 + 609 +6 C + + +0 +7~ + 8990 600 700 80 670 969 006 678790 8 07 / / / /0 /6 / /60 0Thi. prtin f the table is taken by cnsent frm "Statitical Tables" by R. A. Fisber and F. Yates, PlI[,

TABLES OF e VALUES*Cntinued) n= n= I I ~ ~ ~ ~ 0 7 0 +67 0 8 +0 + 680 + 69 7 +7 + 6 7 7 +89 +98 + 60 +9 + 86 69 +6 +097 + 77 +99 + 669 7 98 +6 +886 + 98 +6 + 7708 9 8 6 +6 +7 + 97 + 67 + 788 09 + 9 +899 +6 6 7 + 7088 7 7 90 +609 t 7 7 + 7 0 60 +76 + 8 80 66 + 7 7 8 6 +0608 + 9 9 8 9 9 0 6897 +0 + 8 0 0 98 + 7 099 6 067 + + 9 77 9 79 +8 78 696 0 + +60 8 76 960 +0 0 00 + + + 8 9 7 + + 07 7 07 + +a6 +77 9 696 9 +7 + 899 6 + +0 + +697 + 899 +7 +76 + + 79 +6 +96 +8 +79 +8 +88 +78 +88 +7~ 99 78 7866 090 7760 69969 9779 806 68 69 /6 7/ /0 / / 7/ 7/0 *This prtin f the tahle is taken hy cnsent Crm "Statistical Tahles"?y R. A. Fisher and F. Yates, pu

~.....,...,=~~,~... TABLES OF e VALUES*Cntinued) n=6 n=7 I ~ 6 +8 + 90 0 0 + 8 0 ' 99 + + 760 + 6 + 680 0 6 + + 906 0 67 + +0 7 87 +69 + 70 0 98 + 6 +89 9 6 607 +089 + 88 98 6 + +78 00 + 9 + 87 89 0 + 9 + 97 89 86 + 7706 6 78 69 + 9 +88 0 + 608 7 6 8 +00 7 07 706 + 6 8 0 88 7 +9 9 87 06 + 8 9 86 76 + 786 + 7 9 7 890 0 7 6 +7 69 97l 6 Ii + 7 686 979 + 7 889 8968 + 0 66 80 7 + 0067 + 78 6 9 +07 +78 76 9709 + 8 86 +97 +87 + 86 + + 0...,. 06 96 +9 +0 + + 88 6 + +6 + 7 96 +9 +6 +6 +66 7 +7 +8 + 6 + 78 8 +0 +7 +78 +88 0 076870 9906098 8 978 879 06 9076 888 9809698 0/ 7/ /0 /6 7/ /0 *This prtin f the table is taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yates, pu

TABLES OF e VALUES*Cntinued) n=9 n=0. 0 80 0 +06 0 99 +90 + 67 77 89 + 999 + 09 87 +7 +87 68 7 + 99 + 97 7 9 +6 +97 7 + 789 +669 7 6 +797 +787 706 + 6 +66 9 9 +07 +77 0 8 + 0 +8 0 89 + +6 6 7 99 + 9 +8 9 77 + 8 + 7 0 0 +6667 77 8 79 +00 8 88 09 66 + 7 6 7 7079 + 9 7 0 6 + 8877 9 7 699 +88 0 80 06 89 + 06 9 79 + 8 7 979 0 7 7 9 6 + 88 6 00 + 7 869 9 +7 67 7 6 7 + 9 8 9 6 +08 7 08 0860 9 +77 0999 6 +9 89 +07 + 99 6 6 +88 + 76 6 9 +9 +79 79 7 7 +87 + 867 + 9 007 +7 +88 + 788 8 +9 + + 999 + 78 7 +09 +67 +007 +09 9 +70 +09 +09 +8 9 +7 +99 +8 +99 90 790 98607888 0 6880 6880 9688 67 9660 /6 / /0 0/ / /0.This prtin f the table is taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yates, pub

,... ~~.:...:.. ~ TABLES OF e VALUES*Cntinued) n= n= 0 + 96 + 8070 0 0 +066 0 7 + 977 + 6 +096 + 870 + 87 +8 0 9 + 97 +698 7 0 9 + 706 +96 + 898 + 9 90 66 + +6 8 7 + 7086 +9766 7 9 + 9 +707 9 0 + 6 +0 7 8 + 7 +697 6 8 + 08 +996 6 0 8 +08 7 0 66 + 78 +0 7 78 +88 8 90 8 7 +0 9 8 +999 9 7 9 + 9 79 + 9709 0 9 699 +6 06 98 780 86 87 + 67 + 0 08 970 0 66 08.0 7 + 69 0 7868 + 68 696 9 + 9 6 079 80799 + 89 9 797 +0 906 7 +7 0 7 687 +88 + 6978 8 6 +0 6 07 99 +9 + 98 9 7 + + 79 7 +9 + 8 + 77 6 8 +70 + 87 60 9 +0 + 7 +07 +008 9 +07 +66 + 06 09 +0 +066 +0 +7998 0 +6 +0 +76 +0 +87 +7 +R6 +70889 68 9079 897678 66 676 96006 690 08807 806 87606 / / 7/ /0 /6 7/ 7/0 *This prtin f the tabl~ is laken by cns~t frm "Statistic!>! Tab!e." by R. A. Fisher and F. Yates, publis

t' t' TABLES OF e VALUES*Cntinued) n= n=6 6 0 06 0 + 908 0 88 6 +980 + 00 0 + 898 + 00 87 787 +90 + 97 9 99 + 89 + 870 8 9 +77 +6 79 76 + 78 +09 7 8 778 +0 +069 8 98 + 68 + 9 78 6 +60 +6 60 + 88 +7689 7 69 + 9 +77 6 98 7 + +87 67 977 + +8067 7 9 8 + 68 +86 60 60 + +768 8 96 7 +768 7 68 00 +68 9 6 668 77 +68 9 9 7 +09 0 06 69 767 +0878 69 +99 67 66 + 608 0 + 708 7 9 8 + 8 0 0 868 0 + 6 98 7 7 + 0 9999 + 8 07 8 9 + 7 8 889 +69 980 09 6808 + 98 60 66 6 +6 6 977 0888 + 8 00 7 7 +6 0 8 88 + 6 7 08 8 +66 + 09 607 7 7 + 8 + 777 87 9 +77 + 9 7 69 9 +0 +0 00 0 +69 +60 + 608 9, + +6 + 860 70 +87 +08 +078 + + +0 +6 +99 +96 + +99 +8786 +6 +709 +7 +879 790 9060 0068900 0 9090 786680 906 99660 88 6760 /6 / /0 / / / /0 *This prtin f the table i. taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yates, pu

TABLES OF e VALUES*Cntinued) n=8 n=9 7 +6 + 8 0 00 0 +790 0 69 +87 + 67 99 99 +76 + 9!s67 7 6 +7 + 9 96 9 +67 +97 7 9 777 +08 + 00 9 877 +9 +7767 9 97 +09 + 607 8 6 +96 +9 8 + 8 + 6997 7 9 +08 +089 9 + + 779 6 6 69 + 79 +86 07 + 9 + 70 7 8 + 66 +96 7 9 7 07 + 67097 8 6 97 + 6 +66 9 0 6 67 + 799 9 9 09 99 +98 6 808 + 79 0 00 6 68 +8 79 6 97 + 796 79 89 9769 +9 07 7 7 + 86 6 8 0 +00 7 9 67 697 0 067 609 + 9 + 0 8 979 9 869 090 + 08 8R7 679 + 68 99 08 + 80 807 786 6 + 6 8 0 66 + 6807 806 7 + 89 00 999 66 7 + 7 7 886 8 + 7 7889 06 9 + 6 + 8 8007 9 +6 + 9 89 + 68 +0 6 697 0 +00 + 670 860 8 + 8 +677 + 88 69 + + 79 87 + 9 + +09 + 89 +8 +77 + 99 607 7 +08 + +67 +99 +9 + +70 +67 +76 + +896 +98 688 960080 9088770 9800 670700 70760 760 000 6600 08790 / 7/ /0,6 7/ 7/60 *This prtin f the table is taken by cnsent frm "Statistical Tables" by R. A. Fisher and F. Yates, pub

n= 9 ~ fi TABLES OF e VALUES*Cntinued) 0 60 0 +060 0 67 +076 + 7 68 6 +977 +8 6 9 +886 +077 7 60 6 +606 +66 9 7 0 +0 +009 6 769 +0 +96 7 0 988 + 66 +66 8 8 7 + 676 +86 7 9 07 6 0 +86 9 0 0 6 +88 87 6 967 +7 8 8 8 +0 9 7 + 669 7 6 6 09 870 9 + 060 0 88 6 + 8 78 80 66 7 + 7 8 0 6 8 + 987 869 86 7 9 + 6 009 9 0 + 0 + 70 0 + 67 + 896 86 67 + 80 +77 + 6 78 + 97 +668 +96 6 7 +078 +7 +766 +068 9 + +900 +6060 +7670 00 7700 78660 68 780 78070 /6 7/ /0.This prtin f the table is taken by cnsent frm ' Statistical Tables" by R. A. Fisher and F. Yates, publ

6 7 8 9 0 6 7 8 9 0 6,0 TABLES OF e VALUESCntinued) n= 0 8 09 98 8 70 90 6 8 9 + 90 +7 +66 +07 +0 +9 + +9 +,9,7 70 9 06 70 0 8 76 0 0 6 90 0 7 9 90 70 + 70 + + + 60 + 80 +0,9,870 /6 +0 +60 + +066 +70 +0 +8 +6 + 66 66 0 97 7 0 0 80 00 969 70 90 70 09 + 6 +0 +760 +77,08,70 6 + 900 + 68 + 89 +08 + +08 +8 + +66 +6 +0 + 760 + 8 + 9 896 6776 07 69 609 778 679 869 + 0 +090 +090 8,,867,80 /0 n= 7 9 6 6 6 6 087 79 78 6 +690 +66 +9 +0 +90 + 880 + 8 + 906 +96 +886 7 9 9 0 80 6 9 79 77 760. 68 9 +600 + + 78 + 0 6 +6886 +8 +880 +80 +7097 7 9 7 9 99 66 0 9 9 + + 9 +9 +06 79 8 80 7 8 08 8 9 86 6 0 66 07 790 970 07 97 770 +7 +90 + 90090 + 78 + 78 90 990 999 86 06 7 9 +66 +9 +9 +6 +6 7 + 90 + 9 + + 666.0 7 87 + 90 +890 806 97 87 0870 + 80 +6 +689 + 906 +7 +66 +86 +7790 +099,70,79,7,,99,80 9,86,87,060,9,0,6,60 / / 7/ /0

6 7 8 9 0 6 7 8 9 0 6 7,860 TABLES OF e VALUESCntinue<l) n= 8 6 7 6 0 88 7 08 8 6 7 7 + 7 +09 +8 +89 + +77 + +7 + +77,79,0 77. 79 8 78 087 9 96 79 9 07 09 08 00 8 6 9 9 6 890 7 + 6 +9 + +7 +8 +60 7,8,60 /6 +06 +06 +00 +7 +06 + 97 + 78 + 700 + 66 + 87 79 9 6887 99 79 69 96 999 6999 899 99 89 87999 9999 + 76 +088 +99 +6 879,96,988,70 / + 7 + 900 +7 +7 +007 +8 +767 +08 +9 +76 +879 +908 +07 + 696 9 76 899 96 967. 7897 97 77 666 0 + 878 +60 +708,98,900,877,00 7/0 7 9 6 9 9 n=6 7e 9 86 677 +07 +977 +8 +97 +97 + 089 + 086 + 7 + 079 + 089 7 9 7 9 9 0 89 7 9 0 79 806 969 0 7 07 9 99 07 9.7 +97 +7 +06 + 97 + 7 09 689 88 + 6979 + 069 + 0 + 9 + 0097 + + 8780 + 998 + 967 + 7007 7 9 + + + 8 +9 87 0879 9 788 87 97 70 9 0 87 90 99 78 99 9809 7 9 +9 +0 + +9 +9 +89 + +9 0 9 + 7 + 69 +06 +7 +0 +6 08 67 809 76 + 87 +77 +07 +68 679 6909 99997 89 707 86 + 708 +987 8,0 :I,0,7 6,8,988,90 0/,9,799,8 7/,706,66,80,8 7/0

' TABLES OF e VALUESCntinued) n=7 8 809 800 78 76 8 6 9 +886 +8 +7 +98 +66 + 6 + 0788 + 670 + 9796 6 7 8 9 77 70 66 60 69 8 6 609 + +90 + + 98 + 86 + 7088 + 788876 + 89 + 86 + 8007 0 9 80 0 6 67 686 689 679 89 769 8997 99 + 800 + 7687 + 970 + 68 + 6868 6 7 8 9 7 + + 60 +7 6 66 6 89 99 889 7 607 787 ' 709 + 689 6089 77 7668 0 + 88 + + 60 + 77 + 96 90 6 + 6 + 6 60 9 6767 87 79 976 09 078 9708 7760 6 7 8 +06 +6 +7 +0 + 7 + 89 +089 +86 + 76 +8 +7 +78 68 + 00 + 8867 +909908,8 0,08, 6 9,0,6 8,6,97,8,0,09,,796 /6 7/ /0

"6 TABLES OF e VALUE8Cntinued) n=8 ~I ~I ~ ~I 7 9 0 9 7 0 8 7 76 + +7 +67 +00 +699 + 790 + 877 +87 +8 +7 7 9 9 0 9 869 00 0 +089 +87 +8 + 796 + 09 +79 +87 +986 +9886 +90 7 9 8 7 6 9 79 6 0 9 9 0078 68 90 7 +69 +690 +90 +90 + 767 7 9 7 9 0 + + 0 + 70 + 9 + +6 +60 6 76 999 806 7 0 + + 76 +78 966 88 86 0 0086 806 78 878 666 + 68 6666 09 0 7 67 67 8 970 7 +8 + +8 +66 + +79 +0 +96 + 889 +807 +8 +7900 + 7 +8 +666 6,08 90, 87,,6 6,80,,6 9,097,79, 08 / / 7/ /0

~7 TABLES OF ~, VALUESCntinued) n=9, 0 90 0 + 9 0 89 + + 88 86 86 + 7 + 98 8 8 + 8 + 7 7 686 + + 78 6 070 + 89 + 60 6 9 + 67 + 70 7 ~ 78 + + 78 8 6 0 + 76 + 8 9 09 06 + 9 + 809 0 90 + 9 + 77 69 67 898 + 709 6 778 88 + 60 8 78 + 87 9 80 7 + 60 6 70 6 + 68 6 08 6 7 98 88 8 + 967 97 9 +7 6 68 6099 0 +0 00 606 776 + 778 90 +9 69 9768 +9 + 8 8 9798 +86 +08 78 8908 + +0 86 6870 6 +86 ' + + 07 7 +9 +66 + + 68 8 +9 +68 + 79 + 8778 9 + +77 + +88 7,0,966,098 6,7,90,,9,8,90,776,9 /6 / /0

8 TABLES OF e V ALUE8Cntinued) n=60 899 899 +8 + 8 89 687 +06 + 70 88 +9 + 69689 7 86 6 +89 + 979 9 89 779 +9 +69 809 99 + 979 +77 77 0777 + 80 +786 7 08 + 60 +6 7 68 + 9 +.96 9 69 + 6 +690 69.09 7 +89 0 67 6 +7 97 7 + 7 608 79 + 8779 Q 69 9 06 + 70 79 69 6 + 88 8 707 86 77 + 9 6 96 0 7 + 7 7 6 8997 9 + 06 69 7 + 6 89 6 669 + 87 7 6 799 + 69 0 6 97 7 + 77 + 987 0686 909 9 + 90 + 99 6866 779 +0 + 90 866 06 +07 +6 + 9 68 +69 +98 +79 + 789 7 +7 +897 +89 +7769 9 +7 +09 +09 +799 7,980 8,86,0,06,,0 9,8,9,00,0,80,99,680 0/ /0

"9 TABLES OF VALUESCntinued) n=6 ~I ~I ~I 0 0 0 + 0 09 6 +688 + 0 06 9 +0 +00 0 7 +908 +699 9 806 +868 +889 8 0 +90 +0 6 7 609 +78 +0 7 6 968 +788 +78 8 6 9 +808 +86 9 9 76 + 98 +88 0 0 8 + 7 +8006 89 00 +6 66 8 6 +0 870 +90 97 +90 8 60 88 + 888 6 0 7 68 7 808 9 0 8 + 07 67 08 9 + 6 8 77 0 + 90 60 98 78 + 0 88 909 +7 07 9 +9 97 9 +66 + 6 09 6 + +00 98 060 6 +66 +6 7 906 7 +9 +8 +78 0 8 +7 +78 +768 + 77 9 + +68 +608 +09 0 + 90 +8 +977 +608 8,90,68,898 776,0,0 89,06,899,66 8, 60,099, 86 /6 7/ /0

'0 TABLES OF e VALUESCntinued) n=6 ~I ~I ~I 60 96 + 96 + 7660 9 87 + 979 + 77 7 7 + 079 + 7677 7 68 + 06 + 09 9 0 8 + 676 + 68 00 + 07 + 779 9 7 + 689 + 7997 00 + 090 + 866 7 8 + + 87976 9 9 + 79 + 87090 0 6 + + 87 9 70 76 + 7690 8 70 696 + 67760 7 69 77 0 + 787 9 769 9069 + 97097 0 76 8 + 9 67 76 + 7 7 6 6676 7 + 988 708 9 + 0 7 0 6898 + 0 066 6 706 +7 87 6 9097 + 9 7 007 7 +6 88 096 069 9 +0 + 96 86 0680 +I6 + 69 989 9 +9 + 6768 +8 +60 + 670 9098 7 +6 + + 06 + 6007 9 +7 +89 + 70 +007779 6 +0 +99 +07 +9809 79,,70,7 9,8, 0, 69, 68, 0,98,77,66,98 / / 7/ 7/0

TABLES OF t' VALUE8Cntinued) n=6 99 989 980 96 9 99 97 9 86 + 90 + 8609 + 7 + 69 + + 0 + 868 + 706 + 907876 6 7 8 9 97 88 8 800 79 7 9 67 708 77 + 7079 + 09 + 6 + 9776 + 789 +0878 +9696 +7609 +06 +687 0 69 69 60 8 0 8 869 90 9 9 + 79 06 7989 6 +0 +807 +06700 +080 + 868 6 7 8 9 0 6 7 8 9 7 0 + 9 + 08 + + 60 + 9 + 76 + 88 +06 +9 +60 + 9 90 867 8 7 60 9 07 76 + + + 60 + 88 +89 87 96 99 09 78 796 600 09 989 86 77 9 69 + 96 + 899 + 709 + 90768 809 90 6676 980876 67 9968 666 7980 67 6060 08877 7 + 668 0 +708 +89 + +89 + 779 +69 +66996 +0 0,8 9,9,8 8,99,7 9,7,69,968 96,8,6,66,9 /6 7/ /0!

' TABLES OF e VALUESCntinued) n=6 { 0 + 7 + 869 9 09 + + 88 06 + 97 + 97 7 9 70 + 6 + 769 9 8907 + 8 + 79 070 + 76 + 8889 99 89 + 7 + 979 8 9 + 77 + 98700 7 69 + 89 +070 9 687 + 089 +06 76 + 00 + 99707 09 869 7 + 98 8 907 7 + 8708 7 9 9 7 + 7087 9 97 97 + 97 0 9 6907 + 67 69 8799 707 + 767 79 96 6 7 + 676 7 969 9 + 9 97 787 6669 + 79 967 769 + 0879 977 9689 +6 808 7 097 7 + 8 7 00 9 +9 7 7 778 +09 + 077 67 967 +6 + 779 997 09 + +0 87 779 7 +7 +889 + 7 87 9 +9 +9 + 898 + 699 6 +89 +7 + 8 +79 6 +6 +97 +9 +99 87,60,97,9 7,9,96,60 7,98,8,6,066,69,80,896 0/ 7 7/0

_"B TABLES OF e VALUE8Cntinued) n=6 ~i { 6 0 0 +786 0 7 +76 + 7 8 09 +677 + 6000 6 +7 + 8 6 08 +6796 + 96 7 + + 900 6 6 987 +8707 + 676 7 0 09 +600 + 78 8 88 796 +76 + 77 9 7 + 87 + 797 0 + 6 + 787 697 + 77 + 767 08 89 + 700 8 0 89 + 689 6 0 679 + 08 7 0 6769 + 87 6 96 0 090 + 08 7 6 879 099 + 8 8 8 6 709 8976 9 + 9 999 68 0 + 8 890 0 996 + 89 67 789 60 + 79 9 7976 +77 00 00999 86;9 + 8 70 90 +7 7 9 96 6 + + 9 79 90 7 +77 + 979 78 8 + + + 876 96 9 +89 + 07 +67 99 0 +8 + 666 +666 + 06 +609 + 86 +68. + 96 +67 +06 +676 +ls6,880 6,8,., 80,880,967,0,,60 09,0,08,80 /6 / /0

'i TABLES OF e V ALUE8Cntinued) n=66 + 8 + 60 67 + 877 + 9. 69 + 7969 + 09 7 6 78 + 7 + 800;6 9 76 + 69 + 776 99 709 + 677 + 07 8 667 + 7 + 6 60 760 + + 870 7 6 88 + 7 + 08 9 09 89 + 7 + 87 79 999 + 897 + 007 6 998 68 + 7987 0 00 66 + 880 7 7 09 9 + 88 9 9 070 0 + 7 8 066 08 + 768 6 07 68 + 68 8 0 7 + 7 7 98 88 899 9 + 6 8866 908 96 + 86 79 988 0696 + 9 687 966 0880 + 0 9 9896 7 + 8 98 908 6960 9 + 6 6 868 680 + 9 68 68 + 09 + 7 0 8697 + 90 + 70 66 97 7 + 67 + 76 + 06 9 + 76 +0679 + 97 69 6 + 8 +09 + 877 + 0990 6 + 9 +7808 +9 + 676 6 +00 +80 +9 +7998 9,80,66, 9,9,86,0,76,0,6,68,9,0,8 / / / /0

'; TABLES OF e VALUESCntinued) n=67 0 7 0 + 8976 0 7 + 8896 + 80 70 + 867 + 898 6 + 86 + 79 8 8 + 776 + 906 9 0 + 706 +8 6 8 67 + 60 +766 7 78 + +0 8 0 8 + 9 +88 9 9 888 + 06 + 0 7 9 + 80 +6 0 + 06 +97 0 08 88 +00 0 09 78 +67 78 9 +0878 9 0 8 + 8668 6 8 606 + 6088 7 8 088 708 + 96 8 0 07 8 + 66 9 988 907 0 + 6 90 97 66 + 67 8 0 97 +0 69 06 78 + 0068 8 +0 88 90 700 + 00 8 870 6 +0 + 7079 890 7 + + 8 797 8 +0 + 8 88 60 9 +67 + 8 + 66 9889 0 +6 + + 0 9 +87 +88 + 8976 + 6696 +60 +87 + +9 +7 +88 +09 +6,08 7,9, 9,98,76,,60,6,99, 96, 76 /6 / /0

~6 TABLES OF e VALUESCntinued) n=68 8 +6 + 60 8 69 +688 + 786 79 + +88 7 7 89 +98 +79 9 6 09 +7609 +867 +869 +97 8 +68 +8678 9 8 +808 +08 7 9 +998 +8 9 9 89 + 96 +7 7 08 + 09 +879 ~0 + +6 9 7 67 +90 7 0 99 997 +6 9 7 669 76 +6 68 996 +76 6 6 +7 79 77 + 9 7 9 7 9 069 8 87 + 7 69 7 + 77 7807 + 80 808 86 7 +67 09 76 76 9 + 9 886 770 +6 7 086 990 +7 + 9 87 9909 +7 + 807 709 7 +7 +6 877 0799 9 +8 +8 + 99 07 6 + +89 +7 68 6 +607 +679 +008 +88 6 +67 +786 +768 +8 67 +77 +98 +7668 +7668 0,788 8,068,676,06,9,6 9,79,0,8 6,8,08,6 / 7/ /60 ~\

~I ~I "7 TABLES OF e VALUESCntinued) n=69 { 0 90 0 + 70686 0 87 9 + 7009 + 78 78 8 + 687 + 70 6 76 + 68 + 099 6 + 6 + 66 870 + 686 + 7976 6 08 89 + 007 + 9 7 0 878 + 9 +0066 8 998 + 0 +077 9 97 76 + 6 + 0 890 + 706 +76 87 + 78 +06 78 698 88 +0080 68 90 8 + 9668 60 60 + 800 60 6 + 7066 6 60 98 + 08 7 608 8 + 0068 8 8 87 607 + 608 9 07 86 6798 07 0 + 0 0 78 998 + 77 78078 6969 + 6 80 79 + 97 80608 996 + 8 76 788 678 + 68 80 706 980 6 + 88 89 668 86 7 + 997 + 78 69 8 +6 + 68 ~ 698 6 9 + + 07 6778 0 0 +0 + 6 + 806 6687 +69 + 686 + 80 8 +88 + 87 + 70 + 68 +077 +08 +97 +6 +78 +9 +6877 +6060 7,70 78,9,,8,87,0 7,89,660,0 6, 8,0,9,8 /6 7/ /0

'8 TABLES OF e V ALUESCntinued) n=70 ~I ~I ~I ~I 0 6 +766 + 0 8 +67 + 70777 0 0 +8 + 60807 7 98 +76 + 80 9 9 8 +66 +06 89 67 +80 +60 8 70 +0 +67 76 880 +06 +86 7 68 98 +686 +66006 9 9 00 + 00 +60700 9 097 + 70 +608 8 6 + 076 +600 6. 00 9 +790 7 9 8679 +888 9 99 67 9999 +6 8 77 97 + 9779 68 76 + 6960 9 899 + 09 7 099 79 + 09 9 8 677 906 + 6 07 967 + 7 976 6779 87907 + 9 86 79 9097 7 + 7 7 8 78 9 + 96 88 7 70 + 87 8999 87066 +7 979 90 +7 + 990 79 90798 7 +0 + 686 866 76778 9 + + 6667 7999 6 6 +6 + 99 + 00 99 6 +9 + +0996 77 6 + +70 +9606 + 8966 67 +7 +6 +69 +70 69 +9 +697 +860 +767,0,,9 8,6,7,060 7,76,690,,980 7,0.9,, 00 / / / 7/0

'9 TABLES OF e V ALUE8Cntinued) n= 7 ~ ' 0 0 0 + 79 0 9 69 + 786 + 6 6 > + 767 + 9996 867 + 76 + 87 0 66 + 690 + 9686 9 0 + 6879 + 99667 6 8 99 + 7 + 688708 7 7 + 980 + 7666 8 6 6 + 0 + 8688 9 9 06 + 08 + 8 0 0 6 + 9 + 8608 99 89 + 6 + 860 76 68 + 690 + 8780 _ 67 08 + 7700 6 7 + 6980 9 66 87 + 9 6 6 666 690 + 7 7 66 97 + 97 8 96 677 69 + 87 9 9 6 700 + 6777 0 0 90 796 6 + 09 89 0 + 6 98 888 066 +09 7 90 6676 +6 96 8980 8976 +0 7 867 90 6 +6 79 7977 080 7 +09 60 6970 089 8 +6 + 68 790 0 9 + + 09 76 9099 0 +80 + 60 87 7078 + + 0 + 9 697 +60 + 7 + 60 707 +669 + 96 + 8 + 67 +76 +9 +098 +668 +80 +68 +879 +0769 9,80 0,0,6,9,7,80,667,7,090 0,090,,98,60 /6 7/ 7/0

'0 TABLES OF e VALUESCntinued) n=7 6 9 9 + 867 + 97 89 77 + 86 + 7797 77 8 + 7979 + 9 7 9 78 + 797 + 00 9 7 + 7097 + 99 0 79 + 6767 + 876 69 8 + 70 + 669 7 60 + 9 + 79 7 079 99 + 008 ' + 769 9 0 + 07 + 789697 96 669 + 97 + 7987 899 9 + 89 + 7798 87 7 0 + 76 7 79 80 + 6879 9 66 8 6 + 6 7 9 806 + 9 79 9 + 06 77 9 97 + 78 7 69 6 69 + 6 9 6 780 00 879 8 789 + 9 908 79 + 06 9 97 7 + 6 98 677 9 + 0 89 96 766 + 6 9 90 8686 +8 88 9807 + 97 8 70,967 7 + + 66 7 9697 9 + + 89 78 89 6 +9 + 68 67989 6 +68 + + 70 6 +87 + 60 + 07 67 +07 + 770 + 988 + 9 69 +7 + 999 +987 +07077 7 +8 + +97 +89987 9,80 0,0,6,9,7,80,667,7,090 0,090,,98,60 / 7/ /0

TABLES OF e VALUE8Cntinued) n=7 6 0 8 6 9 +6 +9 +7 +80 + + 099 + 8 + 6 + 7996 6 7 8 9 9 08 9 80 6 6 76 87 980 077 +09 + 99 + 89 + 690 + 99 + 966 +086 +969 + +8687 0 00 7 8 6 0 6 07 + 979 + 69 + 690 0 78 +77 +7 +70 +006 +908 6 7 8 9 9 88 0 8 8 87 66 786 90 08 +0 + 86768 + 660 + 66 + 79 0 + 0 + 8 + 0 0 89 06 07 8 66 996 789 6868 99 800 6 7 8 9 0 +8 + +8 +0 +97 +6 +7 +80 +6 +7 7 70 + 0 + 0 + 87 +00 +9 +0 7 0670 87 76 + 670 + 79 +099 99 700 6897 77 6699 868 79 7076 0 + 889 6 +78 +8 +8 +98 +9 +99 +97 +,,06,60 09,09,70 9,8,,970,,0,07,00 /6 / /0

'' TABLES OF e VALUE8Cntinued) n=7 ~I ~I ~I 7 9 7 9 8 7 8 07 00 9 8 68 07 9 78 6006 79 87 960 0608 7 +8 + +7 +78 +8 +08 + 98 + 80 + 678 + + 0 + 66 +0888 +98 +868 +9967 +8677 +708 +897 +009 7 9 7 6 0 7 9 0 80 7 76 + 60 + 898 + 0 677 97 +09 +0079 +9000 +779 +68 7 9 08 9 7 7 8 00 09 0 76 6 0 706 87 07 7 +66 +7086 +8667 + 780 + 8 7 9 7 9 8 + 8 + 7 + 97 + +0 +78 +07 69 87 80 08 906 79 7 970 8 + 9 98 997 7 8 6 97 7 870 0 87 9697 7 090 670 0608 0 69 688 6 6 6 67 69 +7 +68 +00 + +67 + + 8988 +70 +687 +9 7 + 0 + 866 + 7 8 9 +89 7 7 +0 +8 +986 +098 +78 +098 + +7,0,079,0,0,0,700 0,0,86,0,6,997,98,70 / / / /0

TABLES OF e V ALUE8Cntinued) n=7 6 0 06 0 + 906 0 0 70 + 89996 + 00 9 99 + 790 + 6900 79 086 + 66 +009 8 78 + 806 + 0 + 0706 +6689 6 98 07 + 708 +8660 7 9 6 + 876 +076 8 96 + 8066 +68 9 6 78 + 8096 +608 0 06 69 + 78 +68 0 66 + 6 +68 97 699 + 86 +908 899 706 687 +87 88 7 8979 + 7 770 9 +909 6 68 78 6 +67 7 9 78 78 +0 8 779 899 + 906 9 768 9 + 0 0 06 790 99 + 8006 8 70 88 809 + 6 689 99 896 + 8 606 86 0 + 8 6 780 + 69 0 67 90 6 + 6 67 879 080 7 + 78 7 77 7670 8 + 96 86 6787 96 9 +7 8 979 990 0 +9 + 069 86 +77 + 08 8880 7876 +666 + 86 7 9696 +86 + 67 + 6876 088 +06 + 887 + 0 + 88 +69 +0 + 67006 +7 6 +8 +78 + 8966 +078 7 +70 +606 +066 +7,0 8,6, 890,0,77,60,06,80,96,0,67,8,770,700 /6 / /0

' TABLES OF e V ALUESCntiDucd) n=76 8 + 98 + 8860 79 9 + 8 + 8600 7 76 + 979 +07 7 69 996 + 766 +99 9 6 687 + 8 +9 + 9 +8799 9 789 + 78 +9 0 + 670 +76 7 09 9 + 798 +878 9 9 67 + 88 +978 7 6 + 8 +00 9 89 + 9 +0 97 + 79 +9 7 99 077 07 +777 9 7 697 09 + 779 +0 09 69 +99 7 6 080 +00 7 9 0 77 +77 9 0 77 97 + 69 6 06 807 09 9 899 87 8009 + 698 80 706 7 +7 8 8 60 9 +9 707 90 090 +69 8 90 69070 + 69 77 7 +7 006 9 667 7 + 87 8790 9 +89 + 0997 890 6 +9 + 67 66 6 + + 87 066 6 +7 +060 80 08 67 +6 +8609 + 8 7 69 +709 +78 + 88 + 796 7 +779 +667 + 6066 +6 7 +8 +67 + 89 +7 7 +9 +67 + +988 6,00,07,060 7,97,07,00 6,0,08,00 9,9,909,7,960 0/ 7 7/60

" TABLES OF e VALUE8Cntinued) n=77 0 9 0 +09668 0 9 8 +0898 + 00 90 9 +067 + 6006 8 0 +000 + 887 78 8 + 97968 +66 69 70 + 98 +067 6 8 8 + 876 +6 7 980 + 7780 +88 8 0 00 + 6660 +9668 9 + 08 +07 0 9 + + 7 08 + 898 +669 0 90 + 0 +90 60 + 70 +060 98 67 077 +966 69 660 7 +76976 6 8 688 69 +096 7 0 700 60 +879 8 70 69 690 + 98 9 67 866 + 6 0 9 60 9 + 778 68 08 77 0 8 6 + 80 8860 906 + 8 7 80 + 00 68790 6 +8 9 97 00 7 + 70 00 999 8 +90 90 00 0 9 +7 008 60 0 +06 + 87 6098 +67 + 7 6 8 +0 + 70 700 07 +9 +00 00 67 +66 + + 08 866 +7 +960 + 7788 + 89 6 +80 + +968 +8 7 +87 +960 +89070 +06 8 +90 + +,69 +90 8,08,0,00 8,8,80 70,8,96,80,7,70,07,80 /6 7/ 7/0 I

"6 TABLES OF e VALUE8Cntinued) n=78 6 760 +9 + 7660 77 +77 + 7876 7 7 +07 + 89 7 7 00 +0660 + 8876 9 70 8 +00 + 8797 7 67 + 907 + 76677 697 88 + 8 + 608 676 0 + 780 + 707868 7 6 80 + 660 + 7708 9 6 60 + 67 + 8089 9 807 + 8787 + 87999 6 990 + 80 + 899780 6 0 + 0980 + 89780 7 87 8 6 + 77960 9 9 8 + 769 00 7 8 + 6696 0 880 + 688 0 6 + 6987 7 7 768 + 07 9 90 8 898 + 068 0 6 00868 + 7688 67 6 776 0 97 08. 7 + 68 80 600 8076 9 + 0 8 008 600 + 7 0 67 + 9 8 0 79969 + 7 0 60 8968 7 + 8 90 690 9690 9 + 009 00 6 + 6 + 8 8667 996087 6 + 78 + 80 660 99 6 + 8 +60 60 8077 67 + 9 + 70 608007 69 +0 +97 + 77 6 7 +0 +8 + 8 + 76708 7 +8 +0 +880 + 7800 7 +9 +67 +00 +0996 77 +6 +7 +706 +9778 8,8 6,060,0 69,,0 80,,86,0,067,7,9,,0 / / 7/ /0

'M7 TABLES OF e V ALUESCntinued) n=79 l 0 0 0 + 0 9 779 +07 + 88 6 +8 + 78 7 + + 80 0 066 +0900 +08 9 79 +099 +88 6 8 99 + 9 + 7 7 7 + 87 +709 8 6 8 + 700 +888 9 9 6 + 60 +0009 0 0 696 + 999 +07 99 769 + 7 +08 76 798 + 60 +0970 807 + 6 +06 86 886 +900 9 888 +799 6 6 906 980 +606 7 96 0 +707 8 96 977 698 +09896 9 9 90 888 + 79 0 0 890 96976 + 79 869 088 + 97 6 88 9 88 + 9 7797 76 667 + 6 796 980 0968 + 0 67 78 8 6 + 6 69 890 7607 7 + 09 6 678 067 8 + 6 0 069 9 + 9 777 0 + 80 89 0760 6 + + 6 889 7 + 0 + 600 6 + 69 + 6 0076 + 66 + 69 876 + 70 + 8 + 899 7 6 + 776 +0806 + 90960 + 0 7 + 89 +7 +7 + 8 + 9 +609 + +090 9 +00 +909 +88 +06,080 7,08,06,7, 96,00 90,,96,0,6,,0,0 /6 7/ /0

8 TABLES OF e VALUE8Cntinued) n=80 6 99 + 9 + 08 787 + 9000 + 906 7 79 + 877 + 9 7 0 + 8 + 06 9 09 + 7989 +.76 0 709 + 79 + 09 9 9877 + 6790 + 76 77 8 + 608 + 80 7 6 + 0 + 9 7 + + 979 + 9 + 6 0 77 + 0 + 90 77 7 + + 7 7 98 + 0 + 880 9 6 07 + 00 9 769 87 + 70667 6 7807 97 + 7877 7 8 7 + 7607 7 9 807 7 + 77 9 766 6607 + 097 689 707 + 78679 7 67 867 + 89 7 00 907 7799 7 + 9 9 96997 900 9 + 67 9 07 907 + 7 699 087 809 + 69 77 07 869 + 86 067 89 7 + 79 00 9767 9769 9 + 7 879 9007 09 6 + 97 989 797 7 6 + 9 + 6097 77 6. + +06 707 9987 67 + 89 +87 797 07 69 + 67 +69 + 89 06797 7 + 77 +7 + 9 80 7 + 799 + + 700 + 6 7 + 87 +8 + + 6 77 + 99 +67067 +600 + 6666 79 +07 +79079 +6 +07 70,60 8,90, 8,08,7, 60,909,69,880,9,,880,00 0/ / /0

'89 TABLES OF e VALUE8Cntlnued) n=8 ~I ~I ~I ' 60 67 68 6 9 89 6 7 6 +988 +907 +87 +8 +76 + 989 + 89 + 809 ' + 66 6 7 8 9 6 9 8 97 99 79 6 677 +6 +08 +6 +06 +0 +6 + 7 + 79887 + 699 + 677 0 0 77 08 0 76 7909 898 887 99 + 8 + 6 + 06 + 78 9 + 7006 + 76 + 7780 + 709 + 6700 6 7 8 9 96 87 77 668 7 98 970 98 9897 986 97 7689 9999 9 + 6079 + 78 + 0097 + 68 + 97 0 6 7 8 9 0 7 88 + 88 + + 88 + 7 + 7 + 88 970 999 96 877 86 77 6669 7 66 69 799 99 060 7 879 879 8 09 + 7 + 9669 78 9 800 0 096 69 7906 806 0 +060 + + +67 +88 09 89 + 07 + 89 + 879 8687 669 989 799 89 869 8768 7800 6868 6 7 8 9 0 +0 +8 +67 +69 +9 +60 + 70 + 966 +877 +7 +79 +00 + 8 + 76 +0g +88 +89 +88 7999 000 + 99 + 00 +07 +77 \,80 7,06,76,66,707,0,7, 8,89,,80,6, /6 / /0

{ '0 TABLES OF t V ALUESCntinud) n=8 / ~ Fi 80 68 +0868 + 0 79 0 +99 + 0006 77 8 +8 + 69 7 7 6 +0876 + 6996 9 70 8 +08 + 8 6 79 +60 + 867 9 09 +066 + 86 80 + 9676 + 708 7 6 + 86 + 608 9 907 + 700 + 869 + 6 + 099 8 + 096 + 0800 0 0 + 076 + 080 7 89 77 + 77 + 998 9 7 87 977 + 686 60 968 70 + 6 08 6 + 97 7 09 69 + 8877 7 09 07 78069 + 7767 9 90 08 997 + 078 70 08 0889 + 0708 9 9 9 + 889 7 76 69 80 7 7 88 776 9 + 0 9 680 + 0 87 087 +7 70 609 869 + 98 0 60 660 7 +6 86 6 8 9 + 7 87 766 6 +8 79 97 607 6 +6, 68 80 697 6 +8 + 0 9 97 67 +8 +7 66889 6787 69 + +09 77 8 7 +0 +98 + 8988 66 7 +86 +9 + 796 0 7 + +97 + + 966 77 +6 +608 +7767 + 99 79 +00 +768 +088 + 76896 8 +0 +8 +78 +0076 8,76,,6 987,69,6,87,98,07, 6,00,00,80,90 / / 7/ /0 \

"a TABLES OF t' VALUE8Cntinued) n=8 { { 7 7 70 6 8 7 678 +809 +7 +69 +09 +7 + 980 + 98 + 609 + 706 6 7 8 9 9 8 0 9 80 997 8 9 8 +69 +7867 +07 + 90 + 8 + 70 + 668986 + 79 + 8096 + 8768 0 7 0 0 78 67 778 87 9 + 67867 + 0 + 66 + 9 + 87 + 960 + 9967 + 90 + 907 + 908 6 7 8 9 9 8 8 0 00 07 08 7 8 6008 988 896 690 868 + 88 + 7868 + 706 + 9986 + 8669 0 6 7 8 9 7 90 + + + 0 + + 0 + 67 0 07 0 9 88 700 7 68 6 98 0808 7978 78 96 068 6908 6709 6966 6806 6078 + 99 + 069 + 60 07778 7700 70 990 77 879 9969 0 6 7 8 9 + 6 + 87 + 0 + + 8 + 6 + 7 + 79 + 870 + 97 66 7 8 + 08 + 697 +0 +78 +07 +60 +7 9 008 ~76 9796 67 078 + + 6 +79 +886 08069 8 76 06 0098 86 8778 77 + 90 + 788 0 +06 +07 +780 +8 +69 +98 +908 +7778 7,6,867,678 68, 660, 0,6,67,0,876 6, 00,,6,6 /6 7/ 7/0

~ TABLES OF e V ALUESCntinued) n=8 76 76 + 777 + 87860 77 79 + 7669 + 70 7 876 + 799 + 9086 7 77 0 + 77 + 69 9 70 67 + 68877 + 076 67 88 + 667 + 9 67 009 + 98 + 9086 9 0 + 8 + 979 7 7 79 + 76 + 896 9 9 067 + 08 + 697, 7 + 67 + 907 67 89 + 97 + 6007, 9 77 + 99 + 60078 " 7 7 9 + 707 + 89 9 0977 088 + 66068 0 68 + 888 97 9 0688 + 8668 8 8 996 + 8886 7 77 899, + 689 9 6 07 77 + 869 0 8 60 + 00989 77 699 67 + 07989 8 70686 + 0 7 07 96 7678 9090 9 + 7 787 8778 9870 + 87 + 66 9 878 8798 970 9687 + 0 766 888 89707 7 9 + 67 + 87 867 8787 897 7799 6979 6 +07 99 79908 698 6 + 6909 768 708 6 +0 9 66 7776 ~7 +60 + 769 988 6989708 69 +807 +0 69 6 7 +07 +97 68 7 + +6 897 60 7 + + + 689 0 77 +68 +9 + 6 + 778 9 +97 +66 +0006 + 98698 8 +7 +7897 +98 + 97008 8 +0 +988 +876 +798 97,0 08, 97,8 6,867,9,0 99,9,, 68,00,79, 60,08, 0 / 7 / / 0

' TABLES OF e VALUESCntinued) n=8 0 60 60 98 9 86 90 799 686 8 + 806 + 809996 + 7960 + 776 + 706 + 00 + 8900 +07 +7 6 7 8 9 77 66 8 0 7 60 6796 78 + 7006 + 68 + 60076 + 766 + 68096 +67 +&09 +778 +076 + 0 0 8 8 06 89 88 99 9906 0 + 98 + 6 + 6 + 6 + 0 +0 +09 +0 + +76 6 7 8 9 77 6 78 070 0 9 8 96 6 99 +786 +076 +76896 +08 +0 0 6 7 8 9 0 6 7 8 9 0 6 8 7 6 + + 7 + 7 + 8 + 9 + 98 + 9 + + 87 + + 6 + 69 + 767 + 8 + 99 90 0989 066 08 90 887 797 6986 88 8 6 8 + + 07 + 0 + 678 + 8806 +9 + 99 608 68699 766 87 8667 9079 97 9087 979 8869 8880 787 6 0779 699 + 066 + 790 + 697896 +8 +06 + 008 790 670 790 8690 978 7 8868 8 808 8076 096 68 0806 060 77 88686 0 + 998 +079 +6 +70 +08 +8 +06006 +70096 +990 +96676 +86 +876, 70,6,8 7,9,,670,9,909, 0, 690 8,089,80,69,80 /6 / 7/0

' TABLES OF e VALUE8Cntinued) n=86 ~ I ~ I 08 9 +7078 + 0 07 767 +686 + 08 0 9 +697 + 6667 7 0 698 +978 + 98 9 98 866 +8 +67 9 9889 +9 +7709 87 7 +7 +799 80 60 +08 +7006 7 7 688 +06998 +8968 9 6 6 + 907 +0 779 87 + 79 + 878 +096 +08 0 980 + 08 +00 7 7 08 + 69 +7 9 0 7 + +007 88 760 +97 7 0 760 +800 7 +6889 7 7 6 7787 +997 9 8 686 968 +686 98 6 + 866 77 77 77 + 60 7 + 7 808 66 690 9 8 0776 77 80 + 7 999 87 87 + 7967 9067 00 + 70 670 98 978 7 + 98 098 99 86 9 +7 7 987 9 6 +7 9089 8007 6 +88 6 776 706 6 +0 860 8 997 67 + + 77 7 8687 69 +87 + 669 067 6077 7 + + 896 67 0 7 +8 +78 88 79 7 +9 +87 + 97 09 77 + +97 + 879 7 79 +7 +970 +98 + 80 8 + +86 +98 +876 8 + + +0967 +6897 8 +9 +98 +097 +069,990 6,9,9,.,860,977.07,080,6.00.78,8, / / 7/ /0

'J TABLES OF e VALUESCntinued) n=87. I 0 89 0 + 0 889 89 +07 + 70 880 77 +00 + 7 86 6 + + 789 8 76 +0 + 9068 87 9 +7 + 998 6 78 099 +0787 + 69888 7 7 67 +9 + 787787 8 700 8 +78 + 86 9 69 '8 +7 + 977 0 9 7 +867 + 9766 9 89 +07 +00860 60 98 + 788 +000 8 09 + 09 +0 0 9 + 67 +0076 7 7 6 + 96799 6 78 + 9086 7 0 97 67 + 8 8 90 977 + 708 9 809 6 + 607 0 69 0 8 + 7 69 9 78 + 767 0 87 07 + 676 0 97 + 6709 6 6 68 980 7 6 678 6 + 6 989 769 780 7 + 9 87 867 607 8 + 60 68 9 76796 9 + 6 9 90697 0 + 808 7 8 06 + 99 899 7 607 +80 9 0 0768 +7 7:7 8 +76 + 9 9 96 +78 + 88 69 6 +996 + 966 98 068 7 + + 07 868 8 +0 +97 + 0 9 +67 +09 +867 796 0 +908 +00 +7 + 996 + +7 +97 + 89989 +00 +0 +66 +6988 +6 +7 +6067 +879,868 9,0,8 7,68,778,786,7,78 69,0,00,6, /6 / /0

"6 TABLES OF e V A LUESCntinued) n=88 ~ ' 6 87 +670 + 0 6 9 +67 + 87 69 9 +877 + 9 7 6 68 +07 + 06 9 6 +97 + 887 6 7 +6 + 97 60 89 +0 + 0 89 +97 + 7968 7 7 67 +787 + 699 9 678 +9 + 66979 77 + + 6999 7889 + 99 + 78 89 87 + 77 + 70 7 6 88 + 7 + 78 9 99 + 6 + 700 0 97 67 + 6696 7 9779 7 + 667 9 997 777 + 7097 7 0 00 080 + 0607 9 6 0 767 + 07 667 + 6 8 009 9 + 89 9 98 87 + 9 7 9 9 7 + 09 9 96 697 979 + 8687 7897 8 + 7, 809 9...:. 69 + 7 0 ~U779 7 + 67 66 0 69 9 + 7 07 690 6 + 8 697 977 79 6 + 7 9 8 807 6 + 7 67 8707 67 + 77 87 877097 69 + + 667 9707 8696 7 + 6 + 087 8 7 + 687 + 6 98 760 7 + 76 + 6 8 778 77 + 87 + 89 + 967 769 79 + 9 +007 +96 69 8 + 99 +9 + + 6 8 +077 + +887 + 687 8 +6 +87 +8977 +787 87 +7 +9.9 +697 +797 7,8 9,99, 6,7, 9, 9,6,9,8,8,9,. 98 { {0

'7 TABLES OF e VALUE8Cntinued) n=89 660 69 66 6 6 989 97 97 906 +98 +98 +987 +8696 +808 + 68 + 908 +68 +7988 6 7 8 9 6 6 6 96 79 8 79 66 79 80 +77 +609 +87 +878 +99 +98 +60 +8989 +80 +9 0 60 9 6 9 6 906 9779 08 07 7 +0697' + 86 + 68 + + 7 +60 +77 +860 +878 +7780 6 7 8 9 0 7 6 99 0 7 ~97 09 + 697 98 7 667 897 +689 +7696 +0 +96 + 0 60 9 " 76 8 0 069 90 67 6 06678 77 687 67 806 + +677 + + 6097 8 6 7 8 9 0 + 6 + 69 + + 8 + 0 + 0 + 6 + 9 + 96 7 089 0 9 88 79 89 68 77 90 980 0667 77 6 87 0 67 08 9007 68607 6 6 8807 777 0007 96 9869 06 7 66 6 7 8 9 + 6 + 66 + 709 + 78 + 86 + 08 + 6 + 87 + 8 +089 0 0690 667 6807 + 07 8 760 767 99060 98 0 + 90 +0 +0 +89 +76 +70 +68 +067 +69 +7 +08 +8069 +6 +608 +6678 09 +7 +796 +677 +976 8,70,00,97 0,90,69,60,69,0,,886 9,86,89,8,076 /6 7/ /0

"8 TABLES OF e VALUE8Cntinued) n=90 0 0 +066 + 066 009 0 +0 + 07 00 0 + 998 + 0 7 99 70 + 966 + 69606 9 98 898 + 966 + 87866 967 087 + 870 +0800 99 70 + 8 +0969 98 80 + 7806 +068 7 90 68 + 676 +8868 9 877 780 + 900 +.600 87 97 + 00 +6900 8 076 + 076 +67760 778 00 + 006 +700070 7 79 9 + 986 +69.0; 9 697 7 + 8900 +66700 6 7 7 +6088 60 96 7 +7 69 9 +987 7 99. 6899 6679 +867 9 78 787 +088 8 7 877 + 8886 9 696 69779 + 67779 66 7909 + 8089 7 8 9 8808 + 87 9 088 967 766 7 987 0999 989 + 6 090979 67999 + 00 9 8879 7 + 06 9 66 77 9 + 9 69 7099 9089 6 + 8 7 8999 60987 6 + 76 676 0 796 6 + 7 880 0669 9070 67 + 67 9 98079 0797 69 +77 0 86699 06687 7 + 878 + 698 707 0760 7 + 986 + 7 0 880 7 +097 +97 69 688 77 + +77 67879 986 79 +8 +7 + 966 8860 8 +8 +878 + 766 908 8 +7 +09 + 9609 + 600667 8 +697 +90 +008 +7087 87 +86 +96 + 8996 +760 89 +98 +678 +66 +076,970 7,76,69 7,68,,0 7,7,09,86,60 9,677,06,67,7,60 / / / /0

Z9 TABLES OF e VALUESCntinued) n=9 6 7 8 9 0 6 7 8 9 0 6 7 8 9 0 6 7 8 9 0 6,790 690 689 686 68 67 66 6 6 66 609 90 69 6 9 6 0 66 9 90 9 06 6 6 + 9 + 9 + +0 +7 + + 99 + 66 + + 606 + 679 + 7 + 8 + 90 + 99 +07 +9 +6 +,67, 0 06 08 086 0070 609 698 78 8706 9 07 0978 6 0 70 98 767 96 00 0 89 66 6 80 9 8 068 9686 8 7 808 0 90 + 66 + 9 + 60 + 907 +90 +006 +877 +78 + +970 +08 +00 +09909 + 077 +976 +888 +779 +67 +0 +06 +6 + 979 +77 + 8 + 669 + 0788 86 66 99 86 066 8766 00 7006 886 07 877 066 86 66 87 76 706 086 0 7796 7006 0906 67 006 + 08 +6 +089 +99 +977 +08 + 7788 + 88 + 9 + 6878 + 8 + 9898 +7 +80 +7 +9779 +9 +870 +987 +8960 +988 +8806 +0676 +996 +06 + 907 + 77 + 067 + + 970 7 987 866 0077 96 66 606 76 796696 860 76680 66 00 760 69 7 + 866 +8 +66 +669, 79, S, 90, 89,978, 9,88,9,90,88, 8 /6 7/ 7/0

''60 TABLES OF e V ALUE8Cntinued) n=9 ~I ~I ~I ~I 70 +67 + 860 70 67 +066 + 896 699 0 +08 + 980 7 69 9 +07 +689 9 68 77 +07 +6077 67 + 96077 +97 66 7 + 89986 +998 69 606 + 8986 +778 7 6 678 + 76 +67678 9 6 767 + 666 +8607 9 8 + 707 +009 7 877 + 698 +00 9 97 + 6 +60 7 978 + +60 9 9 07 + +896 6 06 + 6 +06 0967 0 +8799 99 76 +687 7 6 989 +777 9 7 707 +9 8 60 888 +8888 67 7079 +069 99 8 +08 7 9 + 90 9 0 097 0078 + 990 0 08678 670 007 69 8769 + 90 9 9 7 + 07 868 9 87699 9 + 6 787 7 0 6 + 689 768 7088 6 + 87 87 66 0 6 + 6 6 97 67 + 7 8 667 69 + 8 87 0 80689 7 + 99 890 7 + 67 + 799 7 7 + 70 + 99 67 77 + 777 + 67 09 97600 79 + 8 + 766 8 069 8 + 9 +007 + 96 986 8 +07 + + 666 68 8 +0 + +086 +867 87 +87 +8067 +66 +0787 89 +7 +09 +087 +9 9 +6 +97 +67~7 +7707 9, 6,9,0 8,80,067,76 907,80,89,66 696,79,096,7,8 / 7/ 7/0

'6 TABLES OF e VALUE8Cntinued) n=9 6 9 0 6 6 8 +96 +6 +98 +88 +66 + 860 + 6 + 77 + 9 6 7 8 9 087 0 0 970 99 060 6 6 6 8 +0686 +9 +898 +6678 +9796 + 99 + 67 + 886 + 76996 + 68 0 86 799 70 6 7 99 6 06 69 +7 +86 + 89988 + 678 + + 66088 + 6898 + 70760 + 77 + 706 6 7 8 9 87 9 9 90 079 680 776 86 99. 96 + 9896 90 007 77 807 + 699 + 676 + 687 + 98 + 6l 0 6 7 8 9 96 89 70 7 87 + + 90 + 6 990 996 98 9 88 800 69 6 9 0 00 99 87 789 98 00 009 669 + 6666 + 8908 + 098 + 08978 + 0860 + 770 0670 7 7978 8 0 + 8 + 7 + 90 +0 +06 98 76 6 799 669 66 6 7 69 86 6896 76 7878 8 6 7 8 9 + +76 +9 +70 +0 0 6 + + 9 +6 8 876 6 07 606 867 868 87 769690 6688 0 +68 +88 +0 +8 +66 +00 +6 +69 +96 +686 0 + 696 +0 +9798 +7876 09068 098 6806 + 9679 + 699006 6 +9 +86 +60 +679 +76 +88 +86 +766 67,0 7,6, 9,99,6,00,60,00,6 6,0,6,07,9 /6 7/ /0

'i6 TABLES OF e V ALUESCntinued) n=9 68 0 +776 + 90 67 07 +6 + 77 6 9 +8 + 977 7 6 768 +896 +8 9 8 9786 +66 +668 869 +0 +9999 7 897 +80 +99 0 860 +608 +66 7 778 +86 +79888 9 9 +6 +9976 9 +8 + 0 86 +6 +6968 90 0 +08 +760 7 77 7 + 88 +77 9 6 69 + +77 8 80 + 76 +6 89 9 + 97 667 +99 7 97 00 999 +698 9 78 0706 0 +696 8 09 67 +0896 7 097 079 +787 070 667 +089 7 9 068 686 + 8680 9 68 996 98 + 900 8679 99 08 7 707 89 6 +0 6070 679 78 7 + 8 8 80 686 9 + 67 6 99 6 + 97 0069 9779 60 6 +8 77 96 076 6 +60 60 879 67 +9 79 797 69 +7 77 89 9967 7 +6 8 8 0 7 +98 + 8 78 07 7 + + 07 67 89 77 +7 +0087 89 70 79 + +8 88 0888 8 + +76 + 6 88 8 +9 +77 +08 7 8 + +08 +8 09 87 +78 + +776 +6 89 +6 +89 +996 +6 9 +667 +6 +68 +88 9 +7 +688 +8 +89 76,80 0,87, 6,,0,90 89,9,68,88 8,00,08,008, / / / /0

'i6 TABLES OF e VALUE8Cntinued) n=9 ~I ~I ~I ~I 7 7 78 7 76 7 9 6 8 +8608 +8080 +789 +79 +6888 + 0 + 0000 + 977 + 780 6 7 8 9 77 76 70 688 67 687 7609 896 9 +67 + + +768 +90 + 9667 + +77 +00 +09 0 6 6 608 8 6 0 97 09 8 0 +0 + 90 + 768 + 79 + 97 +68 +6899 +700 +766 +7676 6 7 8 9 7 96 6 8 9 0 6 079 7 + 8 + 78 67 607 87 +7 +696 +68 +008 +807 0 68 76 890 967 99 80 8 789 9.';7 0607 787 07 +668 +09 + 8008 + 6 + 960 6 7 8 9 0 7 76 + + 89 + 8 + 09 + 7 + 7 + 0 7 677 09 86 8 07 878 77 9 907 77 807 97 007 0767 0797 06 07 967 + 8 0 8 6988 9 78 688 86 9806 6 7 8 9 + '7 + + 67 + 69 + 769 7 7 + 8 + 869 + 7 79767 67 007 607 7997 088 6 86 098 869 0 + 88 + 99 +0 +097 +8 + 80 +9 +7 + 779 +6 09 + 0 + 79 +689 +808 866 9679 6798 + 07 + 7908 6 7 +7 +6 +7 +8 +9 + +9 +9 +6 +780 +96608 +6 7,0,96,06 7,9, 06,0,7,90,0,90,8,09,7,00 /6 / /60

'6 TABLES OF e VALUE8Cntinued) n=96 0 0 +68 + 897 97 6899 +6 + 6 8 6 +799 + 99 7 67 98 + +9 9 07 +0 +606 78 +08 +98 77 909 +7 + +009 +,9 7 087 7 +898 +7967 9 0 0907 +696 +9697 97 +7 +97 907 7909 +0 +67 8 07 + 999 +6 7 77 99 + 76 +670 9 67 667 + 88 +8 8 899 + 6 +780 87 609 +60 8 67 79 +0000 7 77 6 606 +799 9 6 67 886 +79 0 67 7 +869 97 699 8 +889979 78 668 689 ~ +0787 7 67 600 98 +0860 9 0 687 8 + 667 60 69 + 660 97 6009 80 99 76 70 8677 7 + 88 79 9 + 07 07 9 8009 6 + 87 9 0 0009 6 +67 099 007 789 6 + 86 9 009 66 67 +06 90 9 7 69 +67 07 7898 790 7 +77 9 9807 7 +69 609 06 7 +9 + 0 00 0660 77 + + 89 999 897 79 +77 + 6 7 9987 8 +67 + 87 96007 8 +86 + 706 + 8 867 8 + + 6009 + 889 89 87 +7 + 7979 +797 + 9 89 +67 + 887 + 7 +7009 9 +907 +077 +8 +8799 9 +8 +09 +066 +669 9 +6 +8 +66709 +8777 9,880 07,6, 8 97,70,60,880,6,9,06, 0 87, 06,0,08,90 0/ 7/ /0

~6 TABLES OF e VALUE8Cntinued) n=97 ~ 0 78 0 +7660 0 78 +78 + 9 780 69 +7667 + 976 77 70 +687 + 6 768 90 +7700 + 78 79 +7 + 887 6 78 7 +79 + 67 7 7 89 +07 + 97 8 70 796 +0 + 668 9 70 99 +896 + 979 0 68 8 +66 + 70 66 6 +6 + 909 60 +97 + 060 6 69 + 97 + 06 88 8 + 68 + 76 9 96 + 8 + 088 6 8 080 + 60 + 9886 7 9 79 66 + 887 8 60 6 9 + 66 9 700 + 7 0 8 70 000 + 008 9 86 + 6 00 99 97 + 9806 8 88 + 7889 08 0 070 + 98760 9 7 0 + 688 6 08 8 76 + 660 7 069 706 069 8 0 96 8678 8 9 + 7 7 997 768 0 + 6 096 6088 + 77 6 907 + 0 06 768 7779 + 0 77 06 96087 + 7 008 76 + 08 886 6968 6 + 690 670 96 7 + 8 9 97 998 8 + 660 + 09 08 900 9 + 77 + 7 69 69089 0 + 86 +60 0 778 + 897 +8 7979 + 980 +7 + 7787 668 +06 +9 + 97007 80 + +80 +8680 008 + +60 +878 + 00 6 + +0 +0067 + 8908 7 + +6 +977 + 700799 8 +0 +7 +669 +087 76,08 7,68,096 800,78,00,87,9,67,60,7,068,87,,60 /6 7/ 7/0

,66 TABLES OF e VALUE8Cntinued) n=98 00 0 +8760 + 7900 99 79 +8 + 607 97 9 +806 + 69077 7 9 666 +78 + 7779 9 90 0 +6880 + 7~ 8 8 +7 + 96909 79 09 +88 + 7088 7 60 +88 + 686 7 6 876 +088 + 70886 9 7 +89 + 7676 6 +67 + 800 0 +98 + 880 0 +688 + 89760 7 09 66 + 886 + 8677 9 9 9 + 6 + 866907 80 600 + 0 + 88 6 6 + 88 + 800 7 66 87 + 7909 7 9 677 7 + 77989 9 0 6890 8000 + 6876 90 6970 0 + 6776 69 7009 097 + 90 7 700 7007 + 69 7 696 968 + 888 9 00 6860 60 + 80 7 67 68 + 0669 9 69 6707 8 670 89 98 7 + 6 966 087 697088 9 + 60 9696 6 + 6 8 6 + 96 70 89 6996 6 +8 60 87 706 67 +6 07 886689 69 +9 87 90 9067 7 +0 0 9780 99699 7 +66 7 080600 7 +0 97 08 77 + + 9 09077 08 79 +80 + 80 60 98088 8 +0 + 700 0880 8808 8 +6 + 90 87 7990 8 +0 + 8 + 66 69 87 +6 + 6 +06008 806 89 +90 + 800 +9900 + 9796 9 +6 + 9 +08 + 77 9 +68 +9 +060 + 9607 9 +78 +90 +0088 +88088 97 +776 +7 +69968 +8008,698,7,P0,9,9,60 6,,6,,80,8,698,7,07,760 / / 7/ 7/0.

'67 TABLES OF e VALUE8Cntinued) n=99 ~ ' ~ ' 0 7 8 0 6 86 +99880 +9866 +999 +88906 +806 + 77R6 + 877 + 099 + 9069 6 7 8 9 7 0 8 07 600 769 888 97 06 +6960 +6 +76 +896 +06 + 696 + 9 + 7696 + 80 + 70 0 0 087 08 9 86 6 8 09 86 +8 +606 +66 +0986 + 87 + 676 + 670 + 6600 + 679776 + 680 6 7 8 9 77 68 8 78 67 60 68 678 787 76 + 880 + 66 0 69 667 + 6876 + 6688888 + 66688 + 6978 + 798 0 0 7 998 86 7 780 800 807 80 7876 9660 67 669 868 9 + 90 + 687 + 9866 + 766 + 8676 6 7 8 9 0 7 6 98 + 7 + 0 + + 6 + 87 +08 7600 799 6668 600 96 888 07 889 760 669 88 06 7 97 8 90 609 + 90 + 66 90 86 679 76 9888 0888 60808 680808 6 7 8 9 0 + +8 +67 +88 + +0 +9 +8 +097 +8 70 08 87 + 66 + 0 + 76 +097 +88 +709 870 070 8 089 0 660 08 9 + 996 +76 78809 7990 8788 80670 870 7678996 6898 76 6007 77 6 7 8 9 +6 +898 +77 +6 +7 +080 +77 +89 +68 +80 +0 +0 +6 +706 +76 + 7 + 7786 + 76 +7806 +697776 80,80 7,,70,08,69, 00 7,07,88,6,080,,9,8,09,70 /6 7/ /0

TABLES OF e VALUESCntinued) n=00 7 9 7 9 7 9 7 9 7 9 7 9 6 6 6 67 69 7 7 7 77 79 8 8 8 87 89 9 9 9 97 99,00 8 8 87 8 8 80 79 777 76 7 7 70 677 6 6 9 6 7 9 7 7 8 8 77 + 7 + 97 + 9 + + 89 + 7 + 7 + 99 + 7 + 69 + 77 + 807 + 889 + 97 +09 +7 +7 +9 + +9 +67,7,780 99 787 7 9 699 77 608 0 6 869 7 97 98 6 6069 6707 696 77 776 779 77 70 7 7 799 707 68 60 689 7889 77 80 8 89 067 67 + 7979 + 898 + 079 + + 697 + 789 + 86 +070 +979 +787 +689 + 779688 + 778 + 7600 + 7 + 778 + 687 + 6098 + 60978 + 698 + 08 + 8 + 987 + 800 + 96 + 8888 + 88 + 88 97 7777 967 7687 87 7 9980 6906 606 6997 7777 7977 87 86 88 8987 888 877 8997 7967 787 60 06 96 760 077 + 97 + 6 + 606 + 8j8 +.668 +098 +8888 + 78 + 0968 + 86 + 09 + 7 + 879 + + 998 + 8 + 906 + 676 + 6 + 678 + 6886 + 6860 + 67996 + 6676 + 686 + 609 + 60 + 0877 + 787 + 789 + 096. + 00 + 8 + 97 707 77 67 6 76 706 6966 696 79 798 80 8080 80 7607 6809 679 0869 999 + 707 + 6989 + 77 +8689 +709 96,70,0,700 8,080,76,,600,9,,,600 0 / / /0

'869 TABLES OF e V ALUE~Cntinued) n= lol fi,, 0 80 0 +60 0 C\' 89 7 + 68 + 88 86 +68 + 767 8 80 + 778 +09 8 06 + 8 +0 8 670 + 90 +80 6 8 769 + 996 +68 7 80 868 + 7688 +67 8 786 977 + 098 +78 9 769 0866 + 08 +9776 0 70 9 + 90 +86 79 9. + 98 +00 706 88 + 98 +770 68 7 + 808 +66 6 6 + 9 +6060 6 60 + 9660 +988 6 9 698 + 8 +78 7 6 778 + 78 +88 8 6 8087 87 +068 9 89 806 86 +078 0 0 880 090 +8676 09 90 768 +8 66 97 97 +6 98 69 +8866 7 9076 08 +86 880 80 +090 6 7 899 897 + 78 7 808 0 + 9009 8 66 70 6 9 9 666 778 977 0 + 0 7 996 + 69 6 998 + 7 88 66 888 + 9 0 9008 +06 09 77 8 + 7 8890 90 699 6 + 6 70 960 9960 7 + 9 98 668 98 8 + 9 77 77 70 9 + 67 86 77 60 0 + 70 + 0 90 76 + 8 + 66 9 9778 + 9 + 897 77 0 + 999 +8 ;;6 9067 +086 +89 + 68 0660 +7 +870 + 90 98 6 +66 +7 + + 666 7 +9 +660 + 088 +0096 8 + +0968 + 698 +966 9 + +7 + 8968 +6796 0 +60 +0 +0 +89680 8,80 8,60,80 6,,77,60 7,77,0, 70 9,98,6,6,70 /6 / /0

'>70 TABLES OF e V ALUEBCntinued) n=0 f f 00 60 + 80 + 0 97 779 + 789 + 708 9 9 + 79 978 7 8 806 + 60 + 688 9 70 0 + 0 + 0996 ~ 80 + 7 + 0 7 89 + 079 + 90899 6 760 + 809 + 607 7 9 6 + 9 + 86 9 6 6 + 9 + 8677 07 + 88 + 077 0 7 + 7 + 970 066 80 + 9 + 0790 7 07 60 + 799 + 678 9 98 6 + 9 + 70 90 680 + 870 + 0978 89 708 + 89 + 666 8 7 78 + 998 7 787 7 + 0908 9 70 7670 090 + 80 670 7790 00 + 607 7869 976 + 7 790 8 + 777 7 7 7896 8866 + 00 9 00 780 70 + 780 77 7 + 70 7 779 0 + 88 66 770 06 6 7 8 706 786 660 9 + 678 0 069 6 + 9 60 6 97669 6 +88 96 96 776 6 + 8 60 906 896 67 +8 89 8 7 69 + 8 70 689 7 + 90 0 0 788 7 + 698 77 6 \080 7 + 809 9 808 8 77 + 9 00 90 908 79 +00 0 860 90 8 +60 + 080 0 6 8 +8 + 8 97779 8 +09 + 8 8 06689 87 +8 + 8 76 6008 89 +670 + 60 + 70 7066 9 +80 + 77 + 097 79 9 +9 + 9 + 69 + 67 9 +08 +00 + 9 + 60600 97 +8 +80 + 7 + 0698 99 +7 +68 + 9 + 798 0 + +666 +66 +,70 7,9,780,,,70 87, 69,,060,9,0,68,86,060 / { / /0

~7 TABLES OF e VALUESCntinued) n=0 f ~ I 6 0 88 0 +90 0. 88 6 +006 + 78 880 9 +6097 +6 87 79 +907 + 80 868 00 +00 +087 r 89 0 +86 +87 6 88 +0 +677 7 8 799 +8787 +786 8 80 06 +689 +9808 9 80 6 +78 +6069 0 78 8 +66 + 76 69 +99 +969 70 89 +760 +80 7 08 +07 +607 688 +98 +66 69 + 866 +6 6 68 60 + 070 +66 7 9 689 + 707 +677 8 60 80 686 +697 9 89 + 0 8 970 80 +88 0 97 +9886 00 09 +768 07 8660 +79 08 060 860 +60 9 0 9 + 968 6 08 96 78 + 60060 7 879 09 + 6 8 00 766 98 06 9 6 08 689 0 + 6 69 808 + 77 877 099 + 0 0 98 7 + 0 76 008 9807 + 7 6 0 96 + 9708 9 6 + 770 86790 78796 7 + 8 69 7007 99 8 + 60 9 6 00 9 + 67 079 0 + 76 + 60 760 970.. + 797 + 6 8 09099 + 880 + 778 8788 + 96 +89 0 7 +0 +0 80 060 + + + 9 97 6 + +0 +80 66 7 + +8 +6967 + 69 8 +0 +70 +98 +66 9 + 7 +66 +6 +99 0 +66 +77 +686 +6660 +77 +88 +899 +660 9,0 6,7,76,8,0,90 0,09,9,0,0, 7,9,,660 /6 7/ /60

'7 TABLES OF f VALUESCntinued) n=0. 90 70 +690 + 07 899 89 8099 6 +60 +689 + 60607 +))9 7 889 878 +877 +8977 9 88 07 +8 +7690 87 8.9 98 9 +89 +098 + +687 8 9 +9069 +767 7 9 89 8 ' 9 807 +706 +80 +079 +708 79 9 + +778 769 709 +967 +66 7 607 +689 +779 7 79 679 +8 +86869 9 69 687 +0688 +8909 66 79 + 7 +88709 69 79 + 0 +8069 9 767 + '. 6069 +767 7 9 789 896 +7867 9 8077 60 +787 8 8 9968 +87 9 9 89 868 8 69 +807 +900 7 9 880 09 + 9 0 87 79 +6966 860 6689 +6 99 89 96 + 7608 796 8 + 9 7 89 769 76 707 9 797 6908 806707 6 + 9 70 87 707 6 _ + 9 669 0 8867 6 + 69 06 67 + 8 67 9089 69 + 89 967 69 7009 7 + 9 8 6 787779 7 + 9 9988., 889 7 + 0 697 868 0 77 + 8 79 6 669 79 + 69 87 7780 8 + 79 + 7 807 687 8 + 8 + 86 0 7 8 + 90 + 609 768 887 87 + 99 + 979 06 679 89 +079 + 0 96877 9 +69 + 67977 + 67 0 9 +6 + 87 +70 80 9 + +00 +869 + 6089 97 + +809 +90 +60 99 +9 +66 +600 +9 0 +69 +67 +7 +6897 0 +7 +768 +88 +97680 7,90 67,60,8,9, 0, 90 0,9,908,69,0,9,78,0,,880 0 / 7/ 7/0