NATIONAL BUREAU OF STANDARDS REPORT

2851

Tables of Autoregressive Series

Computation Laboratory

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Sinclair Weeks, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

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Development.

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

1102-40-5126

NBS REPORT

October 12, 1953 2851

Tables of Autoregressive Series

Computation Laboratory

The preparation of this

Office of Naval Research,

report was sponsored by the

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, rep

unless permission is 25,0. C. Such pern

cal ly prepared If th

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

n part, Is prohibited

ndards, Washington

lort has been speclfieort for Its own use,

TABLES OF AUTOREGRESSIVE SERIES

This report contains a number of artifically generated

autoregressive series* compiled for the purpose of testing the

goodness of certain estimates of statistics for stationary time

se ries

The series presented here were generated by means of two

autoregressive schemes*

^ x t+2

~ x t+l

~ x

t + ^t+2

and

(2) x t+2 = 1*1 x t+1 ~ >3 x

t + .09 x

t _x + £ t+2

where the magnitudes E are independently distributed random

numbers. A total of eight series are presented. The first

four are derived from random numbers £ taken from a rectangular

distribution; two of these series are based on scheme (1)* the

other two on scheme (2). The next four series are derived from

random numbers 6^. taken from a Gaussian distribution; again two

of these are based on scheme (1)* two on scheme (2).

For each of these series the statistic

( 3 ) N-r

ZI

5—1

X

s X

s+ r

has been computed for r = 0(1) 30; these values are listed on

pp.24 and

The rectangular numbers were taken from the tables of
2

"Digits of 0(1)9 Drawn at Random" of the Rand Corporation

Pairs of digits were combined into numbers of the set 0( e 01).99,

so that the £ used in these four series actually come from a

V discrete rectangular distribution, whose mean is .

1+95. These

four series of values x were calculated for t ranging from 3

to 300(by putting Xq =x^ =x^ = 0), so that each contains 298

values. Although the summations (3) contain 300 terms, the first

two of these are zero in each case.

The Gaussian random numbers (normal deviates) were taken

from the tables of "Random Gaussian deviates from N(0,1)" of the

2) Rand Corporation. . The original numbers, which are given to 3

decima 1 places, were multiplied by 10 for purposes of presentation,

so that the series given are based on random numbers from

M(0,10) to 2 decimal places. In each series, 300 numbers were

used, giving 300 terms of the series x

t

(t=l (1)300) with

X

0

= X

-1 = x-2

= "°-

In addition to the random number ( £ ) there is a pseudorandom error present in each term x as a result of rounding off

the results of the two or three multiplications occuring in

(1) and (2). The probability distribution of these errors is

not easily ascertained. The limitations of the computing machines

used in the process made it advisable to round each product

separately to 2D (rather than round only the sum of all products).
3

These computations were proposed by M, Rosenblatt and

N, Grenander? of the Statistical Research Center? University of

Chicago? in connection with their investigations on spectral

3) analysis of time series . The computations were sponsored

by the Office of Naval Research under Contract l65~53® They

were carried out by the staff of the Computation Laboratory of

the National Bureau of Standards,, Punched-card machines of

type 604 were used to perform the principal computations*

A related topic is discussed in NBS Report 2776 "Note on

the Simulation of Autoregressive Series".

1) Cf. "A Guide to Tables on Punched Cards"? Math. Tables

and Other Aids to Comp.? V? 36 ? Oct. 1951? P» 209? item 25.1.

Series No, 1? 2? and 3 of this report are taken? respectively?

from cols. 19 and 20? 25 and 26 ? 31 and 32 of cards 0 to 297?

and Series Nof- 4 from cols. 31 and 32 of cards 300 to 597? of

the deck described there.

2) Ibid? item 25„2. The four series of this report are taken

from the second? fourth? sixth? and eighth field? respectively?

of cards 3501 to 3^00.

3) Cf. N. Grenander and M. Rosenblatt? "On Spectral Analysis

of Stationary Time Series"? Memoranda SRC-204l7 Gr Rs 17 and

SRC— 20428 Gr Rs 17? Statistical Research Center? University of

Chicago? April 1952? Also Proc, Nat. Acad. Sci. U.S.A. Vol. 33?

No. 6? June 1952)

.
t

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RECTANGULAR DISTRIBUTION 4

Series No, 1

x t+2

“ x t+l

” x

t + ^ t+2

£

t x

t

t £

t x

t

.00 .00 31 .21 1.04

.00 .00 32 .37 .63

.86 .86 33 .24 .31

.96 1.91 34 .59 .55

.03 1.61 35 .54 .96

.15 .77 36 .42 1.15

.47 .35 37 .86 1.55

.50 .43 38 .41 1.43

.06 .32 39 .04 .68

.92 1.01 40 .79 .68

.48 1.40 41 .46 .80

.78 1.71 42 .51 .98

.07 1.11 43 .04 .64

.32 .51 44 .49 .60

.83 .72 45 .74 1.02

.01 .49 46 .96 1.72

.69 .80 47 .71 1.99

.50 1.09 48 .70 1.86

.15 .87 49 .43 1.29

.14 .45 50 .27 .57

.48 .46 51 .10 - .04

.14 .38 52 .76 .38

.86 1.00 53 .27 .71

.58 1.45 54 .54 1.09

.54 1.54 55 .69 1.46

.40 1.22 56 .49 1.45

.84 1.26 57 .03 .75

.74 1.40 58 .85 .81

.53 1.31 59 .91 1.35

.87 1.47 60 .28 1.28
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

RECTANGULAR DISTRIBUTION

Series No . I 5 x t+2 -1 " 1 x

t-fX

x t 0 69 1.29

.91 1.56

.01 .96

.88 1.00

.57 1.09

.21 .81

.70 .94

.69 1.23

.70 1.49 „ 66 1.56

.31 1.14

.61 .92

.11 .44

.86 .79

.17 .78

.72 1.11

.35 1.10

.72 1.26

.14 .87

.83 1.03

.07 .68

.47 .60

.00 .25

.63 .55

.27 .73

.37 .84

.94 1.42

.10 1.16

.22 .65

.91 .93

x t + € t+2

91 .01 .64

92 .12 .26

93 .84 .75

94 .61 1.28

95 .59 1.55

96 .63 1.57

97 .92 1.72

98 .50 1.45

99 .42 .99

100 .15 .37

101 .73 .55

102 .62 1.01

103 .94 1.72

104 .80 2.08

105 .15 1.41

106 .31 .61

107 .05 - .13

108 .94 .43

109 .73 1.28

110 .02 1.17

111 .17 .69

112 .19 .25

113 .49 .36

114 .42 .67

115 .32 .84

116 .06 .58

117 .08 .22

118 .39 .28

119 .04 .22

120 .28 .35
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

RECTANGULAR DISTRIBUTION

Series No. 1

x

t+2 lo1 x t+l “ ^

x

t + ^ t+2

e t x t

t

.48 .74 151 .31

.86 1.46 152 .77

.26 1.43 153 ,15

. 60 1.29 154 .21

.92 1.48 155 .67

.15 1.01 156 .43

.85 1.07 157 .80

.26 .83 158 .18

.14 .41 159 .60

.15 .10 160 .07

.80 .66 161 .71

.45 1.12 162 .77

.21 1.04 163 .43

.95 1.42 164 .35

.09 1.03 165 .05

.62 .90 166 .87

.46 .83 167 .78

.45 .82 168 .86

.79 1.19 169 .14

.74 1.56 170 .82

,02 1.03 171 .03

.64 .83 172 .94

.93 1.22 173 .19

.76 1.60 174 .60

.20 1.23 175 .61

.00 .39 176 .89

.27 - .04 177 .20

.87 .60 178 .41

.22 .90 179 .05

.47 1.10 180 .22

x

t

1.33

1.31

.79

.29

c52

0 83

L 40

1.22

1.10

.55

066 . 1.17

1.32

lolO

.47

.73

1.30

1.85

1.40

1.25

.57

.82

.75

.94

1.19

1.64

1.29

.85

.22

- .05
RECTANGULAR DISTRIBUTION 7

Series No. 1

X t+2 1,1 x t+l x

t

' ^t+2

t X

t

181 .43 .24

182 .54 .83

183 .21 .98

184 .74 1.32

185 .47 1.33

186 .24 .91

187 .97 1.17

188 .02 .76

189 .80 .94

190 .66 1.23

191 .96 1.75

192 .37 1.56

193 .85 1.52

194 .24 .97

195 .18 .34

196 .36 .15

197 .52 .49

198 .16 .61

199 .17 .55

200 .32 .56

201 .02 .31

202 .70 .70

203 .38 .96

204 .36 1.00

205 .98 1.50

206 .50 1.55

207 .56 1.37

208 .41 .99

209 .83 1.10

210 .22 .84

t

t

211 .72 .98

212 .39 .97

213 .94 1.42

214 .43 1.41

215 .35 1.05

216 .49 .80

217 .41 .66

218 .48 .73

219 .11 .51

220 .95 1.07

221 .36 1.23

222 .58 1,29

223 .40 1.08

224 .69 1.11

225 .90 1.47

226 .81 1.76

227 .35 1.41

228 .36 .85

229 .45 .54

230 .92 1.00

231 .83 1.61

232 .53 1.70

233 .91 1.81

234 .48 1.45

235 .36 .87

236 .55 .64

237 .90 1.08

238 .24 1.05

239 .16 .67

240 .32 .43
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

RECTANGULAR DISTRIBUTION 8

Series No. 1

*t+2

1,1 x t+l • 6,x

t + € t+2

ft x

t

t X

t

.72 .79 271 .58 .94

.82 1.43 272 .01 .61

.74 1.84 273 .43 .54

.08 1.24 274 .36 .58

.01 .27 275 .93 1.25

.69 .25 276 .65 1.68

.36 .48 277 .12 1.22

.35 .73 278 .14 .47

.52 1.03 279 .84 .63

.99 1.68 280 .82 1.23

.41 1.64 281 .25 1.22

.13 .92 282 .80 1.40

.25 .28 283 .24 1.05

.91 .67 284 .26 .58

.18 .75 285 .85 .86

.27 .70 286 .91 1.51

.44 .76 287 .03 1.17

.46 .88 288 .64 1.02

.13 .64 289 .57 .99

.26 .43 290 .87 1.35

,44 .53 291 .96 1.86

.67 .99 292 .15 1.39

.58 1.35 293 .94 1.35

.99 1.89 294 .78 1.44

.45 1.72 295 .28 1.05

.49 1.25 296 .59 .89

.41 .76 297 .67 1.02

.06 .15 298 .23 .82

.99 .70 299 .38 .67

.03 .71 300 .86 1.53
t

1o

L.3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RECTANGULAR DISTRIBUTION 9

Series No, 2 x t+2

= 1#1 *t+l

~ ,6 * x

t + ^ t+2

X

t

t

.00 .00 31 .84

.00 .00 32 .59

.35 .35 33 .25

.52 .91 34 .96

.90 1.69 35 .13

.13 1.44 36 .94

.23 .80 37 .14

.73 .75 38 .70

.34 .69 39 .66

.57 .88 40 .92

.35 .91 41 .79

.83 1.30 42 .88

.94 1.82 43 .90

.56 1.78 44 .54

.67 1.54 45 .12

.66 1.28 46 .10

.60 1.09 47 .02

.77 1.20 48 .01

.82 1.49 49 .51

.60 1.52 50 .17

.68 1.46 51 .53

.75 1.45 52 .40

.28 1.00 53 .08

.73 .96 54 .88

.92 1.38 55 .06

.07 1.01 56 .91

.95 1.23 57 .22

.43 1.17 58 .15

.78 1.33 59 .00

.24 1.00 60 .59

1.14

1.24

.93

1.24

.93

1,22

.92

.98

lol9

1 0 64

1.88

1.97

1.94

1.49

.60

- .13 - .48

- .44

.32

.78

1.20

1.25

.74

.94

.65

1.07

1.01

.62

.07

.30
RECTANGULAR DISTRIBUTION

Series No, 2 X t+2 “ l9i *t+l " ,6 - x t + ^t+2 t X t t X t

61

62

63

64

65

,39

,71

,48

,02

,67

.68

1.28

1.48

.88

.75

91

92

93

94

95

.30

.23

.50

.94

.36

.33 - .05

.24

1.23

1.57

66

67

68

69

70

,99

,71

,66

,43

,27

1,29

1.68

1.74

1.33

.69

96

97

98

99

100

.68

.42

.87

.30

.95

1.67

1.32

1.32

.96

1.22

71

72

73

74

75

,39

,36

,29

.11

,53

.35

.34

.45

.41

.71

101

102

103

104

105

.37

.17

.32

.56

.12

1.13

.68

.39

.58

.53

76

77

78

79

80

,88

,47

.74

.52

.80

1.41

1.59

1.64

1.37

1.33

106

107

108

109

110

.19

.04

.54

.95

.52

.42

.18

.49

1.38

1.75

81

82

83

84

85

.90

,18

,55

.29

.68

1.54

1.07

.81

,54

.78

111

112

113

114

115

.65

.26

.42

.44

.54

1.75

1.14

.62

.44

.65

86

87

88

89

90

.22

,74

.95

.69

.00

.76

1.11

1.71

1.90

1.06

116

117

118

119

120

.76

.92

.04

.49

.80

1.22

1.87

1.37

.88

.95
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

RECTANGULAR DISTRIBUTION 11

Series No . 2

X t+2 x t+i ‘t+1 + £ t+2

Et x

t

t Et x

t

.04 .56 151 .83 1.91

.21 .26 152 .19 1.53

.75 .70 153 .09 .62

.50 1.11 154 .49 .25

0 76 1.56 155 .49 .40

.06 1.11 156 .05 .34

.22 .50 157 .25 .38

.59 .47 158 .05 .27

.12 .34 159 .99 1.06

.94 1.03 160 .00 1.01

.49 1.42 161 .47 .94

.47 1.41 162 .55 .97

.06 .76 163 . 06 .57

.00 - .01 164 .46 .51

.49 .02 165 .22 .44

.78 .81 166 .10 .27

.08 .96 167 .28 .32

.32 .89 168 .04 .23

.90 1.30 169 .87 .93

.25 1.15 170 .49 1.37

.33 .82 171 .24 1.19

.79 1.00 172 .74 1.23

.53 1.14 173 .43 1.07

.21 .86 174 .20 .64

.41 .68 175 .06 .12

.26 .49 176 .18 - .07

.21 .34 177 .20 .05

.20 .28 178 .20 .30

.40 .51 179 .34 .64

.87 1.26 180 .62 1.14
t

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

RECTANGULAR DISTRIBUTION

Series No, 2

*t+2 = la

x t-fi " - 6 x t + £ t+2

.27 1.14 211 .80 .76

.75 1.32 212 .87 1.49 .54 1.31 213 .87 2„05 . 86 1.51 214 .08 1.45

.56 1.43 215 , 66 1.03

.99 1*65, .

216 .95 1.21

.12 1.08 217 .45 1.16

.95 1.15 218 .97 1.52

.38 1.00 219 .89 1.86

.76 1.17 220 .01 1.15

.07 .76 221 .30 .45

.96 1.10 222 .00 - .19

.33 1.08 223 .35 - .13

.63

.10

1.16

.73

224

225

.15

.22

.12

.43

.05 .15 226 .99 1.39

,60 .33 227 .70 1.97

.06 .33 228 .84 2.18

.94 1.10 229 .92 2.14

.97 1.98 230 ,21 1.25

.43 1.95 231 .95 1.05

.35 1.31 232 .65 1.06

.36 .63 233 .42 .96

.87 .77 234 .74 1.16

.95 1.42 235 . 06 .76

.83 1.93 236 .81 .95

.81 2.08 237 .80 1.39

.35 1.48 238 .14 1.10

.37 .75 239 .09 .47

.43 .37 240 .28 .14
RECTANGULAR DISTRIBUTION

Series No, 2

13

x t+2 1,1 x t+l •^' x

t + ^t+2

t x

t

241 „73 60

242 04 62

243 88 1.20

244 61 1.56

245 48 1.48

246 84 1.53

247 58 1.37

248 69 1.28

249 39 98

250 08 39

251 68 52

252 59 93

253 03 74

254 94 1.19

255 78 1.65

256 10 1.21

257 49 83

258 60 78

259 67 1.03

260 62 1.28

261 48 1.27

262 96 1.59

263 20 1.19

264 .07 43

265 47 23

266 75 74

267 68 1.35

268 .08 1.13

269 18 61

270 52 51

£»

271 95 1.14

272 01 95

273 78 1.15

274 30 1.00

275 75 1.16

276 39 1.07

277 73 1.21

278 04 73

279 52 59

280 95 1.16

281 56 1.49

282 36 1.30

283 23 77

284 72 79

285 58 99

286 18 80

287 74 1.03

288 27 92

289 35 74

290 42 68

291 44 75

292 96 1.38

293 47 1.54

294 83 1.69

295 27 1.21

296 75 1.07

297 89 1.34

298 71 1.54

299 41 1.30

300 .62 1.13
t

12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RECTANGULAR DISTRIBUTION lb

Series No.. 3

t+2 x

t+ i

- * 48 x

t + •° 9 xt-i + ^t+2

ft x

t t

.00 .00 31 .03

.00 .00 32 .26

.80 .80 33 .61

.20 1.08 34 .54

.15 .96 35 .77

.88 1.49 36 .13

.98 2.26 37 .93

.65 2.51 38 .86

.86 2.67 39 .18

.73 2.67 40 .66

.28 2.17 41 .59

.60 1.95 42 .01

.60 1.95 43 .39

.29 1.70 44 .88

.18 1.29 45 .25

.90 1.68 46 .74

.93 2.31 47 .05

.73 2.58 48 .52

.21 2.09 49 .56

.45 1.72 50 .09

.76 1.88 51 .32

.96 2.39 52 .10

.94 2.82 53 .83

.53 2.65 54 .91

.57 2.36 55 .27

.96 2.54 56 .95

.43 2.33 57 .20

.65 2.20 58 .04

.82 2.35 59 .32

.91 2.65 60 .28

2.02

lo42

1.44

lo62

lo99

1 0 67

1.96

2.40

2.03

1.92

1.95

1 0 42

1 0 18

1 0 68

1.66

lo87

lo46

1.38

lo55

1.27

1.10

.84

lo33

2 o 07

1.99

2.27

1.93

1.25

.97

.92
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

RECTANGULAR DISTRIBUTION

Series No. 3

15

x t+2 x t+l ,!+ ^ x

t +

X

t

.55 1.20

.48 1.45

.51 1.61

.74 1.92

.07 1.54

.42 1.33

.74 1.63

.58 1.87

.73 2.13

.61 2.20

.85 2.42

.45 2.24

.74 2.24

.47 2.07

.75 2.15

.49 2.07

.08 1.52

.23 1.10

.05 .72

.77 1.17

.53 1.57

.43 1.66

.23 1.42

.17 1.07

.82 1.47

.08 1.32

.17 1.01

.28 .89

.12 .74

.83 1.30

.09 x

t _2 + ft+2

t x

t

91 .63 1.78

92 .88 2.29

93 .17 1.96

94 .63 1.85

95 .69 2.00

96 .76 2.25

97 .26 1.95

98 .49 1.74

99 .12 1.29

100 .97 1.73

101 .85 2.29

102 .45 2.26

103 .84 2.39

104 .29 2.05

105 .59 1.90

106 .76 2.09

107 .29 1.86

108 .61 1.83

109 .17 1.48

110 .10 1.02

111 .35 .92

112 .35 1.00

113 .01 .76

114 .70 1.14

115 .11 1.09

116 .78 1.50

117 .27 1.50

118 .88 1.91

119 .74 2.26

120 .28 1.99
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

RECTANGULAR DISTRIBUTION

Series No, 3

x t+2

~ lal x t+l

“ x

t + * 09 x t-l

+ ^t+2

x

t

t £ t x

t

.74 2.02 151 .46 1.27

.65 2.11 152 .47 1.38

.74 2.27 153 .64 1.67

.61 2.28 154 .01 1.30

.76 2.37 155 .72 1.47

.11 1.83 156 .06 1.21

.92 2.00 157 .57 1.31

.01 1.54 158 .09 1.08

.55 1.44 159 ,61 1.28

.66 1.68 160 .46 1.47

.96 2.26 161 .26 1.37

.43 2.24 162 .87 1.79

.71 2.24 163 .73 2.17

.92 2.50 164 .47 2.12

.04 1.91 165 .43 1.88

.45 1.55 166 .53 1.78

.15 1.17 167 .30 1.55

.01 .73 168 .17 1.20

.38 .76 169 .59 1.33

.66 1.26 170 .83 1.85

.54 1.64 171 .09 1.60

.72 1.99 172 .98 1.97

.18 1.69 173 .95 2.52

.74 1.79 174 . 66 2.62

.32 1.66 175 .80 2.65

.78 1.90 176 .55 2.44

.62 2.07 177 .95 2.60

.12 1.64 178 .90 2.83

.76 1.74 179 .68 2.76

.05 1.36 180 .36 2.27
RECTANGULAR DISTRIBUTION 17

Series No„ 3 x t+2 lo1 x t+l

181 .92 2.35

182 .21 1.96

183 .91 2.14

184 .98 2.60

185 .96 2.97

186 .39 2.60

187 .58 2.24

188 .47 1.95

189 .11 1.41

190 .69 1.50

191 .14 1.29

192 .62 1.45

193 .78 1.90

194 .26 1.77

195 .78 1.95

196 .15 1.62

197 .55 1.55

198 .75 1.86

199 .87 2.33

200 .30 2.11

201 .73 2.10

202 .21 1.72

203 .86 1.93

204 .31 1.79

205 .03 1.22

206 .06 .71

207 .36 .71

208 .71 1.26

209 .03 1.14

210 .58 1.29

t + -O 9 x

t_ 1 + £t+2

£t

211 .49 1.47

212 .35 1.45

213 .70 1.71

214 .34 1.65

215 .72 1.85

216 .06 1.46

217 .23 1.10

218 .70 1.38

219 .29 1.41

220 .52 1.51

221 .21 1.31

222 .94 1.79

223 .14 1.62

224 .87 1.91

225 .52 2.00

226 .71 2.14

227 .64 2.20

228 .69 2.26

229 .02 1.64

230 .18 1.10

231 .72 1.34

232 .54 1.63

233 .86 2.11

234 .23 1.89

235 .54 1.76

236 .29 1.51

237 .07 1.06

238 .92 1.53

239 .18 1.49

240 .10 1.11
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

RECTANGULAR DISTRIBUTION

Series No. 3

1! + CM lol X

t+ JL “ ^5 xt + -09 x

t_x + e t+2

X

t

t £t X

t

.95 1.59 271 .87 1.46

.93 2.28 272 .28 1.54

.43 2.28 273 .62 1.70

.46 2.02 274 .79 2.05

.71 2.05 275 .72 2.30

.42 1.92 276 .95 2.65

.54 1.85 277 .59 2.59

.99 2.29 278 .27 2.06

.77 2.57 279 .92 2.19

.23 2.13 280 .02 1.67

.19 1.51 281 .12 1.10

.81 1.68 282 .36 .97

.01 1.33 283 .71 1.40

.93 1.72 284 .69 1.86

.73 2.13 285 .96 2.43

.54 2.17 286 .56 2.47

.85 2.3? 287 .39 2.11

.41 2.17 288 .79 2.14

.88 2.33 289 .25 1.81

.37 2.10 290 .53 1.68

.08 1.47 291 .45 1.62

.94 1.76 292 . 66 1.79

.67 2.09 293 .23 1.57

.55 2.14 294 .61 1.63

.54 2.05 295 .62 1.82

.87 2.29 296 .58 1.94

.50 2.23 297 .49 1.90

.10 1.63 298 .19' 1.51

.34 1.27 299 .19 loll

.13 .95 300 .25 .92
t

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RECTANGULAR DISTRIBUTION

Series No 0 ^

x

t+2 = ia x t+i " x

t + -°9 x t-i + et+2

19

£ t t

£t X

t

00 o 00

00 .00

84 .84

55 1.47

25 1.47

31 .32 1.45

32 .29 1.30

33 .91 1.78

34 .07 1.54

35 .57 1.53

71 1.70

34 1.63

57 1.67

50 1.71

44 1.67

36 .27 1.37

37 .13 1.05

38 .54 1.18

39 .66 1.58

40 .03 1,29

95 2.12

64 2.32

16 1.84

46 1.56

54 1.59

41 .16 .93

42 .47 1.01

43 .20 .98

44 . 16 .84

45 .84 1.38

64 1.81

61 1.98

23 1.68

01 1.07

79 1.34

46 .58 1.79

47 .65 2.04

48 .89 2.39

49 .91 2.72

50 .49 2.51

19 1.30

50 1.39

05 1.08

86 1.50

62 1.88

51 .39 2.06

52 .79 2.10

53 .29 1.84

54 .95 2.15

55 .61 2.29

22 1.67

58 1.66

76 1.96

01 1.52

65 1.53

56 .28 1.94

57 .07 1.29

58 .31 1.01

59 .70 1.36

60 .65 1.79
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

RECTANGULAR DISTRIBUTION 20

Series No 0 b

x t+2 1.1 x t+1

- .48 x

t + .09 x

t _1 + £ t+ 2

X

t

t x

t

.80 2.21 91 .96 2.36

„20 1.89 92 .57 2.43

.75 1.93 93 .31 2.02

.94 2.35 94 .91 2.17

.21 2.04 95 .03 1.67

.11 1.39 96 .72 1.70

.32 1.08 97 .94 2.21

.70 1.40 98 .57 2.33

.81 1.96 99 .40 2.05

.36 1.95 100 .05 1.39

.35 1.69 101 .45 1.21

.05 1.15 102 .78 1.62

.93 1.57 103 .97 2.30

.48 1.81 104 .00 1.86

.47 1.81 105 .48 1.58

.86 2.12 106 .89 1.95

.84 2.46 107 .48 2.04

.55 2.40 108 .28 1.72

.19 1.84 109 .06 1.15

.75 1.84 110 .68 1.30

.67 2.03 111 .83 1.86

.67 2.19 112 .63 2.16

.81 2.42 113 .71 2.32

.65 2.44 114 .94 2.62

.84 2.56 115 .02 1.98

.82 2.69 116 .17 1.30

.52 2.47 117 .81 1.53

.26 1.92 118 .91 2.15

.55 1.71 119 .70 2.46

.68 1.86 120 .11 1.93
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

RECTANGULAR DISTRIBUTION

Series No. b

21

x

t+2 x t+l x

t + x t-l

+ £ t+2

St x

t

t St x

t

.88 2.01 151 .43 1.13

.08 1.58 152 .37 1.18

o 50 1.45 153 .91 1.78

,86 1.88 154 .65 2.14

,22 1.73 155 .57 2.18

, 16 1.29 156 .19 1.72

,62 1.38 157 .99 2.02

,05 1.11 158 .32 1.91

,99 1.67 159 .10 1.38

,26 1.69 160 .04 .82

,33 1.49 161 .68 1.09

.38 1.36 162 .89 1.82

,38 1.31 163 .79 2.34

.85 1.77 164 .47 2.27

,55 1.99 165 .45 1.99

.89 2.35 166 .94 2.25

.95 2.74 167 .34 2.06

.48 2.54 168 .16 1.53

.58 2.26 169 .84 1.73

.63 2.15 170 .78 2.14

.62 2.14 171 .08 1.74

.89 2.41 172 .26 1.30

.42 2.23 173 .82 1.60

.89 2.37 174 .99 2.29

.97 2.73 175 .93 2.80

.17 2.23 176 .84 2.96

.65 2.00 177 .35 2.48

.65 2.03 178 .08 1.64

.20 1.67 179 .82 1.70

.15 1.20 180 .07 1.37
RECTANGULAR DISTRIBUTION

Series No« 4

x t+2

= l.i x t+1 - .48 x

t + •°9 xt_ x + 4+2

t x

t

t 4 x t

181 = 76 1=60 211 = 40 1=20

182 o 07 1=32 212 = 54 1=42

183 = 59 1=39 213 = 24 1=33

184 = 11 1=15 214 = 39 1=28

185 = 10 = 82 215 = 91 1=81

186 = 48 = 96 216 = 11 1=61

187 = 84 1=61 217 = 38 1=40

188 = 75 2=13 218 = 80 1=73

189 = 79 2=45 219 = 46 1=83

190 = 46 2=28 220 = 87 2=18

191 = 28 1=80 221 = 01 1=69

192 = 89 2=00 222 = 45 1=42

193 = 47 2=02 223 = 24 1=19

194 = 85 2=27 224 = 11 = 89

195 = 40 2=11 225 = 01 = 55

196 = 31 1=72 226 = 84 1=13

197 .90 1=98 227 = 17 1=23

198 = 28 1=82 228 = 55 1=41

199 = 16 1=36 229 = 75 1=81

200 = 61 1=42 230 = 71 2=13

201 = 06 1=13 231 = 28 1=88

202 = 58 1=26 232 = 49 1=70

203 = 31 1=29 233 = 30 1 = 46

204 = 84 1=76 234 = 69 1=65

205 = 08 1=51 235 = 03 1=30

206 = 64 1=58 236 = 78 1=55

207 = 74 1=92 237 = 46 1=70

208 = 02 1=51 238 = 65 1=90

209 = 43 1=31 239 = 45 1=86

210 = 28 1=17 240 .50 1=79
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

RECTANGULAR DISTRIBUTION

Series No 0 *+

23

x t+2 lo1 x t+l

oLf8 x

t + °°9 x t-l

+ ^t+2

X

t

t ft X

t

.51 1.76 271 .57 1.90

.59 1.84 272 .83 2.14

.25 1.59 273 .59 2.21

.31 1.34 274 .57 2.14

.41 1.29 275 .87 2.35

.06 .98 276 .25 2.01

.58 1.16 277 .75 2.02

.60 1.53 278 .43 1.90

.74 1.95 279 .43 1.73

.23 1.75 280 .18 1.35

.84 1.97 281 .49 1.32

.38 1.89 282 .90 1.86

.82 2.11 283 .42 1.96

.10 1.69 284 .39 1.78

.53 1.55 285 .56 1.75

.91 2.00 286 .36 1.62

.64 2.25 287 .67 1.77

.69 2.35 288 .52 1.85

.10 1.79 289 .05 1.39

.56 1.60 290 .63 1.43

.68 1.79 291 .71 1.78

.34 1.70 292 .11 1.51

.83 1.98 293 .73 1.67

.31 1.83 294 .95 2.23

.20 1.41 295 .94 2.73

.39 1.24 296 .69 2.77

.58 1.42 297 .43 2.37

.59 1.68 298 .47 2.00

.92 2.20 299 .26 1.57

.30 2.04 300 .80 1.78
r

0

12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RECTANGULAR DISTRIBUTION 24- N-r

C

p = r. xtxt+ r

Se rie

s

Series

No. 1 No. 2

340 o 99 366.17

318.83 343.11

284.99 305.49

262.91 275.77

260.41 265.78

270.01 271.14

281.44 280.24

284.31 285.54

280.13 284.30

274.42 280.20

270.18 280.30

268.72 284.67

267.02 287.92

264.56 288.19

262.41 284.00

263.97 276.51

267.55 267.39

271.45 263.50

271.77 267.52

269.20 274.82

264.28 277.49

259.82 274.09

257.24 267.02

256.95 258.49

258.18 253.68

258.03 256.97

255.50 262.47

252.97 265.40

254.29 262.83

254.56 258.93

253.08 254.10

Series Se rie

No. 3 No. 4-

1004.49 981.59

988.70 964.25

967.26 941.63

949.06 926.91

935.35 918.99

926.76 913.34

921.32 907.25

919.02 902.22

917.38 899.41

916.55 895.28

914.71 890.82

909.46 888.86

900.80 887.98

894.41 885.60

889.39 880.71

885.60 877.48

881.41 875.65

876.88 873.39

873.18 871.89

870.25 871.26

867.82 872.98

862.79 876.26

855.46 873.40

849.13 865.90

842.44 859.05

837.34 854.41

835.75 851.24

834.70 848.19

834.48 843.82

832.96 839.20

830.99 837.19
t

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

NORMAL DISTRIBUTION 25

Series No e 1

x t+2 101 x t+l

~ - 6 x

t + £ t+2

ft *t

t ft x

t

- 4.81 - 4.81 31 1.93 36.63

- 5.75 -11.04 32 - .06 13.66

- .99 -10.24 33 3.03 - 3192

16.18 11.54 34 - .02 -12.53

.73 19.56 35 - 1.63 -13.06

2.16 16.76 36 - .23 - 7.08

- 5.09 1.61 37 - 3.20 - 3.15

- 7.19 -15.48 38 .43 1.21

- 2.97 -20.97 39 7.54 10.76

- 8.68 -22.46 40 .67 11.78

3.20 - 8.93 41 .43 6.93

-20.99 -17.33. 42 -18.27 -17.72

16.90 3.20 43 .36 -23.29

-11.13 2.79 44 - 2.61 -17.60

6.25 7.40 45 - 5.24 -10.63

23.37 29.84 46 - 9.28 -10.41

.62 29.00 47 -13.73 -18.80

.11 14.11 48 - 2.07 -16.50

5.23 3.35 49 - 1.01 - 7.88

- 4.03 - 8.81 50 - 2.89 - 1.66

-17.21 -28.91 51 7.16 10.06

10.92 -15.59 52 4.67 16.74

- 8.47 - 8.27 53 - 5.69 6.68

- 5.62 - 5.37 54 11.50 8.81

- 4.59 - 5.54 55 - 3.60 2.08

- 5.10 - 7.97 56 4.04 1.04

- 4.15 - 9.60 57 1.99 1.88

6.86 1.08 58 .82 2.27

16.41 23.36 59 -17.57 -16.20

19.24 44.29 60 1.15 -18.03
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

NORMAL DISTRIBUTION 26

Series No. 1

x t+2

= lo1 x t+l x

t +

^ t+2

x

t

t £t X

t

9.16 - .95 91 -17.60 -47.51

- 9.78 - .01 92 - .20 -35.14

- 1.93 - 1.37 93 8.05 - 2.09

18.87 17.37 94 13.33 32.11

3.31 23.24 95 5.46 42.03

- 3.27 11.87 96 - 8.56 18.40

14.46 13.58 97 4.23 - .75

10.95 18.77 98 20.25 8.38

3.64 16.14 99 1.97 11.64

6.12 12.61 100 13.01 20.78

5.28 9.47 101 - 3.75 12.13

- 5.16 - 2.31 102 1.67 2.54

.57 - 7.65 103 - 4.74 - 9.23

- 2.36 - 9.39 104 8.57 - 3.10

- .83 - 6.57 105 - 5.22 - 3.09

- 9.90 -11.50 106 - .29 - 1.83

6.70 - 2.01 107 -14.32 -14.48

2.75 7.44 108 -27.45 -42.28

9.19 18.58 109 - 2.01 -39.83

- 1.28 14.70 110 7.61 -10.83

- 1.41 3.61 111 -20.80 - 8.81

4.74 - .11 112 - 6.65 - 9.84

- 7.05 - 9.34 113 18.21 12.68

21.83 11.63 114 - 1.51 18.34

15.31 33.70 115 - .23 12.33

18.90 48.99 116 12.83 15.39

10.84 44.51 117 6.84 16.37

5.86 25.43 118 - 4.22 4.56

- 4.33 - 3.07 119 - 4.95 - 9.75

-10.22 -28.86 120 9.24 - 4.23
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

NORiviAL distribution 27

Series No 6 1

x t+2

= la x t+l " " 6 x

t + St+2

ft X

t

t ft x

t

2.92 4.12 151 -30.98 - 45.26

- 3.69 3.38 152 2.35 -33.53

- .84 .41 153 5.49 - 4.23

- 3.19 - 4.77 154 - 9.19 6.28

1.90 - 3.60 155 6.61 16.06

8.08 6.98 156 - 6.98 6.92

- 16.37 - 6.53 157 - 13.94 - 15.97

- 10.79 - 22.16 158 5.61 - 16.11

4.81 - 15.65 159 - 1.38 - 9.52

10.06 6.14 160 -20.78 - 21.58

- 3.65 12.49 161 - 10.27 - 28.30

- 19.63 - 9.57 162 9.74 - 8.44

.95 - 17.07 163 - 10.07 - 2.37

- 5.78 - 18.82 164 4.22 6.67

3.52 - 6.94 165 9.22 17.98

16.45 20.11 166 .07 15.85

1.19 27.47 167 - 5.50 1.15

- 17.70 .45 168 - 2.92 - 11.16

10.44 - 5.54 169 4.61 - 8.36

- 12.44 - 18.80 170 - 9.83 - 12.33

- 4.24 - 21.60 171 - .32 - 8.86

4.02 - 8.46 172 1.90 - .45

- .08 3.57 173 - 12.21 - 7.39

- 5.46 3.55 174 2.68 - 5.18

21.94 23.71 175 - 2.28 - 3.55

10.97 34.92 176 - 9.02 - 9.82

- .12 24.06 177 - .71 - 9.38

- 7.57 - 2.05 178 5.33 .90

- 2.00 - 18.70 179 6.47 13.09

- 3.84 - 23.18 180 - 8.36 5.50
t

181

182

183

184

185

3 86

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

NORMAL DISTRIBUTION 28

Series No. 1

x t+2

= la x t+l” - 6 x

t + £t+2

6t x t

t x

t

3.03 1.23 211 - 1.15 - .57

-25.01 -26.96 212 1.31 2.14

- 3.59 -33.99 213 1.08 3.77

1.71 -19.50 214 - 7.83 - 4.96

1.83 .77 215 20.34 12.62

6.71 19.26 216 - 4.87 11.99

- 1.86 18.87 217 - 4.59 1.03

-11.65 - 2.45 218 - 8.47 -14.53

2.26 -11.76 219 - 7.62 -24.22

- 1.06 -12.53 220 - .97 -18.89

.15 - 6.57 221 11.59 5.34

1.52 1.81 222 1.84 19.04

-15.38 - 9.45 223 15.13 32.87

- 8.25 -19.74 224 -19.51 5.23

8.99 - 7.05 225 -10.86 -24.83

2.65 6.73 226 - 3.97 -34.42

- 5.89 5.74 227 - 8.63 -31.59

-16.80 -14.53 228 - 2.70 -16.80

- 9.37 -28.79 229 3.48 3.95

8.11 -14.84 230 - 7.12 7.31

- 9.24 - 8.29 231 6.96 12.63

2.06 1.84 232 -18.85 - 9.35

3.84 10.83 233 - 1.49 -19.36

-10.23 .58 234 - 8.64 -24.33

12.93 7.07 235 3.09 -12.05

- 2.19 5.24 236 11.65 12.99

2.13 3.65 237 - .48 21.04

5.02 5.90 238 12.23 27.58

- 9.73 - 5.43 239 4.22 21.94

7.07 - 2.44 240 - 7.81 - .23
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

NORiviAL DISTRIBUTION 29

Series No. 1

x

t+ 2 = lo1 x t+l 06 xt + ^ t+2

St

X

t

t St X

t

12.30 - 1.11 271 22.05 40.57

- 15.03 - 16.11 272 - 1.12 34.01

- 11.11 - 28.16 273 - 1.19 11.88

- 2.99 - 24.30 274 13.54 6.20

- 2.05 - 11.88 275 15.93 15.62

.90 2.41 276 - 7.42 6.04

- 11.90 - 2.12 277 13.70 10.97

10.21 6.43 278 - 9.14 - .69

- 8.02 .32 279 - 8.35 - 15.69

- 9.95 - 13.46 280 10.00 - 6.85

- 6.17 -21.17 281 8.47 10.34

12.22 - 2.99 282 2.58 18.06

15.08 24.49 283 19.12 32.79

9.73 38.46 284 4.68 29.91

20.09 47.71 285 3.87 17.10

- 1.09 28.31 286 1.23 2.09

- 2.94 - .43 287 - 2.01 - 9.97

2.62 - 14.84 288 - 9.19 -21.41

- 18.75 -34.81 289 - 10.57 - 28.14

- 5.15 - 34.54 290 .59 - 17.51

20.17 3.07 291 - 4.61 - 6.99

12.30 36.40 292 5.35 8.17

- 9.12 29.08 293 - 1.16 12.02

1.73 11.88 294 - 2.18 6.14

- 10.51 - 14.89 295 - .86 - 1.32

- .48 -23.99 296 8.92 3.79

.86 - 16.60 297 12.17 17.13

- 3.89 - 7.76 298 13.89 30.46

- 3.27 - 1.85 299 9.21 32.44

13.21 15.83 300 - 4.62 12.78
t

12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

NORMAL DISTRIBUTION 30

Series No. 2

x t+2

= la x t+l

‘ - 6 x

t + £t+2

X

t

t x

t

2 0 97 2.97 31 -16.65 -14.29

12.05 15.32 32 - 6.30 -30.53

2.93 18.00 33 - 4.69 -29.70

- 2.94 7.67 34 - .13 -14.48

6.46 4.10 35 - 1.43 .46

7.03 6.94 36 5.82 15.02

11.53 16.70 37 - .97 15.27

4.91 19.12 38 13.13 20.92

- 4.40 6.61 39 - .86 12.99

- 3.47 - 7.67 40 -11.81 -10.07

- 8.25 -20.66 41 8.88 - 9.99

- 2.87 -21.00 42 - 2.86 - 7.81

5.75 - 4.95 43 11.12 8.52

.33 7.48 44 3.84 17.90

- 4.20 7.00 45 5.12 19.70

16.07 19.28 46 - 1.59 9.34

- 1.35 15.66 47 3.74 2.19

4.61 10.27 48 -15.88 -19.07

- 2.00 - .10 49 - 9.37 -31.66

-17.40 -23.67 50 - 8.90 -32.29

16.71 - 9.27 51 10.86 - 5.66

- 8.81 - 4.81 52 - 4.98 8.16

- .24 .03 53 - 4.98 7.40

- .86 2.06 54 4.99 8.23

- 1.86 .39 55 - 5.32 - .71

1.01 .20 56 -13.30 -19.02

13.19 13.18 57 - 5.49 -25.98

5.86 20.24 58 -11.01 -28.18

7.71 22.06 59 -11.10 -26.51

2.05 14.18 60 - 9.37 -21.62
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

NORMAL DISTRIBUTION 31

Series No s 2

x t+2

= 1,1 x t+l x

t + ^ t+2

X

t

t x

t

- 8.85 -16.72 91 - 8.86 - .85

-14.36 -19.78 92 3.89 - 4.78

.60 -11.13 93 - 2.42 - 7.17

- 1.97 - 2.34 94 .86 - 4.16

- 8.60 - 4.49 95 12.32 12.04

5.99 2.45 96 3.24 18.98

- 1.50 3.89 97 7.73 21.39

6.91 9.72 98 -13.32 - 1.18

- 5.90 2.46 99 18.41 4.28

14.93 11.81 100 -13.54 - 8.12

9.14 20.65 101 -18.63 -30.13

6.99 22.62 102 3.47 -24.80

17.85 30.34 103 -24.61 -33.81

18.33 38.13 104 14.13 - 8.18

10.22 33.96 105 13.60 24.89

- 2.08 12.40 106 - 3.53 28.76

- 3.46 -10.20 107 16.70 33.41

4.43 -14.23 108 11.88 31.37

- 3.78 -13.31 109 5.13 19.59

- 2.78 - 8.88 110 18.09 20.82

-11.25 -13.03 111 - 5.91 5.24

15.58 6.58 112 - .91 - 7.64

- 9.56 5.50 113 - 1.16 -12.70

- 1.26 .84 114 - 3.51 -12.90

- 9.64 -12.02 115 4.72 - 1.85

10.70 - 3.02 116 - 7.38 - 1.68

4.17 8.06 117 2.12 1.38

3.62 14.30 118 1.61 4.14

- .60 10.29 119 - 9.98 - 6.26

10.15 12.89 120 12.78 3.41
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

NORMAL DISTRIBUTION 32

Series No. 2

x t+2

= ia x t+l

~ - 6 x

t + ft+2

x

t

t St X

t

- o22 7.29 151 8.68 9.29

-11.46 - 5.49 152 -10.03 - 2.46

.76 - 9.65 153 3.62 - 4.66

4.33 - 3.00 154 - 3.14 - 6.79

- 7.81 - 5.32 155 10.06 5.39

-13.29 -17.34 156 -13.72 - 3.72

16.88 1.00 157 - .24 - 7.56

-16.59 - 5.09 158 -14.96 -21.05

- 8.75 -14.95 159 9.00 - 9.62

5.16 - 8.24 160 - 6.45 - 4.40

2.76 2.67 161 .34 1.27

-16.24 - 8.36 162 7.04 11.08

-14.13 -24.93 163 - 4.80 6.63

7.14 -15.26 164 14.57 15.21

-12.42 -14.25 165 -12.35 .40

- .12 - 6.64 166 - 3.50 -12.19

- .02 1.23 167 - 8.56 -22.21

1.06 6.39 168 1.42 -15.70

8.29 14.58 169 2.97 - .97

11.35 23.56 170 - 8.26 .09

10.21 27.38 171 7.39 8.07

14.55 30.53 172 - 6.10 2.73

3.73 20.88 173 5.80 3.96

6.09 10.74 174 -12.36 - 9.64

6.78 6. 06 175 11.23 - 1.75

-10.78 -10.55 176 - 6.03 - 2.18

8.22 - 7.03 177 7.45 6.10

5.60 4.20 178 - 8.76 - .74

- 1.78 7.06 179 3.37 - 1.10

- .84 4.41 180 18.44 17.67
NORMAL DISTRIBUTION

Series No„ 2

33

x t+2 loi x t+i 06 x

t + ^t+2

t

£t X

t

t 6t X

t

181 -ii.il 8.99 211 - 18.57 - 14.73

182 15.55 14.84 212 9.35 - 3.12

183 6.12 17.05 213 - 18.30 - 12.89

184 - 4.68 5.18 214 7.31 - 5.00

185 - 3.68 - 8.21 215 3.43 5.66

186 .40 - 11.74 216 - 2.78 6.45

187 - 13.45 - 21.43 217 10.41 14.11

188 18.03 1.50 218 8.64 20.29

189 1.79 16.30 219 10.48 24.33

190 14.00 31.03 220 2.49 17.08

191 - 17.40 6.95 221 - 7.41 - 3.22

192 - 7.37 - 18.34 222 12.20 - 1.59

193 .96 - 23.38 223 - 16.39 - 16.21

194 10.64 - 4.08 224 - 2.01 - 18.89

195 - 2.93 6.61 225 - 6.87 - 17.92

196 2.72 12.44 226 4.73 - 3.65

197 1.60 11.31 227 17.46 24.19

198 - 13.52 - 8.54 228 - 7.16 21.64

199 4.77 - 11.41 229 18.36 27.65

200 6.59 - .84 230 -36.42 - 18.98

201 2.53 8.46 231 - 19.54 - 57.01

202 1.88 11.69 232 - 3.26 - 54.58

203 4.96 12.74 233 - 3.78 -29.61

204 - 2.96 4.04 234 - 19.23 - 19.05

205 2.20 - 1.00 235 - 6.07 - 9.26

206 7.30 3.78 236 - 9.40 - 8.16

207 - 3.13 1.63 237 17.00 13.58

208 - 17.00 - 17.48 238 11.73 31.57

209 2.43 - 17.78 239 3.29 29.87

210 2.86 - 6.21 240 .14 14.06
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

NORMAL DXSTiUPTOQN 3^ Series No, 2

x t+2 = 1.1 x t+1 - .6 x

t

+ i t+2

it x

t

t x

t

- 9.75 - 12.20 271 - 9.00 - 8.19

4.73 - 17.13 272 10.03 - 1.76

- 11.44 -22.96 273 - 7.41 - 4.44

16.63 1.65 274 - ,23 - 4.05

- 10.86 4.74 275 11.29 9.49

- 2.81 1.41 276 - 1.78 11.09

- 14.05 - 15.34 277 - 5.81 .70

2.81 - 14.91 278 4.04 - 1.84

- 10.07 -17.27 279 5.85 3.41

16.35 6.30 280 3.05 7.90

10.69 27.98 281 - 6.51 .13

- 17.04 9.96 282 20,31 15.71

- 7,63 - 13.46 283 17,96 35.16

2.31 - 18.48 284 - 16.68 12,57

2.18 - 10.07 285 - 13.57 -20.84

15.93 15.94 286 - .72 -31.18

9.77 33.34 287 7.75 -14.05

18.87 45.98 288 - 2.23 1.02

4.89 35.47 289 - 13.54 - 3,99

- 2.09 9.34 290 1.87 - 3.13

17.83 6.82 291 - 6.20 - 7.25

- 4.47 - 2.57 292 .03 - 6.07

11.53 4.61 293 - 8.03 - 10,36

- 5.08 1.53 294 - 16.18 -23.94

11,58 10.49 295 - 11.79 - 31.90

- 5.13 5.49 296 4.07 - 16.66

- 2,81 - 3.06 297 18.29 19.10

3.91 - 2.75 298 - 13,78 17.23

8.33 7.14 299 18.30 25.79

- 4.87 4.63 300 - 1.80 16.23
NORMAL DISTRIBUTION

Series No. 3

35

x

t+2 = la x t+l ‘ ' h8 x

t + •°9 x

t-1 + £t+2

t x

t

1 12.28 12.28

2 - 13 o 39 .12

3 - 17.78 -23.54

4 - 1.47 - 26.31

5 - 4.08 - 21.71

6 8.19 - 5.18

7 - 15.56 - 13.21

8 11.30 - 2.69

9 - 2.63 .28

10 11.29 11.70

11 .50 13.00

12 - 2.61 6.10

13 - 10.93 - 9.41

14 2.36 - 9.75

15 2.72 - 2.94

16 9.20 9.80

17 24.00 35.31

18 - 3.54 30.34

19 - 4.20 13.10

20 1.12 4.15

21 - 11.35 - 10.34

22 2.13 - 10.05

23 - 1.53 - 7.26

24 - 8.05 - 12.15

25 - 1.77 - 12.56

26 8.48 - .16

27 -24.97 -20.21

28 - 2.46 - 25.74

29 .55 - 18.07

30 14.35 5.01

t X

t

31 - .61 11.25

32 2.97 11.32

33 - 3.24 4.26

34 - 7.55 - 7.28

35 - 10.08 - 19.11

36 - 6.45 - 23.60

37 - 12.44 - 29.89

38 14.16 - 9.11

39 21.67 23.88

40 .01 27.96

41 - 6.86 11.62

42 - 6.54 - 5.03

43 - 4.49 - 13.08

44 - 13.20 - 24.13

45 3.81 - 16.90

46 8.76 .57

47 - 16.21 - 9.64

48 5.68 - 6.71

49 - 13.95 - 16.65

50 .40 - 15.57

51 3.48 - 6.26

52 9.66 8.74

53 4.03 15.24

54 - 7.22 4.78

55 10.34 9.07

56 9.78 18.84

57 - 6.23 10.57

58 - 18.02 - 14.61

59 5.58 - 13.86

60 - 2.01 - 9.30
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

NORitiAL DISTRIBUTION 36

Series No. 3

x t+2

= la x t+l" M x

t + - 09 x t-l + £ t+2

x

t

t x

t

12.91 8.02 91 -11.45 -19.74

-15.91 - 3.88 92 - 1.24 -19.71

10.88 1.92 93 - 8.41 -21.22

2.71 7.40 94 3.74 -11.92

-16.20 - 9.33 95 13.36 8.67

3.72 - 9.92 96 1.06 14.41

- 1.87 - 7.63 97 13.22 23.84

-25.40 -29.87 98 - 4.50 15.58

- 1.77 -31.86 99 -13.98 - 6.98

- 7.35 -28.75 100 -10.71 -23.72

3.19 -15.84 101 -13.66 -35.00

8.72 2.23 102 23.11 - 4.63

- 1.86 5.60 103 - .01 9.57

- 6.17 - 2.51 104 - 5.02 4.58

12.98 7.73 105 5.75 5.78

- .76 9.44 106 - .31 4.71

4.84 11.28 107 - 6.09 - 3.27

5.63 14.21 108 - 5.24 -10.58

22.31 33.38 109 2.03 - 7.62

12.31 43.23 110 .97 - 2.62

- 1.01 31.80 111 -12.62 -12.79

- 9.83 7.40 112 - 6.73 -20.23

2.61 - .62 113 - 4.72 -21.07

.19 - 1.18 114 - 9.34 -23.96

-16.09 -16.42 115 1.95 -16.12

-14.10 -31.65 116 - 3.73 -11.86

7.63 -19.42 117 - 9.44 -16.91

- 2.92 -10.57 118 7.40 - 6.96

4.84 - .32 119 - 3.27 - 3.88

- 9.78 - 6.81 120 .64 - 1.81
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

NORMAL DISTRIBUTION 37

Series No, 3

x t+2

= lel x t+l“ oI+8 x

t + ° 09 X t-I

+ £t+2

Ct x

t

t €t x

t

- 1.12 - 1.88 151 7.47 23.33

.68 - .87 152 5.13 24.04

6.92 6.70 153 1.17 17.70

-11.70 - 4.08 154 - 1.43 8.60

-16o32 -24.11 155 - 6.46 - 3.34

- 3.26 -27.22 156 21.46 15.25

- 3o50 -22.24 157 - 3.00 16.15

- 4 0 66 -18.22 158 -15.50 - 5.35

34.75 22.94 159 -11.29 -23.56

- 2.31 29.67 160 - 1.88 -23.78

4 0 26 24.25 161 - .18 -15.51

-12.05 2.45 162 .95 - 6.82

4.57 - 1.70 163 -19.20 -21.40

30.52 29.65 164 - 3.32 -24.99

2.94 36.60 165 11.94 - 5.89

4.04 29.92 166 - 3.77 - .18

3.15 21.16 167 -10.20 - 9.82

- 8.02 4.19 168 - 6.46 -17.70

- 5.22 - 8.08 169 9.47 - 5.31

-15.71 -24.71 170 3.46 5.24

-11.91 -34.83 171 2.67 9.39

18.44 - 8.74 172 13.65 20.98

-12.83 - 7.94 173 -17.49 1.55

-17.32 -24.98 174 2.83 - 4.68

- 1.27 -25.73 175 10.85 6.85

- 4.39 -21.41 176 - 3.33 6.60

22.76 9.31 177 4.72 8.27

- 9.22 8.98 178 .33 6.88

- 1.94 1.54 179 3.28 7.47

16.13 14.35 180 9.23 14.89
t

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

NORMAL DISTRIBUTION 38

Series No„ 3

x t+2 x t+l

~ *

L|’^ x

t + x t-1

+ ^t+2

6t xt

t x

t

-14.58 - 1.17 211 -19.03 13.85

- 2.06 - 9.83 212 4.93 3.82

3.59 - 5.32 213 3.99 4.94

- 2.14 - 3.38 214 14.47 19.32

- .58 - 2.63 215 6.99 26.21

9.59 7.84 216 .23 20.23

3.77 13.35 217 5.10 16.51

-15.13 - 4.44 218 5.82 16.63

-13.35 -23.93 219 6.77 18.96

15.44 - 7.55 220 - 9.56 4.81

.76 3.54 221 - 4.61 - 6.92

8.49 13.85 222 -13.87 -22.08

.26 13.12 223 - 2.21 -22.75

3.22 11.32 224 -20.31 -35.36

-19.73 -12.33 225 1.30 -28.67

-23.86 -41.67 226 - 5.33 -21.95

28.22 -10.68 227 9.44 - 4.13

- 6.49 .65 228 - 1.50 1.92

-18.16 -16.06 229 -15.10 -12.99

- 2.02 -20.96 230 - 2.73 -18.31

- 4.04 -19.33 231 11.12 - 2.61

15.13 2.48 232 - 1.96 2.79

- .09 10.03 233 6.69 9.36

6.01 14.11 234 22.89 31.62

11.02 21.95 235 - 7.70 22.84

8.52 26.80 236 2.90 13.68

4.43 24.64 237 - 1.04 5.90

- 6.48 9.74 238 - 2.64 .66

18.71 20.00 239 .87 - 1.46

18.28 37.82 240 28.87 28.11
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

NORMAL DISTRIBUTION 39

Series No. 3 x

t + 2 = la x

t+ l

" M x

t + - 09 x t-l

+

fit+2

ix x

t

t x

t

- 9„26 22.30 271 8.49 -22.34

1.79 12.70 272 - .07 - 9.73

- 1.38 4.42 273 8.66 5.61

8.31 9.08 274 - 6.32 2.51

6.48 15.49 275 .46 - .35

14.73 27.81 276 2.02 .93

- 7.71 16.26 277 - 1.67 - .25

4.65 10.58 278 - 4.97 - 5.73

- 7.09 - .75 279 16.51 10.41

- 7.98 -12.43 280 - 7.84 6.34

.11 -12.25 281 10.85 12.30

-17.99 -25.57 282 - 7.91 3.52

-11.25 -34.62 283 15.07 13.61

- 7.83 -34.74 284 3.51 17.90

.58 -23.31 285 23.82 37.30

- 8.76 -20.84 286 - 9.99 23.67

3.65 -11.21 287 -10.85 - 1.10

- 8.37 -12.80 288 - 1.62 -10.83

- 1.12 -11.70 289 4.89 - 4.36

2.91 - 4.83 290 3.52 3.82

.34 - .50 291 10.02 15.34

6.23 6.95 292 6.21 20.86

- 2.99 4.47 293 15.28 31.21

-16.93 -15.40 294 1.07 26.77

- 3.54 -22.00 295 - 1.20 15.15

5.34 -11.07 296 - 8.28 - 1.65

-10.85 -13.86 297 - 6.32 -13.00

- .64 -12.56 298 -16.81 -28.96

- 8.22 -16.39 299 -17.21 -42.98

-20.90 -34.15 300 -12.40 -46.95

9
t

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

NORMAL DISTRIBUTION 4q

Series No. ^

x t+2

= 1 ’ 1 x

t+ l " x

t + ’° 9 x t-l

+ ^t+2

x

t

t x

t

9.95 9.95 31 - 5.51 4.56

5 0 45 16.40 32 - 9.31 -10.08

2 0 89 16.15 33 -24.09 -35.90

7 o 40 18.20 34 2.23 -32.01

-29.94 -16.19 35 2.65 -16.24

- 2o55 -27.65 36 4.97 - .76

8.32 -12.69 37 12.44 16.52

1.32 - .83 38 -16.91 .16

- 7.85 - 5.16 39 - 8.86 -16.68

-15.48 -21.90 40 -14.99 -31.93

3.64 -18.04 41 -12.88 -39.98

4.64 - 5.15 42 - .60 -30.75

12.86 13.88 43 15.14 - 2.37

- .64 15.48 44 17.14 25.69

- 6.97 2.94 45 -18.26 8.37

1.96 - .99 46 11.90 8.57

3.37 2.26 47 2.45 10.17

1.74 4.97 48 -12.84 - 5.01

.18 4.48 49 24.11 14.49

10.75 13.49 50 7.28 26.54

5.34 18.48 51 6.25 28.03

- 1.35 12.90 52 - .86 18.53

- 3.29 3.24 53 - 8.36 .96

2.90 1.93 54 12.03 6.72

16.50 18.22 55 - 3.68 4.92

- .04 19.36 56 - 7.59 - 5.32

1.67 14.39 57 6.01 - 1.60

25.85 34.03 58 4.03 5.26

- 9.38 22.88 59 - 2.87 3.21

6.21 16.35 60 - 6.72 - 5.85
t

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

normal distribution hi

Series No. 4-

x t+2

= la x

t+1 - M x

t + - 09 x t-l + £t+ 2

x

t

t x

t

- 1.69 - 9.20 91 -15.83 3.65

7.20 .18 92 16.69 9.29

- 7.81 - 3.72 93 -14.50 - 3.33

1 0 24 - 3.77 94 3.50 - 4.29

2.49 .15 95 17.34 15.06

3.35 5.00 96 .88 19.21

- 2.83 2.26 97 .34 13.85

15.31 15.41 98 20.56 27.94

- 2.26 14.06 99 - 6.73 19.08

3.42 11.69 100 11.02 19.85

- 8.13 - .63 101 .58 15.77

2.17 - 2.86 102 - 6.58 2.96

- 3.60 - 5.40 103 21.14 18.62

- 3.39 - 8.02 104 - 4.68 15.80

- 3.39 - 9.88 105 1.52 10.23

- 8.45 -15.96 106 -15.69 -10.34

- 9.45 -22.99 107 10.31 - 4.55

- 2.83 -21.35 108 - 9.61 - 8.74

-29.05 -42.94 109 16.91 8.55

8.40 -30.65 110 - 8.88 4.32

1.14 -13.89 111 - 6.47 - 6.61

-11.19 -15.62 112 -12.12 -20.69

3.52 - 9.75 113 -11.14 -30.34

5.61 1.13 114 - 1.64 -25.67

- 4.70 - .19 115 1.21 -14.33

7.20 5.57 116 - 5.70 -11.87

8.09 14.41 117 1.97 - 6.52

12.56 25.72 118 - 4.65 - 7.41

11.03 32.90 119 -10.64 -16.73

4.82 29.96 120 20.05 4.62
t

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

NORiviAL DISTRIBUTION 9-2

Series No.„ *+

‘t+2 = 1.1 x t+I

- *98 x, + „09 x t-1 + £ t+2

£t x

t

t x

t

.68 13.12 151 -17.41 -31.02

12.62 23.32 152 2.79 -25.57

-10.11 9.66 153 - 9.95 -24.28

- 7.60 - 6.98 154 - 3.85 -21.08

4.14 - 6.08 155 - 5.63 -19.47

14.50 12.03 156 3.86 - 9.63

- 5.05 10.47 157 2.20 - .94

-14.91 - 9.71 158 -12.72 -10.88

3.58 -11.05 159 1.20 -11.19

- 4.41 -10.97 160 .72 - 6.45

11.13 3.49 161 12.39 9.68

19.21 27.33 162 - 5.54 7.20

5.89 33.28 163 3.37 6.06

4.76 28.56 164 4.19 8.27

9.82 27.73 165 13.75 20.59

- 3.27 16.52 166 6.34 25.57

1.59 9.02 167 -25.17 - 6.18

-25.11 -20.62 168 1.38 -15.84

- 2.25 -27.77 169 3.72 - 8.43

- 6.11 -25.95 170 6.57 4.34

.46 -16.62 171 -12.33 - 4.94

4.67 - 3.65 172 - 6.83 -15.10

- 1.62 .00 173 - 8.19 -22.04

- .78 - .53 174 - 7.54 -24.97

2.69 1.78 175 -15.53 -33.78

-25.80 -23.59 176 7.55 -19.60

8.20 -18.65 177 - 2.73 -10.33

2.17 - 6.87 178 -19.83 -24.82

- .06 - .79 179 -13.37 -37.47

-12.90 -12.15 180 1.27 -28.97
t

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

NOFbiAL DISTRIBUTION ^3

Series No. 4

X t+2

= lel x t+l

- * 1+8 x

t + *° 9 X t-I

+ ^t+2

x

t

t St X

t

- 3 o 50 -19.61 211 - 3.38 -10.99

5.11 - 5.92 212 - 2.51 -12.73

- .13 .16 213 - 7.89 -16.62

.47 1.73 214 4.22 - 8.94

5 0 36 6.65 215 .12 - 2.88

- 4.45 2.05 216 11.77 11.39

- 5.46 - 6.23 217 - 5.16 7.95

2.48 - 4.75 218 6.67 9.69

- 9.15 -11.21 219 14.77 22.64

-14.37 -24.98 220 -15.75 5.22

3.96 -18.57 221 2.53 - 1.73

17.14 7.69 222 6.32 3.95

6.35 21.47 223 - 8.20 - 2.55

6.62 24.88 224 3.99 - .88

- 9.77 7.98 225 - .07 .54

1.52 .29 226 - 8.21 - 7.43

- 4.92 - 6.19 227 -22.01 -30.52

10.75 4.52 228 - 7.97 -37.92

11.49 19.46 229 - 5.55 -33.28

- 5.27 13.41 230 -10.10 -31.26

14.18 20.00 231 15.25 - 6. 58

- .56 16.75 232 5.67 10.43

- 4.53 5.51 233 -11.24 .58

3.25 3.07 234 11.08 6.12

5.61 7.86 235 - 6.39 1.00

- 6.24 1.44 236 8.52 6.73

10.00 8.09 237 -12.34 - 4.87

15.84 24.76 238 16.01 7.51

- 3.22 20.27 239 -16.97 - 5.76

-11.25 - .10 240 12.88 2.50
t

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

NORMAL DISTRIBUTION 9

- 9

- Series No. 4

x t+2

= la x t+l

"- W x

t + - 09 x t-l

+ fl+ 2

x

t

t x

t

8.49 14.68 271 6.99 - 1.19

14.68 29.11 272 - 9.80 - 7.80

1.01 26.21 273 6.27 - 2.33

- 8.11 8.07 274 -20.69 - 19.62

1.31 .23 275 - 6.08 -27.24

- 2.92 - 4.18 276 18.87 - 1.88

- 5.69 - 9.67 277 11.20 20.44

- 15.47 - 24.08 278 3.95 24.88

8.60 - 13.63 279 2.34 19.73

- 16.96 - 21.26 280 11.51 23.11

- 4.84 -23.86 281 3.92 22.11

- 11.03 - 28.31 282 .72 15.73

- 12.05 -33.65 283 - 1.11 7.66

12.11 - 13.47 284 3.71 6.58

21.45 20.23 285 - 1.65 3.33

- 2.89 22.80 286 - 16.76 - 15.57

- 8.26 5.90 287 - 13.56 - 31.70

- 19.08 - 21.71 288 - 12.82 -39.92

- 9.93 - 34.59 289 7.86 - 22.23

- 20.72 - 47.82 290 - 2.61 - 10.75

17.30 - 20.65 291 - 18.85 - 23.60

16.01 13.13 292 - 11.09 - 33.89

9.76 29.81 293 6.97 - 19.95

12.44 37.07 294 - 5.02 - 12.82

- 10.72 16.93 295 12.19 4.62

- 9.41 - 5.90 296 2.19 11.62

.49 - 10.79 297 19.86 29.27

5.37 - 2.15 298 - 3.40 23.64

- .77 1.51 299 6.79 19.79

- 8.33 - 6.61 300 8.85 21.90
r

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

NORMAL DISTRIBUTION

Series Series Series Series

No. 1 No. 2 No. 3 No. 4

908,205 749.104 876.109 893.638

646.291 530.280 648.594 679.268

175.576 191.514 328.783 364.326

-204.509 - 89.688 122.744 125.943

-377.593 -215.787 31.904 10.072

-314.941 -193.587 - .581 - 3.277

-122.512 -105.784 - 25.008 18.082

40.068 - 18.290 - 47.926 16.268

113.183 23.221 - 71.456 - 33.393

115.251 37.713 -140.687 -111.731

48.033 29.908 -195.927 -182.359

- 58.039 - 1.272 -204.423 -194.338

-102.248 - 49.663 -166.641 -156.871

- 61.911 - 78.588 -113.646 -116.771

13.319 -107.208 - 85.311 - 78.797

116.591 -107.707 - 60.199 - 47.310

180.211 - 81.735 - 42.776 - 41.739

140.204 28.382 - 45.784 - 58.376

64.695 .255 - 54.706 -102.964

22.814 24.994 - 76.554 -114.564

- 7.000 52.817 - 57.785 - 78.746

- 25,979 80.024 - 11.741 - 8.708

- 19.549 87.452 45.377 48.507

4.532 54.618 61.117 46.443

23.808 - 6.330 50.599 .188

39.453 62.952 40.314 - 46.705

19.365 -125.320 36.363 - 48.506

- 42.084 -147.746 39.986 - 44.413

- 70.733 -125.014 31.844 - 45.782

- 40.022 - 78.184 10.262 - 36.395

29.089 - 17.196 11.638 3.308
'

.
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. A major portion of the Bureau’s work is performed

for other Government Agencies, particularly the Department of Defense and the Atomic Energy

Commission. The scope of activities is suggested by the listing of divisions and sections on the

inside of the front cover.

Reports and Publications

The results of the Bureau’s work take the form of either actual equipment and devices or published papers and reports. Reports are issued to the sponsoring agency of a particular project or program. Published papers appear either in the Bureau’s own series of publications or in the

journals of professional and scientific societies. The Bureau itself publishes three monthly periodicals, available from the Government Printing Office: The Journal of Research, which presents

complete papers reporting technical investigations; the Technical News Bulletin, which presents

summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions,

which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards ($1.00). Information on calibration services and fees can be

found in NBS Circular 483, Testing by the National Bureau of Standards (25 cents). Both are

available from the Government Printing Office. Inquiries regarding the Bureau’s reports and

publications should be addressed to the Office of Scientific Publications, National Bureau of Standards, Washington 25, D. C.
k