3306
3413
3520
3627
3735
3843
3950
4058
4
.0
4167
4275
4384
4493
4602
4712
4820
4931
5042
5152
5
.0
5263
5374
5485
5596
5708
5820
5932
6044
6156
6269
6
.0
6383
6496
6610
6724
6838
6952
7066
7180
7296
7412
7
.0
7527
7643
7759
7875
7992
8109
8225
8342
8460
8578
8
.0
8696
8814
8933
9051
9170
9290
9408
9528
9649
9770
9
.0
9890
1001
.1013
.1025
.1037
.1050
.1062
.1074
.1086
.1099
.1111
1123
.1136
.1148
.1160
1173
.1186
.1198
.1211
.1223
1
.1236
1248
.1261
.1274
.1287
.1300
.1312
.1325
.1338
.1351
2
.1364
1377
.1390
.1403
1416
.1429
.1442
.1455
.1468
.1481
3
.1494
1507
.1521
.1534
1547
.1561
.1574
.1587
.1601
1615
4
1628
1641
.1655
.1669
.1682
.1695
.1710
.1723
.1737
.1751
5
.1765
1778
.1792
J806
.1821
.1834
.1848
.1862
.1876
.1890
6
.1905
1919
.1933
.1947
.1962
.1976
.1990
.2005
.2019
.2034
7
2048
2063
.2077
.2092
.2106
.2121
.2136
2151
.2165
.2180
1
8
.2195
.2210
.2225
.2240
.2255
2270
.2285
.2300
.2315
.2331
1
9
.2346
.2361
.2376
.2392
.2407
.2423
.2438
.2454
.2469
.2485
2
.2500
2516
.2532
.2547
.2563
.2579
.2595
2610
.2625
.2642
2
1
.2658
.2674
.2630
.2706
.2722
.2739
.2755
.2772
.2788
.2804
2
2
.2820
.2837
.2853
.2870
.2887
2903
.2920
.2937
.2954
.2971
2
3
.2987
.3004
.3020
.3038
.3055
3072
.3089
3106
.3123
.3140
2
4
3157
.3175
.3192
.3210
.3228
.3245
.3262
.3280
.3298
.3316
2
5
.3333
.3351
.3369
3387
.3405
3423
.3440
.3459
.3477
.3495
2
6
.3513
.3532
.3550
.3568
.3587
3606
.3624
3643
.3662
.3681
2
7
.3699
.3717
3736
.3755
.3774
3793
.3812
.3831
.3850
.3869
2
8
.3889
.3908
3928
.3947
.3966
3986
.4005
.4024
.4044
.4064
2
9
.4084
.4104
.4124
.4144
.4164
.4185
.4205
.4225
.4245
.4265
3
.4285
.4306
.4326
.4347
.4368
4389
.4409
4430
.4450
.4471
3
1
.4493
.4514
.4535
.4556
.4577
4598
.4619
4640
.4661
.4683
3
2
4705
.4727
.4749
.4771
.4793
4814
4836
.4858
.4881
.4903
3
3
.4925
.4947
.4969
.4992
.5015
.5038
.5060
.5083
.5106
.5129
3
4
.5152
.5174
5197
.5220
.5244
.5267
.5290
.5313
.5336
.5360
3
5
5384
.5407
.5431
.5455
.5480
5504
.5528
5553
.5576
.5600
3
6
.5625
.5650
5674
.5698
.5723
.5748
.5773
5798
.5823
.5848
3
7
.5873
.5899
5924
.5949
.5974
.6000
.6025
6051
.6077
.6103
3
8
6129
.6155
6181
.6207
.6233
6260
.6286
.6313
.6340
.6367
3
9
.6394
.6420
.6447
.6474
.6502
.6529
.6557
.6584
.6611
.6638
4
.6666
.6694
.6722
.6750
.6778
.6806
.6834
6862
.6891
.6920
4
1
6949
.6978
7007
.7036
.7065
.7094
.7123
.7152
.7181
.7211
4
2
.7241
.7271
.7301
.7331
. 7361
.7391
.7421
.7451
.7482
.7512
4
3
.7543
.7574
7605
.7636
.7667
.7698
.7729
.7760
.7792
.7824
4
4
7857
.7889
.7921
.7953
.7986
.8018
.8050
.8084
.8117
.8150
4
5
8182
.8215
8248
.8282
.8316
.8349
.8382
.8416
.8450
.8484
4
6
.8518
.8552
8586
.8620
.8655
.8691
.8727
.8762
.8798
.8834
4
7
8868
.8904
8939
.8975
.9011
.9048
.9084
.9120
.9157
.9194
4
8
9231
.9267
9304
.9341
.9379
.9417
.9454
.9493
.9531
.9570
4
9
9609
.9649
9687
.9725
.9764
.9803
.9842
.9881
.9920
.9960
363
364
APPENDIX
Values of
1000 -a
Units
100
10
1
2
3
4
5
6
7
8
9
5
1.000
1.004
1.008
1.012
1.016
.020
1.024
1.028
.032
.036
5
1
1.041
1.045
1.049
1.053
1.058
.062
1.066
1.071
.075
.079
5
2
1.083
1.088
1.092
1.097
1.101
.105
1.110
1.114
.119
123
5
3
1.128
1.132
1.137
1.141
1.146
.15
1.155
1.160
.165
.169
5
4
1.174
1.179
1.183
1.188
1.193
.198
1.203
1.208
.212
.217
5
5
1.222
1.227
1.232
1.237
1.242
.247
1.252
1.257
.262
.267
5
6
1.273
1.278
1.283
1.288
1.294
.298
1.304
1.309
.314
320
5
7
1.326
1.331
1.336
1.342
1.347
.353
1.359
1.364
.370
1.375
5
8
.381
1.386
1.392
1.398
1.404
.410
1.415
1.421
.427
1.433
5
9
.439
1.445
1.451
1.457
1.463
.469
1.475
1.481
.487
1.494
6
.500
1 506
1.513
1.519
1.525
.53
1.538
1.544
1.551
1.557
6
1
.564
1.571
1.577
1.584
1.591
.597
1.604
1.611
1.618
1.625
6
2
.632
1.639
1.645
1.652
1.659
.667
1.674
1.681
1.688
1.695
6
3
.703
1.710
1.717
1.724
1.732
.740
1.747
1.755
1.763
1.770
6
4
.778
1.786
1.793
1.801
1.809
.817
1.825
1.833
1.841
1.849
6
5
.857
1.865
1.873
1.882
1.890
.899
1.907
1.916
1.924
1.933
6
6
.941
1.950
1.958
1.967
1.976
.985
1.994
2.003
2.012
2.021
6
7
2.030
2.039
2.048
2.058
2.068
2.078
2.087
2.096
2.106
2.115
6
8
2.125
2.135
2.145
2.155
2.165
2.175
2.185
2.195
2.205
2.215
6
9
2.225
2.236
2.247
2.257
2.268
2.278
2.289
2.300
2.311
2.322
7
2.333
2.344
2.355
2.367
2.378
2.389
2.401
2.413
2.425
2.436
7
1
2.448
2.460
2.472
2.485
2.497
2.509
2.521
2.534
2.546
2.559
7
2
2.571
2.584
2.597
2.610
2.623
2.636
2.650
2.663
2.676
2.690
7
3
2.703
2.716
2.731
2.745
2.759
2.774
2.788
2.802
2.817
2.831
7
4
2.846
2.861
2.876
2.891
2.907
2.922
2.937
2.953
2.968
2.984
7
5
3.000
3.016
3.032
3.049
3.065
3.081
3.098
3.115
3.132
3.150
7
6
3.168
3.185
3.202
3.220
3.237
3.255
3.273
3.291
3.310
3.329
7
7
3.348
3.367
3.386
3.405
3.425
3.445
3.464
3.484
3.505
3.525
7
8
3.546
3.566
3.587
3.608
3.630
3.652
3.674
3.695
3.717
3.740
7
9
3.762
3.785
3.808
3.831
3.854
3.878
3.902
3.926
3.950
3 975
8
4.000
4.025
4.050
4.075
4.102
4.127
4.154
4.181
4.209
4.236
8
1
4.263
4.290
4.319
4.348
4.376
4.405
4.435
4.464
4.494
4.525
8
2
4.556
4.587
4.618
4.650
4.682
4.715
4.748
4.781
4.814
4.848
8
3
4.882
4.917
4.953
4.988
5.025
5.061
5.097
5.135
5.173
5.211
8
4
5.250
5.290
5.330
5.370
5.411
5.451
5.493
5.536
5.580
5.623
8
5
5.666
5.711
5.757
5.803
5.850
5.898
5.945
5.994
6.043
6.093
8
6
6.143
6.194
6.247
6.300
6.353
6.407
6.463
6.519
6.576
6.634
8
7
6.693
6.752
6.812
6.873
6.937
7.000
7.064|
7.129
7.196
7.264
8
8
7.334
7.403
7.474
7.546
7.620
7.696
7.772
7.849
7.928
8.009
8
9
8.091
8.175
8.259
8.346
8.434
8.524
8.616
8.709
8.804
8.901
9
9.000
9.101
9.204
9.309
9.416
9.526
9.638
9.753
9.870
9.989
9
1
10.11
10.23
10.36
10.49
10.63
10.76
10.90
11.05
11.19
11.34
9
2
11.50
11.66
11.82
11.99
12.16
12.33
12.51
12.70
12.89
13.08
9
3
13.28
13.49
13 71
13.93
14.15
14.38
14.62
14.87
15.13
15.40
9
4
15.66
15.95
16.24
16.54
16.86
17.18
17.52
17.87
18.23
18.61
9
5
19.00
19.41
19.83
20.28
20.75
21.22
21.73
22.26
22.81
23.38
9
6
24.00
24.64
25.32
26.03
26.77
27.57
28.41
29.30
30.25
31.26
9
7
32.33
33.49
34.70
36.04
37.46
39.00
40.67
42.48
44.44
46.62
9
8
49.00
51.63
54.55
57.83
61.50
65.67
70.43
75.93
82.33
89.91
9
9
99.00
10.1
24.0
41.9
65.7
99.0
249.0
332.3
99.0
99.0
MATHEMATICAL QUANTITIES AND RELATIONS 365
II. MATHEMATICAL QUANTITIES AND RELATIONS.
(1) Functions of TT and e.
TT is the ratio of the circumference to the diameter of a circle.
e is the basis of the natural logarithms.
TT = 3.14159
- = 0.31830
7T
7T 2 = 9.86960
VT = 1.77245
logio TT = 0.4971498
log e TT = 1.1447298
e = 2.71828
- = 0.36788
e
logio e = 0.4342944
log e e = 1
loge 10 = 2.3025850
logio x = 0.43429 loge x.
loge x = 2.30258 logio x.
If x = e v , then y = log e x.
(2) English-Metric and Metric-English Conversions.
1 inch = 2.54001 centimeters.
1 centimeter = 0.3937 inch.
1 foot = 0.304801 meter.
1 meter = 3.28083 feet.
1 mile = 1.60935 kilometers.
1 kilometer = 0.62137 mile.
1 square inch = 6.452 square centimeters.
1 square centimeter = 0.1550 square inch.
1 cubic inch = 16.3872 cubic centimeters.
1 cubic centimeter = 0.0610 cubic inch.
1 U. S. liquid gallon = 3.78543 liters = 231 cubic inches.
1 liter = 0.26417 U. S. liquid gallon.
1 avoirdupois pound = 0.45359 kilogram.
1 kilogram = 2.20462 avoirdupois pounds.
1 avoirdupois ounce = 28.3495 grams.
1 gram = 0.03527 avoirdupois ounce.
366 APPENDIX
(3) Formulce for the Conversion of Temperature Scales.
If F = Fahrenheit degrees and C = Centigrade degrees, then
C = f(F - 32). C. = + 32 F.
F = | C + 32. F. = - 17.777 C.
20 C. = + 68 F.
- 40 C. = - 40 F.
100 C. = 212 F.
(4) Formulce for Temperature Coefficients.
If a linear relation exists between electrical resistance (or re-
sistivity) and temperature (only true, usually, to a first approxi-
mation and for short ranges of temperature) then these relations
hold,
Pt = PO (1 + 0, (1)
Ptl = PO (1 + cdd, (2)
Pt, Pt ' , Q N
= T- j> (3)
hpt tpti
Pt Po
a = , (4)
tpo
where p = resistance (or resistivity) at temperature degrees,
pt resistance (or resistivity) at temperature t degrees,
p tl = resistance (or resistivity) at temperature t\ degrees,
and a = temperature-resistance coefficient which, by the as-
sumption made, is a constant quantity.
If a linear relation between resistance and temperature does not
hold, then the resistance (or resistivity) at temperature t can be
expressed, sometimes, in terms of the resistance (or resistivity) at
degrees by the relation
Pt = PO (1 + at + fa 2 ), (5)
where a and b are constants which can be determined by experi-
ment.
Let <r t = o-o (1 - 00 (6)
express the variation of electrical conductivity with temperature,
upon the assumption that relation (1) above holds, then
and
<* = T=
MATHEMATICAL QUANTITIES AND RELATIONS 367
(5) Relations between Resistance and Conductivity. (Consult
Chapter VII.)
_ 0.0203 W . n
L * R^r 30>
0.01594 Z0
or C 8 = -g-g- 30.
C 8 = per cent conductivity by Matthiessen's meter-millimeter
standard.
I = length of conductor in meters.
d = diameter in millimeters of conductor of uniform and cir-
cular cross-section.
5 = cross-section in square millimeters of conductor of uniform
cross-section.
R t = resistance in ohms of a length I meters at temperature
t degrees C.
6 = = a temperature coefficient, or the ratio of the re-
Po
sistivity of the material at temperature t degrees C. to the
resistivity of the material at degrees C.
When the temperature is 20 C. d = 1.07968 for copper.
Use for calculation the value 6 = 1.08.
It is nearly the same for all pure metals.
If the cross-section is given in circular mils and is called V and we
write y
S = 1973^2'
then
.
C,= lOO, (4)
and 17Q 72/j
C w per cent conductivity by Matthiessen's meter-gram
standard.
W = weight of I meters expressed in grams.
C.' = ^C.',. . (6)
where C w r and C,' stand for conductivities instead of per cent
conductivities and
5 = density of the material of the conductor.
368 APPENDIX
Example (1).
A copper wire is 2 mm in diameter and 4 m long, and has a
resistance at 20 C. of 0.0223 ohm. By Eq. (1) its per cent con-
ductivity by Matthiessen's meter-millimeter standard is
C, = - Q Q223 X 4 ~ 10 = 9 ^'^ 6 per cent conductivity.
Example (2).
An aluminum wire is 2 m long and weighs 50 grams. Its re-
sistance at C. is 0.005585 ohm. Then 6 = 1 and by Eq. (5) its
per cent conductivity by Matthiessen's meter-gram standard is
14173 X 4 X 1
= 2 3 er Cent
" 0.005585X50
Example (3).
The density of aluminum is 2.7 and its conductivity is 0.615
by the meter-millimeter standard, then by Eq. (6) its conductivity
by the meter-gram standard is
Q OQ
C u ' = ^ X 0.615 = 2.0249 conductivity.
For bimetallic conductors, as copper or aluminum conductors,
with a steel core we have the following relations:
.
A3 ~|~ S
S = cross-section of the outside metal and
s = cross-section of core of the bimetallic conductor.
(7)
S and s may be expressed in terms of any convenient unit pro-
vided the same unit is chosen for each.
C 8 " = conductivity of the outside metal and
C/ = conductivity of the metal of the core, both by the meter-
millimeter standard.
Example (4).
A conductor is made up of a steel core which has a con-
ductivity, by the meter-millimeter standard, 0.16, and of an
aluminum covering which has a conductivity 0.61. The cross-
section of the core is 2000 circular mils and that of the out-
side metal is 4000 circular mils, Then by Eq. (7) the per cent
MATHEMATICAL QUANTITIES AND RELATIONS 369
conductivity by the meter-millimeter standard of the bimetallic
conductor is
4000 X 0.61 + 2000 X 0.16 inn ,. .,
C 8 = - 40QO + 2000 - = Per C6 conductlvlt y-
r TFiO/' + wv ,.
Cw= Wi + W*
Wi = the weight of the outside metal and
W 2 = the weight of the core.
These weights may be expressed in any unit, provided the same
unit is used for both.
C w " = conductivity of outside metal and
CJ = conductivity of core; both by the meter-gram standard.
Example (5).
A conductor has a steel core of conductivity 0.20 by the meter-
gram standard, and an aluminum covering of conductivity 2 by
the same standard.
For a given length of the conductor the steel core weighs 10 Ibs.,
and the aluminum covering 8 Ibs. Then by Eq. (8)
Cw = 8X2+10X0.20 100 = 100 per cent conductivity.
o + lu
" ' nn x q v
8.89 (q + 1)
q = ratio of the cross-section of the outside metal to the
cross-section of the core.
6 2 = density of the outside metal.
61 = density of the metal in the core.
C w f and C w " have the same meaning as in Eq. (8).
Example (6).
In the conductor under example (5) the density 5i of the steel
core is 7, and the density <5 2 of the aluminum covering is 2.7.
The ratio of the cross-section of the outside metal to that of the
core is, for the case chosen,
As in example (5) taking CJ = 0.2 and C w " = 2 then by Eq. (9)
the per cent conductivity by the meter-millimeter standard is
370 APPENDIX
2.074 X 2.7 X 2 + 7 X 0.2
C 8 = 8 89 X (2 074 + 1) : per C conductivity.
0.01594 Id"
R * = SCs + sCa >'
-p
6" = -FT = the temperature coefficient of the bimetallic conductor.
/to
R t = ohmic resistance in ohms at t degrees centigrade of I meters
of the bimetallic conductor.
Other quantities have the same meaning as above.
Example (7).
A bimetallic conductor 304.8 m long has a steel core 16.72 sq.
mm cross-section and a copper covering 25.59 sq. mm. cross-
section. The conductivity by the meter-millimeter standard of
the core is 0.16, and of the covering 1.00. If at 20 C. the coeffi-
cient 0" is found to equal 1.09, then by Eq. (10) the resistance of
this conductor at 20 C. is
0.01594 X 304.8 X 1.09
R " 25.59 X 1 + 16.72 X 0.16 =
0.14173 M"
C w "Wi + C V 'W*
Example (8).
A bimetallic conductor is 1000 m long. The weight Wi of its
steel core is 180,000 grams, and the weight of its aluminum covering
is 59,100 grams. The conductivity of the core by the meter-gram
standard is 0.2, and of the covering 2.03. At 20 C. its tempera-
ture coefficient is found to be 1.09. Then by Eq. (11) its resist-
ance is
0.14173 X 1000 2 X 1.09
2.03 X 59100 + 0.2
,
=
$ = value in dollars of a certain length of a certain conductor
which weighs W Ibs., and has a conductivity C w by the meter-
gram standard, if $1 = the value in dollars of the same length of
100 per cent conductivity (by the meter-gram standard) conductor
which weighs W\ Ibs.
MATHEMATICAL QUANTITIES AND RELATIONS 371
Example (9).
Suppose that 100 Ibs. of a certain length of 100 per cent con-
ductivity copper is worth $20, then by Eq. (12) 250 Ibs. of the
same length of aluminum wire of 2.03 conductivity or 203 per cent
conductivity, by the meter-gram standard, is worth
_ 20 X 250 X 2.03 _
"loo~
This is the value of the aluminum as compared with the copper
wire when considered only as a conveyer of electric power. Equal
weights of the same length of aluminum and copper have values,
as conveyers of electric power, in the ratio of about 2 to 1.
$' = ^sc 8 . (is)
Oi
$' = the value in dollars of a certain length of a conductor which
has a cross-section S and a conductivity C 8 by the meter-millimeter
standard, when $n = the value in dollars of the same length of
100 per cent conductivity conductor (by the meter-millimeter
standard) which has a cross-section Si.
Example (10).
Suppose that 100 feet of copper conductor of 105,625 circular
mils is worth $64, then by Eq. (13) 100 feet of aluminum conductor
of conductivity 0.6, by the meter-millimeter standard, and 133,225
circular mils is worth
64
' 105625 X 133225 X ' 6 = |48 - 44 '
Equal cross-sections of the same lengths of aluminum and copper
have values as conveyers of electric power in the ratio of about
6 to 10.
(6) Conversions from Practical, to Electrostatic, to Electromagnetic
Units. (C.G.S. System.)
v = velocity of light = 3 X 10 10 centimeters per second.
N = any number. Elst = electrostatic. Elmg = electromag-
netic.
N coulombs = N 3 X 10 9 Elst units = N 1Q- 1 Elmg units.
1 Elst unit of electricity = v~ l Elmg unit.
N volts = ^ X lO- 2 Elst units = N 10 8 Elmg units.
372 APPENDIX
1 Elst unit of potential difference = v Elmg units.
N amperes = N 3 X 10 9 Elst units = N lO' 1 Elmg units.
1 Elst unit of electric current = v~ l Elmg unit.
N ohms = ^ X 10- 11 Elst units = N 10 9 Elmg units.
1 Elst unit of resistance = v 2 Elmg units.
N farads = N 9 X 10 11 Elst units = N 1Q- 9 Elmg units.
N microfarads = N 9 X 10 5 Elst units = N 10~ 15 Elmg units.
1 Elst unit of capacity = v~ 2 Elmg unit.
TV
TV henrys = -5- X 10~ u Elst units = N 10 9 Elmg units.
1 Elst unit of self-induction = v 2 Elmg units.
25
Examples : 25 ohms = -=- X 10- u Elst units = 25 X 10 9 Elmg units,
y
5 microfarads = 5 X 9 X 10 5 Elst units of capacity,
or 5 Elst units of capacity = Q 5 microfarads.
y x lu
(7) Approximation Formula.* Certain other Expressions.
In a mathematical expression it sometimes occurs that some
quantities are very small compared with others. In such cases
the expression may often be given a form which is more convenient
for calculation if formulae of approximation are used.
In the expressions considered let a, b, c, d, etc., be magnitudes
which are very small as compared with unity. The formulae of
approximation may then be given forms such that the corrections
are contained in terms which are added to or subtracted from 1.
The following formulae can be shown to hold upon the above
supposition, and will often be found convenient to use. Where
the sign =t or =F is used before a quantity, either the upper or
lower sign must be taken all thru the formula.
In general (when a is very small compared with 1)
(1 + a) m = 1 + ma; (1 a) m = 1 ma. (1)
For m = 2
(1 + a) 2 = 1 + 2a; (1 - a) 2 = 1 - 2 a. (2)
For m = \
Vl + a = 1 + } a; Vl - a = 1 - J a. (3)
* The substance of what is given under this head has been selected from
"Physical Measurements," by Dr. F. Kohlrausch.
MATHEMATICAL QUANTITIES AND RELATIONS 373
For m = 1
For m = - 2
^-1-2-; ^-1 + 2-. (5)
For m = \
I -| -i J- ill /CN
. = 1 | a; T== = 1 + a. (6)
v 1 -f a v 1 a
(1 a) (1 =b 6)(1 =b c) . . . = 1 a d= b c . . . (7)
For the geometrical mean of two quantities, which are very
nearly alike, the arithmetical mean may be used. Thus
. (9)
If 8 signifies a small angle measured in radians (1 radian = 57.2958
degrees) then,
sin (x + 6) = sin x + 5 cos x\ Sin d = 5, (10)
cos (x -\- d) = cos x d sin x; cos 5 = 1, (11)
tan (x + d) = tan x + - - ; tan d = d. (12)
COS X
Also, if a quantity a is very small compared with a quantity
x > 1, then
log e (x + a) = log e x + - x ; log e (1 + a) = a. (13)
The true value of (a + 6) n is given by the expansion
(a + 6)" = a n + na'-ty + "r^ - n ~ 2 ^> 2 + ' (14)
The exact value of (1 d= a) m when a 2 < 1 is given by the ex-
pansion
m(m 1) m (m l)(m 2) a 3
h (15)
Any quadratic may be put in the form x 2 + px = q. Its solu-
tion is then
374
APPENDIX
III. WIRE DATA AND FORMULAE.
(1) Wire Table for Pure Copper; from Standard Underground Cable Co.
The columns of this table are reproduced with the permission of the Standard Under-
ground Cable Co., of Pittsburgh, Pa., from their " XVII Hand-Book, Standard Underground
Cable Co., Copyright, 1906."
B. &S.
G. No.
Diameter in mils
; Area circular mils
Length, feet per
ohm
Resistance in Inter-
national ohms at
68F. = 20C.
Ohms per 1000 feet
0000
460.0
211,600
20,440
0.04893
000
409.6
167,800
16,210
0.06170
00
364.8
133,100
12,850
0.07780
324.9
105,500
10,190
0.09811
1
289.3
83,690
8,083
0.1237
2
257.6
66,370
6,410
0.1560
3
229.4
52,630
5,084
0.1967
4
204.3
41,740
4,031
0.2480
5
181.9
33,100
3,197
0.3128
6
162.0
26,250
2,535
0.3944
7
144.3
20,820
2,011
0.4973
8
128.5
16,510
1,595
0.6271
9
114.4
13,090
1,265
0.7908
10
101.9
10,380
1,003
0.9972
11
90.74
8,234
795.3
1.257
12
80.81
6,530
630.7
1.586
13
71.96
5,178
500.1
1.999
14
64.08
4,107
396.6
2.521
15
57.07
3,257
314.5
3.179
16
50.82
2,583
249.4
4.009
17
45.26
2,048
197.8
5.055
18
40.30
1,624
156.9
6.374
19
35.89
1,288
124.4
8.038
20
31.96
1,022
98.66
10.14
21
28.46
810.1
78.24
12.78
22
25.35
642.4
62.05
16.12
23
22.57
509.5
49.21
20.32
24
20.10
404.0
39.02
25.63
25
17.90
320.4
30.95
32.31
26
15.94
254.1
24.54
40.75
27
14.20
201.5
19.46
51.38
28
12.64
159.8
15.43
64.79
29
11.26
126.7
12.24
81.70
30
10.03
100.5
9.707
103.0
31
8.928
79.70
7.698
129.9
32
7.950
63.21
6.105
163.8
33
7.080
50.13
4.841
206.6
34
6.305
39.75
3.839
260.5
35
5.615
31.52
3.045
328.4
36
5.000
25.00
2.414
414.2
37