8. The unit of electrical resistance, now universally adopted, is called the international ohm. One international ohm is the resistance offered by a column of pure mercury 106.3 centimeters in length and 1 square millimeter in sectional area at 32° F., or the temperature of melting ice. The dimensions of the column expressed in inches are as follows: length 41.85 inches, sectional area .00155 square inch. Hereafter, the word "international" will be omitted, and simply the word "ohm" used; the international ohm, however, as defined above, will always be implied unless otherwise stated.

9. In Table 1 are given various data respecting the copper wire used in electrical installations. In the first column is the gauge number by American Wire Gauge; in the second column is the diameter as measured in mils (one mil = one one-thousandth of an inch); the third column shows the area of cross-section in circular mils. It is usual to adopt this method for a round wire, instead of the old way of expressing the area in fractions of a square inch, in which case the diameter is squared and the product multiplied by .7854, as explained in Geometry and Mensuration. If the second operation be omitted, and the diameter, as measured in thousandths of an inch, be only squared (or multiplied by itself), the result is expressed in circular thousandths, or circular mils.

## Example

What is the area in circular mils of a wire 2 1/2 inches in diameter ?

## Solution

2 1/2 in. = 2,500 mils. 2,5002 = 2,500x2,500 = 6,250,000 circular mils. Ans.

The resistance of copper wire being low, a unit length of 1,000 feet is usually taken in tables of resistance, and this unit is considered in the eighth column.

10. The resistance of a given conductor increases as the length of the conductor increases; that is, the resistance is directly proportional to the length of the conductor. For example, if the length of a conductor be doubled, its resistance will be doubled.

The resistance of any length of conductor may be found by the following formula:

R = LR1

1,000'

(3.) where R = required resistance; L = length of conductor; R1 = resistance per 1,000 feet of conductor.

## Table 1. American, Or B. & S., Gauge

 Gauge No. DiameterMils (d).1 Mil = .001 In. Area. Weight and Length. Resistance. Ohms per 1,000 Feet. Current Allowed. Amperes Gauge No. Circular Mils SquareInches(d2X.7854). Pounds per 1,000Feet. Pounds perMile. Feet perPound. 0000 460.000 211,600.00 .1661900 639.33 3,375.700 1.56 .051 175 0000 000 409.640 167,805.00 .1317900 507.01 2,677.000 1.97 .064 145 000 00 364.800 133,079.00 .1045200 402.09 2,123.000 2.49 .081 120 00 0 324.950 105,592.00 .0829320 319.04 1,684.500 3.13 .102 100 0 1 289.300 83,694.00 .0657330 252.88 1,335.200 3.95 .129 95 1 2 257.630 66,373.00 .0521300 200.54 1,058.800 4.99 .163 70 2 3 229.420 52,634.00 .0413390 159.03 839.680 6.29 .205 60 3 4 204.310 41,742.00 .0327840 126.12 665.910 7.93 .259 50 4 5 181.940 33,102.00 .0259980 100.01 528.050 10.00 .326 45 5 6 162.020 26,250.00 .0206170 79.32 418.810 12.61 .411 35 6 7 144.280 20,817.00 .0163490 62.90 332,110 15.90 .519 30 7 8 128.490 16.509.00 .0129660 49.88 263.370 20.05 .652 25 8 9 114.430 13,094.00 .0102840 39.56 208.880 25.28 .824 9 10 101.890 10,381.00 .0081532 31.37 165.630 31.88 1.040 20 10 11 90.742 8,234.10 .0064670 24.88 137.370 40.20 1.311 11 12 80.808 6,529.90 .0051286 19.73 104.180 50.69 1.653 15 12 13 71.961 5,178.40 .0040671 15.65 82.632 63.91 2,084 13 14 64.084 4,106.80 .0032254 12.41 65.525 80.59 2.628 10 14