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SEC. 5. The Congress shall have power to enforce, by appropriate legislation, the provisions of this act.

ARTICLE XV.

SECTION 1. The right of citizens of the United States to vote shall not be denied or abridged by the United States, or by any state, on account of race, color, or previous condition of servitude.

SEC. 2. Congress shall have power to enforce this article by appropriate legislation.

ELECTORS OF PRESIDENT AND VICE-PRESIDENT.

NOVEMBER 7, 1876.

COUNTIES.

Hayes and

Wheeler,
19 - Republican.

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4953 6308
1219 1280
1520 1142
1965 363

944 1495
3719 2218

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1643 1145 1407 3679 1413 1928 1174 1631 1357 2129 1276 2715 2883

970 466 1145 2265 1881 2421 1601 742

966 1302 4187

4669 703 1140 1695 3160 1996 1142

627 1433 3496 4207

330 611 1315 1015 4177

1928 3768

2578 2040 2071

111

74
604
207
236
112
132
102
277

38
129
65
16 10

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Alexander.
Bond
Boone.
Brown...
Bureau
Calhoun
Carroll
Cass
Champaign
Christian
Clark
Clay
Clinton.....
Coles
Cook
Crawford
Cumberland
De Kalb.
De Witt,
Douglas.
DuPage
Edgar.
Edwards...
Efngham
Fayette
Foru
Franklin.
Fulton..
Gallatin..
Greene
Grundy
Hamilton
Hancock
Hardin
Henderson
Henry.
Iroquois,
Jackson.
Jasper
Jetferson
Jersey
Jo Daviess
Johnson
Kane
Kankakee
Kendall
Knox.
Lake
La Salle
Lawrence.
Lee

94

25 161 61 43 57 204 391

89 282

Livingston..
Logan.
Macon.
Macoupin.
Madison.
Marion..
Marshall..
Mason...
Massac
McDonough
McHenry
McLean
Menard..
Mercer..
Monroe
Montgomery
Morgan
Moultrie
Ogle
Peoria..
Pope
Perry.
Piatt..
Pike..
Pulaski
Putnam
Randolph.
Richland..
Rock Island..
Saline
Sangamon
Schuyler.
Scott.
Shelby
Stark
St. Clair
Stephenson
Tazewell..
Union ...
Vermilion
Wabash..
Warren..
Washington
Wayne
White
Whiteside....
WAL..
Williamson.
Winnebago.
Woodford

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3120 2782 268 16
3567 4076 114
4554 4730 89
2009 2444 209
1553 1430
1566 1939 86 3....
1231 793 20
2952 2811 347
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6363 4410

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1115 1657

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2209 1425
845 1651

7
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3069 3174 109 3
1245 1672

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14 2357 2589 2 1410 1552

55 3912 2838

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29 1522 1804

115 910 1269 182 2069 3553 341 1140 786 96 4708 5891

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3198 2758

26
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8 4372 3031 288 650 936

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PRACTICAL RULES FOR EVERY DAY USE.

How to find the gain or loss per cent. when the cost and selling price are given.

RULE.—Find the difference between the cost and selling price, which wili be the gain or loss.

Annex two ciphers to the gain or loss, and divide it by the cost price; the result will be the gain or loss per cent.

How to change gold into currency.
RULE.—Multiply the given sum of gold by the price of gold.
How to change currency into gold.
Divide the amount in currency by the price of gold.

How to find each partner's share of the gain or loss in a copartnership business.

RULE.—Divide the whole gain or loss by the entire stock, the quotient will be the gain or loss per cent.

Multiply each partner's stock by this per cent., the result will be each one's share of the gain or loss.

How to find gro88 and net weight and price of hogs.

A short and simple method for finding the net weight, or price of hog8, when the gross weight or price is given, and vice versa.

NOTE--It is generally assumed that the gross weight of Hogs diminished by 1-5 or 20 per cent of itself gives the net weight, and the net weight increased by X or 25 per cent. of itself equals the gross weight.

To find the net weight or gross price.
Multiply the given number by .8 (tenths.)
To find the gross weight or net price.
Divide the given number by .8 (tenths.)
How to find the capacity of a granary, bin, or wagon-bed.

RULE.—Multiply (by short method) the number of cubic feet by 6308, and point off ONE decimal place—the result will be the correct answer in bushels and tenths of a bushel.

For only an approximate answer, multiply the cubic feet by 8, and point off one decimal place.

How to find the contents of a corn-crib.
RULE.—Multiply the number of cubic feet by 54, short method, or

(173)

by 4 ordinary method, and point off ONE decimal place—the result wili be the answer in bushels.

NOTE.-In estimating corn in the ear, the quality and the time it has been cribbed must be taken into consideration, since corn will shrink considerably during the Winter and Spring. This rule generally holds good for corn measured at the time it is cribbed, provided it is sound and clean.

How to find the contents of a cistern or tank.

RULE.—Multiply the square of the mean diameter by the depth (al in feet) and this product by 5681 (short method), and point off ONE decimal place—the result will be the contents in barrels of 314 gallons.

How to find the contents of a barrel or cask.

RULE.—Under the square of the mean diameter, write the length (all in inches) in REVERSED order, so that its UNITS will fall under the TENS; multiply by short method, and this product again by 430 ; point off one decimal place, and the result will be the answer in wine gallons.

How to measure boards.

RULE.—Multiply the length (in feet) by the width (in inches) and divide the product by 12—the result will be the contents in square feet.

How to measure scantlings, joists, planks, sills, etc.

RULE.—Multiply the width, the thickness, and the length together (the width and thickness in inches, and the length in feet), and divide the product by 12—the result will be square feet.

How to find the number of acres in a body of land.

RULE.—Multiply the length by the width (in rods), and divide the product by 160 (carrying the division to 2 decimal places if there is a remainder); the result will be the answer in acres and hundredths.

When the opposite sides of a piece of land are of unequal length, add them together and take one-half for the inean length or width.

How to find the number of square yards in a floor or wall.

RULE.—Multiply the length by the width or height,(in feet), and divide the product by 9, the result will be square yards.

How to find the number of bricks required in a building.
RULE.—Multiply the number of cubic feet by 223.

The number of cubic feet is found by multiplying the length, height and thickness (in feet) together.

Bricks are usually made 8 inches long, 4 inches wide, and two inches thick; hence, it requires 27 bricks to make a cubic foot without mortar, but it is generally assumed that the mortar fills 1-6 of the space.

How to find the number of shingles required in a roof.

RULE.—Multiply the number of square feet in the roof by 8, if the shingles are exposed 44 inches, or by 7 1-5 if exposed 5 inches.

To find the number of square feet, multiply the length of the roof by twice the length of the rafters.

To find the length of the rafters, at ONE-FOURTH pitch, multiply the width of the building by .56 (hundredths); at ONE-THIRD pitch, by .6 (tenths); at TWO-FIFTHS pitch, by .64 (hundredths); at ONE-HALF pitch, by .71 (hundredths). This gives the length of the rafters from the apex to the end of the wall, and whatever they are to project must be taken into consideration.

YOTE.-By or pitch is meant that the apex or comb of the roof is to be or % the width of the building higher than the walls or base of the rafters.

How to reckon the cost of hay.

RULE.—Multiply the number of pounds by half the price per ton, and remove the decimal point three places to the left.

How to measure grain.

RULE.—Level the grain ;. ascertain the space it occupies in cubic feet; multiply the number of cubic feet by 8, and point off one place to the left.

NOTE.-Exactness requires the addition to every three hundred bushels of one extra bushel.

The foregoing rule may be used for finding the number of gallons, by multiplying the number of bushels by 8.

If the corn in the box is in the ear, divide the answer by 2, to find the number of bushels of shelled corn, because it requires 2 bushels of ear corn to make 1 of shelled corn.

Rapid rules for measuring land without instruments.

In measuring land, the first thing to ascertain is the contents of any given plot in square yards; then, given the number of yards, find out the number of rods and acres.

The most ancient and simplest measure of distance is a step. Now, an ordinary-sized man can train himself to cover one yard at a stride, on the average, with sufficient accuracy for ordinary purposes.

To make use of this means of measuring distances, it is essential to walk in a straight line ; to do this, fix the eye on two objects in a line straight ahead, one comparatively near, the other remote; and, in walking, keep these objects constantly in line.

Farmers and others by adopting the following simple and ingenious contrivance, may always carry with them the scale to construct a correct yard

measure.

Take a foot rule, and commencing at the base of the little finger of the left hand, mark the quarters of the foot on the outer borders of the left arm, pricking in the marks with indelible ink.

To find how many rods in length will make an acre, the width being given.
RULE.---Divide 160 by the width, and the quotient will be the answer.

How to find the number of acres in any plot of land, the number of rods being given.

RULE.—Divide the number of rods by 8, multiply the quotient by 5, and remove the decimal point two places to the left.

The diameter being given, to find the circumference.
RULE.— Multiply the diameter by 3 1-7.
How to find the diameter, when the circumference is given.
RULE.—Divide the circumference by 3 1-7.

To find how many solid feet a round stick of timber of the same thickness throughout will contain when squared.

RULE.—Square half the diameter in inches, multiply by 2, multiply by the length in feet, and divide the product by 144.

General rule for measuring timber, to find the solid contents in feet.

RULE.—Multiply the depth in inches by the breadth in inches, and then multiply by the length in feet, and divide by 144.

To find the number of feet of timber in trees with the bark on.

RULE.—Multiply the square of one-fifth of the circumference in inches, by twice the length, in feet, and divide by '44. Deduct 1-10 to 1-15 according to the thickness of the bark.

Howard's new rule for computing interest.

RULE.—The reciprocal of the rate is the time for which the interest on any sum of money will be shown by simply removing the decimal point two places to the left; for ten times that time, remove the point one place to the left; for 1-10 of the same time, remove the point three places to the left.

Increase or diminish the results to suit the time given.
NOTE. - The reciprocal of the rate is found by inverting the rate ; thus 3 per cent, per month, in-

When the rate is expressed by one figure, always write it thus: 3-1, three ones.

Rule for converting English into American currency.

Multiply the pounds, with the shillings and pence stated in decimals, by 400 plus the premium in fourths, and divide the product by 90.

verted, becomes * of a month, or 10 days.

U.S. GOVERNMENT LAND MEASURE.

A township—36 sections each a mile square.
A section—640 acres.
A quarter section, half a mile square—160 acres.

An eighth section, half a mile long, north and south, and a quarter of a mile wide—80 acres.

A sixteenth section, a quarter of a mile square-40 acres.

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