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[blocks in formation]

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Light colored.
Denning's Quarry
Light colored.
Red.
Light colored.
Red..
Colored medium.
Sanborn's Quarry.
Carter's Quarry
Wet more & Morse's Quarry
Syepite..
Gray.
Common.
Scranton County Quarry.
Old Dominion Quarry.
Light colored.

Hallowell, Me.
Fox Island, Me.
Mt. Desert, Me..
Rockford, Me.
Red Beach, Calais, Me.
Oak Hill, Me.
Stark, N. H.
Concord, N. H.
Plymouth, N. H
Ryegate, Vi.
Woodbury, Vt.
Barre, Vt..
Quincy, Mass.
Croton, Conn.
Woodstock, Md.
Port Deposit, Md
Richmond, Va.
St. Cloud, Minn.
Stanstead, P. Q.
North Halifax, N. S.
Gananoque, P. O., Can..

2.638
2.642
2.631
2.600
2.636
2.526
2.631
2.636
2.649
2.647
2.654
2.651
2.660
2.800
2.648
2.700
2.727
2.674
2.690
2.833
2.698
2.687

lbs.
164.8
165.1
164.1
162.5
164.7
157.8
164.1
164.7
165.5
165.4
165.8
165.6
166.2
175.0
165.5
168.7
170.5
167.7
168.2
177.0
168.6
167.9

1+790
1+680
1+716
1+482
1+560
1+310
1+534
1+778
1+685
1+790
1+784
1+720
1+650
1+818
1+394
1+816
1+398
1+402
1+280
1+420
1+584
1+736

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Coarse

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[blocks in formation]

1 Freestone.

Seneca Stone.
Sandstone

Montrose Stone
7

Freestone.
8
9 S. Carboniferous.
10 Freestone.
11 Cincinnati Stone
12 Potsdam Sandstone.
13 Berlin Stone..
14

Potsdam ...
15 Euclid Stone.
16 Berea Stone.
17 Amherst Stone.
18 Brown Stone..
19 Potsdam Sandstone.
20 Sandstone
21
22 Freestone.
23 Brown Stone..

Portland, Conn.
North of England.
Montgomery Co., Md.
Salem, Md
Seneca, Md
Ulster Co., N. Y.
Belleville, N. J.
Nova Scotia.
Br. Phillipe, N. S.
Dorchester, N. B.
Cincinnati, O..
McBride's Corners, O.
Cleveland, O..
McBride's Corners, O.
Near Cleveland, O.
Berea, O.
Amherst, 0.
Humbletown, Penn.
Beauharnois, P. Q.
Murray Bay, P. Q
Cheat River, W. Va.
Acqua Creek, Va.
Manasses, Va.

2.380
2.168
2.500
2.452
2.410
2.661
2.350
2.424
2.353
2.363
2.188
2.333
2.210
2.500
2.290
2.254
2.200
2.346
2.512
2.577
2.632
2.183
2.348

148.7
135.5
156.2
153.2
150.6
166.3
146.8
151.5
147.0
147.7
136.1
145.8
138.1
156.2
143.1
140.8
137.5
146.6
157.0
161.0
164.5
136.4
146.7

1+ 27
1+ 27
1+ 26
1+ 24
1+ 40
1+314
1+ 27
1+240
1+ 19
1+ 26
1+ 23
1+ 28
1+ 22
1+ 22
1+ 35
1+ 20
1+ 18
1+ 28
1+ 38
1+ 36
1+ 80
1+ 16
1+ 17

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changes color.

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[blocks in formation]
[blocks in formation]

Tuckahoe.
Ashley Falls.
Snow Flake.
Tennessee.
Duke Marble.
Black Marble.
Sutherland Falls.

4 5 6 7

Westchester Co., N. Y.
Ashley Falls, N. Y..
Westchester Co., N. Y...
Dougherty's Q’y, E. Tenn.
Near Harper's Ferry, Va.
Isle La Morte, Vt.
Rutland, Vt.

2.794 2.742 2.848 2.711 2.812 2.682 2.666

194.6 171.3 178.0 169.4 175.7 176.6 166.6

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1+298 1+280 1+380 1+320 1+340 1+320 1+342

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OUR CENTER OF POPULATION.

By FRANK D. Y. CARPENTER, C. E.
Written for Van NOSTRAND'S ENGINEERING MAGAZINE.

If a man in San Francisco and another certain established units of weight and living in New York should wish to hold measurement. In the subject now under a conference, it requires no mathematical treatment the forces considered are the demonstration to prove that the proper individuals of our population ; and since place for them to meet would be at a all people, rich and poor, large and point half-way between these two cities. small, ignorant and learned, infant and In this manner the burden of travel is adult, male and female, are of uniform shared equally between the two. But, importance in swelling the grand total if one man in San Francisco and two of an enumeration, these forces are taken men in New York should desire to come as of equal intensity, and their moments together, the subject becomes more in- vary directly with the lengths of their volved. It is evident that it would be lever-arms. In ordinary mechanical in. unjust to require the solitary Californian vestigations the value of a moment is to perform the entire journey across the estimated in foot-pounds, the product Continent to meet his colleagues at their being named from its component factors ; homes, and it would be equally unfair a corresponding and appropriate term to oblige the two New Yorkers to with which to measure the moments of travel half-way to San Francisco to con- this special discussion would be “mile. fer with one person from there.

The men. question is, how great a penalty should If, now, with the one Californian and the former pay for his isolation, and how the two New Yorkers aforesaid, we commuch benefit should the latter reap from bine groups of three from Chicago, four their association ?

from New Orleans, and, to make the An equitable compromise is effected problem still more complicated, five from by apportioning the distance in inverse the central city of Saint Louis, it is still ratio to the number of persons con- possible to find, by the appliance of wellcerned. The one from San Francisco known principles in mechanics, some travels two-thirds of the distance while point at which they could assemble with the two from New York come one-third. justice to all, and that would be the cenThus, it will be observed, the amount of ter of this population of fifteen souls. It travel on each side of the rendezvous is is only necessary to assume a center, equal; that is, one man journeys, say, draw a system of rectangular axis two thousand miles, while the two ac- 'through this point, find the moments of complish one thousand each. In other the fifteen persons with regard to each words, to introduce from the science of of these two lines, note the prepondermechanics a term which it will frequently ance of moments on one side of each of be found convenient to use in this dis-, the axis, divide this surplusage by the cussion, the moment of the man from entire population under discussion, and San Francisco about the rendezvous is the result will be the amount of dis. equal to the moment of the two men placement of the axis from its rightful from New York with respect to the same position. Adjust these lines so as to point. The west moment is in equilib- compensate for that error, and their inrium with the east moment, and the ful. tersection will be at the true center of crum about which they balance is the population. center of this population of three per This is the general method to be emsons.

ployed in finding the center of populaA moment is the product of a force by tion of the country at large. But as it its shortest distance from some point, would be an infinite labor to consider its line or plane, to which it is referred, fifty millions of inhabitants individually, this distance being known as the lever- determining their moments one by one, age. The intensity of the force and the it becomes necessary to handle them by length of the leverage are counted in groups, such as states, counties, town.

ships, or square degrees, proceeding there. Through all of these vicissiupon the assumption that the people of tudes, however, there is a constant proeach of these groups are massed either gress to the West, and, its recurring in the geometrical center of the area oc- positions upon a map being ordinarily cupied by them, or at some other point symbolized by a star, this conventional which, from an inspection of the map, sign becomes literally the star of empire aided, perhaps, by local calculations, of whose westward way so much is seems to be their population center. written and said. It is now in Ohio. Whatever divisions of area may be The center of the population of any adopted for this purpose, it is always portion of the earth's surface has been well to obtain separately the moments of aptly compared to the center of gravity those cities which, owing to size or re- of a spherical shell of equal extent, havmoteness from either axis of co-ordi- ing weight, in any locality, in proportion nates, will exert most influence on the to the density of its population; but for center; the gain in accuracy will more tunately the determination of the former than repay for the extra trouble incur- center is not so intricate a problem as red.

that of the latter would prove to be. In The center of population of the United all ordinary discussions of the center of States may, therefore, be defined as that gravity, the objects considered are so point at which, if all of the people should limited in dimension that the forces of assemble there, the amounts of travel gravitation may be supposed to act in performed on any two sides would bal- parallel lines; but in treating a section of ance; in less popular language, the mo- the earth's area, one-eighth of a circumments of the population with respect to ference in extent, this assumption can no any great circle passing through that longer be permitted. Here gravity acts point, taken as an axis, are in equilibrium. along the normals to the surface, which It may sound strange to call an arc of a converge, approximately, at the center circle an “axis," but in the treatment of of the earth. a new subject like this, it is permitted to Again, even supposing that the forces take some liberties with language; in of gravity influencing this spherical shell the words of King John to Katharine : acted in lines parallel to each other, and “ We are the makers of manners." to the normal to the surface through

A knowledge of the whereabouts of their center, the moment of each of these this pivotal point is useful in various forces would then be the product of its ways. It has a practical value in the lo- intensity by its perpendicular distance cation of a national capital, university, from the center ; that is, by the sine of industrial fair, or other institution whose the arc included between its point of apsituation should be central and equally plication and the center. But, in getconvenient of access on all sides. To ting the center of population, it is evithe historian and political investigator dent that the leverage to be taken as a its successive positions, as shown by factor in obtaining the moment of any census after census, graphically exhibit group of people is the distance that they the movement and advance of our peo- would have to travel in order to reach ple in a wave which is at one time accel- that center. People do not travel along erated by the settlement of the Pacific the sine of an arc, however; they follow coast, in the next decade checked by the the arc itself, and in theoretical journeys, loss of life and enterprise incident to as all of the migration of this discussion our civil war, deflected to the North in must be, they take the shortest route, 1870 by the excessive devastation of the that is, the great circle. Southern States ; again to the South By thus considering that all leverages in 1880 by the rapid recovery and growth reaching from the center of population, of that desolated region, and probably or the axis passing through the same, to to be turned northward again in 1890 the distant city or state, are measured by the occupation of the region to be along the earth's surface, we are relieved opened by the Northern Pacific Railway, from one of the embarrassments which and by å rush of emigration to the affect the determination of the center of mineral regions of Alaska, and the es- gravity; and by further assuming that tablishment of a territorial government these measured arcs are stretched out

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