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space described during the time D E, supposed infinitely short, will be proportional to the area DEFG, which is expressed by the product of B C and DE; consequently the whole area A EF, will represent the space described in the time A E, and A HI, the space described in the time A H; but A H I is half of the square H K, and A E F of E L, the space is therefore always as the square of the time, and is equal to half the space that would be described, in the same time, with the final velocity."

Let the preponderating ring be removed at the time A H, the equal weights will continue their motion uniformly with the final velocity, and describe spaces directly as the time. And in the time H M = A H, the space it will describe is represented by the square I M = H K = P N.

The scale, which follows, applied as an income tax on real property, is in accordance with the above law, and whenever it shall please the Almighty that it shall be adopted—it will “ feed the hungry; clothe the naked; and render to every man his due," only by its justice! It begins with yearly incomes from real property of 501., assuming that a person could spare ten shillings or one per cent. from it to preserve general order, leaving him 491. 10s. for necessary subsistence and comforts : or it might begin at a higher income, according to the circumstance of each community:

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per cent. 50 pays 1 or 100

2 150

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6 350

7 400

8 450

9 500

10 550 11 600 12 650 13 700 14 750 15 800 16 850 17 900 18 950 19 1000 20 1050 21 1100 22 1150 23 1200 24 1250 25

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d. Income.
per cent. £.

d. 0 10 0 1300 pays 26 or 338 0 0 2 0 0 1350 27 364 10 0 4 10 0 1400 28 392 0 0 8 0 0 || 1450 29 420 10 0 12 10 0 1500 30 450 0 0 18 0 0 1550 31

0 24 10 0 1600 32 512 0 0 32 0 0 1650 33 544 10 0 40 10 0 1700 34 578 0 50 0 0 || 1750 35

0 60 10 0 1800 36 648 0 0 72 0 0 1850 37 684 10 0 84 10 0 1900 38 722 0 0 98 0 0 || 1950 39 760 10 0 112 10 0 2000 40 800 0 0 128 0 0 || 2050 41 840 10 0 144 10 0 2100 42 882 0 0 162 0 0|| 2150 43 924 10 0 180 10 0 2200 44

0 200 0 0 2250 45 ..1012 10 0 220 10 0 2300 46

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0 242 0 0 2350 47 ..1104 100 264 10 0 2400 48 ..1152 0 0 288 0 0 2450 49 1200 10 0 312 10 0 2500

50

0 0

. . 968 0

.. 1250

The same per centage of equality continued.

The equity of this scale is proved, by the number of persons such incomes will maintain, after paying the tax; being directly as the amount of the several sums required, for the maintenance of so many people; and, which is seen as follows:

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550

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700 ....

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528 0 84 10

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705 10 ... 162 0

738 0 180 10

769 10 200 0

800 0 220 10

829 10 242 0

858 0 264 10

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Pays

Remaining after Sufficient to For each Income.

paying the Tax to spend maintain Person. £. in luxuries above £50. Persons.

£.

income. 1700 578 0 ...... 1122 0

... 34

33 0 1750 612 10 ...... 1137 10

35 32 10 1800 648 0 ...... 1152 0

32 0 1850 684 10

1165 10

37

31 10 1900 722 0 ...... 1178 0

31 0 1950

760 10
...... 1189 10

39 30 10 2000 800 0 ...... 12000

30 0 2050 840 10

1209 10

41 29 10 2100 882 0 ...... 1218 0. ...... 42 29 0 2150 924 10

1225 10

43 28 10 2200 968 0

28 0 2250 ....1012 10

...... 1237 10

.......

45

.. 27 10 2300 ...1058 0 ....... 1242 0

27 0 2350 ....1104 10

1245 10 ...... 47 26 10 2400 ....1152 0 ...... 1248 0

26 0 2450 ....1200 10

1249 10

49 25 10 2500 ...1250 0...... 1250 0

......

50 25 0

...... 1232 0

...... 44

...... 46

...... 48

To explain. The sum allowed for the maintenance of the first person, after paying the tax, is £49. 108. which gradually decreases in amount, the first per centage paid to fifty ; because, that number of persons could live cheaper together, throughout the progressive increase; and, therefore, a just proportion is allowed, for every one maintained in a family, before the scale takes effect. Thus, suppose a person has an income of £5000. per annum, and he maintains in his establishment fifty people: the sum allowed is £25. each, or £1250., which deducted, leaves £3750. to spend in luxuries; and the tax is 50 per cent., or £1875.,

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which is about 37 per cent. from the whole income. Again, let the income be £ 1000. and that ten people are maintained in the establishment; the allowance for each person is £45., which substracted from the £ 1000. leaves £550. on which the tax is paid, and against that sum is 11 per cent. or £60. 10s. ;-or, that five people are maintained, it is then £47. 10s. for each person; which leaves £762. 10s., and on the scale against it is 15 per cent., or £112. 10s. Hence is seen that enough is left for every reasonable want, after deducting a due share to support the social order of the community

Here then is that law which is in accordance with the revealed law of God; namely, to render the same justice to others we desire ourselves under similar circumstances, and also with the meaning of law as interpreted by the wisest of all ages; namely, “to live honestly; to hurt nobody, and to render to every one his due.” Now, as the Almighty Lord in His government of the general creation established and supports this law-Can reasonable beings say it is not his law, when applicable to all their wants as reasonable beings?

This law being established on strict mathematical principles, hence, all mathematical knowledge emanates from the Lord, and no true wisdom does any one possess but directly from Him: and hence His words: “Without me ye can do nothing,” John xv. 5.

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