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give of the reality of our professions: and as such we are assured they will be mercifully accepted by God, through the mediation of Christ.

Since our Lord has given himself for us, he claims on our part the willing dedication of ourselves to his service. He claims not merely our passive abstaining from evil, but our active exertions to live soberly, righteously, and godly in this present world.

Such are the peculiarities of the Christian faith into which we have all been baptized, and according to which we all profess to live: Arising from the free grace of God, and bringing salvation to all men—teaching us to flee from that which is evil, and to cleave to that which is good—opening to our view the most glorious prospects, the blessed hope of heaven, and the appearing of our great God and Saviour Jesus Christ—Declaring his wonderful mercy, in giving himself for us; and the end of the commandment, our redemption from all iniquity, our purification, and sanctification.

These glad tidings are disclosed to man. But he is free to accept, or to refuse them. If he accept them, and persevere in his obedience unto the end, there is laid up for him "a crown of righteousness, which the Lord the righteous Judge shall give" him "at that day." If he

d 2 Tim. iv. 8.

d

refuse, upon his own head will the punishment fall. And how severe that just vengeance will be, the Scriptures declare in language which we can neither misunderstand nor overlook.

May that God whose mercies are infinite, and who wills not the death of a sinner, but rather that he should be converted and live, so direct and rule our hearts, that we may be redeemed by the merits of Christ Jesus, and become purified to him as a peculiar people, zealous of good works.

APPENDIX.

NOTE A. LECTURE IV.
LECTURE IV. p. 67.

On the change produced in the time of rotation of a mass, in consequence of its condensation, or expansion.

THE particular instance, adduced in the text for the sake of illustration, is purposely limited. The conclusion depends upon these principles.

Suppose a mass M, either rigid or not, to revolve uniformly about an axis passing through the center of gravity, with an angular velocity a.

Let m be one particle, at the perpendicular distance r from the axis of rotation.

Then, if the body be projected upon the plane, which is perpendicular to the axis, and passes through the center of gravity,

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projected area described by m, in an unit of time, about the center of gravity;

= 2 mass x area;

.. Emr2a = sum of all these products.

Now a is common to the whole mass.

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And Emr2 = moment of inertia of the whole mass, with respect to the axis of rotation passing through the center of gravity;

cess.

= Mk3: k being found by the usual proSee Whewell's Dynamics, Book III. Chap. 111.

Now if the same mass be either contracted or expanded, and a represent the angular velocity with which it will then revolve; and Mk2 = moment of inertia : by the principle of conservation of areas,

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And if the original figure of the body be similar to its figure after the change has taken place, and r, r' be radii of the respective equatoreal sections, which are considered circular;

ift and

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are the times of revolution with the angular velocities a, a, respectively.

If then the Earth were expanded, without altering the relative arrangement of its particles, until its radius at the equator were equal to that of the Moon's orbit, considered circular, the time of its rotation would be about

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The same conclusion will obtain, if the form of the

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