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bumble Conversation. And may a great Blefling of God croçon our Labours! Let us go on and the Lord prosper us. And again, The un

holy Teacher, let him preach ever so well, discourseth to little Purpose; • there will be no Life in his DoEtrine, because his Life is so deftitute of • the Spirit of Holiness; he will sooner damn his own Soul than save any * Man's else. His Discourses, tho' arm'd with the most powerful Oratory, • will serve to move no other Affection in his Hearers, than that of Indignation against his Hypocrisy and Impudence, to hear him excellent

ly declaim against a Vice, of which himself is notoriously guilty. adly, The most excellent Prelate, the late Bishop of Salisbury.] The

Manners and the Labours of the Clergy, these are real Arguments which • all People do both understand and feel ; they have a much more cona ( vincing Force, they are more visibie and perjúkde more universally than « Books can do, which are little read and less considered. And indeed, • the Bulk of Mankind is so made, that there is no Working on them,

but by moving their Affections, and commanding their Esteem. Zeal . in Devotion, and Diligence in the Pastoral Care, are fallen under too vi. • fible and too fcandalous a Decay. And whereas the Understanding the Scriptures, and an Application to that facred Study was at first the diftinguishing Character of Protestants, for which they were generally nick• named Gospellers; these Holy Writings are now so little Audied, that • such as are obliged to look narrowly into the Matter, find great Cause of Regret and Lamentation, from the gross Ignorance of such as are either in Orders, or that pretend to be put in them. While Men imagine that • their whole Work consists in publick Functions, they reckon that if they

either do these themselves, or procure and bire another person in Hoły • Orders to do thera, that then they answer the Obligation that lies on • them. And the Pastoral Care, the Instructing, the Exhorting, the Ad• monishing, and Reproving, the Directing, and Conducting, the Visiting ! and Comforting the People of the Parish, is generally neglected ; while • the Incumbent does not think fit to look after it, and the Curate thinks • himself bound to nothing, but barely to perform Offices, accord! ing to Agreement.' And again, . But what can we say, when we find

often the poorest Clerks in the richest Livings? whose Incumbents, not • content to devour the Patrimony of the Church, while they feed them, • felves, and not the Flock, out of it, are so scandalously hard in their Allowance to their Curates, as if they intended equally to farve both Cu. rate and people.

Your Conftant Reader, R. D.

An Answer to a Note in a Book of Mr. RUTHERFORTH's,

concerning the Case of ABRAHAM's offering up ISAAC ; in Defence of Mr Warburton,

H. G. Lordon, August 10, 1744: N a late Book of the Learned and Ingenious Mr Rutherforth's, enti

tled, An Esay on the Nature and Obligation of Virtue, I find, in a Nore, in p. 314, 317, fome Exceptions against understanding the Command which God gave to Abraham 19 sacrifice his Son to have been a Revelation

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to him of the Sacrifice of Christ for the Redemption of Mankind; and Shall attempt to confute them as briefly as I can.

Mr Warburton, whose Interpretation the mentioned is of this famous Command, begins his Proof of it from these Words of our Saviour's spoken to the Jews; your Father Abraham rejoiced to see my Day, and be saw it and was glad. He takes it for granted, and Mr. R. proves, elaborately, that the Jews understood our Saviour as if he had affirm'd, that Abra. ham and he were Cotemporaries, and Abraham had beheld him in person; which contains Mr W's Assertion, that they understood him to speak of seeing in the literal Sense, and not figuratively. And there is very little Force in Mr R's Attempt to evade the obvious Consequence from hence. For there is no Reasons to assert the Jews wilfully perverted our Saviour's Meaning with design to have a pretence for stoning him, but it is a mere groundless, not to say most improbable, Fancy; and though they were always captious in their Discourses with him, that has never been efteemid an Objection of any Weight against the very common Argument, in plain Cases, from their Apprehensions of it, to his real Meaning. It was, in all probability, because his Words expressed definitely, and without any Ambiguity, seeing properly and sensibly, either expresly, or by obvious Consequence, that they pafled the Construction they did on the other part of his Affertion, in which, indeed, not being duly qualified, and for want of Ears to hear, they were likely enough to misapprehend him.

It is very strange in Mr R. to affirm, universally, that a Man may not be said to have seen that of which he has seen a Representation, whether the Yokes and Bonds by which a Prophet express'd a certain Caprivity, might take the Name of that which they were designed to make a strong Impression of, or no (which ’ris needless to dispute, or consider), such a Picture, on Resemblance, nevertheless, as Isaac's Sacrifice was of our Saviour's, might very well be itiled it, or his Day, and with as much Propriery, for Instance, as the Memorial of the Lord's Pallover might be called his Passover ; and Abraham's seeing the facrifice of his Son, be said to be feeing that which it fignified to him, as they to eat of the Passover, who partook of the Paschal Lamb; or the Israelites in the Wilderness to drink of a certain Rock, which Rock was Chris. And this certainly was our Saviour's meaning ; that Abraham had seen a sensible Representation of his Day ; because the Word grdw used by the Evangelist, whether taken literally, or figuratively, always denotes a full Intuition; which was what alone, Abraham could have had of that which happened Ages after him. There is no Neceflity, nor Reason, for expounding this Word by Believing, as Mr R. does, in this Text; these all died in Faith, not baving received the Promises, but baving seen them afar of, and were persuaded of them. The persons here spoken of, law thoseTypes, which represented promised Blessings (which, in our Times, have been accomplish'd, and so we have received) and apprehended their whole Nature, and both primary and secondary End; and believed, and did not doubt but that what they foreshewed would çertainly come to pass : But having seen them afar off, and were persuaded of them; first they saw and then believed ; the one of these Acts (I mean in a Vulgar sense) was not the other, but laid the Foundation for, and propounded the Object of it.

Mr R. owns that our Saviour affirms his Redemption of Mankind was reycaled 10 abrabam, And Mr W. has prov'd, not only that our Saviour

would

would not have appealed to it on the Occasion, and to the Persons he did, if it had not been discoverable by them in the Jewish Scriptures; but that cerrainly lo important a Fact would not be omitted in them; after which he shews that no other part of Abraham's History can admit of this Interpretation, but the Command in question. Which determines the Dif pute between Mr W. and Mr i. (to say nothing of the Appendix to a late Examination of Mr W's second Proposition in D.L.) without infifting on the sense of the Word cod w fo fully vindicated. But whereas in the Second part of his Differtation Mr W.

proves

from our Saviour's Words, several Circumstances relating to this Transaction of Offering up ljaar, Mr R. enquires, which of all these particulars could be found in the History of God's Command to Abraham to sacrifice him, related in such a Manner chat fuch Jews as studied their Scriptures might be well acquainted with the Facts and Circumstances to which our Saviour appeals in them? In which he,' certainiy, betrays great Inattention to Mr W's Dissertation, and the Course of his Argument. The CircumItance which Mr W. insists on, and which alone bis Argument requires to be contained in Moses's History, is this; chat Abraham faw a senlible Representation of Christ's Sacrifice for the Redemption and Resurrection of Mankind ; nor is it any where affirm'd by him, or necessary to be, that the Jews might discover this Circumstance, precisely and completely, in the Command to offer up ljaar, before the Doctrine of Christ's suffering for the Sins of Mankind did, or might well explain it to them ; and which both had been, with fufficient plainness, preached to those Jews, whom our Saviour told that their great Ancestor had seen his Day, before he did, and especially was very soon after. And therefore they might well discover it therein; for Mr W. by the foundest Rules of Logic and Criticilm, has proved it to be: Has prov'd, that the History of this Command, so circumstanc'd as it is, demands this Interpretation. The Application of this to the Argument, with which Mr R. concludes his Attack, is very obvious ; and it appears, at first sight that Mofes might, as induitriously, as Mr W. any where contends, conceal from the Jews, the Knowledge of a future State; and yet those Jews our Saviour discoursed with, perceive that Abraham's offering up his Son represented to him Christ's Sacrifice for the Redemption of Mankind to eternal Happiness. And to both Mr W's Premiffes in proof of his Interpretation of this Case, and his Concluifion are very safe, notwithstanding this threatning Dilemma, and all that Mr R. has advanced to the contrary. As, I hope, he will be very senfible, and own with an Ingenuity worthy his Character, especially since he has told us he might give this as an Instance of the Patriarch's Knowledge of a future State ; and seems to apprehend nothing to lie in his Way *20 doing it, but those Difficulties which I cannot but think, now, are very manifeitly and totally removed.

The Curve which the Moon, or any other SATELLITE,

describes about the Sun, determined, on all possible Suplofitions of DISTANCE and VELOCITY. T

HAT the Moon's Path is a protracted Epicycloid, as was aserted in iny * last, needs no Demonstration: it following immediately from

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Sze Gent. Mag. Vol. 13. p. 592.

1

1

the Genesis of that Curve, and from the Periodical Motions of the Earth
and Moon. Dr 'sGravesande, particularly, had considered the Paths of
the Earth and Moon in this Light, long before your Correspondents had
moved any Question on the Subject ; for in his Inštitut.'Philos. Neut. Tab.
XVII. Fig. 2. the Curve which he delineates has the form of an Epiry-
cloid partly cons'ex towards the Sun. It is true, indeed, this learned Author
has here committed an Oversight, facing, beyond certain Limits, the pro-
Fracted Epicycloid becomes every where concave towards the Centre of its
Base, as shall be demonstrated below. A Mistake which he was probably
led in to by a mechanical Construction that did not nearly enough exhibit
the true Distances of the Earth and Moon from the Sun. I followed him,
and unluckily drew after me Mr R. Yate; for which he more justly owes
me a Grudge than for Stealing his † Trencher and Bread. However, as
foon as I had investigated a Theorem for finding the Point of Contrarx
Flexion in these Curves, the Error was corrected of Courle: All is let io
rights again, and the Moon restored to her Path every where (cho' not by
qually) concave towards the Centre.

The Result of my Enquiry was shortly this. That if n represent the
Number of Synodical Months in a Year, oxid) the Distance of the
Earth from the Sun, and m the Distance of the Moon from the Earth;
then will the Epicycloid have a Point of Contrary Flexion, or nut, as d x 192
is greater or less than Unity,
Whence, if

, in the Case of our Moon, we put 11 = 12, and the
Distances of the Sun and Moon from the Earth to be as 327 10 1, m will
be .0413, and d m m less than Unity, that is, there will be no Point of
contrary Flexion. But if n, or m, or both, are any how increased cili dy me
is greater than Unity, then will the Moon's Path be partly concar'e, partiy
convex. As if m=in, that is, if other things remaining, the Moon was
removed to the Distance of a little more than 121 Semediameters of the
Earth, her Path would be convex for some time before and after the Con-
junEtion ; but if 9 was again diminished to the Convexity would 'va-

12,
nish, and the Radius of Curvature in the Moment of Conjun&tion become
infinite. And, by the Way, we see how easily 'sGravejande and others
might be imposed on by a mechanical Description, if they happened noe
to fix the Pencil or describing Point very near the Centre of the Circle.

DEMONSTRATION.
Let the Circle AES whose Centre is R, be the Base upon which a Cir-
ele CAPQ whose Centre is C, revolving describes with the point T the
Curve TtH. Let the revolving Circle, from its first Position, when TCR
were in a right Line, come into the Position cEaq, and the describing
Point T into the Place t. From t, through the Point of Contact E draw
tEB meeting the Axis in B; join likewise gR which will pass thro' the
lame point E ; and draw GF, a Tangent to the Epicycloid in i, cutting CR

in F.

Then because the Curve TtH is described by the continual Rotation of
Et about the Points of contact E, the Angle FeB is right ; and if c is a
Point of contrary Flexiòn, the Fluxion of the Angle BF vanilles. Fur-
ther, cE being to ct in a constant ratio (as of 1 1097) the Sines of the Angles

Point
+ See Gent. Mag, Vol. 13. p. 471, 639,

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1

T с

ctE, cEt will be in the same ratio ; and the Sum of these Angles, or the
Angle acE, will be in a given ratio to the Angle ARE, namely in the ra-
tio of RA 1o CA (or of n to 1). Writing therefore for the Sines of the
Angels cte, cEt, to the Radius
Unity, the Letters z, y, and for
the several Angles mentioned, the

F
Letters that ftand at their angu-
lar Points, we shall have these
shree Equations.
1. y z

t 2. ixE=nR

C

а.
H
3.

B=EXR
Take the Fluxions, and because
of the contrary Flexion, put B=),

G

AL that is E=R; substitute likewise for t, E, their equals

у and

and V1---22'

✓ by an ealy Reduction it will beg=S

B

9

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V 12-1 , d being equal to

2

nary as

* X1. But y is real or imagi

d
X m

is greater or less chan Unity, whence the Reason of the Rule and Limitation above delivered is manifeft. Q. E. D.

VR

COROLLA RIES: 1. The Sine z is found by Equ. 1.. And the Sum of the Angles to which the Sines z, y belong; i. e. the Angle acE, is the Motion of the Satellite in its proper Orbit, from the Time that it was in Opposition at T; as ARE Eń X acE) is the Motion of the Planet for the fame Time.

2. If m=1,y=1. That is, EB touches both Circles in E, where two Points of contrary Flexion meeting are changed into a Point of Rea flexion. If no, the Curve is a Circle with the Semidiameter RC. If m is greater than Unity, it becomes an Epicycloid contracted with Nodes. And if d is infinite, the Bale being now a strait Line, there is generated the protracted, contracted, or common Cycloid, according as m is teffer or greater than Unity, or equal to it: and in the protracted, the Sine of cEi=m.

It is obvious that the Path of the Earth is of the same Species with that of the Moon, only less deviating from the Ecliptic Circle described by their common Centre of Gravity. And,that the same Theory may be applied to the Satellites of Jupiter and Saturn. The Periodic Time of a Satellite compared with that of its Primary will give the quantity 1, and its farthest Heliocentric Elongation from the Primary will determinem; whence it may be readily seen to what species the Epicycloid of that Satela lite belongs, after which the Questions concerning it will be purely Geometrical. Jan. 19, 1743-4. I remain, Sir, &c. X. Y.

Na

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