# Astronomical Dialogues Between a Gentleman and a Lady/Dialogue 6

​About a Month after our last Conference, I waited on the Lady in London, who after the usual Compliments, began thus with me.
Tho' you might be justly afraid to meet such a questionary Creature as I am, I will own, I'm glad to see you in this Place; for I have a great many things to enquire of you, with relation to our late ​Conferences in the Country. Ever since that I have been tumbling over Astronomical Books with the utmost Application; I have dipt it little also into the New Physicks, and I have been running over your Geometry, your Trigonometry, and your Spherick Projection, in order to use myself to Figures, and to get clearer Ideas of what the Astronomical Writers say: And tho' I believe I should have been frighted and deterred from beginning with Geometry, and the abstracted Mathematicks, yet I now find them so necessary that I am resolved to try at them, and will beg your help, when your Leisure will permit. But in the mean time pray tell me, Don't you think that the Elementary Mathematicks, and the Newtonian Physicks, or Natural Philosophy, might be taught to Gentlemen, or even to our Sex, in the easy and delightful way you have instructed me in Astronomy?
Doubtless, said I, Madam, there is no one really Master of any Science, but he can communicate it to another in plain and easy Words, and render it intelligible to any common Capacity and inquisitive Genius.
I entirely agree with you in your Notions, Madam, said I, and your Commands shall be my Delight as well as my Duty; in the mean time, can I serve your Ladyship in any thing now?
You are very obliging, said she, to anticipate your Trouble; but we will lose no time in Compliments: What I want at present is, to be instructed farther by some Diagram or Figure, how by the Earth's revolving round the Sun in her Annual Motion, together with that round her Axis, the different Seasons of the ​Year, Length and Decrease of Day and Night, &c. are accounted for. Have you drawn me such a Scheme as you once promised me, for this purpose?
I have, Madam, said I, and here it is; I took it chiefly from Mr. Flamstead's Doctrine of the Sphere; a Book, I dare say your Ladyship will one time or other dip into.
I have seen it, said she, in Sir Jonas Moor's Mathematicks, and perhaps may consider it further; for tho' I never design to attempt the Calculation or Construction of Eclipses, yet I shall be glad to know how the Astronomers do it. But pray, Sir, go on, and explain the Figures to me.
An Explication of Fig. V.
Let the Circle A B C D represent the Earth's Annual Orbit round the Sun, whose Centre is supposed to describe that Periphery, as it moves round the Sun from A towards B, in the Natural Order of the Signs, and from Aries to Taurus, &c.
N.B. The Figure ♈, ♋, ♎, ♑, should be placed in the Circular Line A B C D.
The 4 lesser Circles d o t i represent the Earth's quadruple Position in the 4 Cardinal Points, as they call them, i.e. at the 2 Equinoxes, and the 2 Solstices, and the Line d t at right Angles to the Colures, may fitly enough be called the Horizon of the Earth's Disk, because it separates that half part of the Earth which the Sun shines on, from the other which lies behind in the Dark.
But pray, said she, what do you mean by the Earth's Disk?
I use the Word, Madam, said I, because you will frequently meet with it in your reading; it signifies that round appearance of the Sun, Moon, or Earth, which we suppose to be the Object of any Spectator's View; and therefore the Earth's Disk is the appearance of that half of it, which because it is enlightened by the Sun, is seen by any remote beholder.
In these 4 Figures of the Earth, the Spectator's Eye is supposed to be below under the Earth's Centre e, which Centre always moves in the Circle A B C D. To an Eye so placed, the Circle d o t i, which divides the Earth's Upper Hemisphere from the Lower, will appear to lie in, or be coincident with the Plane of the Ecliptick; and therefore that may be called the Ecliptick on the Earth's Globe.
The North Pole of the Earth, or the upper End of the Axis, about which her Diurnal Motion is made, will then appear to be at P, 23° 30′ distant from e to the Pole of the Ecliptick; and if you draw a Line thro' those Points connecting the two Poles, that may be called the Line of Direction of the Earth's Axis; and if produced, it will be coincident with, or parallel to the great Solstical Colure, and therefore will describe such a Line on the Earth, to which, when the Sun's Rays run parallel, or whenever the Earth's Centre is in the Points ♑ or ♋, then will the longest, in the latter, and the shortest Days, in the former Case, happen to all the Inhabitants of the Earth.
Pray, said she, what occasions this Parallelism of the Earth's Axis? which I have read much of.
Madam, said I, 'tis not any new Motion, superinduced into the Earth, but only her keeping to the first Position or Direction of that Diameter about which she revolves; which she must always do, without it be changd by the Will of the Great Creator, who at first appointed it to be so as it is, But if you please, I will go on.
The Angle made between the Earth's Axis and that of the Ecliptick, may be learnt best from Fig. VI.Fig. VI.
In which the Ecliptick Line at ♈ C ♎ e represents the Earth's Annual Orbit, as view'd by the Eye, at a vast Distance, and when the Eye is placed a little above its Plane: Here let e be the Pole, and e d be the Axis of the Earth's Ecliptick, which you must suppose to be every where at right Angles to the Plane of the Great Orbit; and let P be the Earth's North Pole, P m the Earth's Axis, about which the Earth turns from West to East in 24 Hours; and suppose the Angle P C e to be always the same, viz. 23° 30′.
These things being supposed, it will be plain that every Point on the Earth's Surface, will, as the Earth revolves in her Diurnal Motion, describe a Circle about the next Pole: And when you consider, that every such Point is Vertical to the Earth's Centre, and answering to what hath usually been called the Zenith, or Vertex, in the Ptolemaick Projections, the Circle so described, is very properly called the Path of the Vertex, because 'tis a Track or Line made by the Motion of that Point.
Exactly right, said I, Madam, and no one could have explained it better. I think then, we shall now go on with Pleasure.
In such Projections as these 4 Figures of the Earth in Fig. V. a Circle equally distant from both the Poles, must be the Earth's Equator; and the Distance of any Place from that Circle, will be the Latitude of that Place; and therefore half the Diameter of any Path will be the Sine Complement of the Latitude of any Place, describing that Path.
If you take any Place on the Earth, and make a Circle pass thro' it, and the two Poles, that will be the Meridian of that Place.
That Point in the Earth's Periphery, which is opposite to the Sun, or which is ​found by a right Line drawn from the Earth to the Sun, is called the Sun's Place in the Ecliptick.
By the Figure it will appear plain, that since the Sun enlightens but one half of the Earth's Globe at a Time, if the Earth be in ♎ or ♈, the Horizon of the Disk will then coincide with the Solstitial Colure; and therefore as the Earth turns round her Axis, which now is coincident with the Line d t, the Paths of the Vertices, or the Equator and all its Parallels will be bissected by the Line d t: and while any particular place on the Earth, or any Vertex is in the Light Part t i d, the Inhabitants of it will see the Sun; and therefore to them it will be Day: And while it is in the Dark Part, it will be Night to them.
But when the Earth is moved on, either from ♈ to ♋, or from ♎ to ♑, the Line of Direction will coincide with the Solstitial Colure, and the Horizon of the Disk will ​become at Right Angles to it on the Pole of the Ecliptick e. Wherefore, when the Earth is in ♑, all places between the two Poles of the Earth and the Ecliptick, and the entire Artick Circle, will, now you see, be illuminated in their whole Revolutions, as the Earth revolves round its Axis i P o. The Vertexes therefore will see the Sun, each one longer than 24 Hours, according as it is more or less distant from the Pole of the Globes; and those that lie under the Artick Circle, touch the Horizon of the Disk; and consequently at this time of the Year, viz. June 10, they will see the Sun 90 Degrees from the Vertex, both on the North and South of their Meridian; so that as soon as he is Set, he will immediately Rise again; and consequently they have no Night: But all Paths without this, you see, do cut, or get within the Horizon of the Disk; and so will have their Days longer than their Nights, in proportion to the Quantity of the enlightned part of their Path, to the dark one; i.e. at London, As the Ark n v m l f, is to the Ark n z f; which is above Two to One: and therefore the Days will then be above 16 Hours long, and the Nights scarce 8.
Again, while the Earth moves from ♎ thro' ♑, and so on to ♈, you see the ​North Pole of the Earth is all that time in the Light part of the Disk; which shews you that to such as live under that Pole there will be 6 Months Day. But while the Earth runs on from ♈ thro' ♋ to ♎, that Pole will, you see, be in the dark part of the Disk; which shews that then, under the Poles, there will be 6 Months Night. For indeed, when the Earth is in ♋, all things will be the very reverse of what they are when she is in ♑; i. e. the Nights longer than the Days, &c.
But when the Earth is in ♈ or ♎, the Axis of the Earth's Revolution being d t, (the Horizon of the Disk) just one half of the Equator, and all its Parallels will be enlightened, and the other half in the Dark; and therefore the Days and Nights must be equal all the World over.
Sir, said the Lady, if you can part with this Figure, I will look it over more carefully another time, when I am by my self. In the mean time I have another trouble to give you, if you will oblige me in it; and that is to get me a sight of the famous Orrery, which I have heard you and others so often speak of; and which I think was made by Mr. Rowley, the famous Mathematical Instrument-​Maker, and Master of the Mechanicks to the King; and whom I find you have always recommended in your Books, as the best Workman of his Profession.
I shall stay in Town about a Week longer, and will enlarge my Time a Day or two, rather than miss seeing so instructive and curious a Piece of Ingenuity.
Madam, said I, the fine Instrument of that Name, which Mr. Rowley made for the East-India Company, is now luckily in a Place where I can come at it; I will go thither to morrow, and then appoint you a Day when I will wait on you to see it.