enlightened hemisphere of the globe from that which is in the dark at any given time, and shewing at what places the general eclipse begins and ends with the rising or setting Sun. 7. A handle M, which turns the globe round its axis by wheelwork, and at the same time moves the penumbra across the frame by threads over the pulleys L, L, L, with a velocity duly proportioned to that of the Moon's shadow over the Earth, as the earth turns on its axis. And as the Moon's motion is quicker or slower according to her different distances from the Earth, the penumbral motion is easily regulated in the machine by changing one of the pulleys.

To rectify the machine for use. The true time To rectify of new Moon and her latitude being known by the it. foregoing precepts, § 353, et seq. if her latitude exceed the number of minutes or divisions on the scales (which are on the side of the frame hid from view in the figure of the machine) there can be no eclipse of the Sun at that conjunction; but if it do not, the Sun will be eclipsed to some places of the Earth; and, to shew the times and various appearances of the eclipse at those places, proceed in order as follows.

To rectify the machine for performing by the light of the Sun. 1. Move the sliders K, K, till their indexes point to the Moon's latitude on the scales, as it is north or south ascending or descending, at that time. 2. Turn the month-plate E till the day of the given new Moon comes to the annual index G. 3. Unscrew the collar a little on the axis of the handle, to loosen the contiguous socket on which the threads that move the penumbra áre wound, and set the penumbra by hand till its centre comes to the perpendicular thread in the middle of the frame; which thread represents the axis of the ecliptic. 4. Turn the handle till the meridian of London on the globe comes just under the point of the crooked wire F; then stop, and turn the hour-circle D by hand, ti!! XII at noon

its use.

comes to its index, and set the penumbra's middle to the thread. 5. Turn the handle till the hourindex points to the time of new Moon in the circle D; and holding it there, screw fast the collar N. Lastly, elevate the machine till the Sun shines through the sight-holes in the small upright plates 0, 0, on the pedestal; and the whole machine will be rectified.

To rectify the machine for shewing by candlelight. Proceed in every respect as above, except in that part of the last paragraph where the Sun is mentioned; instead of which, place a candle before the machine, about four yards from it, so that the shadow of intersection of the cross threads in the middle of the frame may fall precisely on that part of the globe to which the crooked wire F points; then, with a pair of compasses, take the distance between the penumbra's centre and intersection of the threads; and equal to that distance set the candle higher or lower, as the penumbra's centre is above or below the said intersection. Lastly, place a large convex lens between the machine and candle, so as that the candle may be in the focus of the lens, and then the rays will fall parallel, and cast a strong light on the globe.

These things being done, (and they may be done sooner than they can be expressed) turn the handle backward, until the penumbra almost touches the side HF of the frame; then turning gradually forward, observe the following phænomena. 1. Where the eastern edge of the shadow of the penumbral plate I first touches the globe at the solar horizon: those who inhabit the corresponding part of the Earth see the eclipse begin on the uppermost edge of the Sun, just at the time of its rising. 2. In that place where the penumbra's centre first touches the globe, the inhabitants have the Sun rising upon them centrally eclipsed. 3. When the whole penumbra just falls upon the globe, its western edge at the solar horizon touches and leaves the place where

the eclipse ends at Sun-rise on the lowermost edge. Continue turning, and, 4. the cross lines in the centre of the penumbra will go over all those places on the globe where the Sun is centrally eclipsed. 5. When the eastern edge of the shadow touches any place of the globe, the eclipse begins there; when the vertical line in the penumbra comes to any place, then is the greatest obscuration at that place; and when the western edge of the penumbra leaves the place, the eclipse ends there; the times of all which are shewn on the hour-circle; and from the beginning to the end, the shadows of the concentric penumbral circles shew the number of digits eclipsed at all the intermediate times. 6. When the eastern edge of the penumbra leaves the globe at the solar horizon C, the inhabitants see the Sun beginning to be eclipsed on his lowermost edge at its setting. 7. Where the penumbra's centre leaves the globe, the inhabitants see the Sun set centrally eclipsed. And lastly, where the penumbra is wholly departing from the globe, the inhabitants see the eclipse ending on the uppermost part of the Sun's edge, at the time of its disappearing in the horizon.

N. B. If any given day of the year on the plate E be set to the annual-index G, and the handle turned till the meridian of any place comes under the point of the crooked wire, and then the hour, circle D set by the hand till XII comes to its index; in turning the globe round by the handle, when the said place touches the eastern edge of the hoop or solar horizon C, the index shews the time of Sun-setting at that place; and when the place is just coming out from below the other edge of the hoop C, the index shews the time when the evening-twilight ends to it. When the place has gone through the dark part A, and comes about so as to touch under the back of the hoop C, on

the other side, the index shews the time when the morning-twilight begins; and when the same place is just coming out from below the edge of the hoop next the frame, the index points out the time of Sun-rising. And thus, the times of the Sun's rissing and setting are shewn at all places in one rotation of the globe, for any given day of the year: and the point of the crooked wire Fshews all the places over which the Sun passes vertically on that day.

A PLAIN METHOD

OF FINDING THE

DISTANCES OF ALL THE PLANETS

FROM THE SUN,

BY THE

TRANSIT OF VENUS OVER THE SUN'S DISC, IN THE YEAR 1761.

TO WHICH 18 SUBJOINED,

AN ACCOUNT OF MR. HORROX's OBSERVATIONS

OF THE TRANSIT OF VENUS IN

THE YEAR 1639:

AND ALSU,

OF THE DISTANCES OF ALL THE PLANETS FROM THE

SUN, AS DEDUCED FROM OBSERVATIONS OF

THE TRANSIT IN THE YEAR 1761.