quite neglected it at Edinburgh, where I might have improved my knowledge by conversing with those who were very able to assist me.-I began to compare the ecliptic with its twelve signs (through which the sun goes in twelve months) to the circle of twelve hours on the dial-plate of a watch, the hour-hand to the sun, and the minutehand to the moon, moving in the ecliptic; the one always overtaking the other at a place forwarder than it did at their last conjunction before. On this, I contrived and finished a scheme on paper for shewing the motions and places of the sun and moon in the ecliptic on each day of the year, perpetually; and consequently, the days of all the new and full moons.

To this I wanted to add a method for shewing the eclipses of the sun and moon; of which I knew the cause long before, by having observed that the moon was, for one half of her period, on the north side of the ecliptic, and for the other half on the south. But, having not observed her course long enough among the stars by my above-mentioned thread, so as to delineate her path on my celestial map, in order to find the two opposite points of the ecliptic in which her orbit crosses it, I was altogether at a loss how and where in the ecliptic (in my scheme) to place these intersecting points: this was in the year 1739.

At last, I recollected, that when I was with Squire Grant, of Achoynaney, in the year 1730, I had read, that, on the first of January, 1690,

the moon's ascending node was in the 10th minute of the first degree of Aries; and that her nodes moved backward through the whole ecliptic in 18 years and 224 days, which was at the rate of 3 min. 11 sec. every 24 hours. But, as I scarcely knew, in the year 1730, what the moon's nodes. meant, I took no further notice of it at that time.

However, in the year 1739, I set to work at Inverness; and after a tedious calculation of the slow motion of the nodes from Jan. 1690 to Jan. 1740, it appeared to me, that (if I was sure I had remembered right) the moon's ascending node must be in 23 deg. 25 min. of Cancer, at the beginning of the year 1740. And so I added the eclipse-part to my scheme, and called it The Astronomical Rotula.

When I had finished it, I shewed it to the Rev. Mr. Alexander Mac Bean, one of the ministers at Inverness, who told me he had a set of almanacks by him for several years past, and would examine it by the eclipses mentioned in them. We examined it together, and found that it agreed throughout with the days of all the new and full moons and eclipses mentioned in these almanacks; which made me think I had constructed it upon true astronomical principles. On this, Mr. Mac Bean desired me to write to Mr. Mac Laurin, professor of the mathematics at Edinburgh, and give him an account of the methods by which I had formed my plan, requesting him to correct it where it was wrong. He returned me a most polite and friendly

answer (although I had never seen him during my stay at Edinburgh) and informed me that I had only mistaken the radical mean place of the ascending node by a quarter of a degree; and that, if I would send the drawing of my Rotula to him, he would examine it, and endeavour to procure me a subscription to defray the charges of engraving it on copper-plates, if I chose to publish it. I then made a new and correct drawing of it, and sent it to him, who soon got me a very handsome subscription by setting the example himself, and sending subscription-papers to others.

I then returned to Edinburgh, and had the Rotula-plates engraved there by Mr. Cooper.* It has gone through several impressions, and always sold very well till the year 1752, when the style was changed, which rendered it quite useless.Mr. Mac Laurin received me with the greatest. civility when I first went to see him at Edinburgh. He then became an exceedingly good friend to me, and continued so till his death.

One day I requested him to shew me his orrery, which he immediately did. I was greatly delighted with the motions of the earth and moon in it, and would gladly have seen the wheel-work, which was concealed in a brass box, and the box and planets above it were surrounded by an armillary sphere. But he told me, that he never had opened it; and I could easily perceive that it could

* Cooper was master to the justly celebrated Mr. Robert Strange, who was at that time his apprentice.

not be opened but by the band of some ingenious clock-maker, and not without a great deal of time and trouble.

After a good deal of thinking and calculation, I found that I could contrive the wheel-work for turning the planets in such a machine, and giving them their progressive motions; but should be very well satisfied if I could make an orrery to shew the motions of the earth and moon, and of the sun round its axis. I then employed a turner to make me a sufficient number of wheels and axles, according to patterns which I gave him in drawing and after having cut the teeth in the wheels by a knife, and put the whole together, I found that it answered all my expectations. It shewed the sun's motion round his axis, the diurnal and annual motions of the earth on its inclined axis, which kept its parallelism in its whole course round the sun; the motions and phases of the moon, with the retrograde motion of the nodes of her orbit; and consequently, all the variety of seasons, the different lengths of days and nights, the days of the new and full moons, and eclipses.

When it was all completed, except the box that covers the wheels, I shewed it to Mr. Mac Laurin, who.commended it in presence of a great many young gentlemen who attended his lectures. He desired me to read them a lecture on it, which I did without any hesitation, seeing I had no reason to be afraid of speaking before a great and good man who was my friend.-Soon after that, I sent

it in a present to the Reverend and ingenious Mr. Alexander Irvine, one of the ministers at Elgin in Scotland.

I then made a smaller and neater orrery, of which all the wheels were of ivory, and I cut the teeth in them with a file. This was done in the beginning of the year 1743; and, in May that year, I brought it with me to London, where it was soon after brought by Sir Dudley Rider. I have made six orreries since that time, and there are not any two of them in which the wheel-work is alike for I could never bear to copy one thing of that kind from another, because I still saw there was great room for improvements.

I had a letter of recommendation from Mr. Baron Eldin at Edinburgh to the Right Honourable Stephen Poyntz, Esq; at St. James's, who had been preceptor to his Royal Highness the late Duke of Cumberland, and was well known to be possessed of all the good qualities that can adorn a human mind. To me, his goodness was really beyond my power of expression; and I had not been a month in London till he informed me that he had wrote to an eminent professor of mathematics to take me into his house, and give me board and lodging with all proper instructions to qualify me for teaching a mathematical school he (Mr. Poyntz) had in view for me, and would get me settled in it. This I should have liked very well, especially as I began to be tired of drawing pictures, in which, I confess, I never strove to excel, because my mind