It is to be observed that Ferguson makes 2 of 7 days = 1 day 18 hours 28 minutes 46 seconds; whereas 87:7 d. :: 22 produces 1 day 18 hours 28 minutes 58 seconds nearly; also, he makes of 7 days=3 days 13 hours 17 minutes 46 seconds; but 65:7::33 = 3 days 13 hours 17 minutes 323 seconds; lastly; of 7 days 7 days 3 hours 59 minutes 54 seconds; but 42:7 d.:: 43 produces 7 days 4 hours exactly.

=

Ferguson adds that "all the numbers of teeth in the wheels. are here copied from Mr. Roemer's satellite instrument, except those for the second satellite, where Mr. Roemer has a wheel of 63 teeth turning a wheel of 32, instead of which, I make a wheel of 65 turn a wheel of 33, which is much nearer the truth." 176 Ferguson concludes his description by informing us

that

176 By referring to the last column of the above satellite table,-which, as Iready mentioned, is from a manuscript table by Ferguson, it will be seen that the "true period in the heavens," of the second satellite of Jupiter, is set down at 3 d. 13 h. 17 m. 54 s.; and hence, Ferguson's wheels of 5 was a much nearer approach to the true period than Roemer's wheels of . Roemer's wheels of 3 produce a period of 3 d. 13 h. 20 m., while Ferguson's wheels of produce a period of 3 d. 13 h. 17 m. 32-30s., being a period within 21 s. of the true period, as then understood. Sir John Herschell in his Astronomy gives 3 d. 13 h. 14 m. thus throwing Ferguson's wheel-work period about 3 minutes too slow. If Sir John's period of 3 d. 13 h. 14 m. be adopted, then, by continuous fractions, we find that if we make the wheels for the second satellite 8, it will produce a period of 3 d. 13 h. 13 m. 26 s., which is within 57 s. of his period. We may here note that we once had in our possession Ferguson's wheel of 33 which carried the second satellite in his machine; it is of boxwood, and the teeth beautifully cut into it. This wheel is now among the Ferguson relics in the Museum at Banff.

Wheels, used for the 1st satellite, produce a period too slow by about 22 seconds. By the process of continuous fractions, applied to the period of the 1st satellite, from a prime mover of 7 days, we find that the fraction produces a period within 5 seconds of the true time,-thus, let a wheel of 91 teeth turn round in 7 days, and be made to drive a wheel of 23 teeth, this wheel of 23 teeth will turn once round on its axis in 1 d. 18 h. 28 m. 41 5 s.; the true period being 1 d. 18 h. 28 in. 36 s.

There is a rude woodcut figure, and also a full description of Roemer's satellite machine, in "Harris's Lexicon Technicum,' a work which Ferguson says in his Life, that he perused while he was on a visit to Squire Baird at Auchmedden, in 1733 it is probable that Ferguson then copied the woodcut figure and the description. (See Harris's Lexicon Technicum. London, 1725; article "Satellite Machines.")

"About 16 years ago,177 I made one of these instruments to be turned with a winch by hand. It had a dial-plate divided into the months and days of the year, within which was a circle divided into twice twelve hours. On this plate there were two indexes, one of which was moved round over all the 365 days of the annual circle in 365 turns of the winch; and the other index was moved round over all the 24 hours in one turn of the winch, by which means I could, in a very short time, show at what times of the day the satellites would be eclipsed throughout the whole year; 178 and, after having the above numbers for

177 Ferguson here mentions that he made his satellite machine "about 16 years ago," that is, 16 years before the year 1767, when his "Tables and Tracts,' (from which this extract is taken), were published, and consequently refers to the year 1751.

178 Ferguson made three satellite machines,-the one just described was the first he made, simple in its construction, and being copied from Roemer's instrument, it would, like it, have a prime mover of 7 days. Shortly after it was finished, Ferguson discarded the prime mover of 7 days, and added to it one of 24 hours. We have in our possession (pasted on a small piece of mahogany) a short description (in MS. by Ferguson), showing its arrangement in its altered state, and of which the following is a copy,-he says, "On the axis of the handle is an endless screw which turns a wheel of 12 teeth, on whose axis is a pinion of 6 leaves, turning a wheel of 16 teeth, which turns a wheel of 42, on whose axis is a pinion of 7 leaves, turning a wheel of 60 teeth, on whose axis is a pinion of 12 leaves, turning a wheel of 73 teeth, on whose axis is the annual index which goes round the circle of months in 365 revolutions of the hour index, which is on the axis of the first wheel and pinion. The above-mentioned wheel of 42 teeth turns a wheel of the same number, on whose axis three other wheels are fixed, one of which has 87 teeth, the next above it 65, the next above which is the wheel 42, and the next, or uppermost, is a wheel of 28 teeth.' The several wheels and pinions in this part of the train are to be arranged thus,-19× 30×43 1940 and 2943360-8064365 exactly; or simply, × 13 = 1830, and 183960÷504365 as before. We annex a sectional view of the wheels and pinions calculated and adopted by Ferguson for his new prime mover

504

8064

(WHEEL 42 DRIVES ANOTHER WHEEL OF 42 IN THE SATELLITE WHEELWORK)

of 24 hours, in order that it may be the more easily understood. Below our sketch of the wheel-work of Ferguson's satellite machine will be found a very simple plan we adopted to accomplish the same motions;-A is a long endless screw, making a revolution in 24 hours, which turns round a small wheel B of 7 teeth in 7 days, which wheel drives the satellite machinery. The long endless screw also drives a small wheel of 5 round in 5 days, which has an endless screw D that drives wheel 73 round in 365 days, or in 365 turns of the endless screw. By this simple arrangement we obtain movers of 1 day (or 24 hours), of 7 days, and of 365 days.

the motions of the satellites, any clockmaker may easily construct a machine of this sort, by which the times of the immersions and emersions of the satellites may be known before-hand, in order to be prepared for observing them in the heavens." ("Tables and Tracts." Lond., 1767, pp. 158, 159).

We have no other memoranda of Ferguson for the year 1751, excepting, that "he was occasionally occupied towards its close, in delivering lectures on astronomy, and the rectification of the Calendar."

1752.

FERGUSON'S seeming APPLICATION for some VACANT SITUATION. Early in the year 1752, his attention appears to have been directed to some vacant situation or office in or about

To adopt 7 days as the prime mover of the wheel-work in a satellite machine is rather an inconvenient mover; a prime mover of 24 hours is preferable. We. give the reader a tabular view and section of the wheel-work of a satellite machine made in 1805 by the late Dr. Wm. Pearson, having a prime mover of 24 hours, that its wheels and resulting periods may be compared with the Ferguson-Roemer machine just described.

This sectional view of Dr. Pearson's satellite machine will be readily understood from the description of Ferguson's machine. We may just note that wheels 39, 27, 18, and pinion 8, are all fixed on the same axis, and revolve with it in 24 hours, which is the unit or prime mover. Wheel 39, turning round in 24 hours, drives wheel 69 round in 1 d. 18 h. 27 m. 41 s. Wheel 27, turning round in 24 hours, drives wheel 69 round in 3 d. 13 h. 20 m. Wheel 18, turning round in 24 hours, drives wheel 129 round in 7 d. 4 h.; and pinion 8, turning round in 24 hours, drives wheel 134 round in 16 d. 18 h. It is somewhat remarkable that two of the periods in this machine are precisely alike to those in Ferguson's, viz. the periods of the 3d and 4th satellites.

London, and he became a candidate for it; and as the matter is nowhere afterwards mentioned, it is to be presumed that he was one of probably a great many unsuccessful candidates. All our endeavours to ascertain something about this vacant office have proved fruitless.

In reference to it, however, is the following letter from Martin Folkes, Esq., President of the Royal Society, to the Rev. Mr. Birch, its Secretary, at the Royal Society's house in Crane Court:

"I pray the favour of Mr. Birch that he will please to present this recommendation at the meeting of the Society this afternoon, as it is my humble request that any of the gentlemen present, to whom it may not be disagreeable, to promote the success of Mr. James Ferguson, who is very strongly recommended to me as a gentleman of the greatest merit. From the Society's most dutiful,

66 Feby. 20th, 1752."

humble servant,

Copied from the Birch collection of letters in the
British Museum, No. 4308, Vol. 9, p. 282.

M. FOLKES."

During the first months of 1752, we find that "Ferguson was still busy with his lectures on Astronomy, and on the rectification of the Calendar; and it would appear that he had considerable success, principally owing, perhaps, to the curiosity of the public being then aroused on the subject of the Calendar, and the proposal for striking off 11 days from the year 1752." 179

179"The rectification of the Calendar was effected on 3d September, 1752; the 3d of September of this year was called the 14th, thus striking off the 11 days which had been in excess." We have before us "An Almanac for the year of our Lord 1752, and from the World's Creation 5754 years, by Tycho Wing, Philomath." On looking into the September of this year, in it, we find the following notice, which is inserted in a blank space between September 2d and 14th:

Sept. 1752.

"According to an Act of Parliament passed in the 24th year of his Majesty's reign, and in the year of our Lord 1751, the old style ceases here, and the new style takes place; and consequently, the next day, which in the old account would have been the 3d, is now to be called the 14th: so that all the intermediate nominal days, from the 2d to the 14th, are omitted, or rather annihilated this year; and this month contains no more than 19 days."

Although this is not the proper place to enter on a discussion of the Calendar, a few remarks, however, may be made to show the nature of the subject Ferguson had to deal with. In A.D. 325, the vernal equinox occurred on March 21st. About the year 1750, the vernal equinox occurred on March 9, making a differ

THE LUNARIUM.-About the beginning of the year 1752, Ferguson invented a sort of Rotula, which he called "The Lunarium." A few of these Lunariums are still to be found. It consists of several concentric moveable card-discs, the largest of which is about 15 inches in diameter, the smallest, 5 inches, on which are engraven the 294 days of Moon's age; the 24 hours of the day; circles full of dates for 6000 years before and after the year 1800, &c. Within a space on the middle card-disc, we find the following:

“A LUNARIUM, showing the Days of all the New and Full Moons,
and the Moon's Age every day for 6000 years before or after any
year in the 18th century, and the time of the Moon's Southing on
each day of her Age. By James Ferguson."

scarce.

This Lunarium has been long out of print and is now very Our friend Mr. Robert Sim, in Keith, has a MS. copy We have the MS. middle card-disc of one, from which the above note is extracted.

of one.

ence of 11 days; this was occasioned by estimating and using 365 d. 6 h. as the length of the year, taking in the 6 hours every fourth year, as they in that time amounted to 24 hours or 1 day. The true mean length of a year is 365 d. 5 h. 48 m. 52 s., which, on being subtracted from 365 d. 6 h., shows a difference of 11 m. 8 s., that is, the year estimated at 365 d. 6 h. is too long by 11 m. 8 s.; this excess, 11 m. 8 s. x 444 m. 32 s. that had been added to the Calendar every four years since A.D. 325. About the year 1750, these 44 m. 32 s. added every four years since A.D. 325, had amounted to 11 days very nearly; and hence it was necessary to strike off these 11 days in order to restore the vernal equinox again to 21 March. Had the year consisted of 365 d. 6 h. exactly, then, by taking up these 6 hours every fourth year, and making a day of them, would have been perfect, and engendered no error in any time to come; the yearly excess of 11 m. 8 s. amounts to an entire day in about 129 years.

It will be seen from these remarks that the question of the Calendar is simply one of dealing with the 5 h. 48 m. 52 s. What part of a day is 5 h. 48 m. 52 s.? -By continuous fractions it is shown that the fractional equivalents for this 5 h. 48 m. 52 s. are 3654 days, 365 days 365; now, it has been shown that 365 is a term too great by 11 m. s.; then try 365, this gives a nearer approximation to the truth, as 365 days reduced is = 365 d. 5 h. 47 m. 35 s., being a period only 1 m. 17 s. faster than the true period; therefore, by adding 7 entire days to the Calendar every 29 years, the error of a day would not occur in a less period than 992 years. Suppose all the months every 29th year to have 31 days each, this would add these 7 days to the Calendar, and no rectification would be required for near 1000 years. 365 would give a period still nearer, For a full exposition of the Calendar, and how in future it is to be dealt with by leap centenary years, see any work on Astronomy. We have in our possession

a small and very rare volume, entitled, "THE EARL OF MACCLESFIELD'S SPEECH IN THE HOUSE OF PEERS, ON MONDAY THE 18TH DAY OF MARCH, 1750, at the SECOND READING OF THE BILL FOR REGULATING THE COMMENCEMENT OF THE YEAR, &C. LONDON: PRINTED BY CHARLES DAVIS, PRINTER TO THE ROYAL SOCIETY, M.DCC. LI.," which gives a very clear description of the Calendar, and how it was to be rectified.