# Philosophical Transactions of the Royal Society (1665-1886)/Volume 4/Number 47

Contents:
* Contents
* Instructions concerning the Use of Pendulum-Watches for finding the Longitude at Sea; together with a Method of a Iournal for such Watches.⁠
* An extract of a Letter written from Vienna concerning twp Mock-Suns lately seen in Hungary.⁠
* A Relation of the Conferences held in the Royal Parisian Academy for the Improvement of the Arts of Painting and Sculpture.⁠
* An Account of some Books.
** I. INSTITUTIONUM CHRONOLOGICARUM Libri duo, una cum totidem ARITHMETICES CHRONOLOGICÆ Libellis, per Guil. Beveregium M. A.
** II.⁠ ELEMENTS OF SPEECH; An Essay of Inquiry into the Natural Production of Letters together with an Appendix of a Method to instruct Persons Deaf and Dumb; by William Holder D. D. &c.
** III.⁠ GUAGING PROMOTED, begin an Appendix to Stereometrical Propositions formerly publish't by Rob. Anderson. in quarto.
Numb. 47.
PHILOSOPHICAL
TRANSACTIONS.
May 10. 1669.
The Contents.
Instructions
Concerning the Use of Pendulum-Watches, for finding the Longitude at Sea.
WHereas 'tis generally esteemed that there is no Practise for the Finding of the Longitude at sea comparable to that of those Watches, which instead of a Ballance-wheele are regulated by a Pendulum, as now they are brought to great perfection, and made to measure time very equally; and many perhaps here as ​well as elsewhere being not well versed in the ordering and managing of that Instrument: We though, it might be no un-acceptable service, to make known such Directions, as may teach the Use thereof at Sea. Which we shall doe by now giving you our Translation of those instructions, which some yeares since were made publick by tho Worthy M. Christian Hugens of Zulechem, in the Belgick Tongue, as they have been since altered or rather enlarged by two other Eminent Members of the R. Society.And they are these;
1.
THose, that intend to make use of Pendulum-watches at Sea, must have two of them at least; that, if one of them should by mishap or neglect come to stop, or (being by length of time become foul) need to be made clean there may likely always remaine one in motion.
2.
The Person, to whom the Care of these Watches shall be committed, is-to informe himself from the Watch-maker or some other, so as to understand the inward parts of the Watches, the manner of winding them up, and how to set the Indexes, or Hands having the hours, minutes and seconds, &c.
3.
The Watches on Ship-board are to be hung in a close place, where they may be freest from moisture or dust, and out of danger of being disorder'd by knocking or touching.
4.
Before the Watches be brought on ship-board, 'tis convenient, they be adjusted to a middle or mean day (of which more in the next Section:) the use of them being then most easy, it being little or no trouble to the Watchmakers, when they have one that is set Iust, to set others accordingly: But yet, if time or convenience so to doe should happen to be wanting, they may notwithstanding be used at Sea with the like certainty, provided you know, how much they goe too fast or too slow in 24. hours, as is directed in the next Section.
5.
Here take notice, that the Sun or the Earth passetb the 12. Signes, or makes an entire revolution in the Ecliptick in 365 days, 5 hours, 49 min, or there about, and that those days, reckon'd from noon to noon, are of different lengths; as is known to all, that are vers'd in Astronomy. Now between the longest and the shortest of those days, a day may be taken of such a length, as 365 such days, 5. hours &c. (the same numbers as before) make up, or are equall to than revolution: And this is call'd the Equal or Mean day, according to which the Watches are to be set; and therefore the Hour or Minute shew'd by the Watches, though they be perfectly Iust and equal, must needs differ almost continually from those that are shew'd by the Sun, or are reckon'd according to its Motion. But this Difference is regular, and is otherwise call'd the Æquation, and here you have a Table, that shows it.
| | Januar. | Januar. | Februa. | Februa. | Mar. | Mar. | April. | April. | Mai. | Mai. | Jun. | Jun. |
| | m. | sec. | m. | sec. | m. | sec. | m. | sec. | m. | sec. | m. | sec. |
| 1 | 6 | 10 | 0 | 0 | 4 | 46 | 14 | 23 | 19 | 25 | 16 | 24 |
| 2 | 5 | 47 | 0 | 2 | 5 | 3 | 14 | 39 | 19 | 28 | 16 | 13 |
| 3 | 5 | 24 | 0 | 4 | 5 | 21 | 14 | 55 | 19 | 29 | 16 | 1 |
| 4 | 5 | 2 | 0 | 8 | 5 | 39 | 15 | 10 | 19 | 29 | 15 | 49 |
| 5 | 4 | 41 | 0 | 12 | 5 | 57 | 15 | 25 | 19 | 29 | 15 | 37 |
| 6 | 4 | 21 | 0 | 16 | 6 | 15 | 15 | 39 | 19 | 28 | 15 | 24 |
| 7 | 4 | 2 | 0 | 21 | 6 | 33 | 15 | 53 | 19 | 26 | 15 | 11 |
| 8 | 3 | 44 | 0 | 26 | 6 | 51 | 16 | 7 | 19 | 24 | 14 | 58 |
| 9 | 3 | 27 | 0 | 32 | 7 | 9 | 16 | 21 | 19 | 21 | 14 | 45 |
| 10 | 3 | 11 | 0 | 40 | 7 | 27 | 16 | 34 | 19 | 18 | 14 | 32 |
| 11 | 2 | 55 | 0 | 48 | 7 | 45 | 16 | 47 | 19 | 15 | 14 | 19 |
| 12 | 2 | 39 | 0 | 57 | 8 | 3 | 16 | 59 | 19 | 11 | 14 | 6 |
| 13 | 2 | 23 | 1 | 6 | 8 | 22 | 17 | 11 | 19 | 7 | 13 | 53 |
| 14 | 2 | 7 | 1 | 16 | 8 | 41 | 17 | 22 | 19 | 2 | 13 | 50 |
| 15 | 1 | 52 | 1 | 26 | 9 | 1 | 17 | 33 | 18 | 57 | 13 | 27 |
| 16 | 1 | 38 | 1 | 37 | 9 | 21 | 17 | 43 | 18 | 51 | 13 | 15 |
| 17 | 1 | 25 | 1 | 49 | 9 | 41 | 17 | 53 | 18 | 45 | 13 | 3 |
| 18 | 1 | 13 | 2 | 2 | 10 | 1 | 18 | 3 | 18 | 39 | 12 | 52 |
| 19 | 1 | 2 | 2 | 15 | 10 | 21 | 18 | 13 | 18 | 33 | 12 | 41 |
| 20 | 0 | 51 | 2 | 28 | 10 | 40 | 18 | 23 | 18 | 26 | 12 | 30 |
| 21 | 0 | 41 | 2 | 42 | 10 | 59 | 18 | 32 | 18 | 18 | 12 | 19 |
| 22 | 0 | 32 | 2 | 56 | 11 | 18 | 18 | 39 | 18 | 10 | 12 | 8 |
| 23 | 0 | 24 | 3 | 11 | 11 | 37 | 18 | 46 | 18 | 1 | 11 | 58 |
| 24 | 0 | 18 | 3 | 26 | 11 | 56 | 18 | 53 | 17 | 51 | 11 | 48 |
| 25 | 0 | 13 | 3 | 41 | 12 | 15 | 18 | 59 | 17 | 41 | 11 | 38 |
| 26 | 0 | 9 | 3 | 56 | 12 | 34 | 19 | 4 | 17 | 30 | 11 | 28 |
| 27 | 0 | 6 | 4 | 12 | 12 | 54 | 19 | 9 | 17 | 19 | 11 | 18 |
| 28 | 0 | 3 | 4 | 29 | 13 | 12 | 19 | 14 | 17 | 8 | 11 | 9 |
| 29 | 0 | 1 | | | 13 | 31 | 19 | 18 | 16 | 57 | 11 | 0 |
| 30 | 0 | 0 | | | 13 | 49 | 19 | 22 | 16 | 46 | 11 | 52 |
| 31 | 0 | 0 | | | 14 | 6 | | | 16 | 35 | | |
| | Jul. | Jul. | Aug. | Aug. | Sept. | Sept. | Oct. | Oct. | Nov. | Nov. | Dec. | Dec. |
| | m. | sec. | m. | sec. | m. | sec. | m. | sec. | m. | sec. | m. | sec. |
| 1 | 10 | 45 | 11 | 7 | 19 | 41 | 29 | 16 | 31 | 13 | 21 | 14 |
| 2 | 10 | 38 | 11 | 16 | 20 | 1 | 29 | 30 | 31 | 3 | 20 | 44 |
| 3 | 10 | 31 | 11 | 25 | 20 | 22 | 29 | 43 | 30 | 53 | 20 | 14 |
| 4 | 10 | 25 | 11 | 36 | 20 | 43 | 29 | 56 | 30 | 43 | 19 | 44 |
| 5 | 10 | 19 | 11 | 48 | 21 | 4 | 30 | 9 | 30 | 43 | 19 | 14 |
| 6 | 10 | 13 | 12 | 1 | 21 | 25 | 30 | 22 | 30 | 32 | 18 | 44 |
| 7 | 10 | 7 | 12 | 14 | 21 | 47 | 30 | 34 | 30 | 8 | 18 | 14 |
| 8 | 10 | 2 | 12 | 28 | 22 | 9 | 30 | 45 | 29 | 55 | 17 | 44 |
| 9 | 9 | 58 | 12 | 42 | 22 | 31 | 30 | 55 | 29 | 40 | 17 | 14 |
| 10 | 9 | 54 | 12 | 57 | 22 | 52 | 31 | 4 | 29 | 23 | 16 | 44 |
| 11 | 9 | 51 | 13 | 12 | 23 | 13 | 31 | 12 | 29 | 6 | 16 | 14 |
| 12 | 9 | 49 | 13 | 27 | 23 | 33 | 31 | 19 | 28 | 48 | 15 | 44 |
| 13 | 9 | 47 | 13 | 43 | 23 | 53 | 31 | 26 | 28 | 30 | 15 | 14 |
| 14 | 9 | 46 | 13 | 59 | 24 | 13 | 31 | 32 | 28 | 11 | 14 | 44 |
| 15 | 9 | 46 | 14 | 16 | 24 | 33 | 31 | 38 | 27 | 51 | 14 | 12 |
| 16 | 9 | 46 | 14 | 33 | 24 | 53 | 31 | 43 | 27 | 30 | 13 | 41 |
| 17 | 9 | 47 | 14 | 50 | 25 | 13 | 31 | 47 | 27 | 8 | 13 | 10 |
| 18 | 9 | 49 | 15 | 8 | 25 | 33 | 31 | 50 | 26 | 45 | 12 | 40 |
| 19 | 9 | 52 | 15 | 26 | 25 | 52 | 31 | 53 | 26 | 22 | 12 | 10 |
| 20 | 9 | 56 | 15 | 45 | 26 | 11 | 31 | 55 | 25 | 58 | 11 | 40 |
| 21 | 10 | 0 | 16 | 4 | 26 | 30 | 31 | 55 | 25 | 34 | 11 | 10 |
| 22 | 10 | 4 | 16 | 23 | 26 | 49 | 31 | 55 | 25 | 10 | 10 | 40 |
| 23 | 10 | 8 | 16 | 42 | 27 | 8 | 31 | 55 | 24 | 45 | 10 | 10 |
| 24 | 10 | 13 | 17 | 1 | 27 | 26 | 31 | 54 | 24 | 20 | 9 | 41 |
| 25 | 10 | 18 | 17 | 21 | 27 | 43 | 31 | 52 | 23 | 55 | 9 | 13 |
| 26 | 10 | 23 | 17 | 41 | 28 | 0 | 31 | 50 | 23 | 30 | 8 | 45 |
| 27 | 10 | 28 | 18 | 1 | 28 | 16 | 31 | 47 | 23 | 4 | 8 | 17 |
| 28 | 10 | 34 | 18 | 21 | 28 | 32 | 31 | 43 | 22 | 38 | 7 | 50 |
| 29 | 10 | 41 | 18 | 41 | 28 | 47 | 31 | 37 | 22 | 11 | 7 | 23 |
| 30 | 10 | 49 | 19 | 1 | 29 | 2 | 31 | 30 | 21 | 43 | 6 | 28 |
| 31 | 10 | 58 | 19 | 21 | | | 31 | 22 | | | 6 | 34 |
When you first set your Watch by the Sun, you are to subduct from the time observed by the Sun, the Æquation adjoyned to that day of the Month in the Table, and to set the Watches to the remaining hours, minuts and seconds, that is, ills! Watches are to be set so much flower, than the time of the Sun, as (in the Table) is the Æquation of that day; so that the Æquation of the Day, added to the time of the Clock, is the true time by the Sun. And when after some days, you desire to know by the Watch the time by the Sun, you are to add to the time, shew'd by the Watch, the Æquation of that day; and the Aggregate shall be the time by the Sun, if the Watch hath been perfectly well adjusted after the measure of the Mean days; for the doing of which, this will be a Convenient way;
Draw a Meridian line upon a floor (the manner of doing which is sufficiently known; and note, that the utmost exactness herein is not necessary:) and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. foot or more one from the other, as the smalness of the thred will admit. When the middle of the Sun the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly (for the better and more secure discerning whereof, you must be furnish't with a glass of a dark colour, or somewhat black: with the smoak of a Candle,) you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Æquation of that day by the Table. E. g. If it were the 12 of March, the Æquation of that day being by the Table, 8 min. 3 sec; these are to be subducted from 12. hours, and the remainder will be 11. hours, 51. min. 57. sec; to which hours, minutes and seconds you are to set the Index of the Watch respectively: Then after some days you are to observe again in the same manner, and, likewise to note the hour, min, and sec, of the Watch; to which you are to add the ​Æquation of these days, taken out of the Table; And if the Aggregate doe Iust make 1z. hours, the Watch is set adjusted to the right measure; but if it differ, you are to divide the minutes and seconds of that difference by the number of the days between both the Observations, to get the daily difference, Let us suppose, this second Observation to have been made the 20. of March, viz, 8. days after the first, and finding, that the Middle of the Sun being seen in the Meridian in the same line
| | h. | m. | sec. |
| with the two threds, as before, the Watch points | 11 | 51 | 7 |
| The, Æquation of the 20 of March, by the Table, is | 0 | 10 | 40 |
| Which being added to the time, show'd by the Watch, gives | 12 | 1 | 47 |
If this had been Iust 12 hours, the Watch would have been well adjusted, but being 1. min. 47. sec. more than 12, it hath gone so much too fast in 8. days. And these 1 min. 47. sec. that is, 107. sec. being divided by 8, there comes. 13⅛ sec. for the difference of every 24. hours; which difference being known, if you want time, or have no mind to take the pains to adjust the Watch to its right measure (this being not necessary, since you may bring it thus on ship-board) note onely the daily difference, and regulate your self accordingly, as hath been mention'd. But if you will adjust it better, you must remove the less weight of the Pendulum a little downwards, which will make it goe slower; and then you must begin to observe anew by the Sun, as before, If it had gone too slow, you must have remov'd the mention'd weight somewhat upwards. And this is of that importance in the Ending out of Longitudes, that, if it be not observ'd, you may sometimes in the space of 3 months misreckon 7. degrees and more (yet without any fault in the Watches;) which under the Tropicks will amout to above 400 English miles.
Having shew'd, How the Watches may be adjusted at Land, or how their daily difference may be known; next shall follow, How the same may be done, when a Vessel rides at anchor, it being hardly fesible when she is under saile.
In the morning then, when the Sun is just half above the Horizon, note, what hour, min. and sec. the Watch points at, ​if it be going; if not, set it a going, and put the Indexes, at what hour, min, and sec, you please. Let them goe till Sun-set, and when the Body of the Sun is just half under the Horizon, see, what hour, min. and sec. the Indexes of the Watch point at, and note them too; and reckon, how many houres &c. are Pass'd by the Watch between the one and the other: which is done by adding to the Evening-Observation the hours, &c. that the morning-Observation wanted of 12. or 24. in case the Hour-hand hath in the mean time pass'd that hour once or twice; otherwise the difference only gives the time. Then take the half of that number, and add it to the hours, &c. of the morning-Observation, and you shall have the hours, &c. which the Watch did show, when the Sun was in the South; where unto add the Æquation in the Table belonging to that day, and note the summe. Then some days being pass'd (the more the better,) you are to doe Iust the same: and if the hour of this last day be the same, that was noted before, your Watch is well adjusted; but if it be more or less, the difference divided by the number, elapsed between the two Observations, will give the daily difference. And if you will, you may let it rest there, or otherwise, removing the lesser weight of the Pendulum you may adjust it better.
| | H. | m. | sec. | | H. | m. | sec. |
| E. g. Suppose March 11th in the Morning, when, the Sun half appears above the Horizon, the Watch points at | 5 | 30 | 10 | | 0 | 10 | 3 |
| In the Evening, when the Sun appears half set, ay | 5 | 20 | 6 | | 11 | 59 | 57 |
| To know by the Watch the time elaps'd between both, subduct the time of the rising | 5 | 30 | 10 | |
| From | 12 | 0 | 0 | |
| Rests | 6 | 29 | 50 | |
| Whereunto adding the time of the setting | 5 | 20 | 6 | |
| There comes for the time elapsed between them | 11 | 49 | 56 | | 11 | 49 | 56 |
| Whereof the half is | 5 | 54 | 58 | | 5 | 54 | 58 |
| Which added to the time of the Suns rising | 5 | 30 | 10 | | 0 | 10 | 3 |
| There comes the time of the Watch when the Sun was in the South | 11 | 25 | 8 | diff. | 6 | 5 | 1 |
| To which adding the Æquation of the 11th of March | 0 | 7 | 45 | | 0 | 7 | 45 |
| The Summe is | 11 | 32 | 53 | | 6 | 12 | 46 |
| Seven days after, viz. March 18, let the rising of the Sun be observ'd, and the Watch point then at | 5 | 19 | 4 | | 11 | 58 | 57 |
| And at his setting, let the Watch point at | 5 | 25 | 2 | | 0 | 4 | 55 |
| To find the time elaps'd between them, subduct the time of the rising. | 5 | 19 | 4 | Or, | 11 | 58 | 51 |
| From | 12 | 0 | 0 | | 24 | 0 | 0 |
| Rests | 6 | 40 | 56 | | 12 | 1 | 3 |
| To which adde the time of the setting | 5 | 25 | 2 | | 0 | 4 | 55 |
| And you'l find the time past between them | 12 | 5 | 58 | | 12 | 5 | 58 |
| Whereof the half is | 6 | 2 | 59 | | 6 | 2 | 59 |
| Which adde to the time of the rising | 5 | 19 | 4 | | 11 | 58 | 57 |
| And you have the time when the Sun was in the South | 11 | 22 | 3 | | 6 | 1 | 56 |
| Whereunto adding the Æquation of March 18 | 0 | 10 | 1 | | 0 | 10 | 1 |
| The Summe is | 11 | 32 | 4 | | 6 | 11 | 57 |
| Which Summe if it had agreed with the first, viz. | 11 | 32 | 53 | | 6 | 12 | 46 |
then, had the watch been set to the right measure; but seeing the latter is less than the former, the difference being 49. sec; the Watch hath by so much, in 7. days, gone too slow;; which 49 Sec. divided by the number of days, you have 7 Sec. for the daily difference; and by so much the Watch goes too slow in 24. hours.
You may also, instead of the Suns rising and setting, take two equall Altitudes of the Sun, before and after Noon, and having noted the time given by the Watches at the time of both the Observations, proceed with it in the same manner, as was Iust now directed for observing the Sun in the Horizon. In either of which ways there may be some Error, caused by ​the Suns Refraction, which is inconsiderable, and therefore needs not to betaken notice of.
6.
By means of these Watcher to find at Sea the Longitude of the Place, where you are.
Give to each of the Watches a name or a mark, as A. B. C; and before you set saile, set them to the time observ'd by the Sun in the place, where you are, and whence you are departing, allowing for the Æquation of the day, whereon you make your Observation; Which day you are to note, if the Watches be not well adjusted; otherwise it is not necessary.
Then afterwards being at Sea, and desiring to know the Longitude of the place where you are, that is, how many degrees the Meridian of that place is more Easterly or Westerly, than the Meridian of that place where you did set the Watches; you must observe by the Sun or Stars, what time of the day it is, as precisely as is possible, and note at the same time, to what hour, minutes and sec. the Watches doe point (which time, if the Watches be not set to the right measure, is by the known daily difference to he adjusted,) adding thereunto the Æquation of the present day, which gives you the time of the day, shew'd by the Sun, at the place where the Watches were set: And if this time of the day be the same with that, observ'd where you are, then you are under the same Meridian with the place, where the Watches were set by the Sun; but if the time of the day, observ'd where you are, be greater than that shew'd by the Watches, you may be assur'd, that you are come under a more Easterly Meridian; and if less you are come under a more Westerly, And counting for every hour of difference of time, 15 degrees of Longitude, and for every minute, 15. minutes or ¼ of a degree, you shall then know, how many degrees, minutes, &c. the said Meridians doe differ from one another.
E. g. Suppose, the Watches A. B. C. were set at the place, whence you parted, on the 20 of February, to the time of day observ'd by the Sun, abating the Æquaiion of the 20th of Febr. (viz 2 min, 28, sec.) and suppose that the Watch A. be ​set to its right measure, but that B. goes every day 7 sec. to slow, and C. every day 12. see. too fast. Some days after, suppose the 5th of May, desiring to know the Longitude of the place where you are at Sea, you observe the time of the day
| | h. | min. | sec. |
| there to be | 5 | 10 |
| And you find the Watch A. to point at | 2 | 6 | 0 |
| But the Watch B. to point at | 1 | 57 | 22 |
| Going too slow by 7. sec. every day, which makes in 74. days, (viz. |||
| From the 20th of Febr. to the 5th of May) | 0 | 8 | 38 |
| Which being added to its own time, gives the same |||
| | h. | min. | sec. |
| with than of the Watch A. viz. | 2 | 6 | 0 |
| You find also the Watch C to point at | 2 | 20 | 48 |
| Going 12 sec. too fast every day, which makes in 74. days | 0 | 14 | 48 |
| Which being subducted from its owne time gives again | 2 | 6 | 0 |
| The time of day therefore by the Watches being | 2 | 6 | 0 |
| Adde thereunto the Æquation of the 5th of May | 0 | 19 | 29 |
| And so you have for the time of day at the place where the Watches were set | 2 | 25 | 29 |
| But, the time observ'd being | 5 | 18 | 10 |
| Exceeds this by | 2 | 52 | 41 |
| Wherefore the Meridian of the place, where you are May 5th, is more Easterly, than the places where the Watches were set, by | 2 | 52 | 41 |
| | deg. | m. | d. |
| Which being reduced to degrees, reckoning 15 deg. for an hour, comes to | 43 | 10 | 15 |
'Tis true, that from the same reckoning it may be concluded, that you are 180. deg, more Easterly, which happens because the Hour-Index goes round in the space of 12. hours in the Watches; but the difference is so great, that one cannot be deceiv'd in it; else the Watch might be so made, that the Index shall goe round but once in 24 hours.
7.
To find the time of the Day at Sea.
Since that for finding the Longitude, the Time of the day ​at the place where you are must be known (as hath been said above) you must have a care to observe that time as precisely as is possible. For every minute of time, that you misreckon, makes a 4th part of a degree in longitude, which amounts, near the Æquator, to above 15. English miles, but less elsewhere. Wherefore to find the time of the clay with certainty, you are not to trust to the Observation of the Suns greatest Altitude, thence to conclude that 'tis just Noon, or that the Sun is in the South, unless, being betwixt the Tropicks, you have it just in the Zenith. For else the Sun being near the Meridian, remains for some time without any sensible alteration of its Altitude. Wherefore, though the Meridian Altitude may serve well enough for knowing the Latitude or the Hight of the Pole upon occasion; yet it will not serve for finding precisely the Longitude of that place. Much less are you to rely upon the Sea-compasses, thereby to End the precise time of Noon. Neither are the Astronomical Rings or other sorts of Sundyals sure enough for shewing the time to minutes and seconds. But it is better to observe the Suns Altitude, when 'tis in the East or West, (the nearer, the better:) for being there, its Altitude changes in a short time more sensibly than before or after; and thus from the Hight of the Pale, and the Declination of the Sun the Hour may be calculated; the manner whereof is sufficiently taught by others; yet by reason that this Calculation is somewhat troublesome, and that also there may be some Errors in the taking of the Suns Altitude, here follows an easier way.
8.
How by Observing the Rising and Setting of the Sun, and the Time by the Watches, the Longitude at Sea may be found.
This way doth neither require the Knowledg of the Hight of the Pole, nor of the Declination of the Sun, nor the Use of any Astronomical Instruments: Neither can the Refractions of the Sun or Stars cause any considerable Error; the refraction of the Morning differing but little or nothing from that of the Evening of one and the same day, especially at Sea. Thus then you are to proceed;
​At the Rising and Setting of the Sun, when it is half above the Horison, marke the time of the day, which the Watches, then shew; and though you have in the mean time sayl'd on, it is not considerable. Then reckon by the Watches, what time is elaps'd between them, and add the half thereof to the time of the Rising, and you shall have the time by the Watches, when the Sun. was at South; to which is to be added the Æquation of the present day by the Table. And if this together makes 12. hours, then was the Ship at Noon under the same Meridian, where the Watches were set with the Sun. But if the summe be more than 12, then was she at Noon under a more Westerly Meridian; and if less, then under a more Easterly; and that by as many times 15. degrees, as that Summ exceeds or comes short hours of 12: as the Calculation thereof hath been already deliver'd.
Suppose, e. g. that the Watches A and B, as before, were set with the Sun at the place whence you parted, the 20th of Febr; and the Indexes set to the Hour, min, and second, shewed by the Sun, abating the, Æquation of that day, viz. 2. min. and 20. seconds; the Watch A being reduc'd to the right measure, and B going too slow by 7. sec. a day. Afterwards on the 22th of May, desiring to know the Longitude of the place, to which you are come, you observe in the Morning the Sun
| | h. | min. | sec. |
| half above the Horizon when the Watch points at | 2 | 30 | 10 |
| And in the Evening, the Sun being half under the Horizon, when the same Watch points at | 3 | 8 | 40 |
| To find the Time elaps'd between them, subducting the time of the Rising | 2 | 30 | 10 |
| From | 12 | 0 | 0 |
| There remains | 9 | 29 | 50 |
| Adding thereunto the time of the Setting | 3 | 8 | 40 |
| You have for the time elaps'd between the Observations | 12 | 38 | 30 |
| Whereof the half | 6 | 19 | 15 |
| Being added to the time of Rising | 2 | 30 | 10 |
| You have the time by the Watch A, when the Sun was in the South | 8 | 49 | 25 ​ |
| And after the same manner you are to seek the time by the ||
| Watch B, when the Sun was in the South; which let be | 8 | 38 | 48 |
| But this Watch going 7. sec. a day too slow, it is retarded in 91. dayes, (from the 20th of Febr. to the 22 of May) | 0 | 10 | 37 |
| Which therefore added to the said time gives | 8 | 49 | 25 |
| That is the same time given by the Watch A. Now adding to this time of the Watches, the Æquation of the 22th of May | 0 | 18 | 10 |
| You have | 9 | 7 | 35 |
| Which is the same time of the day with that of the place, where the Watches were set when the Sun was in the same Meridian with the Ship, or where the Ship was at Noon. |
| | h. | min. | sec. |
| The difference is | 2 | 52 | 25 |
| Wherefore this last Meridian is by so much more Easterly, than the first; which being reduc'd to degrees (as hath been |
| | deg. | min. | sec. |
| formerly directed) make | 43. | 6 | 15 |
'Tis manifest, that by this way you find precisely enough the Longitude of the place, where you were at Noon, or the Time of the Suns being in the South: which, although it differs from the Longitude of the place, where you are when you observe the Setting of the Sun, yet you may estimate neer enough, how much you have adyanc'd, or chang'd the Longitude in those few hours, by the Log-line, or other Ordinary practises of reckoning the Ships way; or (which is the surer way) by the degrees pass'd in 24. hours by a former days Observation.
You may also, instead of observing the Suns Rising and Setting, observe the setting first, and then next morning the Rising; marking at both times the Time show'd by the Watches; and find thence, after the same manner as before, the Longitude of the place where the Ship was at Midnight.
Finally, you may also, instead of the Rising and Setting of the Sun, observe before and after Noon two equal Altitudes of the Sun, noting the time shown by the Watches, and reckoning in the same manner, as hath been said of the Rising and Setting: Yet it is to be consider'd that the Altitudes of the ​Sun are best taken, when it is about East and West, as hath been already intimated. But note, that in Sailing North and South you make not the Observations at the Suns rising and setting, but at its being; due East and West.
9.
But you may, especially in such Quarters, as lye farr North or South, yea and wherever you will, put the Rule here prescribed in practise, by taking 2. equal Altitudes of some known Starr, that riseth high above the Horizon. For you shall thence, according to the mention'd Rule, know at what time by the Watches the Starr hath been in the South; and so the Right Ascension of that Starr being known, as also the Right Ascension of the Sun, you may thence easily calculate, what time it then was: Which being compar'd with the time of the Watches, as before, shall give the Longitude of the place where you were, when you had the Start in the Meridian.
10.
If the Watches, that have gone exactly for a while, should come to differ from one another (as in length of time it may well happen, that the one or the other faile a minute, more or less;) in that case it will be belt to reckon by that, which goes fastest; unless you perceive an apparent cause, why it goes too fast; seeing it is not so easie for these Pendulum-Watches to move faster than at first, as it is to goe slower. For, the Wire, on which the Pendulum hangs, may perhaps by the violent agitation of the Ship come to stretch a little, but it cannot grow shorter; and the little Weight of the Pendulum perhaps slip clown wards, but cannot get up higher.
11.
When you get sight of any known Country, Island, or Coast, be sure to note the Longitude thereof as exactly as you can by the help of the Rules here prescribed. First, thereby to correct the Sea-Maps, after that the Longitude of a place shall have been found at divers times to be the same, so that you doubt no more of it. For all Mapps are very defective as to the Scituation of Places in respect of East and West, chiefly where Seas are interpos'd/ secondly, to be able always to know in the prosecution of your Iourney, how farr you have sail'd from ​any place to the East or West. And i by any notable mischance or carelesness all the Watches should come to stand still, yet you may at any place, whereof the Longitude is certainly known, set them a going again, and adjust them there by the Sun, and so reckon the Longitudes from that same Meridian. For, you are to know, that you are nor at all oblig'd to put one certain Meridian of any knowne place as a begining of the Longitude-reckoning; this hapening only in Mapps, or Tables of Longitude: As, when you take for that purpose the Meridian of the Pico in Teneriffe, or that of the Islands of Corvo and Flores (the most Westerly of the Azores) or any others. Yet it were very fit, that all Geographers agreed and pitched upon one and the same First Meridian, that so all places might be known by the same Degrees as well of Longitude as of Latitude; though in Voyaging it is sufficient, to observe only the difference of Longitudes, beginning to reckon from the Meridian of any place, you please, as if it were the first.
12.
If it happen, that being at Sea all the Watches stopp, you must, as speedily as is possible, set them a moving again, that you may know, how much you advance from than place towards the East or West: Which is of no small importance, since, for want of this knowledg, you are sometimes by the force of Currents so carried away, that though you saile before the Wind, yet you are driven a Stern; of which there are many Examples.
The Method of a Iournal for the Watches.
The Watches being distinguisht by marks as A. B. or the like, every day about Noon, or when most conveniently you can, observe the time of the day by the Sun, or by the Starrs at night, and subduct thence the minuts and seconds, that are adjoyn'd to that day in the Table, and write the remainder down in a paper, wherein 9. Columns or more are mark't, placing them in the second column, having plac'd the day of the Month in the first. And at the same time write down the hours, minutes and seconds of each Watch in a distinct Column, all ​opposite one to another. Then in another Column write downe the difference between the time taken by Observation, and that given by the Watches or one of them. Then, one Column for the Latitude: one, for the Longitude by the Ordinary way of reckoning: another, for the Longitude taken from the difference between the time found by Observation, and that given by the Watches: and at last, a large Column to note the Accidents, that befall the Watches, &c.
I received the account of the Parhelia's, seen Ianuar. 30th last, st. n. about one of the clock in the afternoon, over the City of Cassovia in Hungary. It was communicated to me from a Learn'd Iesuit, call'd Father Michel, who lives at Presburg, but is now in this City, There were two Parhelia's, one on each side of the true Sun, and they were so resplendent, that the naked Eye could not bear the brightness thereof. One of them (the lesser of the two) began to decay before the other, and then the other grew bigger, and continued well nigh two houres, projecting very long rays from it self. They were both on that part, which was towards the Sun, tinged with a pale yellow, the other parts being somewhat fuscous. There were at the same time seen several Rainbows, together with the Segment of a great white Circle, of a long duration, pulling through the two Pathelia's and the Sun: and all this at at time, when the Air was almost free from Clouds, though here and there were scatter'd some very thin-ones.
These Conferences are held once in a Month by divers Able Masters making reflexions and observations upon the rarest pieces in the Cabinet of his Most Christian Majesty, the ​establisher of that Academy. Monsieur Colbert, who takes a very particular care to make Arts florish in France, being pleased to visit those Artists some while since, to see what progress they made, and having receiv'd an Account of what had been done in their meetings, expressed himself to this effect, That as 'twas necessary, for the Teaching of Arts, to joyn Examples to Precepts, so he thought it proper, that from time to time the Works of the most excellent Painters should be examin'd, and such Observations made thereon, as would informe others, Wherein the perfection of a Picture consists. Which hath been ever since practised amongst them, as the best means to carry the Art of Painting to its higest perfection; such an Examen of the best Pictures disclosing many secrets of that Art, for which there are no Rules, and opening a dore to debate many important questions, hitherto not treated of.
In the particulars, which have been made publick, of these Conferences, we may find
First, A general Idea of the Art of Painting, wherein are consider'd two principal parts, the one belonging to the Theory; the other regarding the Pratice, and the dexterity of the hand. Where 'tis observ'd, that the Authors, that have written of Painting, have not treated of the former part, how considerable soever that be, in regard of the Dissein and Disposition of the Pieces.
Next, a Relation of 7. conferences, whereof fix were made upon as many Pieces of Raphael, Titian, Paul Veronese, and M. Pousin, and the seventh upon that of Laocoon. Where are to be met with many curious remarques, and among many others, these following.
M. le Brun considering a Piece of Raphael, where is represented the Combat of St Michel with the Divel, observes, that the expression particularly depends from the Bodies, which environ the Figures; affirming, that 'tis that, which sets out the Motion and Action in the figure of St Michel, who seems to have life in this Piece: For, as as if the Air were pressed by the Weight of the Body descending, it causeth, whatever it meets with as more light, to be raised, and drives it on high with violence.
​In another Piece, where Titian represents the Body of I. Christ carried to the Grave, M. de Champagne, the Elder, observes the dexterity of the Master in ordering the Colours and the Light. To make the Leggs of the Picture (which first present themselves)to stand out, he hath wrapped them about with a very white linnen sheet, and hath cloathed Nicodemus, who holds them, with a very vivid and very clear Lacque: On the contrary, to link the rest of the Body, he hath io taken the Light of the Picture, that the Shadow of Ioseph of Arimatbea, who helps to support the Leggs, falls on its head and Shoulders; which also contributes to impress on the Body the image of Death. The Order of the Colours is also very remarkable in the Cloaths. For betwixt the Green habit of Ioseph of Arimathea, and the Blew Mantle of the Blessed Virgin, is the yellow habit of Magdalen, wherein what is brown and dusky, is temper'd, and borrows of the different colours about it; that the Eye may pass by degrees from one of these colours to the other. Add because the Sleeve of Magdalen, which is of a bright yellow, is neer the habit of Nicodemus, which is also of a lively Colour; the Artist, to hinder that those two vivid colours may not entrench on one another, hath turn'd up Nicodemus's Sleeve against the yellow so that Rom the Shadow of one of these colours one passeth to the shadow of the other.
The Art of the Picture, spoken of in the fifth Conference, is no less remarkable. In this Piece, done by P. Veronese, is seen a Woman whose Carnation colour is so fresh and bright, that it dazleth the Eyes: M. Nocret examining, what may cause this beauty, observeth, that it proceeds in part from hence, that the Master hath ingeniously drawn before this Woman a Child cloathed in brown; behind her, a man in black; and on her side, a Negro, who maketh an admirable Concert with the great luster an splendor of that Carnation.
The two last Conferences, treating of two pieces of M. Poussin, doe furnish among other things; very elegant Examples of different Characters suting different persons. This Master having to represent many persons gathering Manna, gives to them all different postures, becoming their humor; on the fore-part of the Picture there are two youths; who following ​the genius of their Age, fight about the Manna. Near them are Men, gathering Manna in the mean time, and eating thereof. A little farther off, appears a Girle, who unwilling to take the pains of stooping, holds out her coat to receive the Manna falling down, and looks on it, as if the Heavens dropp'd it for none but her: Which well expresseth (says the observer) the Softness and disdainful Temper of that Sexe, which loves not to take pains, and imagines that all must come to pass, as they wish. In the other piece, which exhibits the Recovery of the Two Blind men, to whom our Saviour restored their Sight, there is an Old man, who comes very near, peeping, and looking as if he doubted of the truth of the Miracle: in which the Artist hath well observ'd the genius of Aged persons, who commonly are more incredulous and diffident than others.
Besides this, there are examin'd here and there in these Conferences divers Questions important in Painting; which would be too long to particularise in this place.
THis Author first taketh notice, that though most Nations have been diligently endeavoring to render a good account of Time (having its Original and Progress from the Motions of the Heavens) yet casting his Eyes upon some of the most famous Chronologers, as Scallger, Petavius, &c. he found Chronology obscur'd with many intricate Questions, fll'd with many knotty Controversies, stuffed with a multitude of uncertain Comments, and deliver'd in such an odd and dark method, that the knowledg thereof was not to be obtain'd without much difficulty, and loss of Time. Whereupon he declareth his Design to be, To deliver the same from Controversy, and only to treat of what concerns meerly the Distinction of Time, omitting matters of less concernment, and yet nothing of what may he requisite to Chronology it self; in which he (truly) asserts, That ​many things, most worthy to be known, may be found for which on may look in vain elsewhere.
And what he performes herein, he doth in a Method different from others, viz. meerly by Arithmetick, without the aid of Chronological Tables; which, even of the best Authors, will hardly be found without manifold faults.
In the first Book he treats of Time in general; of a Moment, (de Scrupulo;) an Hour, a Day, Week, Month: And then of the several sorts of Years, the Celestial, Iulian, Gregorian, Ægyptian, Æthiopick, Persian, Syriack and Grecian; item, the Astronomical, Civil, and Solar Year of the Iews, and the Arabick year.
In the second, the Author (shewing good skill in Astronomy) treats of 'Conjunctions', and Eclipses, of the Æquinoxes and Solstices, the Circle of the Sun, and, the Dominical Letter; the Circle of the Moon or the Golden number, the Roman Indication, and Epacts, of several eminent Periods or Revolutions of Time, as the Metonick, Calippick, the Dionysian and Iulian Period; of several Æra's or fixed Characters or Time, as the Christian and Dioclesian; of the Age of the World according to the Accompt of the Græcians: Moreover of the Iewish Æra; The Æra or Ethnick Accompt from the taking of Troy; and the Antiochenian Epocha: the Olympiads, and Agones Capitolini: Of the Iulian year, the Spanish Æra; the Æra of the Victory at Actium; the Epocha ofNabonassar; as also of the Philippean, Alexandrian, and the Yezdegirdican Epocha; and of the Mahumetan Æra, the Hegira, or Flight of Mahomet.
In the Arithmetical Part, the Author shews not only his great skill in Arithmetick, even in the Speculative parts thereof, accompanied with good knowledge in the Grounds of Geometry but likewise his understanding of Exotick and Ancient Languages; rand, as a Specimen thereof, explains the Common Characters of Arithmetick, as he doth also the Indian, Roman, Hebrew, Smaritan, Græcian, Syriac, Arabick and Æthiopick Characters. And to the End of the second Book he hath annexed an Appendix, wherein, in Roman Letters, he hath explained the Hebrew, Syriack, Persian, Æthiopick and Arabick Words for the respective Months of the Year, for the ayde ​of those, that are not so much excercised in the Oriental Languages.
And the Author, finishing this Book in the Year 1667. shewreth (as a general Example of all his Calculations) in what Yea of all the severall Periods, Æra's, Epocha's and Accompts before mention'd, the Year of our Lord Christ did then happen.
But this is not all, that is to be expected from this Author; since himself intimates pag. 179. Sed mandum de Tabula; de his enim aliisque, quæ ad Annos præsertim Mensesque Orientales pertinent, alibi, Deo volente, fusius agemus: Which doubtless to the Learned (considering what is already publish'd by him) will be very acceptable.
TO give the Reader the summe of what is said in this well considered and useful Tract, it is as follows;
Language is a Connexion of Audible Signs, the most apt and excellent in whole Nature, for Communication of our Thoughts and Notions, by Speaking. Written Language is a Description of the said Audible Signs, by Signs Visible. The Elements of Language are Letters, viz. Simple Discriminations of Breath or Voice, Articulated by the Organs of Speech.
The Alphabet consists of so many Letters, as there are to be found such Simple Difcriminations. And the Written Alphabet ought to be just so many single proper Characters, design'd to signifie the Sound or Power of each Letter. And these are the Storehouse of Nature, the Elements and Materials, out of which all Languages are made. These Letters have their Material and their Formal Causes, and Organs proper to each. Their Matter is various, viz. Breath or Voice, i. e. Breath vocalized by the Operation of the Larynx. Their Form is constituted by the Motions and Figures of the Organs of- Speech, affecting the Breath or Voice with a peculiar Sound, by which each Letter is discriminated.
Now to find out their just Number, First, Find out the different Kinds of Matter, of which Letters are made; and these are in general, Breath, when only Spirit or Breath is articulated; and Voice, when Articulation ​is of Breath vocalized: And these again, more particularly, are either (after they have passed the Larynx) only in the Mouth; or else have passage at the same time through the Nose. So there are four kinds of Matter, Breath Oral, Voice Oral, Breath Ore-Nasal, and Voice Ore-Nasal.
Next, 'Tis to be examin'd, How many different Articulations can be made by several Motions and Postures of the Organs in the parts of the Mouth; which applied severally to the Kinds of Matter, may make several Discriminations of Sound to the Ear, i. e. several Letters; And of these (as to Consonants, viz. Letters made by Appulse) our Author finds, and hath described 9. And if possibly any more may he found out, he judges it to be most likely, that they will not recompense the Discoverers pains, by being of; ready and graceful use, but will be fitter to be cast out among several others; to which in his Scheme of Consonants he hath prefix'd an Obelisk.
Now by these 9 Articulations with Appulse, there will he fram'd Consonants Spirital 9; Vocal 9; Naso-spirital 9; Naso-vocal 9; in all 36. Then rejecting those, that prove not graceful; nor easie to be pronounced; viz. 2. Spiritals, 2 Naso-spiritals, and 6 Naso-vocals, in all 17; there will remain 19 Consonants proper for use, according to the design of Letters. And if those, to whom these 19 Consonants (or about that number) appear'd and stood in such confus'd Order, some in Ternaries, some in Pairs, and some Single, were themselves put into so much Confusion, and so puzzled to give a Methodical and Natural Accompt of them, it is no matter of wonder. But now, looking upon them, as they lie in their Original Differences and Combinations, and as they are selected out of a Natural Stock of 9 Quaternions, or 4 Novenaries, 'tis judged, that their Nature and Differences lie most plain and obvious to be understood.
That which renders this Piece the more commendable; is its Usefulness, to which the Author hath excellently applied his Considerations of this Subject; viz. The instructing of Persons Deaf and Dumb. In the performance of which, he hath first removed the great Objections and Difficulties that lie in the way, and seem to discourage that Design, and to portend it infesible. Which done, he delivers those particulars, that give encouragement to that Undertaking; which he doth from his own practice therein; it being certain, that such a Work as this, is not to be perfected by Study alone, but must and will receive many hints and helps (not to be thought on otherwise) which the Endeavour is excited, being under Experiment and Practice .
IN this small Tract the Author reduceth his former Doctrine of Gauging to farther Practice, and illustrateth the same by Examples.
And first he supposeth the Axis of a Pyramid, Cone, Sphere, Parabolical, and Hyperbolical Conoid, and of a Figure of different Bases, which he calls a Frustrum of a Prisme, which if round, may resemble a Drinking Cup like an Horn, having its top squeezed into an Elliptick form, and the bottom remaining either a Circle, or be likewise compress'd; the said Axis to be divided into equal Segments, and Plains passing through those Segments erect to the Axis; to divide the above-mentioned Solids into divers Portions or Rings: and upon these Foundations, viz. That in the Parabolical Conoid the second differences of the Solid Contents of the whole Figures so divided are equal; but in the rest of these Solids their third Differences are equal: he hath suted his Examples to the Axes cut by the said Plains at 3 Inches distance from each other, shewing first the nature of the differences in hand, and then some easie wayes to attain a first, second, and third difference; and how out of them to compute the several Capacities fought by Additions of Differences plac'd in several Columns. Lastly, He gives directions for the more easie Calculation of the second Segments of the Sphere and Spheroid.
But we must not omit to take notice, that this Author, speaking pag. 23. of such Elliptick Solids, whose Bases are unlike, asserts, That every such Elliptick Solid is equal to the Frustrum or Truncus of an Hyperbolick Conoid, the Circular, Bases whereof are equal to the Elliptick Bases of the Solid propos'd; and the Height of the one Frustrum equal to the Height of the other: the Invention and Demonstration whereof argues good Knowledge in Geometry.
ERRAT. in N°, 46.
P. 928. l. 1. r. punctum D in B, ib. l. 28. r. fortissime omnium aget
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Printed by T. N. for John Martyn Printer to the Royal Society, and are to be sold at the Bell a little without Temple-Bar, 1669.