and poetry to thofe of mufic, and the love of claffical learning to both. For in order to cherish high fentiments in the minds of all, every confiderable family had a historian who recounted, and a bard who fung, the deeds of the clan, and of its chieftain: and all, even the loweft in ftation, were fent to school in their youth; partly because they had nothing elfe to do at that age, and partly becaufe literature was thought the diftinction, not the want of it the mark, of good birth. The feverity of their climate, the height of their mountains, the diftance of their villages from each other, their love of the chale and of war, with their defire to vifit and be vifited, forced them to great bodily exertions. The valtnels of the objects which furrounded them, lakes, mountains, rocks, cataracts, extended and elevated their minds: For they were not in the state of men who only know the way from one market-town to another. Their want of regular occupation led them, like the ancient Spartans, to contemplation, and the powers of converfation: powers which they exerted in ftriking out the original thoughts which nature fuggefted, not in languidly repeating thofe which they had learned from other people. They valued themfelves, without undervaluing other nations. They loved to quit their own country to fee and to hear, adopted cafily the manners of others, and were attentive and infinuating whereever they went: but they loved more to return home, to repeat what they had obferved; and, among other things, to relate with aftonithment, that they had been in the midst of great focieties, where every individual made his fenfe of independence to confift in keeping at a diftance from another. Yet they did not think themfelves entitled to hate or defpife the manners of ftrangers, because these differed from their own. For they revered the great qualities of other nations; and only made their failings the fubjećt of an inoffenfive merriment. When strangers came amongst them, they received them, not with a ceremony which forbids a fecond visit, not with a coldness which caufes repentance of the firft, not with an embarrafiment which leaves both the landlord and his gueft in equal mifery, but with the moft pleafing of all politenefs, the fimplicity and cordiality of affection; proud to give that hofpitality which they had not received, and to humble the perfons who had thought of them with contempt, by fhewing how little they deserved it. Having been driven from the low countries of Scotland by invasion, they, from time immemorial, thought themfelves entitled to make reprisals upon the property of their invaders; but they touched not that of each other: fo that in the fame men there appeared, to thofe who did not look into the caufes of things, a frunze mixture of vice and of virus. For what we call theft and rapine, they termed right and juftice. But, I.om the practice of thefe reptifals, they acquired the habits of being enterprizing, artful, and bold. An injury done to one of a clan, was held to be an injury done to all, on account of the common relation of blood. Hence the highlanders were in the habitual practice of war: and hence their attachment to their chieftain, and to each other, was founded upon the two most active principles of human nature, love of their friends, and refentment against their enemies. But the frequency of war tempered its ferocity. They bound up the wounds of their prifoners while they neglected their own; and, in the perfon of an enemy, refpected and pitied the ftranger. They went always completely armed: a fashion, which by accuftoming them to the inftruments of death, removed the fear of death itself; and which, from the danger of provocation, made the common people as polite, and as guarded in their behaviour, as the gentry of other countries. From thele combined circumstances, the higher ranks and the lower ranks of the highlanders alike, joined that refinement of fentiment, which, in all other nations is peculiar to the former, to that frengh and hardiness of body, which, in other countries, is poffeffed only by the latter. To be modeit as well as brave, to be contented with the few things which nature requires; to act and to fuffer without complaining, to be as much afhamed of doing any thing infolent or injurious to others, as of bearing bearing it when done to themselves, and to die with pleature, to revenge affronts offered to their clan or their country; thefe they accounted their highest accomplishment. Their chriftianity was ftrongly tinc tured with traditions derived from the antient bards of their country for they were believers in ghofts: they marked the appearances of the heavens; and, by the forms of the clouds, which in their variable climate were continually shifting, were induced to guefs at prefent, and to predict future events; and they even thought, that to fome men the divinity had communicated a portion of his own prefcience. From this mixture of fyftem, they did not enter much into difputes concerning the particular modes of christianity; but every man followed, with indifference of fentiment, the mode which his chieftain had affumed. Perhaps to the fame caufe it is owing, that their country is the only one in Europe, into which perfecution never entered. fitty Scotch Officers. LTHOUGH the fate which at tended thofe officers in France falls beyond the period of time to which thefe memoirs are confined, a digreffion will perhaps be pardoned, that defcribes adventures, which were worthy of the happiest days of Athens or Sparta. The officers were an hundred and fifty in number, all of honourable birth, attached to their chieftains and to each other, in their political principles only to blame, yet glorying in them. Úpon their arrival in France, penfions were affigned them by the French king: But, upon the conclufion of the civil war, thefe penfions were withdrawn; becaufe the object no longer exifted for which they had been given. Finding themfelves therefore a load upon the late king, whofe finances could fcarcely fuffice for himfelf, they petitioned that prince, for leave to form themfelves into a company of private centinels, afking no other favour, than that they might be permitted to chufe their own officers. James affented. They repaired to St. German's to be reviewed by him, before they were modelled in the French army. A few days after they came, they pofted themselves in accoutrements borrowed from a French regiment, and drawn up in order, in a place through which he was to pafs as he went to the chace; an amusement of which he became paffionately fond, after the lofs of his kingdom. He afked who they were; and was furprized to find they were the fame men, with whom, in garbs better fuited to their ranks, he had the day before converfed at his levee. Struck with the levity of his own amufement contrafted with the mifery of those who were fuffering for him, he returned penfive to the palace. The day he reviewed them, he paffed along the ranks, wrote in his pocket-book, with his own hand, every gentleman's name, and gave him his thanks in particular; and then removing to the front, bowed to the body, with his hat off. After he had gone away, ftill thinking honour enough was not done them, he returned, bowed again, but burst into tears. The body kneel ed, bent their heads and eyes ftedfaft upon the ground; and then starting up at once, pasled him with the ufual honours of war, as if it was only a common review they were exhibiting. They were fent from thence to the frontiers of Spain, a march of 900 miles, on foot. Wherever they paffed the were received with tears by the women, with refpect by fome of the men,but with laughter at the aukwardnefs of their fituation by most of them. They were alwife the foremost in battle, and the last in retreat. Of all the troops in the fervice, they were the most obedient to orders. Twice only they difobeyed: the first time was at the fiege of Rofes; where they had fallen into diseases, and been ordered to quit the camp for their recovery; but they delayed to obey, until they had fent a remonftrance to Marthal Noailles, France*. MATHEMATICAL IMPROVEMENTS. TH HE bette to elucidate Mr. Lyle's tables we have given a copperplate for the convenience of our readers. Examples with the New Perpetual Pocket Table. By Mr. Lyle. QUESTION I. REQUIRED, what day of the week is New Year's day for any year, fuppofe 1890? This is found by the 13th or inmoft circle in the table. Description of the circle and rule for its use. Noailles, against what they termed an for ever the promises and flatteries of affront. The fecond inftance of their inattention to orders, was upon the following occasion: the Germans had made a lodgement in an island in the Rhine: the French, from an opinion that the river was impaffable without boats, had ordered a number for the paffage: among other troops intended for the fervice, this company was ordered to keep a ftation opposite to the island, until the boats fhould arrive but finding, upon examination, the ford, though difficult, not impaffable, they, according to the cuftom of highlanders in wading thro' rivers, joining their hands together, and entering the river in a line with its current, the ftrongest men in the upper part, and the weaker in the under, so that thofe, who were highest up the stream, broke all its force, and tying their arms and clothes on their fhoulders, paffed to the ifland in fight of both armies on the oppofite banks, and drove ten times their number from the lodgement. The French cried out in ad.niration, "A gentleman, in whatever ftation, is ftill a gentleman." "Le gentilhome, eft toujours gentilhome." The place is called l'Ile d'Ecoffe to this day. The 13th circle contains the number of New Years days of the week for any year paft or to come counting round it backward or forward, adding or omitting one day every 130 years, &c. before or after 1752, 1769 being one Sunday at the beginning of the table. 1890, fubtracting the years from one another, is 121 years after 1769, which begins the table. Instead therefore of counting the numbers round the table forward for every year, beginning with 1769 and ending with 1890, which I might foon do, if I had not pen and ink, I divide 121 by 28, and the remainder, I count to the number required, faying 1 Sunday, 2 Monday, &c. and 9, 4, which is Wednesday. But because this year is a few years more than one, 130 years after 1752, according to the rule, I omit or fubtract one, and the number is 3, which is Tuesday, and New Year's day of the Obf. in time past to week, 1890. count from the end backward. II. Required, the moon's age or New Year's day at 12 o'clock in the morning for any year? Suppofe 1890. This is found by the 12 being one circle carried twice round the table. Defcription of the circle and rule for its ufe. All collective human virtues are fullied with the selfishness of individuals. The officers, to whom they had yielded their independence, and whom they had chofen to command their equals, cheated them of their pay, poor as it was, of their cloaths, and of prefents which the generous had fet them. The French, inattentive to their patience, fatigues, and fervices, fent them from the frontiers of Spain to Alface, a march as long as the former. In this rout, their cloaths fell to tatters: after they paffed Lyons, the country was covered with fnow: they often wanted the neceffaries of life: yet no complaints were heard amongst them, except for the fufferings of him whom they accounted their fovereign. After x years fervice, they were broke, when the peace was concluded, on the higher part of the Rhine, 1500 miles from their homes, and without any provifion made for them. At that time, only fixteen of them had furvived the fate of their companions; and of thefe only four arrived in Scotland, to give warning, by their example, to their countrymen, though, to too many of them, in vain, to diftruft * There are men now living in Scotland who were acquainted with fome of the four. The 11th and 12th article contains the moon's age at 12 o'clock in the morning for any year fubtracting or adding 6 hours (or more exactly 5 hours 52 mins, backward or forward every circle, which is 76 years. In the fame manner as in last example instead of counting round the circle to 1890 to find the moon's age. I fubtract a circle and a half, or 76 and 38 years, and the remainder is 7, which I count forward in the second half of the circle, faying first year, 22 days 11 hrs. zd 2d. year, 3 days 13 hrs. &c. and the 7th year, 29 days 4 hrs to which 5hrs 52 mins.or 6 hours for one complete circle being added, the moon's age at 12 o clock in the morning, 1890 is 29 days and to hours. Obf. in counting backwards, 1 tabular difference always to be fubtracted. III. Required, the fun's diftance from the node for any year at the fame time, fuppofe the fame year? This is found by 9th and 10th circle, being one circle in the fame manner. Description of the circle and rule for its ufe. The 9th and 10th circle contains the fun's diftance from the node for any year at the fame time, adding or omitting, 30°. (or more exactly, 30, 33' 1) for every circle, which is alfo 76 years forward or backward from 1769. This stead of counting, may be found in that year of the circle, in which the moon's age was found the fame time and which correfponds to it in the table. I look, therefore, into the table, and correfponding to 29 days 4 hrs. moon's age, I find 39, 33' to which I add for one complete circle, 30° 33' and the fum is 70° 6' the fan's diftance from the node on New Year's day, at twelve o'clock in the morning, 1890. IV. Required, where Hydra's heart (which is the ftar for the months of January and February) fouths at night in any year, fuppofe the 6th of January the fame year? This is found by the 8th circle. Defcription of the circle, and rule for its ufe. The 8th circle contains the fouthing of fome of the fixed ftars every New Year's day of the week throughout the year, adding one minute for every year for three years after Leap Year, and adding or omitting one minute for every 18 years or 29 minutes every 520 years forward or backward; from which four minutes fubtracted forward every night of the week gives the time of the night. In table the 8th of January, Hydra's heart fouths at 3 minutes after 2 o'clock next morning, and 121 divided by 18 anotes; 6 therefore, according to the rule, adding 6 minutes, and one minute for one year after Leap Year to 3 minutes gives 10 minutes after two o'clock 8th January, adding 28 minutes, for the 1st of January gives the fouthing of Hydra's heart at 38 minutes after 2 o'clock in the morning of New Year's day, 1890.* Obf. The morning hours are in next day. V. Given the day of the week and the number of the weeks in any month of any year to find the day of the month. Any date or appointment, fuppofe the 2d Wednesday of October, 1770, required the day of the month? This is found by 7th circle. Defcription of the circle and its use. The 7th circle contains the day of the month at the fame time, which in Leap years after February is one day lefs. New Year's day of the week, which, as may be found by first example, in 1770, is Monday. Looking therefore into the 7th article, and fecond part of October. I find the 8th of the month is Monday, which is therefore the 2d. Monday, and confequently next Wednefday is the 2d Wednesday and the 10th of the month, VI. Required, the time between any two dates in days or in years and days of the year. This is found by 6th circle. Defcription and ufe of the circle. The 6th circle contains the days of the year, fame time, from which the time in years and days between any two dates may be found by fubtraction. 1. A draught dated June 1, 1770, payable at 30 days, required when it becomes due. June 4, 1770, being Monday the 155th day of the year. Friday is therefore the ft of June and 152d day of the year, to which adding 30 days, the fum is 182 days, the day of the year when the draught becomes due, which Monday the 2d of July being the 183d of the year in the table, correfponds to Sunday the rft of July, when the draught is due. A bond dated March 5, 1739, and The Stars are for January and February Hydra's Heart; March, April and May Virgin's Ops; June, July Eagle's Heart; Auguft, September Markab. Peg. Wing, Odober, November, December Seven Stars, ! paid June 7, 1770, required the time in years and days to calculate the in tereit ? March the 5th in table is the 64th day of the year, and June the 7th is the 158th, the 4th being the 155th; fubtracting therefore 1739 years, 94 days from 1770 years, 158 days, the remainder is 31 years and 94 days, the time in years and days of the year between these two dates. 3. A workman is hired by the day to do a piece of work, and begins May 1, 1770, and finishes his work September the 8th, fame year; required the number of days he has worked? The 7th of May in the table being the 127th of the year, the 1ft is the 121ft; and the 10th of September being the 253d, the 8th must be the 251ft, from which 121 days being subtracted there remains 130 days, and fubtracting the number of weeks in the table between them, which is 18 for the Sundays; the remainder is 112 the number of days he has worked. VII. Required the moon's age for any day in any year? fuppofe September 12, 1770. This is found by 5th circle, and the 11 and 12 already explained. Defcription of the circle and rule for its ufe. The 5th circle contains the moon's annual age, fame time, which being added to the age found by 11 and 12 circle for the year, omitting 29 days, 13 hours, when it exceeds them gives the moon's age at that time, and which being fubtracted from 29 days, 13 hours, leaves the time to new moon. Moon's age for 1770 (being the 2d year in the table) found by 11th and 12th circle is 3 days, 22 hours. Annual age for September the 10th found in 5th circle is 15 days, 18 hours, and confequently on the 12th the moon's annual age is 17 days, 18 hours, which being added together gives 21 days, 16 hours, for the moon's age at 12 o'clock in the morning the 12th of Sepember, 1770. This being fubtracted from 29 days 13 hours, leaves 7 days, 21 hours the time to the next change. Adding therefore 7 days 21 hours to the 12th of September gives the 19th of September and 21 hours, April, 1771. which is 9 o'clock at night for the time of night new moon. VIII. Required whether or no, there is an eclipfe at any new or full moon, fuppofe this new moon in September, 1770. This is found by the fourth, ninth, and tenth circles in the fame manner. Defcription of the circle and rule for its ufe. The fourth circle contains the fun's distance from the node, fame time, which being added to the distance found in the ninth and tenth circle for the year, omitting 360° when it exceeds them, is the fun's distance from the node at twelve o'clock in the morning on new year's day of the week. And adding one degree for every day and three minutes for every hour for any remaining days and hours of the week to new or full moon, gives the fun's diftance from the node at that time, which being within 70° or 12° either of 180° or 360° there must be an eclipse, otherwife not. Sun's diftance from node for 1770, found by the 9th and 10th circle, is 27° 16'. Annual distance for September the 17th (being the neareft new year's day of the week to new moón) is 269° 0'. And therefore on the 19th, at twelve o'clock in the morning, the distance is 270° 0', and three minutes for every hour to nine o'clock at night, the time of change is 1° 3', all which being added together is 299° 19' the fun's diftance from the node at the time of new moon. This fubtracted from 360° the nearest number, leaves 60° 41'the fun's distance from the node, which being far above 17° there can be no eclipfe at this new moon. IX. Required the time of high wa. ter and afpects of the moon at any time? fuppofe at London the 16th day, 12th hour of the moon's age at twelve o'clock in the morning. There are found by the fecond and third circles. Defcription of the circles and rule for their ufe. The fecond circle contains twentyfour hours and the moon's afpects, and the third circle contains the moon's age at the tinte, in fecond circle of high water, counted from this mar *, D d called |