The Writings of Thomas Jefferson, Vol. 6 (of 9)

The Writings of Thomas Jefferson, Vol. 6 (of 9)
Томас Джефферсон

Thomas Jefferson

The Writings of Thomas Jefferson, Vol. VI. (of 9) / Being His Autobiography, Correspondence, Reports, Messages, / Addresses, and Other Writings, Official and Private

PART III.—Continued.

LETTERS WRITTEN AFTER HIS RETURN TO THE U. S. DOWN TO THE TIME OF HIS DEATH.

1790-1826

TO DR. RUSH

    Poplar Forest, August 17, 1811.

Dear Sir,—I write to you from a place ninety miles from Monticello, near the New London of this State, which I visit three or four times a year, and stay from a fortnight to a month at a time. I have fixed myself comfortably, keep some books here, bring others occasionally, am in the solitude of a hermit, and quite at leisure to attend to my absent friends. I note this to show that I am not in a situation to examine the dates of our letters, whether I have overgone the annual period of asking how you do? I know that within that time I have received one or more letters from you, accompanied by a volume of your introductory lectures, for which accept my thanks. I have read them with pleasure and edification, for I acknowledge facts in medicine as far as they go, distrusting only their extension by theory. Having to conduct my grandson through his course of mathematics, I have resumed that study with great avidity. It was ever my favorite one. We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction. I have forgotten much, and recover it with more difficulty than when in the vigor of my mind I originally acquired it. It is wonderful to me that old men should not be sensible that their minds keep pace with their bodies in the progress of decay. Our old revolutionary friend Clinton, for example, who was a hero, but never a man of mind, is wonderfully jealous on this head. He tells eternally the stories of his younger days to prove his memory, as if memory and reason were the same faculty. Nothing betrays imbecility so much as the being insensible of it. Had not a conviction of the danger to which an unlimited occupation of the executive chair would expose the republican constitution of our government, made it conscientiously a duty to retire when I did, the fear of becoming a dotard and of being insensible of it, would of itself have resisted all solicitations to remain. I have had a long attack of rheumatism, without fever and without pain while I keep myself still. A total prostration of the muscles of the back, hips and thighs, deprived me of the power of walking, and leaves it still in a very impaired state. A pain when I walk, seems to have fixed itself in the hip, and to threaten permanence. I take moderate rides, without much fatigue; but my journey to this place, in a hard-going gig, gave me great sufferings which I expect will be renewed on my return as soon as I am able. The loss of the power of taking exercise would be a sore affliction to me. It has been the delight of my retirement to be in constant bodily activity, looking after my affairs. It was never damped as the pleasures of reading are, by the question of cui bono? for what object? I hope your health of body continues firm. Your works show that of your mind. The habits of exercise which your calling has given to both, will tend long to preserve them. The sedentary character of my public occupations sapped a constitution naturally sound and vigorous, and draws it to an earlier close. But it will still last quite as long as I wish it. There is a fulness of time when men should go, and not occupy too long the ground to which others have a right to advance. We must continue while here to exchange occasionally our mutual good wishes. I find friendship to be like wine, raw when new, ripened with age, the true old man's milk and restorative cordial. God bless you and preserve you through a long and healthy old age.

TO WM. A. BURWELL, ESQ

    Poplar Forest, August 19, 1811.

Dear Sir,—I am here after a long absence, having been confined at home a month by rheumatism. I thought myself equal to the journey when I set out, but I have suffered much coming, staying, and shall, returning. If I am not better after a little rest at home, I shall set out for the warm springs. The object of this letter is to inform Mrs. Burwell that a ring, which she left where she washed the morning of leaving Fludd's, is safe and will be delivered to her order or to herself when she passes. I have not seen the President since he came home, nor do I know what has passed with Foster from the fountain head; but through a channel in which I have confidence, I learn he has delivered a formal note in the name of his government, declaring that the circumstances of the war oblige them to take possession of the ocean, and permit no commerce on it but through their ports. Thus their purpose is at length avowed. They cannot from their own resources maintain the navy necessary to retain the dominion of the ocean, and mean that other nations shall be assessed to maintain their own chains. Should the king die, as is probable, although the ministry which would come in stand so committed to repeal the orders of Council, I doubt if the nation will permit it. For the usurpation of the sea has become a national disease. This state of things annihilates the culture of tobacco, except of about 15,000 hhds. on the prime lands. Wheat and Flour keep up. Wheat was at 9s. 6d. at Richmond ten days ago. I have sold mine here at the Richmond price, abating 2s., but 8s. a bushel has been offered for machined wheat. Present me respectfully to Mrs. Burwell, and accept assurances of affectionate respect and esteem.

TO MR. PEALE

    Poplar Forest, August 20, 1811.

It is long, my dear Sir, since we have exchanged a letter. Our former correspondence had always some little matter of business interspersed; but this being at an end, I shall still be anxious to hear from you sometimes, and to know that you are well and happy. I know indeed that your system is that of contentment under any situation. I have heard that you have retired from the city to a farm, and that you give your whole time to that. Does not the museum suffer? And is the farm as interesting? Here, as you know, we are all farmers, but not in a pleasing style. We have so little labor in proportion to our land that, although perhaps we make more profit from the same labor, we cannot give to our grounds that style of beauty which satisfies the eye of the amateur. Our rotations are corn, wheat, and clover, or corn, wheat, clover and clover, or wheat, corn, wheat, clover and clover; preceding the clover by a plastering. But some, instead of clover substitute mere rest, and all are slovenly enough. We are adding the care of Merino sheep. I have often thought that if heaven had given me choice of my position and calling, it should have been on a rich spot of earth, well watered, and near a good market for the productions of the garden. No occupation is so delightful to me as the culture of the earth, and no culture comparable to that of the garden. Such a variety of subjects, some one always coming to perfection, the failure of one thing repaired by the success of another, and instead of one harvest a continued one through the year. Under a total want of demand except for our family table, I am still devoted to the garden. But though an old man, I am but a young gardener.

Your application to whatever you are engaged in I know to be incessant. But Sundays and rainy days are always days of writing for the farmer. Think of me sometimes when you have your pen in hand, and give me information of your health and occupations; and be always assured of my great esteem and respect.

TO MR. CLAY

    Poplar Forest, August 23, 1811.

Dear Sir,—While here, and much confined to the house by my rheumatism, I have amused myself with calculating the hour lines of an horizontal dial for the latitude of this place, which I find to be 37° 22´ 26´´. The calculations are for every five minutes of time, and are always exact to within less than half a second of a degree. As I do not know that any body here has taken this trouble before, I have supposed a copy would be acceptable to you. It may be a good exercise for Master Cyrus to make you a dial by them. He will need nothing but a protractor, or a line of chords and dividers. A dial of size, say of from twelve inches to two feet square, is the cheapest and most accurate measure of time for general use, and would I suppose be more common if every one possessed the proper horary lines for his own latitude. Williamsburg being very nearly in the parallel of Poplar Forest, the calculations now sent would serve for all the counties in the line between that place and this, for your own place, New London, and Lynchburg in this neighborhood. Slate, as being less affected by the sun, is preferable to wood or metal, and needs but a saw and plane to prepare it, and a knife point to mark the lines and figures. If worth the trouble, you will of course use the paper enclosed; if not, some of your neighbors may wish to do it, and the effect to be of some use to you will strengthen the assurances of my great esteem and respect.

TO LEVI LINCOLN, ESQ

    Monticello, August 25, 1811.

It is long, my good friend, since we have exchanged a letter; and yet I demur to all prescription against it. I cannot relinquish the right of correspondence with those I have learnt to esteem. If the extension of common acquaintance in public life be an inconvenience, that with select worth is more than a counterpoise. Be assured your place is high among those whose remembrance I have brought with me into retirement, and cherish with warmth. I was overjoyed when I heard you were appointed to the supreme bench of national justice, and as much mortified when I heard you had declined it. You are too young to be entitled to withdraw your services from your country. You cannot yet number the quadraginta stipendia of the veteran. Our friends, whom we left behind, have ceased to be friends among themselves. I am sorry for it, on their account and on my own, for I have sincere affection for them all. I hope it will produce no schisms among us, no desertions from our ranks; that no Essex man will find matter of triumph in it. The secret treasons of his heart, and open rebellions on his tongue, will still be punished, while in fieri, by the detestation of his country, and by its vengeance in the overt act. What a pity that history furnishes so many abuses of the punishment by exile, the most rational of all punishments for meditated treason. Their great king beyond the water would doubtless receive them as kindly as his Asiatic prototype did the fugitive aristocracy of Greece. But let us turn to good-humored things. How do you do? What are you doing? Does the farm or the study occupy your time, or each by turns? Do you read law or divinity? And which affords the most curious and cunning learning? Which is most disinterested? And which was it that crucified its Saviour? Or were the two professions united among the Jews? In that case, what must their Caiaphases have been? Answer me these questions, or any others you like better, but let me hear from you and know that you are well and happy. That you may long continue so is the prayer of yours affectionately.

TO MR. JAMES L. EDWARDS

    Monticello, September 5, 1811.

Sir,—Your letter of August 20th has truly surprised me. In this it is said that, for certain services performed by Mr. James Lyon and Mr. Samuel Morse, formerly editors of the Savannah Republican, I promised them the sum of one thousand dollars. This, Sir, is totally unfounded. I never promised to any printer on earth the sum of one thousand dollars, nor any other sum, for certain services performed, or for any services which that expression would imply. I have had no accounts with printers but for their newspapers, for which I have paid always the ordinary price and no more. I have occasionally joined in moderate contributions to printers, as I have done to other descriptions of persons, distressed or persecuted, not by promise, but the actual payment of what I contributed. When Mr. Morse went to Savannah, he called on me and told me he meant to publish a paper there, for which I subscribed, and paid him the year in advance. I continued to take it from his successors, Everett & McLean, and Everett & Evans, and paid for it at different epochs up to December 31, 1808, when I withdrew my subscription. You say McLean informed you "he had some expectation of getting the money, as he had received a letter from me on the subject." If such a letter exists under my name, it is a forgery. I never wrote but a single letter to him, that was of the 28th of January, 1810, and was on the subject of the last payment made for his newspaper, and on no other subject; and I have two receipts of his, (the last dated March 9, 1809,) of payments for his paper, both stating to be in full of all demands, and a letter of the 17th of April, 1810, in reply to mine, manifestly showing he had no demand against me of any other nature. The promise is said to have been made to Morse & Lyon. Were Mr. Morse living, I should appeal to him with confidence, as I believe him to have been a very honest man. Mr. Lyon I suppose to be living, and will, I am sure, acquit me of any such transaction as that alleged. The truth, then, being that I never made the promise suggested, nor any one of a like nature to any printer or other person whatever, every principle of justice and of self-respect requires that I should not listen to any such demand.

TO MR. JAMES LYON

    Monticello, September 5, 1811.

Sir,—I enclose you the copy of a letter I have received from a James L. Edwards, of Boston. You will perceive at once its swindling object. It appeals to two dead men, and one, (yourself,) whom he supposes I cannot get at. I have written him an answer which may perhaps prevent his persevering in the attempt, for the whole face of his letter betrays a consciousness of its guilt. But perhaps he may expect that I would sacrifice a sum of money rather than be disturbed with encountering a bold falsehood. In this he is mistaken; and to prepare to meet him, should he repeat his demand, and considering that he has presumed to implicate your name in this attempt, I take the liberty of requesting a letter from you bearing testimony to the truth of my never having made to you, or within your knowledge or information, any such promise to yourself, your partner Morse, or any other. My confidence in your character leaves me without a doubt of your honest aid in repelling this base and bold attempt to fix on me practices to which no honors or powers in this world would ever have induced me to stoop. I have solicited none, intrigued for none. Those which my country has thought proper to confide to me have been of their own mere motion, unasked by me. Such practices as this letter-writer imputes to me, would have proved me unworthy of their confidence.

It is long since I have known anything of your situation or pursuits. I hope they have been successful, and tender you my best wishes that they may continue so, and for your own health and happiness.

TO DOCTOR PATTERSON

    Monticello, September 11, 1811.

Dear Sir,—The enclosed work came to me without a scrip of a pen other than what you see in the title-page—"A Monsieur le President de la Société." From this I conclude it intended for the Philosophical Society, and for them I now enclose it to you. You will find the notes really of value. They embody and ascertain to us all the scraps of new discoveries which we have learned in detached articles from less authentic publications. M. Goudin has generally expressed his measures according to the old as well as the new standard, which is a convenience to me, as I do not make a point of retaining the last in my memory. I confess, indeed, I do not like the new system of French measures, because not the best, and adapted to a standard accessible to themselves exclusively, and to be obtained by other nations only from them. For, on examining the map of the earth, you will find no meridian on it but the one passing through their country, offering the extent of land on both sides of the 45th degree, and terminating at both ends in a portion of the ocean which the conditions of the problem for an universal standard of measures require. Were all nations to agree therefore to adopt this standard, they must go to Paris to ask it; and they might as well long ago have all agreed to adopt the French foot, the standard of which they could equally have obtained from Paris. Whereas the pendulum is equally fixed by the laws of nature, is in possession of every nation, may be verified everywhere and by every person, and at an expense within every one's means. I am not therefore without a hope that the other nations of the world will still concur, some day, in making the pendulum the basis of a common system of measures, weights and coins, which applied to the present metrical systems of France and of other countries, will render them all intelligible to one another. England and this country may give it a beginning, notwithstanding the war they are entering into. The republic of letters is unaffected by the wars of geographical divisions of the earth. France, by her power and science, now bears down everything. But that power has its measure in time by the life of one man. The day cannot be distant in the history of human revolutions, when the indignation of mankind will burst forth, and an insurrection of the universe against the political tyranny of France will overwhelm all her arrogations. Whatever is most opposite to them will be most popular, and what is reasonable therefore in itself, cannot fail to be adopted the sooner from that motive. But why leave this adoption to the tardy will of governments who are always, in their stock of information, a century or two behind the intelligent part of mankind, and who have interests against touching ancient institutions? Why should not the college of the literary societies of the world adopt the second pendulum as the unit of measure on the authorities of reason, convenience and common consent? And why should not our society open the proposition by a circular letter to the other learned institutions of the earth? If men of science, in their publications, would express measures always in multiples and decimals of the pendulum, annexing their value in municipal measures as botanists add the popular to the botanical names of plants, they would soon become familiar to all men of instruction, and prepare the way for legal adoptions. At any rate, it would render the writers of every nation intelligible to the readers of every other, when expressing the measures of things. The French, I believe, have given up their Decada Calendar, but it does not appear that they retire from the centesimal division of the quadrant. On the contrary, M. Borda has calculated according to that division, new trigonometrical tables not yet, I believe, printed. In the excellent tables of Callet, lately published by Didot, in stereotype, he has given a table of Logarithmic lines and tangents for the hundred degrees of the quadrant, abridged from Borda's manuscript. But he has given others for the sexagesimal division, which being for every 10´´ through the whole table, are more convenient than Hutton's, Scherwin's, or any of their predecessors. It cannot be denied that the centesimal division would facilitate our arithmetic, and that it might have been preferable had it been originally adopted, as a numeration by eighths would have been more convenient than by tens. But the advantages would not now compensate the embarrassments of a change.

I extremely regret the not being provided with a time-piece equal to the observations of the approaching eclipse of the sun. Can you tell me what would be the cost in Philadelphia of a clock, the time-keeping part of which should be perfect? And what the difference of cost between a wooden and gridiron pendulum? To be of course without a striking apparatus, as it would be wanted for astronomical purposes only. Accept assurances of affectionate esteem and respect.

TO CLEMENT CAINE, ESQ

    Monticello, September 16, 1811.

Sir,—Your favor of April 2d was not received till the 23d of June last, with the volume accompanying it, for which be pleased to accept my thanks. I have read it with great satisfaction, and received from it information, the more acceptable as coming from a source which could be relied on. The retort on European censors, of their own practices on the liberties of man, the inculcation on the master of the moral duties which he owes to the slave, in return for the benefits of his service, that is to say, of food, clothing, care in sickness, and maintenance under age and disability, so as to make him in fact as comfortable and more secure than the laboring man in most parts of the world; and the idea suggested of substituting free whites in all household occupations and manual arts, thus lessening the call for the other kind of labor, while it would increase the public security, give great merit to the work, and will, I have no doubt, produce wholesome impressions. The habitual violation of the equal rights of the colonist by the dominant (for I will not call them the mother) countries of Europe, the invariable sacrifice of their highest interests to the minor advantages of any individual trade or calling at home, are as immoral in principle as the continuance of them is unwise in practice, after the lessons they have received. What, in short, is the whole system of Europe towards America but an atrocious and insulting tyranny? One hemisphere of the earth, separated from the other by wide seas on both sides, having a different system of interests flowing from different climates, different soils, different productions, different modes of existence, and its own local relations and duties is made subservient to all the petty interests of the other, to their laws, their regulations, their passions and wars, and interdicted from social intercourse, from the interchange of mutual duties and comforts with their neighbors, enjoined on all men by the laws of nature. Happily these abuses of human rights are drawing to a close on both our continents, and are not likely to survive the present mad contest of the lions and tigers of the other. Nor does it seem certain that the insular colonies will not soon have to take care of themselves, and to enter into the general system of independence and free intercourse with their neighboring and natural friends. The acknowledged depreciation of the paper circulation of England, with the known laws of its rapid progression to bankruptcy, will leave that nation shortly without revenue, and without the means of supporting the naval power necessary to maintain dominion over the rights and interests of different nations. The intention too, which they now formally avow, of taking possession of the ocean as their exclusive domain, and of suffering no commerce on it but through their ports, makes it the interest of all mankind to contribute their efforts to bring such usurpations to an end. We have hitherto been able to avoid professed war, and to continue to our industry a more salutary direction. But the determination to take all our vessels bound to any other than her ports, amounting to all the war she can make (for we fear no invasion), it would be folly in us to let that war be all on one side only, and to make no effort towards indemnification and retaliation by reprisal. That a contest thus forced on us by a nation a thousand leagues from us both, should place your country and mine in relations of hostility, who have not a single motive or interest but of mutual friendship and interchange of comforts, shows the monstrous character of the system under which we live. But however, in the event of war, greedy individuals on both sides, availing themselves of its laws, may commit depredations on each other, I trust that our quiet inhabitants, conscious that no cause exists but for neighborly good will, and the furtherance of common interests, will feel only those brotherly affections which nature has ordained to be those of our situation.

A letter of thanks for a good book has thus run away from its subject into fields of speculation into which discretion perhaps should have forbidden me to enter, and for which an apology is due. I trust that the reflections I hazard will be considered as no more than what they really are, those of a private individual, withdrawn from the councils of his country, uncommunicating with them, and responsible alone for any errors of fact or opinion expressed; as the reveries, in short, of an old man, who, looking beyond the present day, looks into times not his own, and as evidences of confidence in the liberal mind of the person to whom they are so freely addressed. Permit me, however, to add to them my best wishes for his personal happiness, and assurances of the highest consideration and respect.

TO MR. EPPES

    Monticello, September 29, 1811.

Dear Sir,—The enclosed letter came under cover to me without any indication from what quarter it came.

Our latest arrival brings information of the death of the king of England. Its coming from Ireland and not direct from England would make it little worthy of notice, were not the event so probable. On the 26th of July the English papers say he was expected hourly to expire. This vessel sailed from Ireland the 4th of August, and says an express brought notice the day before to the government that he died on the 1st; but whether on that day or not, we may be certain he is dead, and entertain, therefore, a hope that a change of ministers will produce that revocation of the orders of council for which they stand so committed. In this event we may still remain at peace, and that probably concluded between the other powers. I am so far, in that case, from believing that our reputation will be tarnished by our not having mixed in the mad contests of the rest of the world that, setting aside the ravings of pepper-pot politicians, of whom there are enough in every age and country, I believe it will place us high in the scale of wisdom, to have preserved our country tranquil and prosperous during a contest which prostrated the honor, power, independence, laws and property of every country on the other side of the Atlantic. Which of them have better preserved their honor? Has Spain, has Portugal, Italy, Switzerland, Holland, Prussia, Austria, the other German powers, Sweden, Denmark, or even Russia? And would we accept of the infamy of France or England in exchange for our honest reputation, or of the result of their enormities, despotism to the one, and bankruptcy and prostration to the other, in exchange for the prosperity, the freedom and independence which we have preserved safely through the wreck? The bottom of my page warns me it is time to present my homage to Mrs. Eppes, and to yourself and Francis my affectionate adieux.

TO MR. PAINE TODD

    Monticello, October 10, 1811.

Dear Sir,—According to promise I send you our observations of the solar eclipse of September 17th. We had, you know, a perfect observation of the passage of the sun over the meridian, and the eclipse began so soon after as to leave little room for error from the time-piece. Her rate of going, however, was ascertained by ten days' subsequent observation and comparison with the sun, and the times, as I now give them to you, are corrected by these. I have no confidence in the times of the first and ultimate contacts, because you know we were not early enough on the watch, deceived by our time-piece which was too slow. The impression on the sun was too sensible when we first observed it, to be considered as the moment of commencement, and the largeness of our conjectural correction (18´´) shows that that part of the observation should be considered as nothing. The last contact was well enough observed, but it is on the forming and breaking of the annulus that I rely with entire confidence. I am certain there was not an error of an instant of time in either. I would be governed, therefore, solely by them, and not suffer their result to be affected by the others. I have not yet entered on the calculation of our longitude from them. They will enable you to do it as a college exercise. Affectionately yours.

TO DOCTOR ROBERT PATTERSON

    Monticello, November 10, 1811.

Dear Sir,—Your favor of September 23d came to hand in due time, and I thank you for the nautical almanac it covered for the year 1813. I learn with pleasure that the Philosophical Society has concluded to take into consideration the subject of a fixed standard of measures, weights and coins, and you ask my ideas on it; insulated as my situation is, I am sure I can offer nothing but what will occur to the committee engaged on it, with the advantage on their part of correction by an interchange of sentiments and observations among themselves. I will, however, hazard some general ideas because you desire it, and if a single one be useful, the labor will not be lost.

The subject to be referred to as a standard, whether it be matter or motion, should be fixed by nature, invariable and accessible to all nations, independently of others, and with a convenience not disproportioned to its utility. What subject in nature fulfils best these conditions? What system shall we propose on this, embracing measures, weights and coins? and in what form shall we present it to the world? These are the questions before the committee.

Some other subjects have, at different times, been proposed as standards, but two only have divided the opinions of men: first, a direct admeasurement of a line on the earth's surface, or second, a measure derived from its motion on its axis. To measure directly such a portion of the earth as would furnish an element of measure, which might be found again with certainty in all future times, would be too far beyond the competence of our means to be taken into consideration. I am free, at the same time, to say that if these were within our power in the most ample degree, this element would not meet my preference. The admeasurement would of course be of a portion of some great circle of the earth. If of the equator, the countries over which that passes, their character and remoteness, render the undertaking arduous, and we may say impracticable for most nations. If of some meridian, the varying measures of its degrees from the equator to the pole, require a mean to be sought, of which some aliquot part may furnish what is desired. For this purpose the 45th degree has been recurred to, and such a length of line on both sides of it terminating at each end in the ocean, as may furnish a satisfactory law for a deduction of the unmeasured part of the quadrant. The portion resorted to by the French philosophers, (and there is no other on the globe under circumstances equally satisfactory,) is the meridian passing through their country and a portion of Spain, from Dunkirk to Barcelona. The objections to such an admeasurement as an element of measure, are the labor, the time, the number of highly-qualified agents, and the great expense required. All this, too, is to be repeated whenever any accident shall have destroyed the standard derived from it, or impaired its dimensions. This portion of that particular meridian is accessible of right to no one nation on earth. France, indeed, availing herself of a moment of peculiar relation between Spain and herself, has executed such an admeasurement. But how would it be at this moment, as to either France or Spain? and how is it at all times as to other nations, in point either of right or of practice? Must these go through the same operation, or take their measures from the standard prepared by France? Neither case bears that character of independence which the problem requires, and which neither the equality nor convenience of nations can dispense with. How would it now be, were England the deposit of a standard for the world? At war with all the world, the standard would be inaccessible to all other nations. Against this, too, are the inaccuracies of admeasurements over hills and valleys, mountains and waters, inaccuracies often unobserved by the agent himself, and always unknown to the world. The various results of the different measures heretofore attempted, sufficiently prove the inadequacy of human means to make such an admeasurement with the exactness requisite.

Let us now see under what circumstances the pendulum offers itself as an element of measure. The motion of the earth on its axis from noon to noon of a mean solar day, has been divided from time immemorial, and by very general consent, into 86,400 portions of time called seconds. The length of a pendulum vibrating in one of these portions, is determined by the laws of nature, is invariable under the same parallel, and accessible independently to all men. Like a degree of the meridian, indeed, it varies in its length from the equator to the pole, and like it, too, requires to be reduced to a mean. In seeking a mean in the first case, the 45th degree occurs with unrivalled preferences. It is the mid-way of the celestial ark from the equator to the pole. It is a mean between the two extreme degrees of the terrestrial ark, or between any two equi-distant from it, and it is also a mean value of all its degrees. In like manner, when seeking a mean for the pendulum, the same 45th degree offers itself on the same grounds, its increments being governed by the same laws which determine those of the different degrees of the meridian.