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

TO GIDEON GRANGER, ESQ

Monticello, March 9, 1814.

Dear Sir,—Your letter of February 22d came to hand on the 4th instant. Nothing is so painful to me as appeals to my memory on the subject of past transactions. From 1775 to 1809, my life was an unremitting course of public transactions, so numerous, so multifarious, and so diversified by places and persons, that, like the figures of a magic lanthern, their succession was with a rapidity that scarcely gave time for fixed impressions. Add to this the decay of memory consequent on advancing years, and it will not be deemed wonderful that I should be a stranger as it were even to my own transactions. Of some indeed I retain recollections of the particular, as well as general circumstances; of others a strong impression of the general fact, with an oblivion of particulars; but of a great mass, not a trace either of general or particular remains in my mind. I have duly pondered the facts stated in your letter, and for the refreshment of my memory have gone over the letters which passed between us while I was in the administration of the government, have examined my private notes, and such other papers as could assist me in the recovery of the facts, and shall now state them seriatim from your letter, and give the best account of them I am able to derive from the joint sources of memory and papers.

"I have been denounced as a Burrite; but you know that in 1800 I sent Erving from Boston to inform Virginia of the danger resulting from his intrigues." I well remember Mr. Erving's visit to this State about that time, and his suggestions of the designs meditated in the quarter you mention; but as my duties on the occasion were to be merely passive, he of course, as I presume, addressed his communications more particularly to those who were free to use them. I do not recollect his mentioning you; but I find that in your letter to me of April 26, 1804, you state your agency on that occasion, so that I have no reason to doubt the fact.

"That in 1803-4, on my advice, you procured Erastus Granger to inform De Witt Clinton of the plan to elevate Burr in New York." Here I do not recollect the particulars; but I have a general recollection that Colonel Burr's conduct had already, at that date rendered his designs suspicious; that being for that reason laid aside by his constituents as Vice President, and aiming to become the Governor of New York, it was thought advisable that the persons of influence in that State should be put on their guard; and Mr. Clinton being eminent, no one was more likely to receive intimations from us, nor any one more likely to be confided in for their communication than yourself. I have no doubt therefore of the fact, and the less because in your letter to me of October 9, 1806, you remind me of it.

About the same period, that is, in the winter of 1803-4, another train of facts took place which, although not specifically stated in your letter, I think it but justice to yourself that I should state. I mean the intrigues which were in agitation, and at the bottom of which we believed Colonel Burr to be; to form a coalition of the five eastern States, with New York and New Jersey, under the new appellation of the seven eastern States; either to overawe the Union by the combination of their power and their will, or by threats of separating themselves from it. Your intimacy with some of those in the secret gave you opportunities of searching into their proceedings, of which you made me daily and confidential reports. This intimacy to which I had such useful recourse, at the time, rendered you an object of suspicion with many as being yourself a partisan of Colonel Burr, and engaged in the very combination which you were faithfully employed in defeating. I never failed to justify you to all those who brought their suspicions to me, and to assure them of my knowledge of your fidelity. Many were the individuals, then members of the legislature, who received these assurances from me, and whose apprehensions were thereby quieted. This first project of Colonel Burr having vanished in smoke, he directed to the western country those views which are the subject of your next article.

"That in 1806, I communicated by the first mail after I had got knowledge of the fact, the supposed plans of Burr in his western expedition; upon which communication your council was first called together to take measures in relation to that subject." Not exactly on that single communication; on the 15th and 18th of September, I had received letters from Colonel George Morgan, and from a Mr. Nicholson of New York, suggesting in a general way the manœuvres of Colonel Burr. Similar information came to the Secretary of State from a Mr. Williams of New York. The indications, however, were so vague that I only desired their increased attention to the subject, and further communications of what they should discover. Your letter of October 16, conveying the communications of General Eaton to yourself and to Mr. Ely gave a specific view of the objects of this new conspiracy, and corroborating our previous information, I called the Cabinet together, on the 22d of October, when specific measures were adopted for meeting the dangers threatened in the various points in which they might occur. I say your letter of October 16 gave this information, because its date, with the circumstance of its being no longer on my files, induce me to infer it was that particular letter, which having been transferred to the bundle of the documents of that conspiracy, delivered to the Attorney General, is no longer in my possession.

Your mission of Mr. Pease on the route to New Orleans, at the time of that conspiracy, with powers to see that the mails were expected, and to dismiss at once every agent of the Post Office whose fidelity could be justly doubted, and to substitute others on the spot was a necessary measure, taken with my approbation; and he executed the trusts to my satisfaction. I do not know however that my subsequent appointment of him to the office of Surveyor General was influenced, as you suppose, by those services. My motives in that appointment were my personal knowledge of his mathematical qualifications and satisfactory informations of the other parts of his character.

With respect to the dismission of the prosecutions for sedition in Connecticut, it is well known to have been a tenet of the republican portion of our fellow citizens, that the sedition law was contrary to the constitution and therefore void. On this ground I considered it as a nullity wherever I met it in the course of my duties; and on this ground I directed nolle prosequis in all the prosecutions which had been instituted under it, and as far as the public sentiment can be inferred from the occurrences of the day, we may say that this opinion had the sanction of the nation. The prosecutions, therefore, which were afterwards instituted in Connecticut, of which two were against printers, two against preachers, and one against a judge, were too inconsistent with this principle to be permitted to go on. We were bound to administer to others the same measure of law, not which they had meted to us, but we to ourselves, and to extend to all equally the protection of the same constitutional principles. These prosecutions, too, were chiefly for charges against myself, and I had from the beginning laid it down as a rule to notice nothing of the kind. I believed that the long course of services in which I had acted on the public stage, and under the eye of my fellow citizens, furnished better evidence to them of my character and principles, than the angry invectives of adverse partisans in whose eyes the very acts most approved by the majority were subjects of the greatest demerit and censure. These prosecutions against them, therefore, were to be dismissed as a matter of duty. But I wished it to be done with all possible respect to the worthy citizens who had advised them, and in such way as to spare their feelings which had been justly irritated by the intemperance of their adversaries. As you were of that State and intimate with these characters, the business was confided to you, and you executed it to my perfect satisfaction.

These I think are all the particular facts on which you have asked my testimony, and I add with pleasure, and under a sense of duty, the declaration that the increase of rapidity in the movement of the mails which had been vainly attempted before, were readily undertaken by you on your entrance into office, and zealously and effectually carried into execution, and that the affairs of the office were conducted by you with ability and diligence, so long as I had opportunities of observing them.

With respect to the first article mentioned in your letter, in which I am neither concerned nor consulted, I will yet, as a friend, volunteer my advice. I never knew anything of it, nor would ever listen to such gossiping trash. Be assured, my dear Sir, that the dragging such a subject before the public will excite universal reprobation, and they will drown in their indignation all the solid justifications which they would otherwise have received and weighed with candor. Consult your own experience, reflect on the similar cases which have happened within your own knowledge, and see if ever there was a single one in which such a mode of recrimination procured favor to him who used it. You may give pain where perhaps you wish it, but be assured it will re-act on yourself with double though delayed effect, and that it will be one of those incidents of your life on which you will never reflect with satisfaction. Be advised, then; erase it even from your memory, and stand erect before the world on the high ground of your own merits, without stooping to what is unworthy either of your or their notice. Remember that we often repent of what we have said, but never, never of that which we have not. You may have time enough hereafter to mend your hold, if ever it can be mended by such matter as that. Take time then, and do not commit your happiness and public estimation by too much precipitancy. I am entirely uninformed of the state of things which you say exists, and which will oblige you to make a solemn appeal to the nation, in vindication of your character. But whatever that be, I feel it a duty to bear testimony to the truth, and I have suggested with frankness other considerations occurring to myself, because I wish you well, and I add sincere assurances of my great respect and esteem.

TO HORATIO G. SPAFFORD

Monticello, March 17, 1814.

Dear Sir,—I am an unpunctual correspondent at best. While my affairs permit me to be within doors, I am too apt to take up a book and to forget the calls of the writing-table. Besides this, I pass a considerable portion of my time at a possession so distant, and uncertain as to its mails, that my letters always await my return here. This must apologise for my being so late in acknowledging your two favors of December 17th and January 28th, as also that of the Gazetteer, which came safely to hand. I have read it with pleasure, and derived from it much information which I did not possess before. I wish we had as full a statement as to all our States. We should know ourselves better, our circumstances and resources, and the advantageous ground we stand on as a whole. We are certainly much indebted to you for this fund of valuable information. I join in your reprobation of our merchants, priests, and lawyers, for their adherence to England and monarchy, in preference to their own country and its constitution. But merchants have no country. The mere spot they stand on does not constitute so strong an attachment as that from which they draw their gains. In every country and in every age, the priest has been hostile to liberty. He is always in alliance with the despot, abetting his abuses in return for protection to his own. It is easier to acquire wealth and power by this combination than by deserving them, and to effect this, they have perverted the purest religion ever preached to man into mystery and jargon, unintelligible to all mankind, and therefore the safer engine for their purposes. With the lawyers it is a new thing. They have, in the mother country, been generally the firmest supporters of the free principles of their constitution. But there too they have changed. I ascribe much of this to the substitution of Blackstone for my Lord Coke, as an elementary work. In truth, Blackstone and Hume have made tories of all England, and are making tories of those young Americans whose native feelings of independence do not place them above the wily sophistries of a Hume or a Blackstone. These two books, but especially the former, have done more towards the suppression of the liberties of man, than all the million of men in arms of Bonaparte and the millions of human lives with the sacrifice of which he will stand loaded before the judgment seat of his Maker. I fear nothing for our liberty from the assaults of force; but I have seen and felt much, and fear more from English books, English prejudices, English manners, and the apes, the dupes, and designs among our professional crafts. When I look around me for security against these seductions, I find it in the wide-spread of our agricultural citizens, in their unsophisticated minds, their independence and their power, if called on, to crush the Humists of our cities, and to maintain the principles which severed us from England. I see our safety in the extent of our confederacy, and in the probability that in the proportion of that the sound parts will always be sufficient to crush local poisons. In this hope I rest, and tender you the assurance of my esteem and respect.

TO MR. GIRARDIN

Monticello, March 18, 1814.

Dear Sir,—According to your request of the other day, I send you my formula and explanation of Lord Napier's theorem, for the solution of right-angled spherical triangles. With you I think it strange that the French mathematicians have not used or noticed this method more than they have done. Montucla, in his account of Lord Napier's inventions, expresses a like surprise at this fact, and does justice to the ingenuity, the elegance, and convenience of the theorem, which, by a single rule easily preserved in the memory, supplies the whole table of cases given in the books of spherical trigonometry. Yet he does not state the rule, but refers for it to Wolf, Cours de Mathematiques. I have not the larger work of Wolf; and in the French translation of his abridgement, (by some member of the congregation of St. Maur,) the branch of spherical trigonometry is entirely omitted. Potter, one of the English authors of Courses of Mathematics, has given the Catholic proposition, as it is called, but in terms unintelligible, and leading to error, until, by repeated trials, we have ascertained the meaning of some of his equivocal expressions. In Robert Simson's Euclid we have the theorem with its demonstrations, but less aptly for the memory, divided into two rules, and these are extended as the original was, only to the cases of right-angled triangles. Hutton, in his Course of Mathematics, declines giving the rules, as "too artificial to be applied by young computists." But I do not think this. It is true that when we use them, their demonstration is not always present to the mind; but neither is this the case generally in using mathematical theorems, or in the various steps of an algebraical process. We act on them, however, mechanically, and with confidence, as truths of which we have heretofore been satisfied by demonstration, although we do not at the moment retrace the processes which establish them. Hutton, however, in his Mathematical Dictionary, under the terms "circular parts," and "extremes," has given us the rules, and in all their extensions to oblique spherical, and to plane triangles. I have endeavored to reduce them to a form best adapted to my own frail memory, by couching them in the fewest words possible, and such as cannot, I think, mislead, or be misunderstood. My formula, with the explanation which may be necessary for your pupils, is as follows:

Lord Napier noted first the parts, or elements of a triangle, to wit, the sides and angles; and expunging from these the right-angle, as if it were a non-existence, he considered the other five parts, to wit, the three sides, and two oblique angles, as arranged in a circle, and therefore called them the circular parts; but chose, (for simplifying the result,) instead of the hypothenuse and two oblique angles, themselves, to substitute their complements. So that his five circular parts are the two legs themselves, and the complements of the hypothenuse and of the two oblique angles. If the three of these, given and required, were all adjacent, he called it the case of conjunct parts, the middle element the MIDDLE PART, and the two others the EXTREMES disjunct from the middle or EXTREMES DISJUNCT. He then laid down his catholic rule, to wit:

"The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT."

And to aid our recollection in which case the tangents, and in which the cosines are to be used, preserving the original designations of the inventor, we may observe that the tangent belongs to the conjunct case, terms of sufficient affinity to be associated in the memory; and the sine complement remains of course for the disjunct case; and further, if you please, that the initials of radius and sine, which are to be used together, are alphabetical consecutives.

Lord Napier's rule may also be used for the solution of oblique spherical triangles. For this purpose a perpendicular must be let fall from an angle of the given triangle internally on the base, forming it into two right-angled triangles, one of which may contain two of the data. Or, if this cannot be done, then letting it fall externally on the prolongation of the base, so as to form a right-angled triangle comprehending the oblique one, wherein two of the data will be common to both. To secure two of the data from mutilation, this perpendicular must always be let fall from the end of a given side, and opposite to a given angle.

But there will remain yet two cases wherein Lord Napier's rule cannot be used, to wit, where all the sides, or all the angles alone are given. To meet these two cases, Lord Buchan and Dr. Minto devised an analogous rule. They considered the sides themselves, and the supplements of the angles as circular parts in these cases; and, dropping a perpendicular from any angle from which it would fall internally on the opposite side, they assumed that angle, or that side, as the MIDDLE part, and the other angles, or other sides, as the OPPOSITE or EXTREME parts, disjunct in both cases. Then "the rectangle under the tangents of half the sum, and half the difference of the segments of the MIDDLE part, is equal to the rectangle under the tangents of half the sums, and half the difference of the OPPOSITE PARTS."

And, since every plane triangle may be considered as described on the surface of a sphere of an infinite radius, these two rules may be applied to plane right-angled triangles, and through them to the oblique. But as Lord Napier's rule gives a direct solution only in the case of two sides, and an uncomprised angle, one, two, or three operations, with this combination of parts, may be necessary to get at that required.

You likewise requested for the use of your school, an explanation of a method of platting the courses of a survey, which I mentioned to you as of my own practice. This is so obvious and simple, that as it occurred to myself, so I presume it has to others, although I have not seen it stated in any of the books. For drawing parallel lines, I use the triangular rule, the hypothenusal side of which being applied to the side of a common straight rule, the triangle slides on that, as thus, always parallel to itself. Instead of drawing meridians on his paper, let the pupil draw a parallel of latitude, or east and west line, and note in that a point for his first station, then applying to it his protractor, lay off the first course and distance in the usual way to ascertain his second station. For the second course, lay the triangular rule to the east and west line, or first parallel, holding the straight or guide rule firmly against its hypothenusal side. Then slide up the triangle (for a northerly course) to the point of his second station, and pressing it firmly there, lay the protractor to that, and mark off the second course, and distance as before, for the third station. Then lay the triangle to the first parallel again, and sliding it as before to the point of the third station, there apply to it the protractor for the third course and distance, which gives the fourth station; and so on. Where a course is southwardly, lay the protractor, as before, to the northern edge of the triangle, but prick its reversed course, which reversed again in drawing, gives the true course. When the station has got so far from the first parallel, as to be out of the reach of the parallel rule sliding on its hypothenuse, another parallel must be drawn by laying the edge, or longer leg of the triangle to the first parallel as before, applying the guide-rule to the end, or short leg, (instead of the hypothenuse,) as in the margin, and sliding the triangle up to the point for the new parallel. I have found this, in practice, the quickest and most correct method of platting which I have ever tried, and the neatest also, because it disfigures the paper with the fewest unnecessary lines.

If these mathematical trifles can give any facilities to your pupils, they may in their hands become matters of use, as in mine they have been of amusement only.

Ever and respectfully yours.