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."