Dispatching to mr Ticknor my packet of letters for Paris, it occurs to me that I committed an error in a matter of information which you asked of me while here. it is indeed of little importance, yet as well corrected as otherwise; and the rather as it gives me an occasion of renewing my respects to you. you asked me in conversation what constituted a mulatto by our law? and I believe I told you 4 crossings with the whites. I looked afterwards into our law, and found it to be in these words. ‘every person, other than a negro, of whose grandfathers or grandmothers any one shall have been a negro, shall be deemed a mulatto, and so every such person who shall have one fourth part or more of negro blood; shall in like manner be deemed a mulatto.’ L. Virga. 1792. Dec. 17 the case put in the first member of this paragraph of the law is exempli gratiâ. the latter contains the true Canon, which is that ¼ of negro blood, mixed with any portion of white, constitutes the mulatto. as the issue has one half of the blood of each parent, and the blood of each of these may be made up of a variety of fractional mixtures, the estimate of their compound, in some cases, may be1 intricate. it becomes a Mathematical problem of the same class with those on the mixtures of different liquors or different metals. as in these therefore, the Algebraical notation2 is the most convenient & intelligible. let us express the pure blood of the white in the capital letters of the printed3 alphabet, the pure blood of the negro in the small letters of the printed alphabet, and any given mixture of either, by way of abridgment in MS. letters.

let the 1st crossing be of a, pure negro, with A. pure white. the Unit of blood of the issue being composed of the half of that of each parent, will be a/2 + A/2 call it, for abbreviation, h (half-blood)

let the 2d crossing be of h. and B. the blood of the issue will be h/2 + B/2, or substituting for h/2 it’s equivalent, it will be a/4 + A/4 + B/2. call it q (quarteroon) being ¼ negro blood

let the 3d crossing be of q. and C. their offspring will be
q/2 + C/2 = a/8 + A/8 + B/4 + C/2. call this e. (eighth) who having less than ¼ of a. or of pure negro blood, to wit ⅛ only, is no longer a mulatto. so that a 3d cross clears the blood.

from these elements let us examine other compounds.

for example, let h. and q. cohabit. their issue will be
h/2 + q/2 = a/4 + A/4 + a/8 + A/8 + B/4 = ⅜ + ⅜ + B/4 wherein we find ⅜ of a. or of negro blood.

let h. and e. cohabit. their issue will be
h/2 + e/2 = a/4 + A/4 + a/16 + A/16 + B/8 + C/4 = 5a/16 + 5A/16 + B/8 + C/4 wherein 5/16a. makes still a mulatto.

let q. and e. cohabit. the half of the blood of each will be
q/2 + e/2 = a/8 + A/8 + B/4 + a/16 + A/16 + B/8 + C/4 = 3a/16 + 3A/16 + ⅜ + C/4 wherein 3/16 of a is no longer mulatto.

and thus may every compound be noted & summed, the sum of the fractions composing the blood of the issue being always equal to Unit. it is understood in Natural history that a 4th cross of one race of animals with another gives an issue equivalent for all sensible purposes to the original blood. thus a Merino ram being crossed 1st with a country ewe, 2dly with this daughter, 3dly with this grandaughter, and 4thly with the great grandaughter, the last issue is deemed pure Merino, having in fact but 1/16 of the country blood. our Canon considers 2. crosses with the pure white, and a 3d with any degree of mixture, however small, as clearing the issue of the negro blood. but observe that this does not reestablish freedom, which depends on the condition of the mother, the principle of the civil law, partus sequitur ventrem, being adopted here. but if e. be emancipated, he becomes a free white man, and a citizen4 of the US. to all intents and purposes—so much for this trifle, by way of correction.

 

I sincerely congratulate you on the peace, and more especially on the close of our war with so much eclat. our 2d and 3d campaigns have, I trust, more than redeemed the disgraces of the 1st and proved that altho a republican5 government is slow to move, yet, when once in motion, it’s momentum becomes irresistable, and I am persuaded it would have been found so in the late war, had it continued. experience had just begun to elicit those among our officers who had talents for war, and under the guidance of these one campaign would have planted our standard on the walls of Quebec, and another on those of Halifax. but peace is better for us all, and if it could be followed by a cordial conciliation between us and England it would ensure the happiness and prosperity of both. the bag of wind however on which they are now riding must be suffered to blow out, before they will be able soberly to settle on their true bottom. if they adopt a course of friendship with us, the commerce of 100. millions of people, which some now born will live to see here, will maintain them for ever as a great Unit of the European family. but if they go on checking, irritating, injuring, and hostilizing us, they will force on us the motto ‘Carthago delenda est.’ and some Scipio Americanus will leave to posterity the problem of conjecturing where stood once the antient and splendid city of London? nothing more simple or certain than the elements of this calculation. I hope the good sense of both parties will concur in travelling rather the paths of peace, of affection and reciprocations of interests.  I salute you with sincere and friendly esteem, and if the homage offered to the virtues of your father can be acceptable to him, place mine at his feet.

Th: Jefferson