I know not what apology to make for the trouble I am about to give you. I am sure I must call your publick spirit in aid of your private friendship to me.

You will see by the head of the inclosed report, that the house of representatives have instructed me to lay before them a plan for establishing uniform weights, measures and coins. Five and twenty years ago I should have undertaken such a task with pleasure, because the sciences on which it rests were then familiar to my mind and the delight of it. But taken from them thro’ so great a length of time, and forced by circumstances into contemplations of a very different nature and much less pleasing, I have grown rusty in my former studies. To render me more unequal to the task, it comes on me in the moment when I am separated from all my books and papers, which had been left in Paris and Virginia: and this place yeilds fewer resources in the way of books than could have been imagined. Thus situated, I have done what I could towards fulfilling the object of the house of representatives, and I think myself happy in having such a resource as your friendship and your learning to correct what I have prepared for them. The necessity I am under must be my apology. It is desirable for the public that the plan should be free from errors: it is desireable for me that they should be corrected privately by a friend, rather than before the world at large, by the unfeeling hand of criticism. Do then, my dear Sir, read it over with all that attention of which you are so much the master, and correct with severity every thing you find in it which is not mathematically just. And while I ask your attention to every part of it, I will make some notes on particular things.—It was not till after I had got through the work that I was able to get a sight of Whitehurst’s on the same subject. Mr. Madison procured it for me from a library in Philadelphia. But on perusal of it, his plan of two pendulums appeared to me on the whole less eligible than Leslie’s of the vibrating rod.—How has it been inferred that Sr. Isaac Newton’s calculation of the length of the pendulum for the latitude of London is 39.2 Inches? From his general table in the Principia. B. 3. I deduce 39.1682. Am I wrong? If so, I may be equally wrong in the calculation of 39.1285 I. for lat. 38.° in which an error would be fundamentally important, and therefore I ask your peculiar attention to that. What do you think of the vibrating rod? Is it not clear of some objections which lie against the pendulum? And is it liable to any of which that is clear? And which is best on the whole?—I am too little familiar with the mechanism of the clock to know how the rod can be adapted to a machinery which shall maintain and count it’s vibrations, without accelerating them by it’s power, or retarding them by it’s friction, in short which shall leave the rod free to make it’s vibrations uninfluenced by any circumstance but it’s own length. On this point no man in the world can judge or contrive better than yourself. On these then and all the other parts of the report pray give me the full benefit of your assistance. In the trouble I am giving you I feel it as a circumstance of additional misfortune that I am pressed in time. The session of Congress is drawing to a close. Nothing will keep them together after the money bills are got through, and this will be pretty soon. I am obliged therefore to ask your immediate attention to this subject, as I must give in the report before they rise. I suppose they will have it printed for consideration, to be taken up at their next meeting.

I will not weary you with apologies, tho I feel powerfully the necessity of them. I am in all times and places Your sincere friend & humble servt,