middle, and other smaller drains, laid it perfectly dry. This, having first taken up all the rubbish, I ploughed up, and harrowed it many times over, till it was smooth. Its soil is blackish; but, in about a foot or ten inches, you come to a sand of the same color with the upland. From the birch that grew upon it, I took it to be of a cold nature, and therefore I procured a grass which would best suit that kind of ground, intermixed with many others, that I might thereby see which suited it best. On the 8th of September, I laid it down with rye, which being harrowed in, I threw in the following grass seed; a bushel of Salem grass or feather-grass, half a bushel of timothy or herd-grass, half a bushel of rye-grass, a peck of burden-grass or blue bent, and two pints of red clover per acre, (all the seed in the chaff, except the clover,) and bushed them in. I could wish they had been clean, as they would have come up sooner, and been better grown before the frost; and I have found by experiment, that a bushel of clean chaff of timothy or Salem grass will yield five quarts of seed. The rye looks well, and there is abundance of timothy or Salem grass come up amongst it; but it is yet small, and in that state there is scarce any knowing those grasses apart. I expect from the sand lying so near the surface, that it will suffer much in dry weather.

B. FRANKLIN.

*

TO THOMAS HOPKINSON.*

On the Vis Inertia of Matter.

Philadelphia, 1747

ACCORDING to my promise, I send you in writing my observations on your book; † you will be the better able to consider them; which I desire you to do at your leisure, and to set me right where I am wrong.

I stumble at the threshold of the building, and there. fore have not read farther. The author's vis inertia

*Thomas Hopkinson was born in London, in April, 1709. He possessed a fine genius, and a finished education, having been a student at Oxford. He came to America while young, and married and settled in Philadelphia, where he died in 1751. He was distinguished for his classical attainments, general learning, the brilliancy of his conversation, and his fondness for philosophical studies. Being an intimate friend of Franklin, he was associated with him in his electrical and philosophical experiments. In a note to one of his letters on electricity, Franklin says; "The power of points to throw off the electrical fire was first communicated to me by my ingenious friend, Mr. Thomas Hopkinson, since deceased, whose virtue and integrity in every station of his life, public and private, will ever make his memory dear to those who knew him, and knew how to value him." He mentions other assistance derived from the observations and experiments of his friend. It is an honorable proof of Mr. Hopkinson's talents, learning, and character, that he was chosen the first president of the American Philosophical Society, instituted in the year 1744. (See above, p. 29.) He also took an active part in founding the City Library and the Colege of Philadelphia, and was a zealous promoter of public institutions and improvements. He left several children, among whom was Francis Hopkinson, one of the signers of the Declaration of Independence, well known as a writer of genius, wit, and ability, and for his valuable public services during the revolution and subsequently to that event.-EDITOR.

It was a book by Andrew Baxter, entitled An Inquiry into the Nature of the Human Soul, wherein its Immateriality is evinced, &c. One of the chief objects of this book was to prove, that a resistance to any change is essential to matter, consequently inconsistent with active powers in it; and that, if matter wants active powers, an immaterial being is necessary for all those effects, &c. ascribed to its own natural powers. After stating the several proofs, questioned by Dr. Franklin, of a Vis

essential to matter, upon which the whole work is founded, I have not been able to comprehend. And I do not think he demonstrates at all clearly (at least to me he does not), that there is really such a property in matter.

He says, No. 2, "Let a given body or mass of matter be called a, and let any given celerity be called c. That celerity doubled, tripled, &c., or halved, thirded, &c., will be 2c, 3c, &c., or c, c, &c., respectively. Also the body doubled, trepled, or halved, thirded, will be 2a, 3a, or a, a, respectively." Thus far is clear. But he adds, "Now to move the body a, with the celerity c, requires a certain force to be impressed upon it; and to move it with a celerity as 2c, requires twice that force to be impressed upon it, &c." Here I suspect some mistake creeps in, by the author's not distinguishing between a great force applied at once, and a small one continually applied, to a mass of matter, in order to move it. I think it is generally allowed by the philosophers, and, for aught we know, is certainly true, that there is no mass of matter, how great soever, but may be moved by any force how small soever, (taking friction out of the question,) and this small force, continued, will in time bring the mass to move with any velocity whatsoever. Our author himself seems to allow this

inertiæ, or "force of inertness," in matter, the author adds; "If the immateriality of the soul, the existence of God, and the necessity of a most particular, incessant providence in the world, are demonstrable from such plain and easy principles, the atheist has a desperate cause in hand." 'See the third edition, pp. 1–8.) In fact, Mr. Baxter's doctrine seems to establish, rather than disprove, an activity in matter, and consequently to defeat his own conclusion, were not that conclusion to be found from other premises. Primâ facie, it seems better for Mr. Baxter's system to suppose matter incapable of force or effort, even in the case, as he calls it, of resisting change; which case appears to me no other than the simple one, of matter not altering its state without a cause, and a ca ise exactly proportioned to the effect. B. V.

towards the end of the same No. 2, when he is subdividing his celerities and forces; for as in continuing the division to eternity by his method of c, c, c, śc, &c. you can never come to a fraction of velocity that is equal to Oc, or no celerity at all; so, dividing the force in the same manner, you can never come to a fraction of force that will not produce an equal fraction of celerity.

Where then is the mighty vis inertia, and what is its strength, when the greatest assignable mass of matter will give way to, or be moved by, the least assignable force? Suppose two globes equal to the sun and to one another, exactly equipoised in Jove's balance; suppose no friction in the centre of motion, in the beam or elsewhere; if a musqueto then were to light on one of them, would he not give motion to them both, causing one to descend and the other to rise? If it is objected, that the force of gravity helps one globe to descend, I answer, the same force opposes the other's rising. Here is an equality that leaves the whole motion to be produced by the musqueto, without whom those globes would not be moved at all. What then does vis inertiæ do in this case? and what other effect could we expect if there were no such thing? Surely, if it were any thing more than a phantom, there might be enough of it in such vast bodies to annihilate, by its opposition to motion, so trifling a force!

Our author would have reasoned more clearly, I think, if, as he has used the letter a for a certain quantity of matter, and c for a certain quantity of celerity, he had employed one letter more, and put ƒ, perhaps, for a certain quantity of force. This let us suppose to be done; and then, as it is a maxim that the force of bodies in motion is equal to the quantity of matter multiplied by the celerity, (or f = cx a); and as the force

received by and subsisting in matter, when it is put in motion, can never exceed the force given; so, if f moves a with c, there must needs be required 2f to move a with 2c; for a moving with 2c would have a force equal to 2f, which it could not receive from 1f; and this, not because there is such a thing as vis inertiæ, for the case would be the same if that had no existence; but because nothing can give more than it has. And now again, if a thing can give what it has, If If can to la give lc, which is the same thing as giving it If, (that is, if force applied to matter at rest, can put it in motion, and give it equal force,) where then is vis inertia? If it existed at all in matter, should we not find the quantity of its resistance subtracted from the force given?

In No. 4, our author goes on and says, "The body a requires a certain force to be impressed on it to be moved with a celerity as c, or such a force is necessary; and therefore it makes a certain resistance, &c.; a body as 2a requires twice that force to be moved with the same celerity, or it makes twice that resistance; and so on." This I think is not true; but that the body 2a, moved by the force If, (though the eye may judge otherwise of it) does really move with the same celerity as it did when impelled by the same force; for 2a is compounded of la+la; and if each of the la's, or each part of the compound, were made to move with lc (as they might be by 2f), then the whole would move with 2c, and not with lc, as our author supposes. But If applied to 2a makes each a move with c; and so the whole moves with 1c; exactly the same as la was made to do by If before. What is equal celerity but a measuring the same space by moving bodies in the same lime? Now if 1a, impelled by lf, measures one hundred yards in a minute; and in 2a, impelled by If, each