Scientific Memoranda 

Trees and Fountains

Written at Paris, in 1788, and left with Jefferson, residing at Challiot. 
 
Dear Sir: I enclose you a problem, not about bridges, but trees; and to explain my meaning I begin with a fountain.  The idea seems far-fetched-but fountains and trees are in my walk to Challiot.  Suppose Figure 1, a fountain.  It is evident that no more water can pass through the branching tubes than passes through the trunk.  Secondly that, admitting all the water to pass with equal freedom, the sum of the squares of the diameters of the two first branches must be equal to the square of the diameter of the trunk; also the sum of the squares of the four branches must be equal to the two; and the sum of the squares of the eight branches must be equal to the four.  And therefore 8,4,2, and the trunk, being reciprocally equal, the solid content of the whole will be equal to the cylinder (figure 2) of the same diameter of the trunk, and height of the fountain.
 
Carry the idea of a fountain to a tree growing.  Consider the sap ascending in capillary [begin page 211] tubes like the water in the fountain, and no more sap will pass through the branches than passes through the trunk.  Secondly, consider the branches as so many divisions and subdivisions of the trunk, as they are in the fountain, and that their contents are to be found by some rule - with the difference only of a pyramidal figure instead of a cylindrical one.  Therefore, to find the quantity of timber (or rather loads) in the tree (figure 8) draw a pyramid equal to the height of the tree (as in figure 4) taking for the inclination of the pyramid the diameter at the bottom, and at any discretionary height above it (which in this is as three and two). 

P.S. - As sensible men should never guess, and as it is impossible to judge without some point to begin at, this appears to me to be that point; and [one] by which a person may ascertain near enough the quantity [of] timber and loads of wood in any quantity of land.  And he may distinguish them into timber, wood, and faggots.
 
Attraction

Your saying last evening that Sir Isaac Newton's principle of gravitation would not explain, or could not apply as a rule to find the quantity of the attraction of cohesion, and my replying [begin page 212] that I never could comprehend any meaning in the term "Attraction of Cohesion" - the result must be, that either I have a dull comprehension, or that the term does not admit of comprehension.  It appears to me an Athanasian jumble of words, each of which admits of a clear and distinct idea, but of no idea at all when compounded. 

The immense difference there is between the attracting power of two bodies, at the least possible distance the mind is capable of conceiving, and the great power that instantly takes place to resist separation when the two bodies are incorporated, prove to me that there is something else to be considered in the case than can be comprehended by attraction of gravitation.  Yet this matter appears sufficiently luminous to me, according to my own line of ideas.
 
Attraction is to matter, what desire is to the mind; but cohesion is an entirely different thing, produced by an entirely different cause - it is the effect of the figure of matter. 

Take two iron hooks - the one strongly magnetical - and bring them to touch each other, and a very little force will separate them for they are held together only by attraction.  But their figure renders them capable of holding each other [begin page 213] with infinitely more power to resist separation than attraction can; by hooking them.
 
Now if we suppose the particles of matter to have figures capable of interlocking and embracing each other we shall have a clear distinct idea between cohesion and attraction, and that they are things totally distinct from each other and arise from as different causes. 

The welding of two pieces of iron appears to me no other than entangling the particles in much the same manner as turning a key within the wards of a lock-and if our eyes were good enough we should see how it was done. 

I recollect a scene at one of the theaters that very well explains the difference between attraction and cohesion.  A condemned lady wishes to see her child and the child its mother -this call attraction.  They were admitted to meet, but when ordered to part they threw their arms round each other and fastened their persons together.  This is what I mean by cohesion - which is a mechanical contact of the figures of their persons, as I believe all cohesion is.
 
Though the term “attraction of cohesion" has always appeared to me like the Athanasian Creed, yet I think I can help the philosophers to a better explanation of it than what they give themselves [begin page 214] which is, to suppose the attraction to continue in such a direction as to produce the mechanical interlocking of the figure of the particles of the bodies attracted.
 
Thus suppose a male and female screw lying on a table, and attracting each other with a force capable of drawing them together.  The direction of the attracting power to be a right line till the screws begin to touch each other, and then, if the direction of the attracting power be circular, the screws will be screwed together.  But even in this explanation, the cohesion is mechanical, and the attraction serves only to produce the contact.
 
While I consider attraction as a quality of matter capable of acting at a distance from the visible presence of matter, I have as clear an idea of it as I can have of invisible things, 

And while I consider cohesion as the mechanical interlocking of the particles of matter, I can conceive the possibility of it much easier than I can attraction, because I can, by crooking my fingers, see figures that will interlock-but no visible figure can explain attraction, Therefore to endeavor to explain the less difficulty by the greater appears to me unphilosophical.  The cohesion which others attribute to attraction and [begin page 215] which they cannot explain, I attribute to figure, which I can explain. 

A number of fish hooks attracting and moving toward each other will show me there is such a thing as attraction, but I see not how it is performed, but their figurative hooking together shows cohesion visibly. And a handful of fish hooks thrown together in a heap explains cohesion better than all the Newtonian philosophy. It is with gravitation, as it is with all new discoveries, it is applied to explain too many things. 

It is a rainy morning, and I am waiting for Mr. Parker, and in the meantime, having nothing else to do, I have amused myself with writing this. 

On the Means of Generating Motion for Mechanical Uses

Sent to Jefferson, from Paris, June 25, 1801. 

As the limit of the mechanical powers, properly so called, is fixed - in nature no addition or improvement otherwise than in the application of them, can be made.  To obtain a still greater quantity of power we must have recourse to the natural powers, and for usefulness, combine them with the mechanical powers.  Of this kind are wind and water, to which has since been [begin page 216] added steam.  The first two cannot be generated at pleasure.  We must take them where and when we find them. 

It is not so with the steam engine.  It can be erected in any place and act in all times where a well can be dug and fuel can be obtained.  Attempts have been made to apply this power to the purpose of transportation, as that of moving carriages on land and vessels on the water.  The first I believe to be impracticable, because I suppose, that the weight of the apparatus necessary to produce steam is greater than the power of the steam to remove that weight and consequently that the steam engine cannot move itself. 

The thing wanted for purposes of this kind, and if applicable to this may be applicable to many others, is something that contains the greatest quantity of power in the least quantity of weight and bulk, and we find this property in gunpowder.  When I consider the wisdom of nature I must think that she endowed matter with this extraordinary property for other purposes than that of destruction.  Poisons are capable of other uses than that of killing. 

If the power which an ounce of gunpowder contains could be detailed out as steam or water can be, it would be a most commodious natural [begin page 217] power, because of its small weight, and little bulk; but gunpowder acts, as to its force, by explosion.  In most machinery operations the generating power is applied to produce a rotary motion on a wheel, and I think that gunpowder can be applied to this purpose.

But as an ounce of gunpowder or any other quantity when on fire, cannot be detailed out so as to act with equal force through any given space of time, the substitute in this case is, to divide the gunpowder into a number of equal parts, and discharge them in equal spaces of time on the wheel, so as to keep it in nearly an equal and continual motion; as a boy's whipping top is kept up by repeated floggings.  Every separate stroke given to the top acts with the suddenness of explosion, but produces, as to continual motion, the effect of uninterrupted power.

When a stream of water strikes on a water wheel, it puts it in motion, and continues it.  Suppose the water removed and that discharges of gunpowder were made on the periphery of the wheel where the water strikes, would they not produce the same effect? 

I mention this merely for the simplicity of the case.  But the wheel on which gunpowder is to act must be fitted for the purpose.  The buckets [begin page 218] or boards placed on the periphery of a water wheel are the whole breadth of the stream of water; but the parts corresponding to them on a gunpowder wheel should be of iron and concave like a cup, and of no larger size than to receive the whole of the explosion.  The back of them should be convex or oval, because in that shape they meet with less resistance from the air. 

The barrels from which the discharges are to be made, should, I think, be in the direction of a tangent with the cups.  But if it should be found better to make the discharge on the solid periphery of the wheel the barrels should be a tangent of a circle something less than the periphery of the wheel.  A wheel put and continued in motion in this manner is represented by holding the axis of a wheel in one hand and striking the periphery with the other.

If acting on the solid periphery of the wheel should be found preferable to acting on the cups, 
the wheel should be shod with iron, the edges ,ii should be turned up and the middle part fluted cross.  By this means the explosion cannot well escape sideways and the fluting will be preferable to a plain surface. 

That the power of any given quantity of gunpowder can be detailed out by this means to act [begin page 219] through any given quantity of time, and that a wheel can be put and continued in motion thereby, there is I think no doubt.  Whether it will answer profitably in practise is another question.  But the experiment, I think is worth making, and the more so, because it appears one of things in which a small experiment decides almost positively for a large one, which is not the case in many other small experiments.  I think the wheel for a great work should be large, 30 or 40 feet diameter, because the explosions would give too much velocity to a small one, and because the larger the wheel is, the longer the explosion would rest upon it and the motion will be less irregular.

The machine which it seems to come into competition with is the steam engine. In the first place a steam engine is very expensive to erect.  In this only a few iron barrels are required.  In a steam engine the expense and consumption of fuel is great, and this is to be compared to the expense of gunpowder, with the advantage that the interest of the money expended in erecting a steam engine goes toward the expense of the gunpowder. 

A steam engine is subject to be out of order, and for this reason they frequently have two, that when one is repairing the other can suppl- [begin page 220] its place, or all the works dependent upon it must stand still.  But nothing of this kind can happen to the gunpowder engine, because if a barrel burst, which is all that can happen, its place can be immediately supplied by another; but if a boiler bursts there must be a new one.  But I will not take up your time with calculations of this kind.  The first thing to know is, if the experiment will succeed. 

If in your retirement from business you should be disposed to vary your mechanical amusements, I wish you would try the effect of gunpowder on a wheel of two or three feet diameter; the smallest bored pistol there is, about the size of a quill, would give it considerable velocity.  The first experiment will be to observe how long it will revolve with one impulse, and then with two.  If the wheel revolves perpendicularly fast to its axis, and a cord be fastened to the axis with a weight to the end of the cord which, when the wheel is in motion, will wind on the axis and draw up the weight, the force with which it revolves will be known. 

Perhaps there may be some difficulty in starting a great wheel into motion at first, because gunpowder acts with a shock.  In this case, might not gunpowder be mixed with some other [begin page 221] material, such as is used to make sky-rockets ascend? because this lessens the shock and prolongs the force.  But I conceive that after the wheel is in motion, there will be scarcely any sensible shock from the gunpowder. 

As it is always best to say nothing about new concerts till we know something of their effects I shall say nothing of this till I have the happiness to see you, which I hope will not be long, and which I anxiously wish for.

T.P.