thoughts, and sometimes enters the regions of Natural Theology and Metaphysics, this I think is very allowable, and is not to be considered a part of his Physics, which are contained in his propositions and corollaries. Even his queries and conjectures are valuable; but I think he never intended that they should be taken for granted, but made the subject of inquiry.

THO. REID.

From Dr REID to Lord KAMES.

On the Laws of Motion.-Pressure of Fluids, &c.

January 25. 1781.

MY LORD, To what cause is it owing that I differ so much from your Lordship in Physics, when we differ so little in Metaphysics? I am at a loss to account for this phenomenon. Whether is it owing to our having different conceptions to the same words? Or, as I rather think it is, to your being dissatisfied with the three general laws of motion? Without them, I know not indeed how to reason in physics. Archimedes reasoned from them both in mechanics and hydrostatics, Galileo, Huygens, Wren, Wallis, Mariotte, and many others, reasoned from them, without observing that they did so...

I have not indeed any scruples about the principles of hydrostatics. They seem to me to be the necessary consequences of the definition of a fluid, the three laws of motion, and the law of gravitation; and, therefore, I cannot assent to your Lordship's reasoning, either about the pressure of fluids, or about the suspension of the mercury in the barometer.

J...

As

As to the first, the experiments which shew that fluids do in fact press undequaque, are so numerous, and so well known to your Lordship, that I apprehend it is not the fact you question, but the cause. You think that gravity is not the cause, Why? Because gravity gives to every part of the fluid a tendency downwards only; and what is true of every part is true of the whole: therefore, the whole has no other tendency but downward. This argument is specious, but there is a fallacy in it. If the parts did not act upon one another, and counteract one another, the argument would be good; but the parts are so connected, that one cannot go down but another must go up, and, therefore, that very gravity which presses down one part presses up another: so that every part is pressed down by its own gravity, and pressed up at the same time by the gravity of other parts; and the contrary pressures being equal, it remains at rest.

This may be illustrated by a balance equilibrating by equal weights in both scales. I say each arm of the balance is equally pressed upwards and downwards at the same time, and from that cause is at rest; although the tendency of the weights in each of the scales is downwards only. I prove it à posteriori; because the arm of a balance being moveable by the least force, if it was pressed in one direction only, it would move in that direction: But it does not move. I prove it à priori; because the necessary effect of pressing one arm down, is the pressing the other up with the same force: Therefore, each arm is pressed down by the weight in its own scale, and equally pressed up by the weight in the other scale; and being pressed with equal force in contrary directions, it remains at rest. Your Lordship will easily apply this reasoning to a fluid, every part of which is as moveable as the balance is about its fulcrum; and no one part can move, but an equal part must be moved in a contrary

direction.

direction. And I think it is impossible we should differ in this, but in words.

Next, as to the barometer. You say the mercury is kept up by the expansive power of the air: But you say further, that it is not kept up by the weight of the air. I agree to the first, but not to the last. The expansive power of the air is owing to its being compressed; and it is compressed by the weight of the incumbent atmosphere. Its expansive force is exactly equal to the force that presses and condenses it; and that force is the weight of the air above it, to the top of the atmosphere. So that the expansive force of the air is the causa proxima, the weight of the atmosphere the causa remota of the suspension of the mercury. Your Lordship knows the maxim, Causa causæ est causa causati. The barometer, therefore, while it measures the expansive force of the air which presses upon the lower end of the tube, at the same time measures the weight of the atmosphere, which is the cause of that expansive force, and exactly equal to it. If the air was not pressed by the incumbent weight, it would expand in boundless space, until it had no more expansive force.

As to the observation in the postscript. It is true, that the gravity of the air, while it rests upon an unyielding bottom, will give no motion to it; but the mercury in the lower end of the tube yields to the pressure of the air upon it, until the weight of the mercury is balanced by the pressure of the air.

What your Lordship is pleased to call the Opus Magnum, goes on, but more slowly than I wish.-I am, most respectfully, my Lord, yours,

From Dr REID to Lord KAMES.

On the accelerated Motion of Falling Bodies.

MY LORD,

Glasgow College, November 11. 1782.

My hope that your Lordship is in no worse state of health than when I left you, and that the rest of the good family are well, is confirmed by your continuing your favourite speculations. I promi sed to call upon you in the morning before I came away. I sent in Samuel to see if you was awake: he reported that you was sleeping sound; and I could not find it in my heart to disturb your repose.

When we say, that, in falling bodies, the space gone through is as the square of the velocity, it must be carefully observed, that the velocity meant in this proposition, is the last velocity, which the body acquires only the last moment of its fall: But the space meant is the whole space gone through, from the beginning of its fall to

the end.

As this is the meaning of the proposition, your Lordship will easily perceive, that the velocity of the last moment must indeed correspond to the space gone through in that moment, but cannot correspond to the space gone through in any preceding moment, with a less velocity; and, consequently, cannot correspond to the whole space gone through in the last and all preceding moments taken together. You say very justly, that, whether the motion be equable or accelerated, the space gone through in any instant of time corresponds to the velocity in that instant. But it does not follow from this, that, in accelerated motion, the space gone through in many

succeeding

succeeding instants will correspond to the velocity of the last in

stant.

If any writer in physics has pretended to demonstrate mathematically this proposition, That a body falling by gravity in vacuo, goes through a space which is as the square of its last velocity; he must be one who writes without distinct conceptions, of which kind we have not a few.

pro

The proposition is not mathematical, but physical. It admits not of demonstration, as your Lordship justly observes, but of proof by experiment, or reasoning grounded on experiment. There is, however, a mathematical proposition, which possibly an inaccurate writer might confound with the last mentioned. It is this, That a body uniformly accelerated from a state of rest, will go through a space which is as the square of the last velocity. This is an abstract position, and has been mathematically demonstrated; and it may be made a step in the proof of the physical proposition. But the proof must be completed by shewing, that, in fact, bodies descending by gravitation are uniformly accelerated. This is sometimes shewn by a machine invented by S'Gravesend, to measure the velocities of falling bodies: Sometimes it is proved by the experiments upon pendulums; and sometimes we deduce it by reasoning from the second law of motion, which we think is grounded on universal experience. So that the proof of the physical proposition always rests ultimately upon experience, and not solely upon mathematical demonstration. I am, my Lord, respectfully yours,

THO. REID.

APPEN