Sir Henry H. Cunynghame

“ The only thing we can do is to watch its motions, and see how it flies. If it goes more and more quickly, we say, “There is propelling force acting on it”; if it begins to stop, we say again, “There is retarding force acting on it.” So long as it does not change its speed or direction, we say, “There is no force acting on it.” By this method, therefore, we tell whether a body is being acted on by force, simply by observing its speed or its change of speed. Merely to say a body is moving does not tell us that force is acting on it. All we know is that, if it is moving, force has acted on it. ”

“ It is like a man who has an increasing income and always goes on saving it. His total mounts up not merely in proportion to the time, but the very rate of increase also increases with the time, so that the total increase is in proportion to the time multiplied into the time, in other words to the square of the time. So then, if I let a body drop from rest under the action of any force capable of producing an acceleration, the space passed through will be as the square of the time.
Now let us see what the speed will be if the force is gravity, that is the attraction of the earth. ”

“ Thus, for instance, we are all apt to think we know what is meant when force, weight, length, capacity, motion, rest, size, are spoken of. And yet when we come to examine these ideas more closely, we find that we know very little about them. Indeed, the more elementary they are, the less we are able to understand them.
The most primordial of our ideas seem to be those of number and quantity; we can count things, and we can measure them, or compare them with one another. Arithmetic is the science which deals with the numbers of things and enables us to multiply and divide them. ”

“ The truth is that each body is occupied in moving itself without troubling about moving its neighbour, so that if you put any number of marbles into a bag and let them drop they all go down individually, as it were, and all in the time which a single marble would take to fall. For any other result would be a contradiction. If you cut a piece of bread in two, and put the two halves together, and tie them together with a thread, will the mere fact that they are two pieces make each of them fall more slowly than if they were one? ”

“ We are not entitled to say that all other ideas are formed from and compounded of these ideas, but we are entitled to say that our correct understanding of physics, that is of the study of nature, depends in no slight degree upon our clear understanding of them. The three fundamental ideas are those of space, time and mass.
Space appears to be the universal accompaniment of all our impressions of the world around us. Try as we may, we cannot think of material bodies except in space, and occupying space. Though we can imagine space as empty we cannot conceive it as destroyed. ”

“ So that we may say that the test of the strength of the force is how much motion it can give to a body of a given mass in a given time. It does not matter how the force acts. It may act by means of a string and pull it; it may act by means of a stick and push it; it may act by attraction and draw it; it may act by repulsion and repel it; it may act as a sort of little spirit and fly away with it. In all these cases it acts. The more it acts, the more effect it has. In double the time it produces double the motion. If the mass is big, it takes more force to make the mass move ”

“ They will smile when they observe that our highest university degrees, our most lucrative rewards, were given for the study of dead languages or archæological investigations, and that science, our glory and that for which we have shown real ability, should only have occupied a secondary place in our education.
They will smile when they learn that we considered that a knowledge of public affairs could only be acquired by a grounding in Greek particles, or that it could ever have been thought that men could not command an army without a study of the tactics employed at the battle of Marathon. ”

“ But mass is quantity of matter. Knock a brick against your head, and you will know what mass is. It is not the weight of the brick that gives you a bump; it is the mass. Try to throw a ball of lead, and you will know what mass is. Try to push a heavy waggon, and you will know what mass is. Weights, that is earth attractions on masses, are proportional to the masses at the same place. This, as we have seen, is known by experiment.
Therefore, when a force acts for a certain time on a mass that is free to move, however small the force and however small the time, that body will move. ”

“ Galileo had partly seen the same thing, but he never saw it so clearly as Newton. Great discoveries are only made by seeing things clearly. What required the force of a genius in one age to see in the next may be understood by a child.
Hence then we say a force is that which in a given time produces a given motion in a given mass which is free to move. ”

“ When we read the works of Homer, or Virgil, or Plato, or turn to the later productions of Dante, of Shakespeare, of Milton, and the host of writers and poets who have done so much to instruct and amuse us, and to make our lives good and agreeable, we are apt to look with some disappointment upon present times. And when we turn to the field of art and compare Greek statues and Gothic or Renaissance architecture with our modern efforts, we must feel bound to admit our inferiority to our ancestors. ”

“ Gravity is, of course, not the only accelerating force with which we are acquainted. If a spring be suddenly allowed to act on a body and pull it, the body begins to move, and its action is gradually accelerated, just as though it were attracted, and the acceleration of its motion will be proportional to the time during which the accelerating force acts. Similarly, if gunpowder be exploded in a gun-barrel, and the force thus produced be allowed to act on a bullet, the motion of the bullet is accelerated so long as it is in the barrel. ”

“ He is, as it were, the slave of the machine, watching it and answering to its calls. Or shall we rather say that he is the machine’s employer and master? He has here a servant who never tires nor ever disobeys him. All the machine requires is that its cutting edges should be exactly true and sharp and microscopically perfect; then it will cut away and make wheel after wheel. It oils itself. It only wants the man to act as superintendent, and stop it if any cutting edge gets unduly worn. ”

“ It may be useful to give a simple form of proof of the law which governs the time of oscillation of a pendulum whose length is given.
Unfortunately, it is impossible to give one so simple as to be comprehended by those who know nothing whatever of mathematics. It is, however, possible to give a proof that requires very little mathematical knowledge.
We know that when a mass of matter is whirled round at the end of a string it tends to fly outwards and puts a strain on the string. The faster the speed at which the mass is whirled, the stronger will be the strain on the string. ”

“ If when a particular star got to Greenwich a gong were sounded which could be heard all over the earth, then of course, by seeing what stars were overhead, everyone would know their longitude at once. ”

“ This would not be the case with other methods of setting a body in motion. If I kick a small ball with all my might, I shall send it further than a kick of equal strength would send a heavier ball. Why? Because the impulse is the same in each case, but the masses are different. But if those balls are pulled by gravity, then, by the very nature of the earth’s attraction (the reason of which we cannot explain) , the small ball receives a little pull, and the big ball receives a big pull, the earth exactly apportioning its pull in each case to the mass of the body on which it has to act. ”

“ When a baby in a temper stamps upon the earth it makes the earth move—not much, it is true, but still it moves; nay, more, in theory, not a fly can jump into the air without moving the earth and the whole solar system. Only, as you may imagine they do not show it appreciably. Still, in theory the motion is there. ”

“ The mistaken astronomy of the Greeks was also much forwarded by Aristotle, the tutor of Alexander the Great. This great genius in politics and philosophy was only in the second rank as a man of science, and, as I think, hardly equal to Archimedes or Hipparchus, or even to Ptolemy. Aristotle wrote a book concerning the heavens which bristles with the most wantonly erroneous scientific ideas, such as, for instance, that the motion of the heavenly bodies must be circular because the most perfect curve is a circle, and similar assumptions as to the course of nature. ”

“ We are in the habit of estimating mass by its weight, and we do so rightly, for at any place on the earth, as London, the weights of masses are always proportioned to the masses, and if you want to find out what mass of tea you have got, you weigh it, and you know for certain. Hence in our minds we confuse mass with weight. ”

“ Whence then we see that for motion in a circle of a mass under the attraction of a centripetal force, or pull of a string, the time of rotation will be uniform, provided that the centripetal force always varies as the radius of the path. From this it is evident that a body fixed on to an elastic thread where the pull varies as the extension would make its rotations always in equal times. If your sling consists of elastic, whirl as you will, you can only whirl the body round so many times in a second, and no more. ”

“ It is possible, of course, with a file and scraper and days of labour to get two flat surfaces of metal so perfect that when put together one will lift the other like a sucker on a stone, but it is waste labour. A small machine will do it as well in a few minutes. No longer is a watch built up as one would build a house, fitting part to part. By expensive machines thousands of watch parts are stamped and cut out to pattern, and then a watch is made by taking one of each indiscriminately and just putting them into their places. ”

“ The attraction of the earth on masses of matter that are not free to move gives rise to forces which are called weights. Thus the attraction of gravitation on a mass of one pound produces a pressure equal to a weight of one pound. ”

“ To our age is reserved the glory of being easily the foremost in scientific discovery. Future ages may despise our literature, surpass us in poetry, complain that in philosophy we have done nothing, and even deride and forget our music ”

“ I repeat again, when a body is free to move, then, if no further force acts on it, it will go on in a straight line at a uniform speed, but if a force continues to act on it in any direction, then that force produces in each unit of time a unit of acceleration in the direction in which the force acts, and the result is that the body goes on moving towards the direction of acceleration at a constantly increasing speed, and hence passing over spaces that are greater and greater as the speed increases. ”

“ The ancient Pythagorean philosophers thought that all nature moved to music, and that dying souls could begin to hear the tones to which the stars moved in their orbits. They called it, as you know, the music of the spheres. ”

“ If a ball be attached to a piece of elastic thread, and thrown from the hand, so that it flies out, and then stops and is brought back by the elastic force of the thread, the time of the outward motion and the return is the same whatever be the force of the throw. And so if a pendulum be impelled outwards from a position of rest, the time of the swing out and back is the same, however big (within limits) is the impelling force and the consequent length of the swing. The use of a pendulum as a measure of time is to impel it outwards, and then let it fly freely out and back. ”

“ It was compensated for heat expansion by a cunning use of the unequal expansion of brass and steel, in a manner analogous to the way this unequal expansion of metals had been employed to compensate the pendulum, and became the beautiful and accurate time-measurer that we see to-day, with its pivots mounted in jewels to diminish friction, and with screws round the rims of the balance wheel to enable the centre of gravity to be exactly adjusted to its centre of rotation, and with a delicate hair-spring of tempered steel that is a marvel of microscopic work. ”

“ If a crowd of persons are rushing out of a building, the total force of the crowd will be greater than the force of one man, but the speed at which they can get out will not be greater than the speed of one man; in fact, each man in the crowd has only force enough to move his own mass. ”

“ The idea of a state of things in which time existed no more was quite familiar to mediæval thinkers, and was regarded by many of them as the condition that would exist after the Day of Judgment. In recent times Kant propounded the theory that time was only a necessary condition of our thoughts, and had no existence apart from thinking beings—in fact, that it was our way of looking at things. ”

“ Some philosophers think that the limitation is in us, not in the world, and that perhaps when our minds are free from the limitations imposed by their sojourn in our bodies, and death has set us free, we may see not only what is the length and breadth and height, but a great deal more also of which we can now form no conception. ”

“ Fire appeared always to desire to go upwards, so they thought that fire had an earth-repellent, heaven-seeking character. Water they thought partly earth-seeking, partly heaven-seeking, for it appeared in the ocean or floated as clouds. ”

“ The great manufacturers of our Midlands do not seem to understand that there is no object in making a towel-horse as geometrically accurate as a turning lathe. It will apparently be years before they learn to put art and precision each in the place where it is wanted—precision in the works of the watch, art in the face and the case of it; machine work in the inside of a watch, hand work on the outside. ”

“ If the earth suddenly stood still, everything on it would be shaken to pieces. It is bad enough to have the concussion of a train going thirty miles an hour when dashed against some obstacle. But the concussion due to the earth’s stoppage would be as of a train going about 800 miles an hour, which would smash up everything and everybody.
Thus, then, the first effect of the new ideas formulated by Galileo was to show that the Copernican theory that the earth moved round on its axis, and round the sun, was in agreement with the laws of motion. ”

“ The reason why there are two arms is that, if they come together and recede, they balance, and hence the instrument as a whole does not shake on its base. This balance of moving parts of a rapidly moving machine is very important. Some motor cars are arranged so that the engines are “balanced,” and the moving parts come in and out simultaneously, leaving the centre of gravity unchanged whatever be the position of the motion. This makes the vibration of the car very small.
The tuning fork is therefore balanced. Being elastic, it obeys Hook’s law, “As the force, so the deflection.” ”

“ As long as the force acts, the force keeps putting more and more motion into the body, like pouring water into a jug, the longer you pour the faster the motion becomes. The body keeps all the motion it had, and keeps adding all the motion it gains. ”

“ The earth they thought must be at rest; for if it was in motion things would fly off from it. They saw that either the sun must be moving round the earth, or else the earth must be turning on its axis. They chose the former hypothesis, because they argued that if the earth were twisting round once in twenty-four hours then such a country as Greece must be flying round like a spot on the surface of a top, at the rate of about 18,000 miles in twenty-four hours, that is, at the rate of about 180 yards in a second, or faster than an arrow from a bow. ”