Physical law

“ A physical law does not say "A will be followed by B," but tells us what acceleration a particle will have under given circumstances, i.e. it tells us how the particle's motion is changing at each moment, not where the particle will be at some future moment. ”

“ I always considered this the most fundamental law in all physical sciences. It is applicable to all motions no matter what the thing is which moves, whether ponderable matter or imponderable electricity. ”

“ The same kind of questions recur as regards the solution or absorption of gases in liquids, the pressure as well as the temperature having then a most decided effect, and Professor Roscoe’s researches on the subject present an excellent example of the successive determination of various complicated laws.‍184
There is hardly a branch of physical science in which similar complications are not ultimately encountered. In the case of gravity, indeed, we arrive at the final law, that the force is the same for all kinds of matter, and varies only with the distance of action. ”

“ Physical Law It is odd, but on the infrequent occasions when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics. ”

“ Civilization, Commerce, Christianity.
Before considering these it may be well to note Newton's first law of motion, that every body will continue in a state of rest or of uniform motion in a straight line unless acted on by some external force; for though this law was affirmed of material bodies, yet its applicability to large groups of men is striking and suggestive. Not only do human beings have the physical attributes of weight and inertia like other material bodies, but their mental organism, while of a higher order than the physical, is as powerfully affected by external forces. ”

“ I mean in just the same sense as the researches of physical philosophers have shown that heat is convertible into electricity, that electricity is convertible into magnetism, magnetism into mechanical force or chemical force, and any one of them with the other, each being measurable in terms of the other,--even so, I say, that great law is applicable to the living world. ”

“ The simple fact is that the agreement of cell-forms with the forms which physical experiment and math­e­mat­i­cal theory assign to liquids under the influence of surface tension, is so frequently and often so typically manifested, that we are led, or driven, to accept the surface tension hypothesis as generally applicable and as equivalent to a universal law. The occasional difficulties or apparent exceptions are such as call for further enquiry, but fall short of throwing doubt upon our hypothesis. ”

“ Experimental research proves that the conservation of force is an unalterable law of nature—“a principle in physics as large and sure as that of the indestructibility of matter or the invariability of gravity. No hypothesis should be admitted, nor any assertion of a fact credited, that denies this principle. ”

“ All physics is rooted in the notion of law, the belief that we live in an ordered universe that can be understood by the application of rational reasoning. ”

“ In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – ”

“ It offends reason to believe that a well-established natural law can admit of exceptions. A natural law must hold everywhere and always, or be invalid. I cannot believe, for example, that the universal law of gravitation, which governs the physical world, is ever suspended in any instance or at any point of the universe. Now I consider economic laws comparable to natural laws, and I have just as much faith in the principle of the division of labor as I have in the universal law of gravitation. I believe that while these principles can be disturbed, they admit of no exceptions. ”

“ Now we have a problem. We can deduce often from one part of physics, like the Law of Gravitation, a principle which turns out to be much more valid than the derivation. This does not happen in mathematics; theorems do not come out in places where they are not supposed to be. ”

“ We have these wide principles which sweep across the different laws, and if we take the derivation too seriously, and feel that one is only valid because another is valid, then we cannot understand the interconnections of the different branches of physics. Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced. But while we do not know all the laws, we can use some to make guesses at theorems which extend beyond the proof. ”

“ Physicists like to think that all you have to do is say, ‘These are the conditions, now what happens next?’ But all our sister sciences have a completely different problem: in fact all the other things that are studied – history, geology, astronomical history – have a problem of this other kind. ”

“ Among the forces which determine the forms of cells, whether they be solitary or arranged in contact with one another, this force of surface-tension is certainly of great, and is probably of paramount importance. But while we shall try to separate out the phenomena which are directly due to it, we must not forget that, in each particular case, the actual conformation which we study may be, and usually is, the more or less complex resultant of surface tension acting together with gravity, mechanical pressure, osmosis, or other physical forces. ”

“ But unless the body could recover its original figure by elasticity, there was no potential energy and force was annihilated. It is now believed, and to a large extent demonstrated, that the force, apparently lost, has been transformed into heat, electricity, or some other kind of molecular motion, of which the change of shape is only the outward sign. The establishment on a firm foundation of theory and experiment of the so-called conservation of energy, the child of the correlation of physical forces, is one of the first fruits of molecular mechanics. ”

“ There, though the weight of a given mass of matter is different from what it is with us, it is nevertheless determined by the law that determines here—the law of gravitation. There energy is indestructible, and is measured as it is measured among us, by work. Then is there any boundary that we can assign to natural law—is it not omnipresent, universal? ”

“ One of these properties is that its particles shall attract one another by a certain force; one of these laws is that this force shall operate by an invariable and fixed rule of direct action, and by an invariable and fixed rule of diminution, according to the distance of the particles from each other; and another law is that a body projected into space, by any force, shall continue to move in a straight line until and unless it is deflected from that line by some other force. ”

“ Mechanics, physics, and chemistry teach the rules and laws according to which the forces of impenetrability, gravitation, rigidity, fluidity, cohesion, elasticity, heat, light, affinity, magnetism, electricity, &c., operate; that is to say, the law, the rule which these forces observe whenever they enter time and space. But do what we will, the forces themselves remain qualitates occultæ. ”

“ By likening the molecule to a system of bodies in a state of motion—for instance, to the sum total of the sun, planets, and satellites, existing in conditions of mobile equilibrium—then we should expect the action of one part, in this system, to be equal and opposite to the other, according to Newton's third law of mechanics. ”

“ The inherent nature of cause may be so constituted and fixed, that the nisus by which it determines itself to produce phenomena, shall take place according to invariable and necessary laws. This we believe to be true with respect to all physical causes. Heat, electricity, galvanism, magnetism, gravitation, mechanical forces in general, and the powers at work in chemical of affinities, produce their phenomena according to fixed, and, with respect to the powers themselves, necessary laws. ”

“ From what precedes, it results that a quantity of mechanical action and a quantity of heat passing from a hot to a cold body, are quantities of the same nature, and that it is possible to substitute the one for the other reciprocally; in the same manner as in mechanics a body falling from a certain height, and a mass endowed with a certain velocity, are quantities of the same order, and can be transformed one into the other by physical agents. ”

“ On the remaining pages of this paper I desire to direct attention to some of the facts connected with the main subject of my present inquiry—the concept force.
Physical forces are distributed by modern science into two classes, molecular and molar forces. Molecular forces are those which determine the internal changes of a body, while molar forces cause the motion of the entire mass. ”

“ Molecular forces, therefore, are the agencies which determine the particular state of the body in its physical relations, considering it as an independent whole—or, as it is termed in modern mechanics, as an independent conservative system—while the molar forces determine the physical relations of the body to other bodies which, together with it, are integrant parts of a greater whole, i. ”

“ We cannot place a body in the condition of being unacted upon by any forces. But we may convince ourselves of the truth of the law by some such reasoning as the following. If a stone be thrown along the road, it soon comes to rest. The body leaves the hand with a certain initial velocity and is not further acted upon by it. Hence, if no other force acted on the stone, we should expect, if the first law be true, that it would continue to run on for ever with the original velocity at the moment of leaving the hand. ”

“ For, as we have seen in our Third Book, the primary object of mechanical science is to reduce the course of events to rigid laws of uniform sequence, and thus to facilitate the formulation of practical rules for our own interference with it. It is therefore a legitimate postulate of mechanical science that—for its special object—desire and will shall be excluded from our conception of the conditions which determine events, and the whole course of nature treated as if conditioned only by physical antecedents. ”

“ In all the operations of chemical transmutations no material is lost and no power wasted, and, by the law of the conservation and correlation of force, both energy and material must exist as correlatives. [Pg 55] This places the nature of matter upon the same basis as the origin of power. The transformation of force into material is impossible. Force follows the laws of motion, and atoms the law of form obedient to the lines of motion. ”

“ This force does not depend on the material phenomena of motion, and is quite independent of the mechanics of atoms. The highest law of modern natural science, the law of [51] the conservation of force, has, therefore, no application in the region of soul-life, and that mechanical causality which prevails throughout all the processes of nature does not exist for the soul. ”

“ Without presuming to dissent from such authorities on a point of 467 anatomical probability, we may venture to observe, that these hypotheses do not tend at all to elucidate the physiological principle which is here involved; for this principle cannot be mechanical, chemical, or physical, and therefore cannot be better understood by embodying it in a fluid; the difficulty we have in conceiving what the moving force is, is not got rid of by explaining the machinery by which it is merely transferred. ”

“ Thus, in order to determine the case of the direct action of bodies upon one another, we require no new law of motion. The equality of action and reaction, which enters necessarily into every conception of mechanical operation, combined with the measure of action as given by the third law of motion, enables us to trace the consequences of every case, whether of pressure or of impact. ”

“ The fundamental principle of action in such media must be in accordance with elastic impact, for upon that the dynamic theory of heat and conservation of force rests as a foundation. The statical and dynamical characteristics of gravitation and transfusion of force conform to it, so that all the forces that hold the molecules of bodies together must also be in subjection to it. ”

“ Every particle that enters into the composition of a nerve, a muscle, or a bone, has been placed in its position by molecular force. And unless the existence of law in these matters be denied, and the element of caprice introduced, we must conclude that, given the relation of any molecule of the body to its environment, its position in the body might be determined mathematically. ”

“ But does not a force equal to two hundred weight, actually contain in itself two forces each equal to one hundred weight, which, if employed apart, would separately raise the two bodies in question? The fact, therefore, that when exerted jointly they raise both bodies at once, results from the Composition of Causes, and is a mere instance of the general fact that mechanical forces are subject to the law of Composition. ”