NEWTON

In speaking of Newton we are tempted to paraphrase a line from the

Scriptures: Before Newton the Solar System was without form, and void;

then Newton came and there was light. To have discovered a law not

only applicable to matter on this earth, but to the planets and sun

and stars beyond, is a triumph which places Newton among the super-men.

What Newton's law of gravitation must have meant to the people of his

day can be pictured only if we conceive what the effect upon us would

be if someone--say Marconi--were actually to succeed in getting into

touch with beings on another planet. Newton's law increased confidence

in the universality of earthly laws; and it strengthened belief in

the cosmos as a law-abiding mechanism.

Newton's Law. The attraction between any two bodies is proportional

to their masses and inversely proportional to the square of the

distance that separates them. This is the concentrated form of

Newton's law. If we apply this law to two such bodies as the

sun and the earth, we can state that the sun attracts the earth,

and the earth, the sun. Furthermore, this attractive power will

depend upon the distance between these two bodies. Newton showed

that if the distance between the sun and the earth were doubled the

attractive power would be reduced not to one-half, but to one-fourth;

if trebled, the attractive power would be reduced to one-ninth. If,

on the other hand, the distance were halved, the attractive power

would be not merely twice, but four times as great. And what is true

of the sun and the earth is true of every body in the firmament, and,

as Professor Rutherford has recently shown, even of the bodies which

make up the solar system of the almost infinitesimal atom.

This mysterious attractive power that one body possesses for another is

called "gravitation," and the law which regulates the motion of bodies

when under the spell of gravitation is the law of gravitation. This

law we owe to Newton's genius.

Newton's Predecessors. We can best appreciate Newton's momentous

contribution to astronomy by casting a rapid glance over the state

of the science prior to the seventeenth century--that is, prior to

Newton's day. Ptolemy's conception of the earth as the center of the

universe held undisputed sway throughout the middle ages. In those days

Ptolemy was in astronomy what Aristotle was in all other knowledge:

they were the gods who could not but be right. Did not Aristotle say

that earth, air, fire and water constituted the four elements? Did

not Ptolemy say that the earth was the center around which the sun

revolved? Why, then, question further? Questioning was a sacrilege.

Copernicus (1473-1543), however, did question. He studied much and

thought much. He devoted his whole life to the investigation of the

movements of the heavenly bodies. And he came to the conclusion that

Ptolemy and his followers in succeeding ages had expounded views which

were diametrically opposed to the truth. The sun, said Copernicus,

did not move at all, but the earth did; and far from the earth being

the center of the universe, it was but one of several planets revolving

around the sun.

The influence of the church, coupled with man's inclination to exalt

his own importance, strongly tended against the acceptance of such

heterodox views. Among the many hostile critics of the Copernican

system, Tycho Brahe (1546-1601) stands out pre-eminently. This

conscientious observer bitterly assailed Copernicus for his

suggestion that the earth moved, and developed a scheme of his own

which postulated that the planets revolved around the sun, and planets

and sun in turn revolved around the earth.

The majority applauded Tycho; a small, very small group of insurgents

had faith in Copernicus. The illustrious Galileo (1564-1642)

belonged to the minority. The telescope of his invention unfolded

a view of the universe which belied the assertions of the many, and

strengthened his belief in the Copernican theory. "It (the Copernican

theory) explains to me the cause of many phenomena which under the

generally accepted theory are quite unintelligible. I have collected

arguments for refuting the latter, but I do not venture to bring

them to publication." So wrote Galileo to his friend, Kepler. "I do

not venture to bring them to publication." How significant of the

times--of any time, one ventures to add.

Galileo did overcome his hesitancy and published his views. They

aroused a storm. "Look through my telescope," he pleaded. But the

professors would not; neither would the body of Inquisitors. The

Inquisition condemned him: "The proposition that the sun is in

the center of the earth and immovable from its place is absurd,

philosophically false and formally heretical; because it is expressly

contrary to the Holy Scriptures." And poor Galileo was made to utter

words which were as far removed from his thoughts as his oppressors'

ideas were from the truth: "I abjure, curse and detest the said errors

and heresies."

The truth will out. Others arose who defied the majority and the

powerful Inquisition. Most prominent of all of these was Galileo's

friend, Kepler. Though a student of Tycho, Kepler did not hesitate to

espouse the Copernican system; but his adoption of it did not mean

unqualified approval. Kepler's criticism was particularly directed

against the Copernican theory that the planets revolve in circles. This

was boldness in the extreme. Ever since Aristotle's discourse on the

circle as a perfect figure, it was taken for granted that motion

in space was circular. Nature is perfect; the circle is perfect;

hence, if the sun revolves, it revolves in circles. So strongly

were men imbued with this "perfection," that Copernicus himself fell

victim. The sun no longer moved, but the earth and the planets did,

and they moved in a circle. Radical as Copernicus was, a few atoms

of conservatism remained with him still.

Not so Kepler. Tycho had taught him the importance of careful

observation,--to such good effect, that Kepler came to the conclusion

that the revolution of the earth around the sun takes the form of an

ellipse rather than a circle, the sun being stationed at one of the

foci of the ellipse.

To picture this ellipse, we shall ask the reader to stick two pins

a short distance apart into a piece of cardboard, and to place over

the pins a loop of string. With the point of a pencil draw the loop

taut. As the pencil moves around the two pins the curve so produced

will be an ellipse. The positions of the two pins represent the

two foci.

Kepler's observation of the elliptical rotation of the planets was the

first of three laws, quantitatively expressed, which paved the way

for Newton's law. Why did the planets move in just this way? Kepler

tried to answer this also, but failed. It remained for Newton to

supply the answer to this question.

Newton's Law of Gravitation. The Great Plague of 1666 drove Newton

from Cambridge to his home in Lincolnshire. There, according to the

celebrated legend, the philosopher sitting in his little garden one

fine afternoon, fell into a deep reverie. This was interrupted by the

fall of an apple, and the thinker turned his attention to the apple

and its fall.

It must not be supposed that Newton "discovered" gravity. Apples

had been seen to fall before Newton's time, and the reason for their

return to earth was correctly attributed to this mysterious force of

attraction possessed by the earth, to which the name "gravity" had been

given. Newton's great triumph consisted in showing that this "gravity,"

which was supposed to be a peculiar property residing in the earth,

was a universal property of matter; that it applied to the moon and the

sun as well as to the earth; that, in fact, the motions of the moon

and the planets could be explained on the basis of gravitation. But

his supreme triumph was to give, in one sublime generalization,

quantitative expression to the motion regulating heavenly bodies.

Let us follow Newton in his train of thought. An apple falls from a

tree 50 yards high. It would fall from a tree 500 yards high. It would

fall from the highest mountain top several miles above sea level. It

would probably fall from a height much above the mountain top. Why

not? Probably the further up you go the less does the earth attract

the apple, but at what distance does this attraction stop entirely?

The nearest body in space to the earth is the moon, some 240,000 miles

away. Would an apple reach the earth if thrown from the moon? But

perhaps the moon itself has attractive power? If so, since the apple

would be much nearer the moon than the earth, the probabilities are

that the apple would never reach the earth.

But hold! The apple is not the only object that falls to the

ground. What is true of the apple is true of all other bodies--of all

matter, large and small. Now there is the moon itself, a very large

body. Does the earth exert any gravitational pull on the moon? To

be sure, the moon is many thousands of miles away, but the moon is

a very large body, and perhaps this size is in some way related to

the power of attraction?

But then if the earth attracts the moon, why does not the moon fall

to the earth?

A glance at the accompanying figure will help to answer this

question. We must remember that the moon is not stationary, but

travelling at tremendous speed--so much so, that it circles the entire

earth every month. Now if the earth were absent the path of the moon

would be a straight line, say MB. If, however, the earth exerts

attraction, the moon would be pulled inward. Instead of following

the line MB it would follow the curved path MB'. And again, the moon

having arrived at B', is prevented from following the line B'C, but

rather B'C'. So that the path instead of being a straight line tends

to become curved. From Kepler's researches the probabilities were that

this curve would assume the shape of an ellipse rather than a circle.

The only reason, then, why the moon does not fall to the earth is on

account of its motion. Were it to stop moving even for the fraction

of a second it would come straight down to us, and probably few would

live to tell the tale.

Newton reasoned that what keeps the moon revolving around the earth is

the gravitational pull of the latter. The next important step was to

discover the law regulating this motion. Here Kepler's observations of

the movements of the planets around the sun was of inestimable value;

for from these Newton deduced the hypothesis that attraction varies

inversely as the square of the distance. Making use of this hypothesis,

Newton calculated what the attractive power possessed by the earth must

be in order that the moon may continue in its path. He next compared

this force with the force exerted by the earth in pulling the apple

to the ground, and found the forces to be identical! "I compared,"

he writes, "the force necessary to keep the moon in her orb with the

force of gravity at the surface of the earth, and found them answer

pretty nearly." One and the same force pulls the moon and pulls the

apple--the force of gravity. Further, the hypothesis that the force

of gravity varies inversely as the square of the distance had now

received experimental confirmation.

The next step was perfectly clear. If the moon's motion is controlled

by the earth's gravitational pull, why is it not possible that the

earth's motion, in turn, is controlled by the sun's gravitational

pull? that, in fact, not only the earth's motion, but the motion of

all the planets is regulated by the same means?

Here again Kepler's pioneer work was a foundation comparable to

reinforced concrete. Kepler, as we have seen, had shown that the earth

revolves around the sun in the form of an ellipse, one of the foci of

this ellipse being occupied by the sun. Newton now proved that such

an elliptic path was possible only if the intensity of the attractive

force between sun and planet varied inversely as the square of the

distance--the very same relationship that had been applied with such

success in explaining the motion of the moon around the earth!

Newton showed that the moon, the sun, the planets--every body in space

conformed to this law. The earth attracts the moon; but so does the

moon the earth. If the moon revolves around the earth rather than the

earth around the moon, it is because the earth is a much larger body,

and hence its gravitational pull is stronger. The same is true of

the relationship existing between the earth and the sun.

Further Developments of Newton's Law of Gravitation. When we speak of

the earth attracting the moon, and the moon the earth, what we really

mean is that every one of the myriad particles composing the earth

attracts every one of the myriad particles composing the moon, and

vice versa. If in dealing with the attractive forces existing between

a planet and its satellite, or a planet and the sun, the power exerted

by every one of these myriad particles would have to be considered

separately, then the mathematical task of computing such forces

might well appear hopeless. Newton was able to present the problem

in a very simple form by pointing out that in a sphere such as the

earth or the moon, the entire mass might be considered as residing

in the center of the sphere. For purposes of computation, the earth

can be considered a particle, with its entire mass concentrated at

the center of the particle. This viewpoint enabled Newton to extend

his law of inverse squares to the remotest bodies in the universe.

If this great law of Newton's found such general application beyond our

planet, it served an equally useful purpose in explaining a number of

puzzling features on this planet. The ebb and flow of the tides was one

of these puzzles. Even in ancient times it had been noticed that a full

moon and a high tide went hand in hand, and various mysterious powers,

were attributed to the satellite and the ocean. Newton pointed out that

the height of the water was a direct consequence of the attractive

power of the moon, and, to a lesser extent, because further away,

of the sun.

One of his first explanations, however, dealt with certain

irregularities in the moon's motion around the earth. If the solar

system would consist of the earth and moon alone, then the path of the

moon would be that of an ellipse, with one of the foci of this ellipse

occupied by the earth. Unfortunately for the simplicity of the problem,

there are other bodies relatively near in space, particularly that huge

body, the sun. The sun not only exerts its pull on the earth but also

on the moon. However, as the sun is much further away from the moon

than is the earth, the earth's attraction for its satellite is much

greater, despite the fact that the sun is much huger and weighs far

more than the earth. The greater pull of the earth in one direction,

and a lesser pull of the sun in another, places the poor moon between

the devil and the deep sea. The situation gives rise to a complexity of

forces, the net result of which is that the moon's orbit is not quite

that of an ellipse. Newton was able to account for all the forces that

come into play, and he proved that the actual path of the moon was

a direct consequence of the law of inverse squares in actual operation.

The "Principia." The law of gravitation, embodying also laws of motion,

which we shall discuss presently, was first published in Newton's

immortal "Principia" (1686). A selection from the preface will disclose

the contents of the book, and, incidentally, the style of the author:

"... We offer this work as mathematical principles of philosophy; for

all the difficulty in philosophy seems to consist in this--from the

phenomena of motions to investigate the forces of nature, and then from

these forces to demonstrate the other phenomena; and to this end the

general propositions in the first and second book are directed. In the

third book we give an example of this in the explication of the system

of the world; for by the propositions mathematically demonstrated

in the first book, we there derive from the celestial phenomena the

forces of gravity with which bodies tend to the sun and the several

planets. Then, from these forces, by other propositions which are

also mathematical, we deduce the motions of the planets, the comets,

the moon and the sea. I wish we could derive the rest of the phenomena

of nature by the same kind of reasoning from mechanical principles;

for I am induced by many reasons to suspect that they may all depend

upon certain forces by which the particles of bodies, by some causes

hitherto unknown, are either mutually impelled towards each other,

and cohere in regular figures, or are repelled and recede from each

other...."

At this point we may state that neither Newton, nor any of Newton's

successors including Einstein, have been able to advance even a

plausible theory as to the nature of this gravitational force. We

know that this force pulls a stone to the ground; we know, thanks

to Newton, the laws regulating the motions due to gravity; but what

this force we call gravity really is we do not know. The mystery is

as deep as the mystery of the origin of life.

"Prof. Einstein," writes Prof. Eddington, "has sought, and has not

reached, any ultimate explanation of its [that is, gravitation]

cause. A certain connection between the gravitational field and the

measurement of space has been postulated, but this throws light rather

on the nature of our measurements than on gravitation itself. The

relativity theory is indifferent to hypotheses as to the nature of

gravitation, just as it is indifferent to hypotheses as to the nature

of light."

Newton's Laws of Motion. In his Principia Newton begins with a series

of simple definitions dealing with matter and force, and these are

followed by his three famous laws of motion. The nature and amount

of the effort required to start a body moving, and the conditions

required to keep a body in motion, are included in these laws. The

Fundamentals, mass, time and space, are exhibited in their various

relationships. Of importance to us particularly is that in these laws,

time and space are considered as definite entities, and as two distinct

and widely separated manifestations. We shall see that in Einstein's

hands a very close relationship between these two is brought about.

Both Newton and Einstein were led to their theory of gravitation

by profound studies of the mathematics of motion, but as Newton's

conception of motion differed from Einstein's, and as, moreover,

important discoveries into the nature of matter and the relationship

of motion to matter were made subsequent to Newton's time, we need not

wonder that the two theories show divergence; that, as we shall see,

Newton's is probably but an approximation of the truth. If we confine

our attention to our own solar system, the deviation from Newton's

law is, as a rule, so small as to be negligible.

Newton's laws of motion are really axioms, like the axioms of Euclid:

they do not admit of direct proof; but there is this difference,

that the axioms of Euclid seem more obviously true. For example,

when Euclid informs us that "things which are equal to the same

thing are equal to one another," we have no hesitation in accepting

this statement, for it seems so self-evident. When, however, we are

told by Newton that "the alteration of motion is ever proportional

to the motive force impressed," we are at first somewhat bewildered

with the phraseology, and then, even when that has been mastered,

the readiness with which we respond will probably depend upon the

amount of scientific training we have received.

"Every body continues in its state of rest or of uniform motion in a

straight line, unless it is compelled to change that state by forces

impressed thereon." So runs Newton's first law of motion. A body does

not move unless something causes it to move; to make the body move

you must overcome the inertia of the body. On the other hand, if a

body is moving, it tends to continue moving, as witness our forward

movement when the train is brought to a standstill. It may be asked,

why does not a bullet continue moving indefinitely once it has left

the barrel of the gun? Because of the resistance of the air which it

has to overcome; and the path of the bullet is not straight because

gravity acts on it and tends to pull it downwards.

We have no definite means of proving that a body once set in motion

would continue moving, for an indefinite time, and along a straight

line. What Newton meant was that a body would continue moving provided

no external force acted on it; but in actual practise such a condition

is unknown.

Newton's first law defines force as that action necessary to change

a state of rest or of uniform motion, and tells us that force alone

changes the motion of a body. His second law deals with the relation

of the force applied and the resulting change of motion of the body;

that is, it shows us how force may be measured. "The alteration of

motion is ever proportional to the motive force impressed, and is made

in the direction of the right line in which that force is impressed."

Newton's third law runs--"To every action there is always opposed

an equal reaction." The very fact that you have to use force means

that you have to overcome something of an opposite nature. The forward

pull of a horse towing a boat equals the backward pull of the tow-rope

connecting boat and horse. "Many people," says Prof. Watson, "find a

difficulty in accepting this statement ... since they think that if the

force exerted by the horse on the rope were not a little greater than

the backward force exerted by the rope on the horse, the boat would not

progress. In this case we must, however, remember that, as far as their

relative positions are concerned, the horse and the boat are at rest,

and form a single body, and the action and reaction between them, due

to the tension on the rope, must be equal and opposite, for otherwise

there would be relative motion, one with respect to the other."

It may well be asked, what bearing have these laws of Newton on the

question of time and space? Simply this, that to measure force the

factors necessary are the masses of the bodies concerned, the time

involved and the space covered; and Newton's equations for measuring

forces assume time and space to be quite independent of one another. As

we shall see, this is in striking contrast to Einstein's view.

Newton's Researches on Light. In 1665, when but 23 years old,

Newton invented the binomial theorem and the infinitesimal calculus,

two phases of pure mathematics which have been the cause of many a

sleepless night to college freshmen. Had Newton done nothing else his

fame would have been secure. But we have already glanced at his law

of inverse squares and the law of gravitation. We now have to turn

to some of Newton's contributions to optics, because here more than

elsewhere we shall find the starting point to a series of researches

which have culminated so brilliantly in the work of Einstein.

Newton turned his attention to optics in 1666 when he proved that

the light from the sun, which appears white to us, is in reality a

mixture of all the colors of the rainbow. This he showed by placing

a prism between the ray of light and a screen. A spectrum showing

all the colors from red to violet appeared on the screen.

Another notable achievement of his was the design of a telescope which

brought objects to a sharp focus and prevented the blurring effects

which had occasioned so much annoyance to Newton and his predecessors

in all their astronomical observations.

These and other discoveries of very great interest were brought

together in a volume on optics which Newton published in 1704. Our

particular concern here is to examine the views advanced by him as

to the nature of light.

That the nature of light should have been a subject for speculation

even to the ancients need not surprise us. If other senses, as

touch, for example, convey impressions of objects, it is true to say

that the sense of sight conveys the most complete impression. Our

conception of the external world is largely based upon the sense

of sight; particularly so when we deal with objects beyond our

reach. In astronomy, therefore, a study of the properties of light

is indispensable. [1]

But what is this light? We open our eyes and we see; we close our eyes

and we fail to see. At night in a dark room we may have our eyes open

and yet we do not see; light, then, must be absent. Evidently, light

does not wholly depend upon whether our eyes are open or closed. This

much is certain: the eye functions and something else functions. What

is this "something else"?

Strangely enough, Plato and Aristotle regarded light as a property of

the eye and the eye alone. Out of the eye tentacles were shot which

intercepted the object and so illuminated it. From what has already

been said, such a view seems highly unlikely. Far more consistent with

their philosophy in other directions would have been the theory that

light has its source in the object and not in the eye, and travels

from object to eye rather than the reverse. How little substance the

Aristotelian contribution possesses is immediately seen when we refer

to the art of photography. Here light rays produce effects which are

independent of any property of the eye. The blind man may click the

camera and produce the impression on the plate.

Newton, of course, could have fallen into no such error as did Plato

and Aristotle. The source of light to him was the luminous body. Such

a body had the power of emitting minute particles at great speed,

and these when coming in contact with the retina produce the sensation

of sight.

This emission or corpuscular theory of Newton's was combated

very strongly by his illustrious Dutch contemporary, Huyghens, who

maintained that light was a wave phenomenon, the disturbance starting

at the luminous body and spreading out in all directions. The wave

motions of the sea offer a certain analogy.

Newton's strongest objection to Huyghens' wave theory was that it

seemed to offer no satisfactory explanation as to why light travelled

in straight lines. He says: "To me the fundamental supposition itself

seems impossible, namely that the waves or vibrations of any fluid can,

like the rays of light, be propagated in straight lines, without a

continual and very extravagant bending and spreading every way into

the quiescent medium, where they are terminated by it. I mistake if

there be not both experiment and demonstration to the contrary."

In the corpuscular theory the particles emitted by the luminous

body were supposed to travel in straight lines. In empty space the

particles travelled in straight lines and spread in all directions. To

explain how light could traverse some types of matter--liquids, for

example--Newton supposed that these light particles travelled in the

spaces between the molecules of the liquid.

Newton's objection to the wave theory was not answered very

convincingly by Huyghens. Today we know that light waves of high

frequency tend to travel in straight lines, but may be prevented from

doing so by gravitational forces of bodies near its path. But this

is Einstein's discovery.

A very famous experiment by Foucault in 1853 proved beyond the shadow

of a doubt that Newton's corpuscular theory was untenable. According

to Newton's theory, the velocity of light must be greater in a denser

medium (such as water) than in a lighter one (such as air). According

to the wave theory the reverse is true. Foucault showed that light

does travel more slowly in water than in air. The facts were against

Newton and in favor of Huyghens; and where facts and theory clash

there is but one thing to do: discard the theory.

Some Facts about Newton. Newton was a Cambridge man, and Newton made

Cambridge famous as a mathematical center. Since Newton's day Cambridge

has boasted of a Clerk Maxwell and a Rayleigh, and her Larmor, her

J. J. Thomson and her Rutherford are still with us. Newton entered

Trinity College when he was 18 and soon threw himself into higher

mathematics. In 1669, when but 27 years old, he became professor of

mathematics at Cambridge, and later represented that seat of learning

in Parliament. When his friend Montague became Chancellor of the

Exchequer, Newton was offered, and accepted, the lucrative position

of Master of the Mint. As president of the Royal Society Newton was

occasionally brought in contact with Queen Anne. She held Newton in

high esteem, and in 1705 she conferred the honor of knighthood on

him. He died in 1727.

"I do not know," wrote Newton, "what I may appear to the world,

but, to myself, I seem to have been only like a boy playing on the

seashore, and directing myself in now and then finding a smoother

pebble or a prettier shell than ordinary, whilst the great ocean of

truth lay all undiscovered before me."

Such was the modesty of one whom many regard as the greatest intellect

of all ages.