SCIENCE AS MEASUREMENT--TYCHO BRAHE, KEPLER, BOYLE
Considering the value for clearness of thought of counting, measuring
and weighing, it is not surprising to find that in the seventeenth
century, and even at the end of the sixteenth, the advance of the
sciences was accompanied by increased exactness of measurement and by
the invention of instruments of precision. The improvement of the simple
microscope, the invention of the compound microscope, of the telescope,
the micrometer, the barometer, the thermoscope, the thermometer, the
pendulum clock, the improvement of the mural quadrant, sextant, spheres,
astrolabes, belong to this period.
Measuring is a sort of counting, and weighing a form of measuring. We
may count disparate things whether like or unlike. When we measure or
weigh we apply a standard and count the times that the unit--cubit,
pound, hour--is found to repeat itself. We apply our measure to uniform
extension, meting out the waters by fathoms or space by the sun's
diameter, and even subject time to arbitrary divisions. The human mind
has been developed through contact with the multiplicity of physical
objects, and we find it impossible to think clearly and scientifically
about our environment without dividing, weighing, measuring, counting.
In measuring time we cannot rely on our inward impressions; we even
criticize these impressions and speak of time as going slowly or
quickly. We are compelled in the interests of accuracy to provide an
objective standard in the clock, or the revolving earth, or some other
measurable thing. Similarly with weight and heat; we cannot rely on the
subjective impression, but must devise apparatus to record by a
measurable movement the amount of the pressure or the degree of
temperature.
"God ordered all things by measure, number, and weight." The scientific
mind does not rest satisfied till it is able to see phenomena in their
number relationships. Scientific thought is in this sense Pythagorean,
that it inquires in reference to quantity and proportion.
As implied in a previous chapter, number relations are not clearly
grasped by primitive races. Many primitive languages have no words for
numerals higher than five. That fact does not imply that these races do
not know the difference between large and small numbers, but precision
grows with civilization, with commercial pursuits, and other activities,
such as the practice of medicine, to which the use of weights and
measures is essential. Scientific accuracy is dependent on words and
other means of numerical expression. From the use of fingers and toes, a
rude score or tally, knots on a string, or a simple abacus, the race
advances to greater refinement of numerical expression and the
employment of more and more accurate apparatus.
One of the greatest contributors to this advance was the celebrated
Danish astronomer, Tycho Brahe (1546-1601). Before 1597 he had completed
his great mural quadrant at the observatory of Uraniborg. He called it
with characteristic vanity the Tichonic quadrant. It consisted of a
graduated arc of solid polished brass five inches broad, two inches
thick, and with a radius of about six and three quarters feet. Each
degree was divided into minutes, and each minute into six parts. Each of
these parts was then subdivided into ten seconds, which were indicated
by dots arranged in transverse oblique lines on the width of brass.
[Illustration: THE TICHONIC QUADRANT]
The arc was attached in the observation room to a wall running exactly
north, and so secured with screws (_firmissimis cochleis_) that no force
could move it. With its concavity toward the southern sky it was closely
comparable, though reverse, to the celestial meridian throughout its
length from horizon to zenith. The south wall, above the point where the
radii of the quadrant met, was pierced by a cylinder of gilded brass
placed in a rectangular opening, which could be opened or closed from
the outside. The observation was made through one of two sights that
were attached to the graduated arc and could be moved from point to
point on it. In the sights were parallel slits, right, left, upper,
lower. If the altitude and the transit through the meridian were to be
taken at the same time the four directions were to be followed. It was
the practice for the student making the observation to read off the
number of degrees, minutes, etc., of the angle at which the altitude or
transit was observed, so that it might be recorded by a second student.
A third took the time from two clock dials when the observer gave the
signal, and the exact moment of observation was also recorded by
student number two. The clocks recorded minutes and the smaller
divisions of time; great care, however, was required to obtain good
results from them. There were four clocks in the observatory, of which
the largest had three wheels, one wheel of pure solid brass having
twelve hundred teeth and a diameter of two cubits.
Lest any space on the wall should lie empty a number of paintings were
added: Tycho himself in an easy attitude seated at a table and directing
from a book the work of his students. Over his head is an automatic
celestial globe invented by Tycho and constructed at his own expense in
1590. Over the globe is a part of Tycho's library. On either side are
represented as hanging small pictures of Tycho's patron, Frederick II of
Denmark (d. 1588) and Queen Sophia. Then other instruments and rooms of
the observatory are pictured; Tycho's students, of whom there were
always at least six or eight, not to mention younger pupils. There
appears also his great brass globe six feet in diameter. Then there is
pictured Tycho's chemical laboratory, on which he has expended much
money. Finally comes one of Tycho's hunting dogs--very faithful and
sagacious; he serves here as a hieroglyph of his master's nobility as
well as of sagacity and fidelity. The expert architect and the two
artists who assisted Tycho are delineated in the landscape and even in
the setting sun in the top-most part of the painting, and in the
decoration above.
The principal use of this largest quadrant was the determination of the
angle of elevation of the stars within the sixth part of a minute, the
collineation being made by means of one of the sights, the parallel
horizontal slits in which were aligned with the corresponding parts of
the circumference of the cylinder. The altitude was recorded according
to the position of the sight attached to the graduated arc.
Tycho Brahe had a great reverence for Copernicus, but he did not accept
his planetary system; and he felt that advance in astronomy depended on
painstaking observation. For over twenty years under the kings of
Denmark he had good opportunities for pursuing his investigation. The
island of Hven became his property. A thoroughly equipped observatory
was provided, including printing-press and workshops for the
construction of apparatus. As already implied, capable assistants were
at the astronomer's command. In 1598, after having left Denmark, Tycho
in a splendid illustrated book (_Astronomiæ Instauratæ Mechanica_) gave
an account of this astronomical paradise on the Insula Venusia as he at
times called it. The book, prepared for the hands of princes, contains
about twenty full-page colored illustrations of astronomical instruments
(including, of course, the mural quadrant), of the exterior of the
observatory of Uraniborg, etc. The author had a consciousness of his own
worth, and deserves the name Tycho the Magnificent. The results that
he obtained were not unworthy of the apparatus employed in his
observations, and before he died at Prague in 1601, Tycho Brahe had
consigned to the worthiest hands the painstaking record of his labors.
Johann Kepler (1571-1630) had been called, as the astronomer's
assistant, to the Bohemian capital in 1600 and in a few months fell heir
to Tycho's data in reference to 777 stars, which he made the basis of
the Rudolphine tables of 1627. Kepler's genius was complementary to that
of his predecessor. He was gifted with an imagination to turn
observations to account. His astronomy did not rest in mere description,
but sought the physical explanation. He had the artist's feeling for the
beauty and harmony, which he divined before he demonstrated, in the
number relations of the planetary movements. After special studies of
Mars based on Tycho's data, he set forth in 1609 (_Astronomia Nova_) (1)
that every planet moves in an ellipse of which the sun occupies one
focus, and (2) that the area swept by the radius vector from the planet
to the sun is proportional to the time. Luckily for the success of his
investigation the planet on which he had concentrated his attention is
the one of all the planets then known, the orbit of which most widely
differs from a circle. In a later work (_Harmonica Mundi_, 1619) the
title of which, the _Harmonics of the Universe_, proclaimed his
inclination to Pythagorean views, he demonstrated (3) that the square of
the periodic time of any planet is proportional to the cube of its mean
distance from the sun.
Kepler's studies were facilitated by the invention, in 1614 by John
Napier, of logarithms, which have been said, by abridging tedious
calculations, to double the life of an astronomer. About the same time
Kepler in purchasing some wine was struck by the rough-and-ready method
used by the merchant to determine the capacity of the wine-vessels. He
applied himself for a few days to the problems of mensuration involved,
and in 1615 published his treatise (_Stereometria Doliorum_) on the
cubical contents of casks (or wine-jars), a source of inspiration to all
later writers on the accurate determination of the volume of solids. He
helped other scientists and was himself richly helped. As early as 1610
there had been presented to him a means of precision of the first
importance to the progress of astronomy, namely, a Galilean telescope.
The early history of telescopes shows that the effect of combining two
lenses was understood by scientists long before any particular use was
made of this knowledge; and that those who are accredited with
introducing perspective glasses to the public hit by accident upon the
invention. Priority was claimed by two firms of spectacle-makers in
Middelburg, Holland, namely, Zacharias, miscalled Jansen, and
Lippershey. Galileo heard of the contrivance in July, 1609, and soon
furnished so powerful an instrument of discovery that things seen
through it appeared more than thirty times nearer and almost a thousand
times larger than when seen by the naked eye. He was able to make out
the mountains in the moon, the satellites of Jupiter in rotation, the
spots on the revolving sun; but his telescope afforded only an imperfect
view of Saturn. Of course these facts, published in 1610 (_Sidereus
Nuncius_), strengthened his advocacy of the Copernican system. Galileo
laughingly wrote Kepler that the professors of philosophy were afraid to
look through his telescope lest they should fall into heresy. The German
astronomer, who had years before written on the optics of astronomy,
now (1611) produced his _Dioptrice_, the first satisfactory statement of
the theory of the telescope.
About 1639 Gascoigne, a young Englishman, invented the micrometer, which
enables an observer to adjust a telescope with very great precision.
Before the invention of the micrometer exactitude was impossible,
because the adjustment of the instrument depended on the discrimination
of the naked eye. The micrometer was a further advance in exact
measurement. Gascoigne's determinations of, for example, the diameter of
the sun, bear comparison with the findings of even recent astronomical
science.
The history of the microscope is closely connected with that of the
telescope. In the first half of the seventeenth century the simple
microscope came into use. It was developed from the convex lens, which,
as we have seen in a previous chapter, had been known for centuries, if
not from remote antiquity. With the simple microscope Leeuwenhoek before
1673 had studied the structure of minute animal organisms and ten years
later had even obtained sight of bacteria. Very early in the same
century Zacharias had presented Prince Maurice, the commander of the
Dutch forces, and the Archduke Albert, governor of Holland, with
compound microscopes. Kircher (1601-1680) made use of an instrument that
represented microscopic forms as one thousand times larger than their
actual size, and by means of the compound microscope Malpighi was able
in 1661 to see blood flowing from the minute arteries to the minute
veins on the lung and on the distended bladder of the live frog. The
Italian microscopist thus, among his many achievements, verified by
observation what Harvey in 1628 had argued must take place.
In this same epoch apparatus of precision developed in other fields.
Weight clocks had been in use as time-measurers since the thirteenth
century, but they were, as we have seen, difficult to control and
otherwise unreliable. Even in the seventeenth century scientists in
their experiments preferred some form of water-clock. In 1636 Galileo,
in a letter, mentioned the feasibility of constructing a pendulum clock,
and in 1641 he dictated a description of the projected apparatus to his
son Vincenzo and to his disciple Viviani. He himself was then blind, and
he died the following year. His instructions were never carried into
effect. However, in 1657 Christian Huygens applied the pendulum to
weight clocks of the old stamp. In 1674 he gave directions for the
manufacture of a watch, the movement of which was driven by a spring.
Galileo, to whom the advance in exact science is so largely indebted,
must also be credited with the first apparatus for the measurement of
temperatures. This was invented before 1603 and consisted of a glass
bulb with a long stem of the thickness of a straw. The bulb was first
heated and the stem placed in water. The point at which the water, which
rose in the tube, might stand was an indication of the temperature. In
1631 Jean Rey just inverted this contrivance, filling the bulb with
water. Of course these thermoscopes would register the effect of varying
pressures as well as temperatures, and they soon made way for the
thermometer and the barometer. Before 1641 a true thermometer was
constructed by sealing the top of the tube after driving out the air by
heat. Spirits of wine were used in place of water. Mercury was not
employed till 1670.
Descartes and Galileo had brought under criticism the ancient idea that
nature abhors a vacuum. They knew that the _horror vacui_ was not
sufficient to raise water in a pump more than about thirty-three feet.
They had also known that air has weight, a fact which soon served to
explain the so-called force of suction. Galileo's associate Torricelli
reasoned that if the pressure of the air was sufficient to support a
column of water thirty-three feet in height, it would support a column
of mercury of equal weight. Accordingly in 1643 he made the experiment
of filling with mercury a glass tube four feet long closed at the upper
end, and then opening the lower end in a basin of mercury. The mercury
in the tube sank until its level was about thirty inches above that of
the mercury in the basin, leaving a vacuum in the upper part of the
tube. As the specific gravity of mercury is 13, Torricelli knew that his
supposition had been correct and that the column of mercury in the tube
and the column of water in the pump were owing to the pressure or weight
of the air.
Pascal thought that this pressure would be less at a high altitude. His
supposition was tested on a church steeple at Paris, and, later, on the
Puy de Dôme, a mountain in Auvergne. In the latter case a difference of
three inches in the column of mercury was shown at the summit and base
of the ascent. Later Pascal experimented with the siphon and succeeded
in explaining it on the principle of atmospheric pressure.
Torricelli in the space at the top of his barometer (pressure-gauge) had
produced what is called a Torricellian vacuum. Otto von Guericke, a
burgomaster of Magdeburg, who had traveled in France and Italy,
succeeded in constructing an air-pump by means of which air might be
exhausted from a vessel. Some of his results became widely known in
1657, though his works were not published till 1673.
Robert Boyle (1626-1691), born at Castle Lismore in Ireland, was the
seventh son and fourteenth child of the distinguished first Earl of
Cork. He was early acquainted with these various experiments in
reference to the air, as well as with Descartes' theory that air
is nothing but a congeries or heap of small, and, for the most
part, flexible particles. In 1659 he wrote his _New Experiments
Physico-Mechanical touching the Spring of the Air_. Instead of _spring_,
he at times used the word _elater_ (ἐλατὴρ). In this treatise he
describes experiments with the improved air-pump constructed at his
suggestion by his assistant, Robert Hooke.
One of Boyle's critics, a professor at Louvain, while admitting that air
had weight and elasticity, denied that these were sufficient to account
for the results ascribed to them. Boyle thereupon published a _Defence
of the Doctrine touching the Spring and Weight of the Air_. He felt able
to prove that the elasticity of the air could under circumstances do far
more than sustain twenty-nine or thirty inches of mercury. In support of
his view he cited a recent experiment.
He had taken a piece of strong glass tubing fully twelve feet in length.
(The experiment was made by a well-lighted staircase, the tube being
suspended by strings.) The glass was heated more than a foot from the
lower end, and bent so that the shorter leg of twelve inches was
parallel with the longer. The former was hermetically sealed at the top
and marked off in forty-eight quarter-inch spaces. Into the opening of
the longer leg, also graduated, mercury was poured. At first only enough
was introduced to fill the arch, or bent part of the tube below the
graduated legs. The tube was then inclined so that the air might pass
from one leg to the other, and equality of pressure at the start be
assured. Then more mercury was introduced and every time that the air in
the shorter leg was compressed a half or a quarter of an inch, a record
was made of the height of the mercury in the long leg of the tube. Boyle
reasoned that the compressed air was sustaining the pressure of the
column of mercury in the long leg _plus_ the pressure of the atmosphere
at the tube's opening, equivalent to 29-2/16 inches of mercury. Some of
the results were as follows: When the air in the short tube was
compressed from 12 to 3 inches, it was under a pressure of 117-9/16
inches of mercury; when compressed to 4 it was under pressure of
87-15/16 inches of mercury; when compressed to 6, 58-13/16; to 9,
39-5/8. Of course, when at the beginning of the experiment there were 12
inches of air in the short tube, it was under the pressure of the
atmosphere, equal to that of 29-2/16 inches of mercury. Boyle with
characteristic caution was not inclined to draw too general a conclusion
from his experiment. However, it was evident, making allowance for some
slight irregularity in the experimental results, that air reduced under
pressure to one half its original volume, doubles its resistance; and
that if it is further reduced to one half,--for example, from six to
three inches,--it has four times the resistance of common air. In fact,
Boyle had sustained the hypothesis that supposes the pressures and
expansions to be in reciprocal proportions.
REFERENCES
Sir Robert S. Ball, _Great Astronomers_.
Robert Boyle, _Works_ (edited by Thomas Birch).
Sir David Brewster, _Martyrs of Science_.
J. L. E. Dreyer, _Tycho Brahe_.
Sir Oliver Lodge, _Pioneers of Science_.
Flora Masson, _Robert Boyle; a Biography_.