CHAPTER VII
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.
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 292⁄16 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 1179⁄16 inches of mercury; when compressed to 4 it was under pressure of 8715⁄16 inches of mercury; when compressed to 6, 5813⁄16; to 9, 395⁄8. 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 292⁄16 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.
