Part 6 (2/2)

SUMMARY OF FACTS FOR LECTURES IV AND V

In 1564, Michael Angelo died and Galileo was born; in 1642, Galileo died and Newton was born. Milton lived from 1608 to 1674.

For teaching the plurality of worlds, with other heterodox doctrines, and refusing to recant, Bruno, after six years' imprisonment in Rome, was burnt at the stake on the 16th of February, 1600 A.D. A ”natural”

death in the dungeons of the Inquisition saved Antonio de Dominis, the explainer of the rainbow, from the same fate, but his body and books were publicly burned at Rome in 1624.

The persecution of Galileo began in 1615, became intense in 1632, and so lasted till his death and after.

Galileo Galilei, eldest son of Vincenzo de Bonajuti de Galilei, a n.o.ble Florentine, was born at Pisa, 18th of February, 1564. At the age of 17 was sent to the University of Pisa to study medicine. Observed the swing of a pendulum and applied it to count pulse-beats. Read Euclid and Archimedes, and could be kept at medicine no more. At 26 was appointed Lecturer in Mathematics at Pisa. Read Bruno and became smitten with the Copernican theory. Controverted the Aristotelians concerning falling bodies, at Pisa. Hence became unpopular and accepted a chair at Padua, 1592. Invented a thermometer. Wrote on astronomy, adopting the Ptolemaic system provisionally, and so opened up a correspondence with Kepler, with whom he formed a friends.h.i.+p. Lectured on the new star of 1604, and publicly renounced the old systems of astronomy. Invented a calculating compa.s.s or ”Gunter's scale.” In 1609 invented a telescope, after hearing of a Dutch optician's discovery. Invented the microscope soon after.

Rapidly completed a better telescope and began a survey of the heavens.

On the 8th of January, 1610, discovered Jupiter's satellites. Observed the mountains in the moon, and roughly measured their height. Explained the visibility of the new moon by _earth-s.h.i.+ne_. Was invited to the Grand Ducal Court of Tuscany by Cosmo de Medici, and appointed philosopher to that personage. Discovered innumerable new stars, and the nebulae. Observed a triple appearance of Saturn. Discovered the phases of Venus predicted by Copernicus, and spots on the sun. Wrote on floating bodies. Tried to get his satellites utilized for determining longitude at sea.

Went to Rome to defend the Copernican system, then under official discussion, and as a result was formally forbidden ever to teach it. On the accession of Pope Urban VIII. in 1623, Galileo again visited Rome to pay his respects, and was well received. In 1632 appeared his ”Dialogues” on the Ptolemaic and Copernican systems. Summoned to Rome, practically imprisoned, and ”rigorously questioned.” Was made to recant 22nd of June, 1633. Forbidden evermore to publish anything, or to teach, or receive friends. Retired to Arcetri in broken down health. Death of his favourite daughter, Sister Maria Celeste. Wrote and meditated on the laws of motion. Discovered the moon's libration. In 1637 he became blind. The rigour was then slightly relaxed and many visited him: among them John Milton. Died 8th of January, 1642, aged 78. As a prisoner of the Inquisition his right to make a will or to be buried in consecrated ground was disputed. Many of his ma.n.u.scripts were destroyed.

Galileo, besides being a singularly clear-headed thinker and experimental genius, was also something of a musician, a poet, and an artist. He was full of humour as well as of solid common-sense, and his literary style is brilliant. Of his scientific achievements those now reckoned most weighty, are the discovery of the Laws of Motion, and the laying of the foundations of Mechanics.

_Particulars of Jupiter's Satellites, Ill.u.s.trating their obedience to Kepler's third law._

-------------------------------------------------------------------------- | | | Distance| | | T^2 | | Time of | from | | | ---- Satellite.|Diameter revolution | Jupiter, | T^2 | d^3 | d^3 | miles.| in hours. |in Jovian | | | which is | miles | (T) | radii. | | |practically | | | (d) | | | constant.

----------|-------|------------|----------|---------|---------|----------- No. 1. | 2437 | 4247 | 6049 | 18037 | 22144 | 8149 No. 2. | 2188 | 8523 | 9623 | 72641 | 89111 | 8152 No. 3. | 3575 | 17772 | 15350 | 29488 | 39168 | 8153 No. 4. | 3059 | 40053 | 26998 |160426 |19679 | 8152 --------------------------------------------------------------------------

The diameter of Jupiter is 85,823 miles.

_Falling Bodies._

Since all bodies fall at the same rate, except for the disturbing effect of the resistance of the air, a statement of their rates of fall is of interest. In one second a freely falling body near the earth is found to drop 16 feet. In two seconds it drops 64 feet altogether, viz. 16 feet in the first, and 48 feet in the next second; because at the beginning of every second after the first it has the acc.u.mulated velocity of preceding seconds. The height fallen by a dropped body is not proportional to the time simply, but to what is rather absurdly called the square of the time, _i.e._ the time multiplied by itself.

For instance, in 3 seconds it drops 9 16 = 144 feet; in 4 seconds 16 16, or 256 feet, and so on. The distances travelled in 1, 2, 3, 4, &c., seconds by a body dropped from rest and not appreciably resisted by the air, are 1, 4, 9, 16, 25, &c., respectively, each multiplied by the constant 16 feet.

Another way of stating the law is to say that the heights travelled in successive seconds proceed in the proportion 1, 3, 5, 7, 9, &c.; again multiplied by 16 feet in each case.

[Ill.u.s.tration: FIG. 35.--Curve described by a projectile, showing how it drops from the line of fire, _O D_, in successive seconds, the same distances _AP_, _BQ_, _CR_, &c., as are stated above for a dropped body.]

All this was experimentally established by Galileo.

A body takes half a second to drop 4 feet; and a quarter of a second to drop 1 foot. The easiest way of estimating a quarter of a second with some accuracy is to drop a bullet one foot.

A bullet thrown or shot in any direction falls just as much as if merely dropped; but instead of falling from the starting-point it drops vertically from the line of fire. (See fig. 35).

The rate of fall depends on the intensity of gravity; if it could be doubled, a body would fall twice as far in the same time; but to make it fall a given distance in half the time the intensity of gravity would have to be quadrupled. At a place where the intensity of gravity is 1/3600 of what it is here, a body would fall as far in a minute as it now falls in a second. Such a place occurs at about the distance of the moon (_cf._ page 177).

The fact that the height fallen through is proportional to the square of the time proves that the attraction of the earth or the intensity of gravity is sensibly constant throughout ordinary small ranges. Over great distances of fall, gravity cannot be considered constant; so for things falling through great s.p.a.ces the Galilean law of the square of the time does not hold.

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