A Short History of Astronomy, Arthur Berry [large screen ebook reader .TXT] 📗

to B, where he sees it setting. When he is at C, on the line joining the centres of the earth and moon, the point O appears to be in the centre of the moon’s disc, and the portion c O c′ is visible, c R c′ invisible. But when the observer is at A, the point P, on the right of O, appears in the centre, and the portion a P a′ is visible, so that c′ a′ is now visible and a c invisible. In the same way, when the observer is at B, he can see the portion c b, while b′ c′ is invisible and Q appears to be in the centre of the disc. Thus in the course of the day the portion a O b′ (dotted in the figure) is constantly visible and b R a′ (also dotted) constantly invisible, while a c b and a′ c′ b′ alternately come into view and disappear. In other words, when the moon is rising we see a little more of the side which is the then uppermost, and when she is setting we see a little more of the other side which is uppermost in this position. A similar explanation applies when the observer is not on the earth’s equator, but the geometry is slightly more complicated. In the same way, as the moon passes from south to north of the equator and back as she revolves round the earth, we see alternately more and less of the northern and southern half of the moon. This set of changes—the simplest of several somewhat similar ones which are now known as librations of the moon—being thus thought of as likely to occur, Galilei set to work to test their existence by observing certain markings of the moon usually visible near the edge, and at once detected alterations in their distance from the edge, which were in general accordance with his theoretical anticipations. A more precise inquiry was however interrupted by failing sight, culminating (at the end of 1636) in total blindness.

But the most important work of these years was the completion of the great book, in which he summed up and completed his discoveries in mechanics, Mathematical Discourses and Demonstrations concerning Two New Sciences, relating to Mechanics and to Local Motion. It was written in the form of a dialogue between the same three speakers who figured in the Dialogue on the Systems, but is distinctly inferior in literary merit to the earlier work. We have here no concern with a large part of the book, which deals with the conditions under which bodies are kept, at rest by forces applied to them (statics), and certain problems relating to the resistance of bodies to fracture and to bending, though in both of these subjects Galilei broke new ground. More important astronomically—and probably intrinsically also—is what he calls the science of local motion,80 which deals with the motion of bodies. He builds up on the basis of his early experiments (§ 116) a theory of falling bodies, in which occurs for the first time the important idea of uniformly accelerated motion, or uniform acceleration, i.e. motion in which the moving body receives in every equal interval of time an equal increase of velocity. He shews that the motion of a falling body is—except in so far as it is disturbed by the air—of this nature, and that, as already stated, the motion is the same for all bodies, although his numerical estimate is not at all accurate.81 From this fundamental law he works out a number of mathematical deductions, connecting the space fallen through, the velocity, and the time elapsed, both for the case of a body falling freely and for one falling down an inclined plane. He gives also a correct elementary theory of projectiles, in the course of which he enunciates more completely than before the law of inertia already referred to (§ 130), although Galilei’s form is still much less general than Newton’s:—

Conceive a body projected or thrown along a horizontal plane, all impediments being removed. Now it is clear by what we have said before at length that its motion will be uniform and perpetual along the said plane, if the plane extend indefinitely.

In connection with projectiles, Galilei also appears to realise that a body may be conceived as having motions in two different directions simultaneously, and that each may be treated as independent of the other, so that, for example, if a bullet is shot horizontally out of a gun, its downward motion, due to its weight, is unaffected by its horizontal motion, and consequently it reaches the ground at the same time as a bullet simply allowed to drop; but Galilei gives no general statement of this principle, which was afterwards embodied by Newton in his Second Law of Motion.

The treatise on the Two New Sciences was finished in 1636, and, since no book of Galilei’s could be printed in Italy, it was published after some little delay at Leyden in 1638. In the same year his eyesight, which he had to some extent recovered after his first attack of blindness, failed completely, and four years later (January 8th, 1642) the end came.

134. Galilei’s chief scientific discoveries have already been noticed. The telescopic discoveries, on which much of his popular reputation rests, have probably attracted more than their fair share of attention; many of them were made almost simultaneously by others, and the rest, being almost inevitable results of the invention of the telescope, could not have been delayed long. But the skilful use which Galilei made of them as arguments for the Coppernican system, the no less important support which his dynamical discoveries gave to the same cause, the lucidity and dialectic brilliance with which he marshalled the arguments in favour of his views and demolished those of his opponents, together with the sensational incidents of his persecution, formed conjointly a contribution to the Coppernican controversy which was in effect decisive. Astronomical textbooks still continued to give side by side accounts of the Ptolemaic and of the Coppernican systems, and the authors, at any rate if they were good Roman Catholics, usually expressed, in some more or less perfunctory way, their adherence to the former, but there was no real life left in the traditional astronomy; new advances in astronomical theory were all on Coppernican lines, and in the extensive scientific correspondence of Newton and his contemporaries the truth of the Coppernican system scarcely ever appears as a subject for discussion.

Galilei’s dynamical discoveries, which are only in part of astronomical importance, are in many respects his most remarkable contribution to science. For whereas in astronomy he was building on foundations laid by previous generations, in dynamics it was no question of improving or developing an existing science, but of creating a new one. From his predecessors he inherited nothing but erroneous traditions and obscure ideas; and when these had been discarded, he had to arrive at clear fundamental notions, to devise experiments and make observations, to interpret his experimental results, and to follow out the mathematical consequences of the simple laws first arrived at. The positive results obtained may not appear numerous, if viewed from the standpoint of our modern knowledge, but they sufficed to constitute a secure basis for the superstructure which later investigators added.

It is customary to associate with our countryman Francis Bacon (1561-1627) the reform in methods of scientific discovery which took place during the seventeenth century, and to which much of the rapid progress in the natural sciences made since that time must be attributed. The value of Bacon’s theory of scientific discovery is very differently estimated by different critics, but there can be no question of the singular ill-success which attended his attempts to apply it in particular cases, and it may fairly be questioned whether the scientific methods constantly referred to incidentally by Galilei, and brilliantly exemplified by his practice, do not really contain a large part of what is valuable in the Baconian philosophy of science, while at the same time avoiding some of its errors. Reference has already been made on several occasions to Galilei’s protests against the current method of dealing with scientific questions by the interpretation of passages in Aristotle, Ptolemy, or other writers; and to his constant insistence on the necessity of appealing directly to actual observation of facts. But while thus agreeing with Bacon in these essential points, he differed from him in the recognition of the importance, both of deducing new results from established ones by mathematical or other processes of exact reasoning, and of using such deductions, when compared with fresh experimental results, as a means of verifying hypotheses provisionally adopted. This method of proof, which lies at the base of nearly all important scientific discovery, can hardly be described better than by Galilei’s own statement of it, as applied to a particular case:—

“Let us therefore take this at present as a Postulatum, the truth whereof we shall afterwards find established, when we shall see other conclusions built upon this Hypothesis, to answer and most exactly to agree with Experience.”82