Another question concerns the oscillations of pendulums, and it falis into two parts. One is whether all oscillations, large, medium, and small, are truly and precisely made in equal times. The other concerns the ratio of times for bodies hung from unequal threads; the times of their vibrations, I mean…. As to the prior question, whether the same pendulum makes all its oscillations – the largest, the average, and the smallest – in truly and exactly equal times, I submit myself to that which I once heard from our Academician [Galileo]. He demonstrated that the moveable which falls along chords subtended by every arc [of a given circle] necessarily passes over them all in equal times….

As to the ratio of times of oscillations of bodies hanging from strings of different lengths, those times are as the square roots of the string lengths; or should we say that the lengths are as the doubled ratios, or squares, of the times.

We have seen that the gaseous and liquid states are only distant stages of the same condition of matter, and are capable of passing into one another by a process of continuous change. A problem of far greater difficulty yet remains to be solved, the possible continuity of the liquid and solid states of matter. The fine discovery made some years ago by James Thomson, of the influence of pressure on the temperature at which liquefaction occurs, and verified experimentally by Sir. W. Thomson, points, as it appears to me, to the direction this inquiry must take; and in the case at least of those bodies which expand in liquefying, and whose melting-points are raised by pressure, the transition may possibly be effected. But this must be a subject for future investigation; and for the present I will not venture to go beyond the conclusion I have already drawn from direct experiment, that the gaseous and liquid forms of matter may be transformed into one another by a series of continuous and unbroken changes.

Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances.

And with respect to the general cause, it seems manifest to me that it is none other than God himself, who, in the beginning, created matter along with motion and rest, and now by his ordinary concourse alone preserves in the whole the same amount of motion and rest that he placed in it. For although motion is nothing in the matter moved but its mode, it has yet a certain and determinate quantity, which we easily see may remain always the same in the whole universe, although it changes in each of the parts of it.

The initial shock [of acceleration] is the worst part of it, for he is thrown upward as if by an explosion of gun powder…. Therefore he must be dazed by opiates beforehand; his limbs must be carefully protected so that they are not torn from him and the recoil is spread over all parts of his body. Then he will meet new difficulties: immense cold and inhibited respiration…. When the first part of the journey is completed, it becomes easier because on such a long journey the body no doubt escapes the magnetic force of the earth and enters that of the moon, so that the latter gets the upper hand. At this point we set the travellers free and leave them to their own devices: like spiders they will stretch out and contract, and propel themselves forward by their own force – for, as the magnetic forces of the earth and moon both attract the body and hold it suspended, the effect is as if neither of them were attracting it – so that in the end its mass will by itself turn toward the moon.

First of all, it is necessary to note that each pendulum has its own time of vibration, so limited and fixed in advance that it is impossible to move it in any other period than its own unique natural one. Take in hand any string you like, to which a weight is attached, and try the best you can to increase or diminish the frequency of its vibrations; this will be a mere waste of effort. On the other hand, we confer motion on any pendulum, though heavy and at rest, by merely blowing on it. This motion may be quite large if we repeat our puffs; yet it will take place only in accord with the time appropriate to its oscillations. If at the first puff we shall have moved it half an inch from the vertical, by adding the second when, returned toward us, it would commence its second vibration, we confer a new motion on it; and thus successively with more puffs given at the right time (not when the pendulum is going toward us, for thus we should impede the motion and not assist it), and continuing with many impulses, we shall confer on it impetus such that much greater force than a breath would be needed to stop it.

The heavenly motions are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which, through discordant tensions, through sincopes and cadenzas, as it were (as men employed them in imitation of those natural discords), progresses towards certain predesigned, quasi six-voiced clausuras, and thereby sets landmarks in the immeasurable flow of time, tt is, therefore, no longer surprising that man, in imitation of his creator, has at last discovered the art of figured song, which was unknown to the ancients. Man wanted to reproduce the continuity of cosmic time within a short hour, by an artful symphony for several voices, to obtain a sample test of the delight of the Divine Creator in His works, and to partake of his joy by making music in imitation of God.

Nature and Nature's law lay hid in night.

God said: “Let Newton be”; and all was light.

Everybody knows that heat can cause movement, that it possesses great motive power; steam engines so common today are a vivid and familiar proof of it. … The study of these engines is of the greatest interest, their importance is enormous, and their use increases every day. They seem destined to produce a great revolution in the civilized world….

Despite studies of all kinds devoted to steam engines, and in spite of the satisfactory state they have reached today, the theory of them has advanced very little and the attempts to improve them are still directed almost by chance.

“Also I do not at all believe that the judgment wch is given can be taken for a final judgment of the [Royal] Society. Yet Mr Newton has caused it to be published to the world by a book printed expressly for discrediting me, and sent it into Germany, into France and into Italy in the name of the Society …

As for me I have always carried myself with the greatest respect that could be towards Mr Newton. And tho it appears now that there is great room to doubt whether he knew my invention before he had it from me; yet I have spoken as if he had of himself found something like my method; but being abused by some flatterers ill advised, he has taken the liberty to attaque me in a manner very sensible. Judge now Sr, from what side that should principally come wch is requisite to terminate this controversy.”