divide into smaller units, and to find the differences in pulses at any moment in both healthy and sick individuals.
XXIII. To compare the speed of the preceding oscillations with the speed of other natural or artificial motions.
XXIV. Given the motion of heavy bodies, or any other, to provide the sound produced by an equal motion of strings. See the two Corollaries on the motion of heavy bodies toward the center.
XXV. Given a string, to provide the number of motions, or oscillations, that it can make.
XXVI. If a string is held by a nail at one end but hangs freely at the other with a weight attached, the ratio of the length of the strings will be at least the square of the ratio of the number of oscillations.
XXVII. To reveal the use that the aforementioned oscillations of strings can have in Medicine, and in Mechanics or Mathematics. See the six Corollaries on the circular motion of heavy bodies.
XXVIII. To construct, in a moment, a clock that marks seconds.
XXIX. All oscillations of a string maintaining the same tension are nearly isochronous original Greek: ἰσόχρονοι, that is, they are completed in the same space of time.
XXX. To define the duration of the oscillations of a given string, that is, to assign the time in which a complete period of all oscillations is finished.
XXXI. When a string stretched by a given force makes a certain number of oscillations, the same string stretched by four times the force makes an equal number of oscillations, but in half the time: which is always shorter as the oscillations are faster, when the greater speed proceeds from the brevity of the string alone.
XXXII. To define the ratio of the spaces which the oscillations of a given string traverse from the first larger one to the very last and smallest.
XXXIII. To define how great the frequency of oscillations of a given string must be to produce a sensible and harmonious sound.
XXXIV. To define how great the speed of oscillations must be, or what space must be traversed, so that a sound may be heard.
XXXV. To define and explain the causes of the low pitch Latin: grauitas and high pitch Latin: acumen of sounds.
XXXVI. To define whether a string emits a lower sound at the end of its motion than at the beginning, since it moves more slowly: and from where high pitch arises.
XXXVII. The greater the quantity of air moved in a shorter or equal time, the greater and more vehement is the sound.
XXXVIII. To define by what method and when a harmonic sound begins to be made by a string.
XXXIX. To define the sphere of a given sound, that is, to assign the space from which a given sound can be heard.
XL. To define the speed of sounds according to those things observed during the siege and capture of La Rochelle, and in other places. Mersenne refers to his experiments timing the delay between the flash and the sound of cannons during the 1627-1628 siege of the city of La Rochelle.
XLI. To define why strings, metals, and other bodies sound higher or lower than remaining bodies: and the origin of the hardness of bodies.
XLII. To explain the qualities of bodies, both active and passive, which can contribute to the diversity of sounds.
XLIII. To derive the reason for hardness, rigidity, and other qualities from the atoms of Epicurus and Democritus.

BOOK TWO,

ON THE CAUSES OF SOUNDS,

ON SOUND-PRODUCING BODIES.

A decorative woodcut initial 'T' featuring floral and foliate motifs within a square frame.

So many and such great difficulties occur in bodies that produce sound that they require a specialized book. In this book, there will hardly be anyone who cannot note many things hitherto unknown, whatever part of Philosophy they embrace. This will be supported by illustrious and accurate experiments, which I bring forward in individual books, especially in this one and the fourth. We shall encompass this book in the following propositions.

PROPOSITION I.

The difference in sizes and shapes seen in bodies causes differences in sounds.

This is proven by experience, for as homogeneous bodies are larger, they produce lower sounds; as they are smaller, they produce higher sounds. If their shapes are changed, the sound is changed, as can be seen in metal formed into a bell. This produces a sound very distinct from that which it produces when it is drawn into a thin plate or takes on any other shape. Moreover, a larger body produces a lower sound because it moves a larger or equal quantity of air more slowly.
Whether a larger quantity of air alone, even if moved at an equal or the same speed, is sufficient to emit a lower sound will be discussed further below.