Abstract
D’Alembert counted as physics in general disciplines such optics, acoustics, positional astronomy, cosmology, magnetism and electricity. For the sake of space, this chapter deals with optics and electricity only. A good deal of the optical works, concerned the theories of propagation of light, with those of undulatory character that required complex mathematical treatments and the use of partial differential equations, becoming a fertile ground for mathematical physics. The experience with which the theories were compared was mostly based on experiments conducted in the 17th century by Newton and Huygens. Relevant new experimental work, on a quantitative basis, was carried out only relatively to what is today known as photometry with Bouguer and Lambert. The creation of the 18th century was the science of electricity. It assumes in the chapter the paradigmatic role of the development of the experimental sciences starting from the ascertainment of the phenomena at a qualitative level—remaining partially in the footsteps of the traditional natural philosophy—up to their quantification. The number and quality of experiments on electricity grew dramatically, especially after the 1750s when the discovery of the Leyden jar made it possible to accumulate large charges. After a brief mention to the situation in the 17th century, the chapter passes to the examination of the English experimenters and the continental ones to stop before Alessandro Volta’s studies at the end of the century.
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Notes
- 1.
pp. 2–3.
- 2.
p. 47.
- 3.
pp. 631–632.
- 4.
p. 95.
- 5.
pp. IV–V.
- 6.
pp. VII–VIII.
- 7.
pp. VII–XII.
- 8.
p. 4.
- 9.
p. 315.
- 10.
p. 62, p. 323.
- 11.
pp. 55–56.
- 12.
p. 25.
- 13.
p. 42.
- 14.
p. 11.
- 15.
pp. 21–22.
- 16.
p. 22.
- 17.
pp. 47–48.
- 18.
p. 48.
- 19.
p. 4.
- 20.
p. 27.
- 21.
p. 3.
- 22.
Vol. 2, p. 495.
- 23.
Vol. 2, p. 496.
- 24.
p. 24.
- 25.
pp. 24–25.
- 26.
Vol. 1, Livre premiere des movemens, p. 14.
- 27.
p. 12.
- 28.
p. 771–772.
- 29.
Vol. 2, p. 525.
- 30.
Vol. 2, pp. 483–484.
- 31.
Vol. 2, p. 486.
- 32.
p. 6.
- 33.
p. 6.
- 34.
p. 8.
- 35.
p. 9.
- 36.
p. 10.
- 37.
p. 12.
- 38.
p. 12.
- 39.
pp. 11, 26.
- 40.
p. 17.
- 41.
p. 18.
- 42.
p. 15.
- 43.
p. 27.
- 44.
p. 25.
- 45.
p. 35.
- 46.
pp. 77–80.
- 47.
p. 26. A trochoid is the curve described by a point linked to a disk. If the distance of the point is equal to (lower than) the radius of the disk, the curve is also called (curtate) cycloid and looks like a sinusoid.
- 48.
p. 135.
- 49.
Corresponding to 300 m/s. The value obtained by Newton was distorted downwards. Later, Pierre-Simon Laplace saw the flaw and ultimately corrected Newton’s result. He assumed that the process of sound transmission was not isothermal as Newton had thought, but adiabatic. Bernoulli suggested his own reasons why the actual speed, then estimated in 1080 pieds d’Angleterre, was grater than that found by Newton [35], pp. 38–39.
- 50.
p. 46.
- 51.
p. 44.
- 52.
p. 57.
- 53.
p. 529.
- 54.
p.149.
- 55.
p.75.
- 56.
p. 198. Translation adapted from [124].
- 57.
p. 205.
- 58.
p. 192.
- 59.
Following the standard symbols, the speed v of sound according to the modern theories is given by the relation \(v=\sqrt{E/\uprho }\), where \(\uprho \) is the mass density of the medium, not to be confused with the weight density D, and E its modulus of longitudinal elasticity, also known as Young modulus, which stands for the elastic force. Factor 2 in Euler’s formula derives from the values he assumed for the acceleration of gravity g: \(D=\uprho g=\uprho \times 2\).
- 60.
p. 193.
- 61.
pp. 91–97.
- 62.
p. 192.
- 63.
p. 229.
- 64.
p. 208.
- 65.
p. 228.
- 66.
p. 255.
- 67.
pp. 217–218.
- 68.
pp. 219–220.
- 69.
Vol. 1, pp. 106–107, letter 26. See also [92], pp. 234–235.
- 70.
p. 239.
- 71.
p. 9.
- 72.
pp. 237–239.
- 73.
p. 23.
- 74.
p. 113.
- 75.
p. 278.
- 76.
p. 50.
- 77.
p. 378. English translation in [141].
- 78.
p. liv.
- 79.
pp. 6–7.
- 80.
Index capitum. English translation in [141].
- 81.
Preface.
- 82.
Preface. English translation in [141].
- 83.
p. 3.
- 84.
184a.
- 85.
pp. 1–2. English translation in [141].
- 86.
p. 3.
- 87.
Section 46, p. 24. English translation in [141].
- 88.
Section 226, p. 105. English translation in [141].
- 89.
Section 58, pp. 29–30.
- 90.
Section 251, p. 117.
- 91.
Section 257, p. 122.
- 92.
Section 269, p. 128.
- 93.
p. 24.
- 94.
p. 250.
- 95.
Section 79, p. 40.
- 96.
pp. xcviii-xcix.
- 97.
pp. clxvi-clxxxiii.
- 98.
pp. 52–53. Translation in [104].
- 99.
pp. 59–60. Translation in [104].
- 100.
p. 183.
- 101.
p. 185.
- 102.
p. 192.
- 103.
Vol. 3, p. 399.
- 104.
pp. 192–194.
- 105.
p. 194.
- 106.
p. 496.
- 107.
pp. 496–497.
- 108.
pp. 186–187.
- 109.
Vol. 19, p. 615.
- 110.
Vol. 3, pp. 250-251.
- 111.
p. 102.
- 112.
p. 255.
- 113.
p. 432.
- 114.
pp. 52–53.
- 115.
pp. 2, 17.
- 116.
p. 260.
- 117.
pp. 71–72.
- 118.
pp. 206–209.
- 119.
p. 424.
- 120.
Preface, pp. 11–12 (not numbered pages); 595, 597.
- 121.
p. 350.
- 122.
Letter of Symmer to Michell, July 10. p.17.
- 123.
p. 10.
- 124.
p. 10.
- 125.
p. 584.
- 126.
p. 585.
- 127.
p. 659.
- 128.
p. 593.
- 129.
pp. 607-608.
- 130.
All the following measurements in cm in the following are approximated.
- 131.
pp. 105–108.
- 132.
p. 140.
- 133.
pp. 111–112. The mathematical proof of this assertion is given at pp. 112–113.
- 134.
Vol. 6, pp. 407–410.
- 135.
p. 416.
- 136.
pp. 104–105.
- 137.
p. 107.
- 138.
p. 106.
- 139.
Reference is to his second experiment referred to in the letter: “If when the feather is come to the Glass, it be held at about 6 or 8 in. Distance from the side of a wall edge of a Table Arme of a Chair or the like it will be drawn to it and thence to the Glass together without ceasing it flies to object at a greater Distance but then does not so often Return” [60], pp. 34–35.
- 140.
p. 36. Punctuation added.
- 141.
pp. 18–19.
- 142.
pp. 19–20.
- 143.
p. 42.
- 144.
p. 246.
- 145.
p. 22.
- 146.
p. 24.
- 147.
p. 25.
- 148.
p. 26.
- 149.
pp. 26–27.
- 150.
p. 29.
- 151.
p. 31.
- 152.
pp. 39-40
- 153.
p. 42.
- 154.
p. 35.
- 155.
p. 42.
- 156.
pp. 40–42; 53–63.
- 157.
p. 423; 398.
- 158.
p. 40.
- 159.
p. 399.
- 160.
p. 176. English translation in [122].
- 161.
- 162.
Introductory remarks, p. 5, p. 239.
- 163.
Introductory remarks, p. 7.
- 164.
Introductory remarks, pp. 7–8. Translation in [5].
- 165.
pp. 375–376. Translation in [122].
- 166.
p. 402.
- 167.
p. 426.
- 168.
p. 402.
- 169.
p. 202.
- 170.
p. 401.
- 171.
pp. 9–10; p. 241.
- 172.
pp. 14–15; p. 244.
- 173.
Section 6, pp. 14–16.
- 174.
Section 29, p. 37.
- 175.
p. 247; see footnote 16.
- 176.
Section 30, p. 38.
- 177.
Section 31, p. 39. Translation in [5].
- 178.
Section 31, pp. 39–40.
- 179.
Section 34, p. 46.
- 180.
Section 107, p. 114, p. 304.
- 181.
Section 124, pp. 127–128.
- 182.
This equation has been corrected according the suggestion of [5], p. 269, footnotes 29, 30.
- 183.
Section 45, pp. 54–55.
- 184.
p. 338.
- 185.
p. 144.
- 186.
Section 133, pp. 135–136, 318.
- 187.
Section 138, pp. 139–140,.
- 188.
Section 142, p. 143.
- 189.
Section 144, p. 144; pp. 323–324.
- 190.
Section 147, pp. 146–147, 325.
- 191.
p. 120.
- 192.
Section 76, p. 83.
- 193.
pp. 23–24.
- 194.
p. 395.
- 195.
p. 40.
- 196.
p. 126.
- 197.
p. 252.
- 198.
To the readers, first rows.
- 199.
p. 14.
- 200.
Vol. 1, p. 194.
- 201.
Deferent (deferente) is the term used by Beccaria for conductors. The English translation of his treatise replaced everywhere deferent with conductor.
- 202.
Beccaria in one occasion compared his measures, in particular his inch, with a physical magnitude, which allows to give it a value: “supposing the common height of mercury in the barometer in Turin to be twenty-seven inches and an half” [29], p. 165. Which gives for the inch the value of 2.76 cm, greater than the current English value.
- 203.
pp.10–11; p. 11.
- 204.
pp. 56–58.
- 205.
pp. 53–54.
- 206.
pp. 155–156.
- 207.
p. 175.
- 208.
p. 175.
- 209.
p. 173; p. 179.
- 210.
p. 244.
- 211.
p. 174. Translation into English in [31].
- 212.
p. 155.
- 213.
p.174. Translation into English in [31].
- 214.
p. 180.
- 215.
p. 181. Translation into English in [31].
- 216.
p. 181.
- 217.
p. 181.
- 218.
pp. 182–183.
- 219.
pp. 184–185.
- 220.
p. 185. Translation into English adapted from [31].
- 221.
pp. 325–326.
- 222.
p. 187; pp. 688–689.
- 223.
Vol. 1, p. 434.
- 224.
p. 47.
- 225.
p. 48.
- 226.
Vol. 6., p. 486.
- 227.
pp. 515–516. Translation into English adapted from James Parsons.
- 228.
p. 40.
- 229.
pp. 524–525.
- 230.
p. 278.
- 231.
p. 401.
- 232.
p. 1.
- 233.
p. 48. Translation in to English [31].
- 234.
pp. 196–199; 1–3.
- 235.
pp. 1–3.
- 236.
p. 619.
- 237.
p. 53.
- 238.
p. 6.
- 239.
p. 55.
- 240.
p. 58.
- 241.
Vol. 6, p. 343.
- 242.
p. 27.
- 243.
p. 27.
- 244.
pp. 28–30.
- 245.
p. 45.
- 246.
p. 61.
- 247.
Section 200, pp. 192–193.
- 248.
Section 202, pp. 194–196.
- 249.
pp. 62–63.
- 250.
pp. 120–121.
- 251.
pp. 247–248.
- 252.
pp. 259–266.
- 253.
p. 43; p. 263.
- 254.
p. 52; p. 263.
- 255.
pp. 270–271.
- 256.
p. 51.
- 257.
p. 132.
- 258.
p. 55; p. 272.
- 259.
pp. 55–56, p. 272.
- 260.
pp. 87–88.
- 261.
p. 17.
- 262.
p. 370.
- 263.
p. 39.
- 264.
p. 95.
- 265.
pp. 310–313.
- 266.
pp. 298–301.
- 267.
p. 303.
- 268.
p. 361.
- 269.
p. 361.
- 270.
p. 363.
- 271.
p. 363.
- 272.
pp. 12–15.
- 273.
p. 16.
- 274.
vol V/1, pp. 332–334.
- 275.
p. 332–333.
- 276.
p. 343.
- 277.
pp. 80–82.
- 278.
Most of biography information comes from [106].
- 279.
p. 8.
- 280.
p. 27.
- 281.
p. 689.
- 282.
pp. 298-299.
- 283.
p. 258.
- 284.
p. 579.
- 285.
p. 191.
- 286.
pp. 162–165.
- 287.
The measurements are expressed in French inches, equal to about 2.7 cm.
- 288.
A ligne is about 1/12 of an inch, or 2.2 mm.
- 289.
One French grain is about \(5\times 10^{-4} N\), the weight of a mass of 50 mg.
- 290.
p. 574.
- 291.
Coulomb used the symbol D, which is here avoided to not confuse with the product of electric masses introduced later.
- 292.
p. 247.
- 293.
p. 572. Translation in Gillmor 1971.
- 294.
pp. 572–573.
- 295.
If the electric force is proportional to the inverse square of distance, that is \(f \propto \displaystyle \frac{1}{d^2}\), the product \(fd^2\) is constant.
- 296.
p. 174.
- 297.
p. 547.
- 298.
p. 579. Coulomb used the symbol D instead of M; it has be changed here not to confuse it with the diameter of the torsion wire.
- 299.
pp. 579–580.
- 300.
Book 1, section XII, Proposition 71, Theorem 31. Actually, because of the induction between the globe Gr and the small disk l, the electricity is not exactly uniformly distributed on Gr and Theorem 31 does not hold exactly [64], vol. 1, p. 43.
- 301.
p. 583.
- 302.
p. 584.
- 303.
p. 611. Translation in [105].
- 304.
p. 593.
- 305.
p. 40.
- 306.
p. 586.
- 307.
pp. 443–444.
- 308.
p. 228.
- 309.
By making explicit that the distribution of electricity was in a stable state, Coulomb avoided the then almost impossible to solve problem of determining the laws of spatial distribution of electricity during the process of charging.
- 310.
p. 67. Translation in [105].
- 311.
p. 74.
- 312.
pp. 620–621.
- 313.
pp.105–107; p. 232.
- 314.
pp. 75-76. Translation in [105].
- 315.
pp. 587–588. Coulomb proof is strictly connected to that reported by Cavendish in his paper of 1771 [55], pp. 586–587. This suggests that even though Coulomb did not cite him he knew Cavendish’s writings.
- 316.
p. 430.
- 317.
pp. 432–436.
- 318.
p. 457.
- 319.
p. 443–444.
- 320.
p. 445.
- 321.
p. 445.
- 322.
pp. 446–447.
- 323.
The year 1811 is the date attributed to the publication of the Institute; in [126], the true dates of presentation are referred to.
- 324.
pp. 60, 66, 80.
- 325.
p. 675.
- 326.
pp. 674–675.
- 327.
The origin of factor 2 in the expression of \(f_1\) is commented upon in the endnote III.
- 328.
p. 447.
- 329.
pp. 675–676.
- 330.
p. 74.
- 331.
Vol. 1, p. 277.
- 332.
Vol. 1, p. 281. The expression for the ratio between the density of the proof plane and that of the electrified body is given by \(1+8 \displaystyle \frac{z}{r} \ln \displaystyle \frac{8 \uppi r}{z}\), with z the thickness and r the radius.
- 333.
pp. 677–678.
- 334.
p. 676.
- 335.
pp. 488–491.
- 336.
p. 672.
- 337.
p. 673.
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Capecchi, D. (2021). Physics in General. In: Epistemology and Natural Philosophy in the 18th Century. History of Mechanism and Machine Science, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-030-52852-2_4
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