Mossotti, Ottaviano Fabrizio
MOSSOTTI, OTTAVIANO FABRIZIO
(b. Novara, Italy, 18 April 1791; d. Pisa, Italy, 20 March 1863)
Mossotti came from a moderately well-to-do family. Little is known directly of his life. He attended the University of Milan, and spent ten years as an assistant at the Milan observatory before leaving to seek a position in England. Following four years without an appointment, Mossotti accepted the post of astronomer at the topographical bureau in Buenos Aires and also served as professor of physics at the university. He remained in Argentina for several years, returning to become a professor of mathematics at the Ionian University at Corfu, founded by Frederick North in 1824. In 1841 he became professor of mathematics, theoretical astronomy, and geodesy at the University of Pisa, where he remained until his death.
As is evident in his first work (1815), Mossotti’S outlook and methods derived from that French group of analysts best exemplified by Laplace, Poisson, and Ampère. Like them, he believed that the proper way to explain all physical phenomena was by means of forces acting centrally at a distance between various fluids. Given such a force and its subject, the correct application of mathematics to the equilibrium situations of the fluids in all circumstances should, they believed, lead one to the observed phenomena. Poisson had been the first to subject Coulomb’s magnetic and electrical fluids to extensive analysis, while Ampère had postulated a central force acting between the elements of galvanic circuits. While most scientists granted the general applicability of these forces and fluids, they were utilized fully only by the Continental “action-at-a-distance” group. Indeed, after Faraday’s work of the 1830’s and 1840’s many refused to grant even the existence of the requisite fluids. Mossotti, however, held firmly to the outlook of Poisson and others, and much of his work derived from this belief.
Between 1815 and 1832 Mossotti concentrated on the question of which forces were responsible for cohesion and aggregation in liquids and solids. In accordance with the French tradition, Mossotti thought that these forces were best explained by means of a fluid distributed in an atmosphere about the particles of the ordinary matter that constituted all bodies. Mossotti’s “ether” was subject to the two central forces of self-repulsion and attraction to “natural matter”—these two were the only electrical forces he imagined. In the absence of an external concentration of the electrical ether the molecules of a body were evenly surrounded by the electrical fluid, and the whole existed in stable equilibrium under the action of the two forces, with the self-repulsion of the ether atmospheres balancing the mutual attraction of the ether and the matter. Mossotti thought these two forces were suflicient to explain cohesion as well as a number of other phenomena, including the propagation of light in transparent bodies.
In the mid-1840’s Mossotti read of Faraday’s investigation of dielectric, or nonconducting, bodies. Until then it was believed that nonconductors were unlike conductors only in opposing the motion of electrical fluid. Faraday sought an explanation predicated upon the ability of an intervening medium to propagate electrical force from point to point between “charged” bodies. Faraday assumed that all dielectrics—solid and liquid as well as gaseous—were constituted so that their smallest parts were somehow “polarized” under electrical influence, each part transmitting the action to its neighbor by its “polarity.” Although Faraday rejected the notion of an absolute electrical fluid, Mossotti ignored this rejection and accepted Faraday’s assumption of dielectric polarity, preferring to explain polarity by means of ether-bearing molecules.
Mossotti thought that all bodies were built of ether-matter molecules in which the ether acted as an electrical fluid. The difference between conductors and nonconductors resulted from a variation in the abilities of bodies to retain the ethereal atmosphere about a single molecule under electrical action. A conductor had no retentive strength, while a dielectric retained the ether, but in a condition of varying density about the molecule. Mossotti believed this conception to be in the tradition of Franklin’s single electrical fluid.
When Mossotti’s dielectric was placed near an element of ether, its molecules became polarized in the sense that the ether density about each particle varied from point to point. The variation resulted in a net force on the molecule because of the change in distance of the ether and matter from the external fluid. In Mossotti’s notation, if ρ is the distance from a volume element dψ dξ dς of the ether to the electricity, then μ dψ dξ dς/ρ2 represents the force produced on the electricity by dψ dξ dς. The function μ was positive if the density in dψ dξ dς was greater than the equilibrium value, and negative if it was less, since a decrease in ether density yielded an attraction. Mossotti was thus able to show that, if k′ represents the ratio of ether volume to total volume, then the force on a unit of electrical fluid is given by the negative coordinate derivatives of
integrating over the dielectric. The functions α′, β′, γ′ are the “dipole moments” of a molecule, their form being α′ = ∫∫∫ μψ dψ dξ dσ integrating over a molecule.
Mossotti made an extensive analysis of the internal conditions in a dielectric subject to electrical action. Employing the mathematics derived by Poisson in 1826 for the actions of magnetic molecules, he obtained expressions like for the force in a small element of the dielectric resulting from the distribution of the molecules therein. This result is the Clausius-Mossolti relation in its original form. In addition Mossotti showed that the action of a polarized dielectric can be fully represented by an imaginary distribution of ether on its boundary surfaces. By means of this equivalent surface distribution Mossotti demonstrated in 1846 that “[because of] the polarization of the atmospheres of its molecules the dielectric simply transmits the action between conducting bodies…” (“Sull’influenza…” , p. 73).
Mossotti reached this last result—which he considered his most important—only after an extensive analysis. In Faraday’s view such a transmission was an elementary proposition. The difference between Mossotti’s and Faraday’s work—and, eventually, between the proponents of mediated action and those of electrical matter—was a deep one, hinging on the acceptance or rejection of fluids acting directly at a distance. Thus, Mossotti felt called upon to explain why electrical fluid does not fly off the surface of a conductor under its self-repulsion; while Faraday considered the question unnecessary because he did not employ an electrical fluid like Mossotti’s ether. Mossoiti’s success in accounting for dielectric behavior may be considered together with the impact of Faraday’s work to illustrate the conceptual tlux that characterized the study of electricity and magnetism from 1840 to 1870. Mossotti’s work wan not very influential theoretically; it remained in the Continental aetion-at-a-distance tradition and used none of Faraday’s newer ideas on the distribution of force in space. However it was an important formal development in that it showed that one could explain dielectric behavior without abandoning the scheme of central forces and subtle fluids as Faraday had. During the late 1840’s and early 1850’s, electrical fluids came to be viewed with increasing distrust both because of Faraday’s work and because they seemed to imply unacceptable behavior for the fluid qua fluid.
I. Original Works. Mossotti’s writings include “Del movimento di un fluido elastico che sorte da un vase e della pressione che fa sulle pareti dello stesso,” in Memorie di matematica e di fisica della Società italiana delle scienze, 17 (1815), 16–72; Sur les farces qui régissent la constitution intérieure des corps, aperçu pour servir à la détermination de la cause et des lois de l’action moléculaire (Turin, l836), repr. in Richard Taylor, ed., Scientific Memoirs, I (London, 1837), 448; Dell’azione delle forze moleculari nella produzione dei fenomeni della capillarità (Milan, 1840), repr. in Scientific Memoirs (London, 1841); Lezioni elementari di fisica matematica, 2 vols. (Florence, 1843–1845); and “Sull’influenza che l’azione di un mezzo dielettrico ha sulla distribuzione dell’elettricità alla superfice di più corpi elettrici disseminati in esso,” in Memorie di matematica e di fisica della Società italiana delle scienze, 24 pt. 2 (1850), 49–74.
II. Secondary Literature. On Mossotti and his work, see Salvatore de Beuedetti, Ottaviano Fabrizio Mossotti. Elogio pronunziato nella inaugurazione del monumento all’illustre scienziato li di 16 giugno 1867, e le interpretazioni del Mossotti ai versi astronomici della Divina Commedia (Pisa, 1867).
Related works are Samuel Earnshaw, “On the Nature of the Molecular Forces Which Regulate the Constitution of the Luminiferous Ether,” in Transactions of the Cambridge Philosophical Society, 7 (1839), 97–112; Michael Faraday, Experimental Researches in Electricity, I (London, 1839); George Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Nottingham, 1828), repr. in his Mathematical Papers (New York, 1970), 3–115; James Clerk Maxwell, A Treatise on Electricity and Magnetism (Cambridge, 1891); and William Thomson, Reprint of Papers on Electrostatics and Magnetism (London, 1872).
Jed Zachary Buchwald