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E.g. extension, hardness, impenetrability, mobility, inertia, etc. [RK].
However, astronomical data are provided by Newton as evidence only for phenomena 1, 2 and 4.
Kepler’s 2nd law: In their orbits (planets or satellites), a line drawn to them from the orbited body sweeps out equal areas in equal times. Kepler’s 3rd law: The square of their periods of revolution is proportional to the cubes of their respective distance from the orbited body.
It is quite well known that these rules appeared in their final version only in the third edition of the Principia (1726), which seems quite a strong argument in favor of the a posteriori thesis. Unfortunately, no mention or discussion about this fact is found in Achinstein’s book.
In mathematics, probability is defined as the ratio of the favorable cases to the whole number of cases possible. It is therefore, a number that varies from 0 to 1. Having this mathematical definition in mind, speaking about the “probability that there is an explanatory connection between h and e” does not make sense to me. How can one calculate such probability?
By mathematical I mean essentially geometrical. Newton’s style in Book I resembles a lot a geometry book like Euclid’s Elements.
The interested reader can find a detailed explanation at Feynman (1985, pp. 41–45).
The whole argument is far from being trivial. For the interested reader (especially the interested physics instructor), I strongly recommend the didactical approach proposed by Prentis et al. (2007).
Newton concludes that the centripetal force is inversely proportional to the volume of the solid \( \frac{{SP^{2} \cdot QT^{2} }}{QR} \). This stresses how mathematical Newton’s concept of force is.
This demonstration demands a profound knowledge of the basic elements of conic sections and their properties.
These case studies are certainly relevant, but they are far from being sufficient to provide a general view of Maxwell’s work. Moreover, no explicit justification for choosing these particular manuscripts is offered. Overall, it seems that Achinstein knows in advance the aspects he wants to discuss and looked for Maxwell’s papers that contain them.
Another pedagogical reason for using analogies in teaching and learning physics is due to different types of learners. According to Maxwell “for the sake of persons of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid colouring of a physical illustration [or analogy] or in the tenuity and paleness of a symbolical expression” (p. 140).
This is the first time in the book that a relatively technical derivation is presented and explained. Achinstein, however, does not seem to regard this derivation as essential, since he recommends his readers who “want to avoid formulas and get to the bottom line” (p. 146) to move directly to the last expression. In my view, Achinstein could have been more honest to his readers and make them aware of the limitations involved in avoiding formulas and geometrical derivations when trying to understand the “Scientific Strategies of Isaac Newton and James Clerk Maxwell”.
Achinstein sustains that Maxwell also employs “An Exercise on Mechanics” (and not Physical Analogy) in another seminal paper on electricity (On Physical Lines of Forces), since the British physicist “shows how a purely mechanical fluid containing rotating vortices to act as idle wheels could produce electromagnetic properties.” (p. 153).
References
Achinstein, P. (2001). The book of evidence. New York: Oxford University Press.
Achinstein, P. (2010). Evidence, explanation and realism: Essays in philosophy of science. New York: Oxford University Press.
Aubusson, P. J., Harrison, A. G., & Ritchie, S. M. (Eds.). (2006). Metaphor and analogy in science education. Dordrecht, NL: Springer.
Bork, A. M. (1963). Maxwell, displacement current, and symmetry. American Journal of Physics, 31, 854–859.
Chalmers, A. F. (1975). Maxwell and the displacement current. Physics Education, 10, 45–49.
Feynman, R. P. (1985). The character of physical law. Cambridge Mass: The MIT Press.
Prentis, J., Fulton, B., Hesse, C., & Mazzino, L. (2007). Elliptical orbit → 1/r2 force. The Physics Teacher, 45, 20–25.
Rivadulla, A. (2005). Theoretical explanations in mathematical physics. In G. Boniolo, P. Budinich, & M. Trobok (Eds.), The role of mathematics in physical sciences (pp. 161–178). Dordrecht: Springer.
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Karam, R. Peter Achinstein: Evidence and Method: Scientific Strategies of Isaac Newton and James Clerk Maxwell . Sci & Educ 23, 2137–2148 (2014). https://doi.org/10.1007/s11191-014-9717-7
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DOI: https://doi.org/10.1007/s11191-014-9717-7