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Books I and III seem to receive the bulk of attention by Newton scholars, and historians more generally. However, I'm sure an in-depth study of Book II would shed light on Newton as a thinker -- for that reason it must be of import, no?

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    $\begingroup$ You might find more interest in your question if you identified particular topics in Book 2 that you would like to see studied. $\endgroup$ – Carl Witthoft Apr 1 at 13:47
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It can certainly be agreed that Book 2 of the Principia has received less attention than Books 1 and 3. According to I B Cohen (1999):--

"Book 2 of the Principia differs from books 1 and 3 in a variety of ways. One of the most striking of these is the fact that its major contents, the theoretical and experimental study of the forces of resistance to motion in various types of fluids, is usually not discussed and often not even mentioned by historians of science or even by some historians of mechanics, ... ".

Cohen went on to offer a contributory reason, that:--

"Newton himself was in part responsible for this rather cavalier treatment of book 2 since he suggested to readers that they confine their study to the beginning of book 1 and then skip over to book 3, on the system of the world. For the intellectual historian and philosopher of science, the system of the world has always been a more glamorous field of study than an investigation of the properties of fluids."

(Quoted from p.161 of I B Cohen (1999), "A Guide to Newton's Principia", pp.1-370 accompanying "The Principia: A New Translation", I B Cohen and Anne Whitman (1999, Berkeley, CA, Univ. Cal. Press); for Book 2 see especially pages 161-194.)

There is also another and short possible answer: that Book 2 of the Principia was less successful than Books 1 and 3, it has not stood the test of time to anything like the same extent, and it interests fewer people also on that account.

Part of the reason for relative lack of success is that the subject of Book 2 really needed for its study experimental observations and data not available until long after Newton's lifetime. The motion of bodies in resisting (fluid) media is affected by phenomena such as viscosity and turbulence and temperature effects. These were hardly accessible to systematic study and observation in the state of experimental and observational science in Newton's time. The effects they contributed therefore remained largely or entirely beyond Newton's observational reach, and their absence from his reasoning limited the correctness and validity of some of his conclusions.

To give just one example, Newton in Book 2 calculated or estimated the speed of sound in air; he obtained a poor result, and later, after experimental estimations showed something closer to the true value, he put forward essentially wrong conjectures to account for the difference. The real cause of the errors lay in the temperature component of the gas laws and in temperature effects unknown in his time, thus:--

"The error in the speed of sound ... reflects nothing more than the impossibility of Newton recognizing the distinction between adiabatic and isothermal expansion in an era before thermometry. Newton’s derivation of the speed of sound from first principles is correct save for the need to replace Boyle’s law" [which considers gas pressure and volume but not the effects of temperature] "with the corresponding adiabatic relationship" [in which the effect of temperature is also taken into account] "for expansions and contractions in sound waves." (emphasis, comment [ ] and links added):

quoted from p.128 in George E Smith's chapter: "Was Wrong Newton Bad Newton?", pp.127-160 in "Wrong for the Right Reasons", ed. J Z Buchwald and A Franklin (2005).)

(G E Smith in the same chapter also draws attention to errors by Newton in Book 2 arising from incomplete development of some concepts in Book 1: showing, for example, how Newton did not see how to reformulate his second law of motion for the case of angular motion.)

Besides the references given above, other sources showing scholarly study of Principia Book 2 include:

George E Smith (2001), "The Newtonian Style in Book II of the Principia", ch.9 (pp.249-298) in "Isaac Newton's Natural Philosophy", eds. J Z Buchwald, I B Cohen, (2001, MIT Press, Cambridge, MA); and

Clifford Truesdell (1968), "Essays in the history of mechanics", pp.138-183 (chap. III): "Reactions of Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia".

Altogether it seems hard to tell how much more would be revealed of Newton's thinking by further in-depth study of Book 2. The examples already mentioned show how such study could be specially burdened by the need to distinguish between (a) limitations arising because Newton only partly developed some of the concepts for which foundations are laid in Book 1, and (b) limitations arising from the impossibility of Newton's foreseeing experimental data and phenomena still unknown and inaccessible in his lifetime.

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