In relation to the "tilting the head while looking the astigmatic wheel with one eye" experiment (http://forum.gettingstronger.org/index.php/topic,1114.0.html
Not 100% surely but if it was the cornea or the lens that causes diplopia then with this experiment the darkest lines shouldn't change but they do.
But if the oblique muscles can change the shape of the cornea then with tilting the head we have a huge relation to the changing of shape fo the oblique muscles with this movement, while having the cornea not moving so having it change according to the moving oblique muscles. The "moving" darkest lines could then correspond to the changes in shape (but bot moving) cornea due to the 2 oblique muscles changing shape.
Also if there are some myopic meridians in the myopic astigmatism they could change with this head tilting since the two oblique muscles are moving in relation to the still eyeball and these muscles zone the eyeball like a belt. "The left eye, which was the poorer of the two, showed a minimum of 3.00D. of Ast. against the rule, and this amount would actually double for a few seconds and then return to the minimum. This change was evidently due to some action of the oblique muscles and occurred when the eye was directed toward the tube, while there was a slight turning of the head.""After six or seven vigorous muscle treatments, the ophthalmometer showed a decrease in Ast. Subjectively,"
...the point I want to bring out is: That corneal astigmatism does change and often lessens and sometimes disappears after thorough muscle treatments.
Likewise, the symptoms attributed to refractive errors often vanish after muscular treatments, even through the refractive error remains. In other words, the symptoms may be due to wrong muscular condition and not to the refraction. This will account for some of the "miraculous" cures made by the kind of doctors whose slogan is "throw away your spex.""
from the "Changes in Corneal Astigmatism" http://www.i-see.org/parker.html
Bierly JR, Hainsworth DP, Schmeisser ET, Baker RS. Effect of extraocular muscle surgery on corneal topography. Invest Ophthalmol Vis Sci 1993;31(suppl):1249.
Bowman KJ, Smith G, Carney LG. 1979. Corneal Topography and Monocular Diplopia Following Near Work. Am J Optom & Physiol Opt 55:818-823.
Fairmaid, J.A. 1959. The Constancy of Corneal Curvature: An Examination of Corneal Response to Changes in Accommodation and Convergence.
Home, Everard. 1795. The Croonian Lecture on Muscular Motion. Philosophical Transactions of the Royal Society of London, vol. 85, p. 1ff.
Knoll, Henry A. 1975. Bilateral Monocular Diplopia After Near Work. American Journal of Optometry and Physiological Optics 52:139-40, 432 (errata).
Kwitko S; Feldon S; McDonnell PJ. 1992. Corneal topographic changes following strabismus surgery in Grave's disease. Cornea 11: 36-40.
Parker, J.W. 1930. Changes in Corneal Astigmatism. Optical Journal and Review, April 11, 1930, 21-22.
Preslan MW; Cioffi G; Min YI. 1992. Refractive error changes following strabismus surgery. J-Pediatr-Ophthalmol-Strabismus 29:300-4.