My dear Sir
It may be very right to apply “elliptic transcendents” even to the eating of an egg: but it seems to me that bearing in mind the well known equilibrium of a point within a spherical shell, it is obvious that a spherical shell would remain in neutral equilibrium about a point, or about the centre of a gravitating sphere, because the attraction of every part of such a shell is proportionate to
the its angular extent, and the opposite parts must balance each other. Now if we take a narrow zone or ring of such a shell, and suppose it to approach the centre at any part, it is clear that the angular extent of that part of the ring as seen from the centre, will be increased in the direction perpendicular to its plane – and will therefore preponderate over the attraction in the opposite direction, and the equilibrium must be as unstable as that of an egg placed on its narrow end –
I do not wish to “crucify” the Newtonian <1> theory upon Fraunhofer’s <2> experiments: but will any Newtonian assert that the velocities of rotation which you mention can by any imaginable mechanism be caused to vary in the direct ratio of the velocity of the particles themselves, or of the refractive density of the medium – until this is done, the undulatory theory has the advantage
I do not apprehend that your three undulations can destroy each other except at the supposed points where they afford intervals of 120° or ⅓ of a whole undulation but between x = 0 and x = 120° there would be several alternations: first, at x = 90°,
and the sum is 1 + 0 – 1 = 0: then there must be a maximum between this and the disappearance at 120°: and it is by no means universally true that any number whatever, if equidistant, will destroy each other, “except in one case”.
The maxima of my formula are indicated, I believe, by the equation nx = tanx very nearly –
The lovers of “living forces” are satisfied with the general law that assures them light cannot be destroyed: Fresnel <3> has pursued it through some cases of interference: but I do not pretend to understand why light is not lost in the most ordinary case of transmission according to the Huygenian law of equal dispersion of the elementary motions – and I must suppose this equal dispersion to be a mathematical fiction only by which the true direction of the force is determined: at least I am inclined to take this view of a very dark subject, which confounds me the more the more I study it.
My eye may perhaps be different from yours in its perceptions, but I should call the monochromatic yellow rather green than orange yellow: as [sic] least the cadaverous countenances of the little masters and misses playing at snap dragon are just such as are imitated by the conteur monstre of the theatre, which is a greyish green. I certainly do not agree with Fraunhofer in seeing the Newtonian gradations in the true striated spectrum: the red to my eye is unmixed with orange except a small portion, the green is uniform, as well as the blue and the violet, with scarcely any variation from what Wollaston <4> describes – and I have coloured the spectra accordingly in my Lectures –
yours very truly
1. Sir Isaac Newton (1642–1727).
2. Joseph von Fraunhofer (1787–1826), optician, Munich.
3. Augustine Jean Fresnel (1788–1827), French physicist.
4. William Hyde Wollaston (1766–1828), physicist.