Seeliger's Dust Fit Too Well
In May 1909 William Wallace Campbell, director of Lick Observatory, printed a table in Popular Science Monthly. One column held Simon Newcomb’s ten unexplained secular motions of the inner planets; the other held what Hugo von Seeliger’s model of zodiacal dust predicted for each. All ten matched within their probable errors. For Mercury’s perihelion the model gave 8.49″ and Newcomb measured 8.48″ (both as e·ΔΠ per century). Campbell said the work “marks an epoch” and that it was “scarcely possible to doubt” the dust was the cause. The Damn Interesting piece that sent me here goes straight from the failed hunt for Vulcan to Einstein and never mentions this rival, yet for six years it was the leading explanation. Seeliger’s version was two flattened ellipsoids of matter around the Sun, totalling about twice Mercury’s mass. As Harold Jeffreys later spelled out, the fit was a least-squares solve for the two densities plus a slow rotation of the stellar reference frame: at least three knobs.
The dispute had more than two sides. Erwin Freundlich, Einstein’s astronomer ally, argued in February 1915 that no Newtonian matter could account for the anomalies of Mercury and Venus; Seeliger answered in print, and when he later caught a formula error in another Freundlich paper he took it apart in public. A private letter explained why he bothered: “I happened to hear that Einstein sets great store in Dr. F’s line of reasoning” (Hentschel). Einstein, in his paper of 18 November 1915, reproduced four rows of Newcomb’s table “which I owe to Dr. Freundlich” and left the verdict “to professional astronomers” (Janssen & Renn). All four were perihelion rows; the node and inclination rows, where his theory predicts zero, were absent. The sharpest paper came from a 25-year-old Jeffreys in MNRAS 77:112 (Dec 1916), and it cut against everyone. Against Seeliger he used photometry: at de Sitter’s density, the outer ellipsoid would either need particles some 10⁷ cm across (small planets, not a glow) or would make the zodiacal light 200–600 times brighter than observed. Against Einstein he noted that relativity cannot tilt an orbital plane, so Venus’s node residual of 0.60″ ± 0.17 stayed unexplained; fitting solar matter to the plane motions alone pushed Mercury’s perihelion to 13.6″, half again the observed excess.
Scoring both models against Campbell’s table, with relativity’s predictions of 43.0, 8.6, 3.8 and 1.35″ per century times each planet’s eccentricity, gives this:
| fitted parameters | χ² over 10 rows | how likely by chance | |
|---|---|---|---|
| Einstein | 0 | 8.9 | p ≈ 0.54 (ordinary scatter) |
| Seeliger | ≥3 | 0.8 | P(fit this good) ≈ 0.25% on 7 dof |
Relativity’s worst misses are Mars’s perihelion (1.8 probable errors) and Venus’s node (3.5 PE, about 2.4σ); with ten rows, the chance that at least one lands that far out is around 16%. That is what honest noise looks like, from a theory with nothing to tune. Seeliger’s ten-for-ten is the improbable result, and anyone holding Campbell’s table in 1916 could have computed it. (One caveat: Campbell calls Newcomb’s ± values probable errors, Jeffreys calls them “mean errors.” If they are standard errors, relativity’s χ² rises to 19.5, p ≈ 0.03, and Jeffreys’s worry about Venus was fair, but Seeliger’s chance of fitting that well is still only about 3%.)
The anomaly ended by dissolving rather than being refuted. Newcomb’s tables carried Asaph Hall’s fudged force law, r^-(2+1.612×10⁻⁷), until JPL’s development ephemerides dropped it (Lieske, JPL TR 32-1206). Duncombe (1956) re-reduced two centuries of Venus observations and found a perihelion advance of 8.4″ ± 4.8 against relativity’s 8.6. INPOP10a now bounds any extra motion of Venus’s node at 0.2 ± 1.5 mas per century, roughly 6,700 times smaller than the 10,100 mas Newcomb’s residual implied. I could not find the paper that formally retired that residual; it seems to have faded through successive re-reductions. Seeliger’s dust had perfectly explained an anomaly that wasn’t there, and Jeffreys’s main objection to Einstein went with it. The lesson the record supports is narrow and usable: when a flexible model fits a table of residuals better than the table’s own errors allow, suspect the table. Within three years Jeffreys had begun writing with Dorothy Wrinch on the simplicity postulate, the line that led to priors penalizing adjustable parameters and eventually to the Bayes factor. I can’t show the Mercury dispute caused that work, but it posed exactly the problem the work answers. My bet: re-reduce Newcomb’s 1895 Venus normal places with modern masses and IAU precession, and the node residual comes out below 0.1″ in sin i·ΔΩ.