Tolman's own starting position: the independence of light speed from source speed "has hitherto lacked experimental justification" and came from the ether theory. He states the alternative, that light speed and source speed add (an emission hypothesis), "would be very simple, would be no contradiction to the first postulate of relativity, and would directly explain all our failures to detect an ether drift."
Kinematic argument: with source speed independent of light speed, a moving source changes wavelength (lambda = lambda0(1 - v/c)); with additive speeds the wavelength is unchanged (lambda = lambda0) while frequency changes by nearly the same first-order amount. Grating measurements could decide, but a reflecting grating might act "as a new source", hiding the difference; he recommends transmission gratings.
Tolman's own experiment (sun's limbs): a Lloyd's-mirror interferometer (plate-glass mirror about 25 cm long, about 10 cm from mirror end to eyepiece), sunlight focused by a lens of about 9 cm aperture and 80 cm focus (solar image about 8 mm). Light from the approaching and then the receding limb of the sun was let into the slit. Expected shift on the emission hypothesis about two fringes (speed difference about 1.5 km/s each way; path 10 cm; 0.5e-4 cm delay each way; wavelength 5e-5 cm). Result: "No shift in the fringes was observed." He estimates that the lens would remove only about half the difference (Fresnel drag coefficient 0.51 for mu = 1.5), still leaving about one fringe. He notes the possibility that the difference is destroyed near the earth "is not entirely excluded".
Second argument: from the Kaufmann-Bucherer mass law m/sqrt(1-beta²) plus the first postulate, he deduces time dilation, length contraction, clock offset v/c² and then the constancy of light speed. He adds his own caution: "the Kaufmann-Bucherer experiment may not really indicate an increase in the mass of an electron in motion", since forces at high speed might instead be smaller than Maxwell's fifth equation gives, an application which "certainly lacks experimental justification".
Footnotes: Lewis and Tolman, Proc. Amer. Acad. 44, 711-724 (1909); Phil. Mag. 18, 510-523 (1909); Comstock, Phys. Rev. 30, 267 (1910); Tolman, Phys. Rev. 30, 291 (1910); N. R. Campbell's Faraday-tube emission model (Modern Electrical Theory, 1907).
Classifies three emission theories by what happens on reflection: (a) the mirror re-emits at c relative to itself (the theory Tolman himself had suggested in 1910); (b) O. M. Stewart's theory (Phys. Rev. 32, 418, 1911): reflected light takes the velocity of the mirror image of the source; (c) Ritz's theory: light keeps the source velocity component along its whole path.
Against (a) and (b): canal-ray Doppler measurements with a concave grating (Stark, Ann. d. Phys. 28, 974, 1909; Paschen, Ann. d. Phys. 23, 247, 1907). Tolman quotes a letter from Johannes Stark (in German) saying both grating arrangements gave matching Doppler spectrograms. On (a) no Doppler shift would appear for the Rowland-type arrangement; on (b) the shift would go to the red for an approaching source, opposite to observation.
On Ritz: says it "does not seem to have received the critical attention which it deserves" and is "the only emission theory which has been developed with any completeness". Proposes the decisive test: a Michelson-Morley interferometer fed with sunlight, which on Ritz's theory should show a fringe shift of time interval 2 l v²/c³ on rotation through 90 degrees, and on Einstein's none. Summary: "A definite experimental decision between the relativity theories of Ritz and Einstein is a matter of the highest importance."
Thanks P. Ehrenfest for suggestions.
Bearing on the claims
Claim 6 (emission theories ruled out): the 1917 book (pp.41-43) cites Comstock and de Sitter; these two papers show Tolman's own route: he first treated the emission hypothesis as a live, simpler alternative, ran his own null experiment on the sun's limbs (1910), and in 1912 still regarded Ritz's theory as undecided and in need of a specific test. Priority 1 material by the author; it supplies the apparatus and numbers the book lacks.
Claim 1 and claim 2: the 1910 paper derives the kinematics from the Bucherer mass law, the reverse of the book's order, and records Tolman's own caveat that the electron experiments might be explained by a change in force rather than mass. This is pertinent for the Kaufmann-Bucherer point in claim 6 and for any reviewer weighing claim 2.
Next run: read the 1909 Lewis-Tolman paper (lever paradox origin, claim 3; colliding-spheres mass argument, claim 2) and the three "Non-Newtonian Mechanics" papers (1911-1912; transverse/longitudinal mass and force-acceleration direction).