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125). Thus from both McGaugh’s phenomenological study and from the phenomenological Eq. (125), we see that it is indeed an acceleration scale (or equivalently an inverse distance scale times the square of the speed of light) which determines exactly when luminous Newtonian matter fails to account for observed data. As such, the acceleration criterion which Milgrom originally identified has to be regarded as being a bona fide property of nature. As formulated, the MOND theory actually possesses not one but two logically independent components.
A cosmology where ρC = 3Mc2 /4πL3 = 3H 2 c2 /8πG), the Hubble radius happens to be equal to the Schwarzschild radius of the matter within it (viz. 2MG/c2 = L). For such a cosmology the centripetal acceleration of a test particle located at the Hubble radius is given by v 2 /L = MG/L2 = cH/2. 5 × 10−8 cm/sec/sec, and with this value being very close to the values found for both the MOND a0 and the acceleration γ0 c2 /2 associated with Eq. (125), we see that the centripetal accelerations of Newtonian cosmology occur precisely in the acceleration regime where luminous Newtonian matter falls short for galaxies.
To treat the luminous Newtonian contribution more accurately we need to allow for the fact that the optical disk actually has a thickness (with its own scale height z0 ), that the HI gas comes with its own surface brightness distribution and can have a total mass as high as 15 per cent or so of the luminous mass, and that the two largest galaxies in the sample also have a central bulge. Using the calculational tools presented in Appendices A, B and C the contributions of all of these various components can readily be determined for each galaxy in the sample, with the exact luminous Newtonian expectation for v(R) reported in the typical calculation of  being exhibited as the dashed curves in Fig.