Tee,
You don't indicate what book it is from which you are studying and who might have written it. I note that there are a great many books around which are full of imaginative ideas.
Is the book talking TAS, IAS, CAS, or EAS ? And are we looking at constant TOW ?
To add a little to Tinstaafl's commentary (I might not agree with his V1 comments) and I suspect that Quid might have made a typo or two -
(a) Vmcg tests normally are predicated on no nosewheel steering (ie the nosewheel is rigged to be free to caster to reduce the stabilising effect of nosewheel tyre forces). This allows some margin for contaminated (ie slippery) runway surfaces. The AFM figure is based on the reasonably expected maximum engine thrust. It may be reasonable to talk about the day to day variation in the "real" Vmca/Vmcg as you are suggesting, but the AFM figure is fixed at a reasonably high value. Similarly, the AFM figure for Vmca would normally be fixed.
(b) V2 normally is limited by Vs1 unless, in the lower weight (ie lower Vs1) range, Vmca becomes limiting. So it would appear that the book might be looking at the low speed end of the range. What you are suggesting is not a reasonable statement to make to students without some appropriate clarification. And, in any case, Vmca is declared for reasonably critical conditions so it is generally not going to vary in the Flight Manual.
(c) Vr normally is predicated, within certification boundaries, on a value which, following a failure, will permit the aircraft to end up pretty close to V2 as it goes through 35 feet. I would have expected to see Vr follow whatever V2 does as the main consideration is the rotation rate specified by the manufacturer.
(d) V1, within AFM limits (usually from around, say, 0.85 Vr up to Vr), is not tied to what V2 or Vr are doing and may be varied to suit in the unbalanced field length case. The book probably is talking about a specific presumed situation so we might need to know a bit more about the information it is purporting to give you.
My thought is that one would need to read the book's story in a little more detail (to get the whole story) before talking in excessively sombre tones about its usefulness.
[ 11 July 2001: Message edited by: john_tullamarine ]