Chris,
Most of the world refers to "Vref" as a landing speed, i.e. "reference" as you noted. The guy whose book you're looking at is using notation different from most everybody else these days, and that's what's caused the confusion. Not an invalid way of looking at life and performance and such, but a rather nonstandard notation. The way the Air Force taught takeoff performance, you had a "decision speed" which was really a MINIMUM speed at which you could continue a takeoff having lost an engine, a "refusal speed" which was the MAXIMUM speed at which you could stop on the runway available, having just lost an engine. If "decision speed" is below "refusal speed," life is good, and if you lose one between those two speeds you should be able to successfully execute an abort but also you could successfully take off. If "decision speed" is ABOVE "refusal speed," then life is very bad, because if you lose one between the two, you can neither stop nor go... that's not good!
The Air Force wouldn't let you fly on days when "decision speed" was above "refusal speed," and (not wanting their fledgling pilots taking bad aircraft into the air unnecessarily) told you that until you reached "refusal speed" you weren't committed to the takeoff. They didn't use the terminology "V1," but if they had, they'd have set it = "refusal speed." That's not a universal preference, by the way... if you have a range of speeds where the aircraft can successfully stop AND successfully go, some operators will set their V1 to a value below the maximum "refusal speed" since they figure that stopping on the last brick with smoking brakes is more dangerous than taking the jet airborne... particularly since nobody notices or cares if you had 34' of obstacle clearance instead of the engineers' 35', but EVERYBODY cares if you go one foot into where the approach lights are set up!
Limo,
You're not wrong in anything you said, but bringing balanced field into it complicates life tremendously. V1 is your (make a) DECISION SPEED: before V1 you can stop the airplane, after V1 you won't try to. Period. (note: this is NOT the same as what the USAF called "decision speed"!)
Doesn't mean that on this runway with today's conditions you couldn't continue with a problem that occurs before V1, and it doesn't mean that you couldn't stop the airplane with a problem after V1. With a long enough runway, you can lose an engine well before V1 and continue the takeoff successfully; with a long enough runway you can initiate a stop well above V1 and do so successfully. If the runway is long enough, there's no reason you MUST base V1 on anything related to balanced field whatsoever... if you have enough performance, you (actually, whoever has done all the performance calculations) can set V1 = Vr, thus not having to commit yourself to taking a bad airplane airborn when there's ample room to safely stop. Or, on that same runway, a legal V1 could also be incredibly low... for instance, most 4-engine jets are approved to do 3-engine takeoffs for ferry purposes... so with 4 engines operating, their minimum speed to continue the takeoff should they lose one engine could be as low as 0 knots. Why would you WANT to have a V1 as low as possible, I don't know... but you could. (maybe, getting out of Dodge with bad guys shooting at you)
There is a LOT of stuff that can go into how the V1's are set and calculated and affected by winds and brake cooling and balanced field length and what wiggle room the performance engineers have to set it anywhere they choose within some range, but the simple pilot definition is, it's your decision speed. Before I get to V1, I can stop. Don't have to, but can. After V1, I won't try to. (Might be able to, but won't try, unless the aircraft is incapable of safe flight, in which case the choice is between running off the end of the runway really fast or somewhat slower, but that's beyond the scope of "normal" emergencies that get considered.)
K.I.S.S., V1 is the speed after which I'm not going to try to stop the airplane on takeoff. Questions?