I understand what you are saying now but I'm not convinced by the argument: It does not seem plausible that transaction volume will be affected by value of the medium of exchange. Can you show your reasoning applies to other conventional currencies? Specifically that the transaction volume changes in direct proportion to some numeraire, say USD?
(That book is about DCF and bitcoin and other currencies don't give off cash flows).
The definition of velocity is not at issue, the relationship between "price" and transaction volume is. If tomorrow the US gov decreed that every $1 of USD will immediately be exchanged for $2 of USDX you wouldn't expect, in theory, for the USDX transaction volume, denominated in USD, to change.
Put another way, I fail to see how the BTC/USD exchange rate is related to BTC transaction volume except for tangential reasons like sentiment.
BTC value is directly related to its velocity and the value of the goods and services that are transacted in BTC. I held the purchasing power of USD constant, simply to derive a value of BTC in 2013 dollars. If USD experiences a large shift in PP (unlikely), that would affect BTC/USD. But either way that's not an inherent source of value to BTC.
This is my last comment, as I cannot possibly respond to an endless string of unfounded criticisms.
I'm not an expert, frankly I don't even have a passing knowledge of how to value currency. My "string of criticisms" is actually one probative question: How does transaction volume imply a given value of a unit of currency?
Obviously an increase in transaction volume increases the value of currency. What is not obvious, at least to me, is that it is in direct proportion.
(That book is about DCF and bitcoin and other currencies don't give off cash flows).