It might be a fun exercise to re-write another's literature because we do not like the way they said it, or we do not think they said what we think they should have said. In fact, there is a thread about that very thing:
http://forums.mikeholt.com/showthread.php?t=126834
However, the authors in this case were perfectly capable of saying "two phase conductors" when they wanted to and saying "two-phase" when they wanted to and, in fact, they did. In the spirit of getting to the "true meaning" however, why don't we investigate what it means to call a wire a "phase"?
When looking at the "phases" we are really talking about the voltages (voltage waveforms). If we have voltages (sinusoidal for us) that peak at different times, we say they have a difference in phase. Because they have a difference in phase, we have traditionally labeled these voltages as "phases".
Brief history: Counting phases in a system:
When we group voltages into different systems, we group those that have significantly the same magnitude. We have 120 volt systems, 240 volt systems, 208 volt systems, 277 volt systems, etc. Inside the system group, we create sub-groups of voltages that have the same phase angle in order to separate the voltages into unique sub-groups. The number of sub-groups determines the highest phase order (# of phases) of the system.
That does not mean the voltages have to be used by loads of that same order, and many times they are not. Often, the load type might determine the name we use for our group of voltages. Regardless of the traditional name used for the system of voltages, the physics of the voltages remains the same. For example, we could have three (3) single-phase-voltage systems or one (1) three-phase system. We even have supplies that have a mixture of different systems.
If the unique voltages are evenly displaced with phase angles that sum to 360 degrees, the system is said to be a regular system, like a 3-phase wye or delta. Otherwise, the system is said to be an irregular system, like the 90-degree displaced 2-phase system of old (also known as a quarter-phase system).
There is a particularly interesting regular system, and that is the system with two voltages displaced by 180 degrees. These voltages are exactly those of the center-tapped 3-wire single-phase system and, as such, represent a single-phase system. That is why we call it single-phase instead of two-phase. But one should not forget the twofold nature of this system; a fact that is not over-looked when the 3-wire single-phase system is grouped with multiphase systems when studying the application of the method of symmetrical components, where it is actually assigned a characteristic angle of 180 degrees (see Wagner/Evans "Symmetrical Components" 1933).
Here is another quote on the matter:
From "Engineering Circuit Analysis" by William Hayt, 1962:
The name single phase arises because the voltages Ean and Enb, being equal, must have the same phase angle. From another viewpoint however, the voltages between the outer wires and the central wire, which is usually referred to as the neutral, are exactly 180? out of phase. That is, Ean = -Ebn and Ean + Ebn = 0. In a following section we shall see that balanced polyphase systems are characterized by possessing a set of voltages of equal magnitude whose (phasor) sum is zero. From this viewpoint, then, the single-phase three-wire system is really a balanced two-phase system. "two-phase", however, is a term that is traditionally reserved for something quite different, as we shall see in the following section.
So what does all that mean for the wires? It depends on if the source voltages (EMFs) are in a wye or delta configuration. With a delta configuration, the phase voltages are the line-to-line voltages (commonly called the "line" voltage). In the delta case, the "line" voltage and "phase" voltage is the same. In a wye configuration, the phase voltages are the line-to-neutral/common voltages. In the wye case, the "line" voltage is equal to sqrt(3) times the "phase" voltage.
So how about the utility distribution? For the delta case (no neutral available), bringing out two wires results in a single-phase system (one line-line voltage). Bringing out three wires results in a three-phase system (there are three line-line voltages, even if we have a one missing transformer coil). There is no two-phase case because we have no neutral. Jim's line-line voltage phase-counting method works great for this because the line-line voltages
are the original "phase" voltages.
For the wye case (neutral/common available), bringing out two wires results in a single-phase system (one line-line voltage or one line-common voltage). Bringing out three wires could result in a three-phase system (three line-line voltages) or a two-phase system (two line-neutral voltages). The line-neutral voltages
are the original "phase" voltages. Of course, bringing out four lines is a three-phase system (three line-line voltages or three line-neutral voltages).
Jim's method does not work too well for a wye system. If you insist on line-line voltages being the phase count, you get one phase for two lines + the neutral (one line-to-line voltage). The problem is you get zero phases for one line + the neutral as you have no line-line voltage. The problem is that the method ignores the fact that the line-to-neutral voltages
are the "phase" voltages in a wye system.
Jim's method also does not work well for the quarter-phase system because there are four line-line voltages in the 5-wire 2-phase system (the truth of the matter is that the 3-wire quarter-phase system is a sub-set of a 4-phase system).
All that to say: There are two phase voltages in a wye system that has two ungrounded conductors plus the neutral. As such, it can be called a two-phase system using the general definition for poly-phase systems.