Let's look at how the Part of Fortune is calculated. For a daytime birth, you take the Ascendant, add the Moon, and then subtract the Sun. For a nighttime birth, you take the Ascendant, add the Sun, and subtract the Moon. I'll do the first calculation to show what I mean.
Ascendant ---- 12 Taurus 17. Taurus is the 2nd sign, so let's write it as 2 - 12 - 17
Moon----------- 15 Gemini 13. Gemini is the 3rd sign, so let's write it as 3 - 15 - 13
Sun----------- 10 Aries 00 Aries is the 1st sign, so let's write it as 1 - 10 - 00
The math would be:
2 - 12 - 17
+ 3 - 15 -13
5 - 27 - 30
-1 - 10 - 00
4 - 17 - 30. The 4th sign is Cancer, so this person would have a Part of Fortune at 17 Cancer 30, which would fall in this person's 3rd house.
But where in the sky is this part? What angle, what actual point? There isn't an actual physical point in this person's chart at 17 Cancer 30. It is only a mathematically derived position.
Now, to give some support to those who use this body, I will say that the Part of Fortune in a daytime chart is in the same house the the Moon will be in that person's Solar Chart. So using the above example, if you put the Sun on the cusp of the first house (thus making it a solar chart), the Moon will be in the 3rd house of the Sun. So one could say that the Part of Fortune is symbolic of the relationship the Moon has to the Sun, and that is the reason to use it.
But I have never been able to get my mind around the way this point is derived.