Stylus force digital scales

@nrenter wrote The only change in the vertical force vector is as the stylus is raised vertically is due to the change in gravitational force as you move [mm to cm] further away from the center of gravity, and therefore the force of gravity changes. This is why it's called "Vertical" tracking force - vertical states the direction of the force vector.

This statement is incorrect and you gave the reason in the body of your response. The force of gravity is at its greatest when perpendicular to the earth's surface (you call it vertical).  With a pivoted tonearm, the cartridge travels in an arc and within that arc, there can only be one position in which the stylus tip is perpendicular to the playing surface and it is in this position in which the force of gravity is at it's maximum.  Any deviation from perpendicular will result in a less gravitational force. 

This is the same rationale as why weigh scales must be place on a flat surface to read accurately, otherwise the weight will not be transferred perpendicular to the earth's surface.

Folkfreak,  I took a powerful magnet to the weigh pan of my digital VTF scale, and there was zero attraction of the magnet to the weigh pan or even to the body of the scale itself.  Seems that even though your plastic-bodied scale and my metal-bodied scale look alike (maybe exactly alike), there actually was a good reason why mine cost more money, other than the metal outer shell. For once in my life, my extravagance paid off.

nrenter and brf, You both got it right for the wrong reasons.  My physics professor in college would have given you both an "F", but he was mean.  The force of gravity never changes.  What changes is the magnitude of the force vector in the vertical direction, when you rotate the tonearm in a vertical arc away from or down towards the LP surface.  The magnitude of the vertical force vector due to gravity changes because you are shifting the center of mass toward the pivot (if you raise the tonearm) or away from the pivot (if the arm wand moves toward the LP surface).  It's like a seesaw. When you raise the tonearm, some of its mass is shifted toward the pivot and thus the pull of gravity on the cartridge is partly borne by the pivot, not the cantilever, during that moment.  

Lewm, I believe we are saying the same thing if I replace force of gravity "on an abject" with force vector. An object perpendicular to the earth’ surface will experience only one force vector. Anything other than perpendicular, results in more than one force vector and that is (as you obviously know) why balls roll downhill and objects topple if not supported. Thanks for the additional clarification.

All physically true, but, does it matter? The optimal VTF for any given cartridge is an unknown. We could try to measure by incremental adjustments while taking measurements, but the results would always be a range that is dependent on the accuracy and precision of our measuring devices. Plus the recording being played will also determine the outcome and define the parameters and conditions under which the analysis was performed i.e., the so-called asterisk in the footnote. So, the optimal VTF will always be a range, it can't be anything other than that, and, as long as we are in that range, slight variations of up and down motion on the cartridge imparted by the record and that change the VTF ever so slightly as described above simply          won’t          matter.

All physically true, but, does it matter? The optimal VTF for any given cartridge is an unknown

I agree, I only use the stylus force gauge to set the vtf at the manufacture's recommended force and then perform fine adjustments by ear.  Personally, I don't need a scale that measures to the 1,000 of a gram.