Originally Posted by **kiwiheretic** Well, one experiment might be to fire an object to a known velocity at a spring oriented horizontally and then finding the maximum compression of the spring and using Hooke's law, calculate the inertial mass, then conduct the same experiment place the object on a spring scale and then again measure the gravitational mass and then check if these two quantities are equal. |

That won't work because you must first define those quantities. For example: how does one determine the gravitational constant?

As I mentioned, you can choose constants of motion so that they will be equal

*numerically*. Its only through observation that the equality can be determined. Its important to realize that these terms were never defined merely to give different names to the same quantities. That'd be absurd.

Originally Posted by **kiwiheretic** Not sure if its possible to measure relativistic mass in this way |

There are other ways of doing it. You can accelerate a body at a constant rate using a spring scale where the body is moving along the face of the scale. That would tell you the inertial mass of the body. What's important to know here is that in reality you'd be measuring the transverse mass. But that's numerically equal to the relativistic mass. I think Einstein mentions this in his 1905 SR paper in fact.

Then you place the scale at rest on the surface of the Earth then slide the body along the scale.

See

Weight of a Moving Body
However to be precise one must use inertial mass as how its properly define, i.e. using Newton's definition. Weyl also, in effect, defined mass in that way.