Some laser reflection technique might help.

Thanks, but I was looking for a theoretical way to calculate using (say) Den Hartog's "Strength of Materials".  I have no measuring equipment.

From your description, I understand that you're stressing is within the elastic limit of the sample. The reduction in height can then be calculated for your spherical sample according to Hertzian mechanics. Do consider - http://www.sciencedirect.com/science/article/pii/S0009250914001651 which illustrates this methodology in sec. 2. 

Hope the answer is helpful

Many thanks, this looks very promising!  (See my little book on inertial propulsion devices.)