You have to know if you have a US style moisture meter or European style. European moisture meters (Gann, etc) are calibrated to read across the grain and US meters are calibrated to read along the grain. Across grain readings are impossible from the edge. At very low MCs (under 12% MC), pin orientation will not affect the readings. When going into the lumber from the edge, go at the thickness midpoint if you want the core, and use the 1/4 points for average values.
Consider researching:
ASTM D4442
Direct Moisture Content Measurement of Wood and Wood-Base Materials
ASTM D1037 (Part A, Sec. 126-127)
Evaluating the Properties of Wood-Base Fiber and Particle Panel Materials, Part A, Sec. 126-127: Moisture Content and Specific Gravity
Drying Oak Lumber by Eugene M. Wengert
Department of Forestry
University of Wisconsin
Madison, WI
Cost: $25 plus $5 postage and handling (plus WI residents add $1.65 tax)
Payment: Check, money order, P.O.
Order from:
Department of Forest Ecology and Managemen
1630 Linden Drive
University of WIsconsin-Madison
Madison, WI 53706
Also search the archives for a site at the US Forest Products Lab.