Optimizing of Balances of the Second Generation

At the 3rd Conference on Vacuum Microbalance Techniques in Los Angeles in 1962, we suggested the use of the equation of motion of a balance T=J+α+kα+Cα for the calculation of the unknown torque T, and the measurement for that purpose of the values of all the other quantities in this equation. The present paper discusses the consequences of two sources of error relevant for this method. First, the errors caused in the first and second derivatives of the deflection are considered, deduced from two or three deflection measurements separated by small time intervals. Secondly, the consequences of the errors caused by the uncertainties in the deflection measurements are discussed. Consideration of the two errors together leads to an optimal set of values of parameters for the balance handling. This revised version was published online in July 2006 with corrections to the Cover Date.