Many years ago I was given a problem involving the calibration of sets of weights. Each of two sets consisted of weights of 1.0 kg, 500.0 g, 300 g, 200 g, and 100 g. The two 1.0 kg weights were calibrated by the international agency in France and I was permitted to assume that their masses were known absolutely, i.e., 1.0 kg +/- a known correction.(adsbygoogle = window.adsbygoogle || []).push({});

The calibration of the remaining weights was carried out using a balance which would give the difference between the weights in the left pan and the weights in the right pan. This. was carried out in a vacuum to eliminate bouyancy.

Designating one set a A and the other as B the following comparisons were made:

A[1000] vs. B[1000]

A[500] + B[500] vs. A[1000]

A[500] + B[500] vs. B[1000]

A[500] + B[300] + B[200] vs. A[1000]

A[500] + B[300] + B[200] vs. B[1000]

Etc., etc.

Every possible combination of weights from either set which would nominally add to 1000 g was compared. It's been a long time but I think that every possible combination that would add to 500 (or 300 or 200) was also compared.

Now here my question: I was to use this data to solve for the most probable mass of each weight in the two sets with the exception of the 1.0kg weights. I was directed to usethe method of least squares. Now I am familiar with using the method of least squares to find a straight line. For the life of me I could not, and still cannot, see any way of arranging this data so that the solution is a straight line. Was I using the wrong approach. Can the method of least squares be used to find something other than a straight line? Or a plane, etc.

The solution was found in a computer program written at the National Institute of Standards and Technology. I never figured out how the program worked but it compiled and my supervisors considered the problem solved. I was directed to move on the the next project. But to this day the whole thing bugs me.

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# I Calibration of weight sets

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