The Abbe principle and Abbe error
The Abbe principle and Abbe error
The Abbe principle
The Abbe principle states that maximum accuracy is obtained only when the measuring scale (the standard) lies in line with the axis of the dimension being measured. In other words, the instrument's line of measurement and the measured dimension must be collinear, one as the continuation of the other, with no lateral offset between them. It was formulated by Ernst Abbe, who also designed the corresponding length-measuring machine in 1890.
The Abbe error
When the measuring scale is not collinear but offset by a distance h from the line of measurement, any small angular deviation (tilt) in the guideways or moving parts of the instrument turns into a length error. This is the Abbe error. The greater the distance h between the line of measurement and the axis of the instrument, the greater the error for the same angular deviation. That is why the degree to which an instrument conforms to the Abbe principle determines its inherent accuracy.
