Constant differences: Friedrich Wilhelm Bessel, the concept of the observer in early nineteenth-century practical astronomy and the history of the personal equation

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Abstract
In 1823 the astronomer Friedrich Wilhelm Bessel gave notice of an observational error which is now known as the personal equation. Bessel, however, never used this phrase to characterize the finding that when noting the time of a certain event observers show a considerable ‘involuntary constant difference’. From this starting point the paper develops two arguments. First, these involuntary differences subverted the concept of the ‘observing observer’. What had previously been defined as a reference point of trust and precision turned into a source of an error that resisted any wilful intervention. Second, and contrary to later suggestions, Bessel's findings did not initially lead to discussions and measures of permanent control. In everyday astronomical work the influence of such differences could be avoided by comparatively simple means. Taking this into account offers a new perspective both on the history of the personal equation and on the significance of Bessel's findings. Whereas the former has to be read as the history of a rather particular reaction to the phenomenon of constant differences, the latter is connected with a rather fundamental transition in the epistemology of the observer.