No investigator did more to popularize the idealization of instruments and experimental conditions than Bessel. In addition to numerous applications of and elaborations upon the method of least squares, Bessel contributed significantly to the theory of astronomical and related instruments. Wanting to assemble a fixed star catalogue based on James Bradley's observations from 1750-1762, Bessel found he needed an alternative theory of refraction in order to refine Bradley's data. For this he developed theories of the thermometer and the barometer, as well as of their errors. Later he applied the same method of analysis to other physical instruments, and in 1826 produced a theory for the calibration of a thermometer of imperfect cylindrical shape. Combined with the method of least squares and the personal equation, Bessel's theory of instruments convinced him that errors could not be eliminated from an experiment, but could at best be determined quantitatively. Good measurements, he argued, accounted for instrumental errors in the result.

A paradigmatic experiment exemplifying Bessel's investigative style and having lasting influence throughout the century upon those who sought to idealize instruments was his seconds pendulum investigation, begun in 1823 and completed in early 1828. Constructed by the instrument-maker Johann Georg Repsold, Bessel's seconds pendulum was the focal point for a series of smaller investigations that identified and quantified the constant errors of the experiment, including the theory of the micrometer, chronometer, thermometer, and barometer. He developed a new method of coincidence observations (comparing the vibrations of two pendula) so that certain errors would cancel out. To Isaac Newton's hydrostatic correction for the pendulum's movement, Bessel added a hydrodynamic one, demonstrating that the pendulum carried air with it as it moved, adding to its weight and changing its center of gravity. His auxiliary investigations paid off. His determination of gravity had an accuracy greater than Newton’s (1/60,000 compared to l/1,000), and with the aid of his analytical determinations, he was able to measure 0.02 seconds, the smallest interval of rime then measurable. In the end Bessel's protocol transcended the material conditions of the instrument and its environment. "The idea" of his method, he claimed, was to design a protocol for which "the accuracy of the result is limited not by the apparatus, bur above all by the diligence one applies to the observations and to their repetition." Convinced that "too many instruments" were "just as detrimental as too few," Bessel was never convinced that the way to achieve more accurate results was by improving instruments. "The task of the present-day art of observation," he stated unequivocally, was "to eliminate the apparatus from the results." Bessel's seconds pendulum investigation became a model in the nineteenth century for experimental protocols aiming to use the method of least squares to reduce data.