It is quite to be expected that the earliest experimenters in any branch of science will overlook errors which afterwards become most apparent. The Arabian astronomers determined the meridian by taking the middle point between the places of the sun when at equal altitudes on the same day. They overlooked the fact that the sun has its own motion in the time between the observations. Newton thought that the mutual disturbances of the planets might be disregarded, excepting perhaps the effect of the mutual attraction of the greater planets, Jupiter and Saturn, near their conjunction.9 The expansion of quicksilver was long used as the measure of temperature, no clear idea being possessed of temperature apart from some of its more obvious effects. Rumford, in the first experiment leading to a determination of the mechanical equivalent of heat, disregarded the heat absorbed by the apparatus, otherwise he would, in Dr. Joule’s opinion, have come nearly to the correct result.
It is surprising to learn the number of causes of error which enter into the simplest experiment, when we strive to attain rigid accuracy. We cannot accurately perform the simple experiment of compressing gas in a bent tube by a column of mercury, in order to test the truth of Boyle’s Law, without paying regard to—(1) the variations of atmospheric pressure, which are communicated to the gas through the mercury; (2) the compressibility of mercury, which causes the column of mercury to vary in density; (3) the temperature of the mercury throughout the column; (4) the temperature of the gas, which is with difficulty maintained invariable; (5) the expansion of the glass tube containing the gas. Although Regnault took all these circumstances into account in his examination of the law,10 there is no reason to suppose that he exhausted the sources of inaccuracy.
The early investigations concerning the nature of waves in elastic media proceeded upon the assumption that waves of different lengths would travel with equal speed. Newton’s theory of sound led him to this conclusion, and observation (p. 295) had verified the inference. When the undulatory theory came to be applied at the commencement of this century to explain the phenomena of light, a great difficulty was encountered. The angle at which a ray of light is refracted in entering a denser medium depends, according to that theory, on the velocity with which the wave travels, so that if all waves of light were to travel with equal velocity in the same medium, the dispersion of mixed light by the prism and the production of the spectrum could not take place. Some most striking phenomena were thus in direct conflict with the theory. Cauchy first pointed out the explanation, namely, that all previous investigators had made an arbitrary assumption for the sake of simplifying the calculations. They had assumed that the particles of the vibrating medium are so close together that the intervals are inconsiderable compared with the length of the wave. This hypothesis happened to be approximately true in the case of air, so that no error was discovered in experiments on sound. Had it not been so, the earlier analysts would probably have failed to give any solution, and the progress of the subject might have been retarded. Cauchy was able to make a new approximation under the more difficult supposition, that the particles of the vibrating medium are situated at considerable distances, and act and react upon the neighbouring particles by attractive and repulsive forces. To calculate the rate of propagation of disturbance in such a medium is a work of excessive difficulty. The complete solution of the problem appears indeed to be beyond human power, so that we must be content, as in the case of the planetary motions, to look forward to successive approximations. All that Cauchy could do was to show that certain quantities, neglected in previous theories, became of considerable amount under the new conditions of the problem, so that there will exist a relation between the length of the wave, and the velocity at which it travels. To remove, then, the difficulties in the way of the undulatory theory of light, a new approach to probable conditions was needed.11