SCIENCE IN THE LAST HALF CENTURY. 67 



that those who refuse to go beyond fact rarely get as far as fact ; and 

 any one who has studied tlio history of science knows that almost every 

 great step therein has been made by the " anticipation of nature," that 

 is, b3' the invention of hypotheses, which though verifiable, often had 

 very little foundation to start with; and not unfrequently, in spite of a 

 long career of usefulness, turned out to be wholly erroneous in the 

 long run. 



HYPOTHESES FRUITFUL EVEN WHEN ERRONEOUS. 



The geocentric system of astronomy, with its eccentrics and its epi- 

 cycles, was an hypothesis utterly at variance with fact, which never- 

 theless did great things for the advancement of astronomical knowledge. 

 Kepler was the wildest of guessers. Newton's corpuscular theory of 

 light was of much temporary use in optics, though nobody now believes 

 in it; and the uudulatory theory, which has superseded the corpus- 

 cular theory, and has proved one of the most fertile of instruments of 

 research, is based on the hypothesis of the existence of an " aether," the 

 properties of which are defined in propositions, some of which, to ordi- 

 nary apprehension, seem physical antinomies. 



It sounds paradoxical to say that the attainment of scientific truth 

 has been effected, to a great extent, by the help of scientific errors. 

 But the subject-matter of physical science is furnished by observation, 

 which can not extend beyond the limits of our faculties; while, even 

 within those limits, we can not be certain that any observation is abso- 

 lutely exact and exhaustive. Hence it follows that any given generali- 

 zation from observation may be true, within the limits of our powers of 

 observation at a given time, and yet turn out to be untrue, when those 

 powers of observation are directly or indirectly enlarged. Or, to put 

 the matter in another way, a doctrine which is untrue absolutely, may 

 to a very great extent be susceptible of an interpretation in accordance 

 with the truth. At a certain period in the history of astronomical science 

 the assumption that the planets move in circles was true enough to 

 serve t he purpose of correlating such observations as were then possible ; 

 after Kepler, the assumption that they move in ellipses became true 

 enough in regard to the state of observational astronomy at that time. 

 We say still that the orbits of the planets are ellipses, because, for all 

 ordinary purposes, that is a sufficiently near approximation to the truth ; 

 but, as a matter of fact, the center of gravity of a planet describes 

 neither an ellipse nor any other simple curve, but an immensely compli- 

 cated undulating line. It may fairly be doubted whether any generali- 

 zation, or hypothesis, based upon physical data is absolutely true, in 

 the sense that a mathematical proposition is so ; but, if its errors can 

 become apparent only outside the limits of practicable observation, it 

 may be just as usefully adopted for one of the symbols of that algebra 

 by which we interpret nature, as if it were absolutely true. 



The development of every branch of physical knowledge presents 



