126 PART II. SOME IMPORTANT METHODOLOGICAL TERMS. 



51. The case for measurement can be perhaps best stated 

 by allowing an old writer, the founder of methodology, one 

 who has been regarded as unfriendly to mathematics, to speak 

 (Bacon, Novum Organum, bk. 2, 44, 45, and 46): "The chief 

 cause of failure in operation (especially after natures have been 

 diligently investigated) is the ill determination and measurement 

 of the forces and actions of bodies. Now the forces and actions 

 of bodies are circumscribed and measured, either by distances of 

 space, or by moments of time, or by concentration of quantity, 

 or by predominance of virtue; and unless these four things 

 have been weH and carefully weighed, we shall have sciences, 

 fair perhaps in theory, but in practice inefficient." "The powers 

 and motions of things act and take effect at distances, not in- 

 definite or accidental, but finite and fixed ; so that to ascertain 

 and observe these distances in the investigation of the several 

 natures is of the greatest advantage. . . . But whether the 

 distances at which these powers act be great or small, it is 

 certain that they are all finite and fixed in the nature of things, 

 so that there is a certain limit never exceeded; and a limit 

 which depends either on the mass or quantity of matter in the 

 bodies acted on ; or on the strength or weakness of the powers 

 acting; or on the helps or hindrances presented by the media 

 in which they act; all which things should be observed and 

 brought to computation. Moreover, the measurements of violent 

 motions (as they are called), as of projectiles, guns, wheels, 

 and the like, since these also have manifestly their fixed limits, 

 should be observed and computed." "All these things with 

 their measures should in the investigation of nature be explored 

 and set down, either in their certitude, or by estimate, or by 

 comparison as the case will admit." "All motion or natural 

 action is performed in time; some more quickly, some more 

 slowly, but all in periods determined and fixed in the nature 

 of things. Even those actions which seem to be performed 

 suddenly and (as we say) in the twinkling of an eye, are found 

 to admit of degree in respect of duration. First, then, we see 

 that the revolutions of heavenly bodies are accomplished in 

 calculated times; as also the flux and reflux of the sea. The 

 motion of heavy bodies to the earth, and of light bodies towards 

 the heavens, is accomplished in definite periods, varying with 

 the bodies moved and the medium through which they move. 

 The sailing of ships, the movements of animals, the transmission 

 of missiles, are all performed likewise in times which admit (in 

 the aggregate) of measurement. As for heat, we see . boys in 

 winter time bathe their hands in flame without being burned, 

 and jugglers by nimble and equable movements turn vessels 

 full of wine or water upside down and then up again, without 

 spilling the liquid; and many other things of a similar kind. 

 The compressions also and expansions and eruptions of bodies 

 are performed, some more slowly, according to the nature of 



