THE UNDERLYING FACTS OF SCIENCE 565 



sible because it is infinitely large or infinitely small ; no time must seem 

 impossible on account of its infinite length or of its infinite shortness; 

 the grains of sand of the ocean bed and the bubble capacity of a million 

 tons of soap are crude and inadequate figures of comparison. "We must 

 remember that in extra-mathematical investigation we judge everything 

 by human standards, but that in reality anything which can be ex- 

 pressed as a mathematical formula is as simple in nature and in opera- 

 tion as the facts of every-day life. If we do not get away from the 

 habit of setting limits to every conception — limits based upon our own 

 surroundings — we shall find our speculations conflicting with science 

 at every turn. 



The knowledge of principles clears the fog in which the speculative 

 mind wanders in search of resting spaces, and the secret of clear con- 

 ception lies in the ability of ridding oneself of pre-conceptions. If in 

 attempting to conceive the speed of propagation of light we bring to 

 mind the speed of a railway train or of a rifle bullet, we set a limit to 

 our mental grasp, just as a student who can not assimilate an alge- 

 braical formula without an arithmetical parallel shuts himself out of 

 the higher mathematics. 



The greatest limitation from which our forefathers suffered was 

 the rushing to conclusions from analogies, and the shallowness of the 

 results can not be better illustrated than by quoting from a book called 

 " The Art of Metals," published in the year 1640, and at one time con- 

 sidered an authority in matters metallurgical. Referring to blue cop- 

 peras, or sulphate of copper, the learned author writes: 



It is admirable to see its effect in Aqua-Fortis, (in which all Mettals like 

 Salt dissolve and are turned into water) and an occular demonstration of th« 

 possibility of the transmutations of Mettals one into another, for with Copperas 

 dissolved in Aqua-Fortis, (without any other artifice) Iron, Lead and Tin 

 become fine Copper, and Silver will lose of its value, and be turned into 

 Copper also. 



When discussing the principles of physical science we are confronted 

 by a condition which continually vitiates clearness of exposition. Con- 

 ceptions of energy and of matter are now becoming more and more con- 

 vergent and we find ourselves in the dilemma of having at times to 

 think of matter as energy and at the same time to describe energy in 

 material terms. The world of science is becoming daily more accus- 

 tomed to the convertibility of the terms energy and matter ; but there is 

 a natural tendency to incredulity, for, as some one recently stated : 



In the estimation of material beings matter must necessarily assume a 

 position of special importance; but nature may not perhaps regard it other- 

 wise than as one of numerous forms of force, between which (as Newton wrote) 

 it " delights in effecting transmutations." 



We shall return to this subject later. 



There exists a public impression that the dreams of the old alche- 



