July 7, 1916] 



SCIENCE 



21 



size is twice as great when it pulls on two 

 exactly like objects together as it is when it 

 pulls on only one of them; and conversely we 

 use this pull to measure the elastic force of a 

 spring, the relative magnitudes of different 

 bodies, etc. This notion, that the magnitude 

 of earth pull is proportional to the number of 

 otherwise equal things on which it acts, is 

 fundamental, and so familiar as to seem 

 axiomatic; it is instinctive, as E. Mach would 

 say. 



The study of the downward motion of bodies 

 affected by their own weight and only slightly 

 by friction was a lifelong interest of Galileo. 

 Directly or indirectly he showed two things; 

 that they fall equal distances in equal times, 

 and that unequal distances of fall are pro- 

 portional to the squares of the times of fall. 

 Differentiation of the latter showed that the 

 gravitational acceleration is constant during 

 the time of fall ; the former showed it to be the 

 same for all things, independently of their 

 weight or material. 



The last conclusion leads to an appreciation 

 of another difficulty in the study of mechanics, 

 if we take into account a law of psychology, 

 well stated in the following quotation from 

 William James: 



. . . any number of impressions, from any number 

 of sensory sources, falling simultaneously on a 

 mind which has not yet experienced them sepa- 

 rately, will yield a single undivided object to that 

 mind. The law is that all things fuse that cau 

 fuse, and that nothing separates except what 

 must. 



The singling out of elements in a compound. It 

 is safe to lay down as a fundamental principle that 

 any total impression made on the mind must be un- 

 analyzable so long as its elements have never been 

 experienced apart or in other combinations else- 

 where. The components of an absolutely change- 

 less group of not-elsewhere-occurring attributes 

 could never be discriminated. If all cold things 

 were wet, and all wet things cold, if all hard 

 things pricked our skin, and no other things did 

 so: is it likely that we should discriminate be- 

 tween coldness and wetness, and hardness and 

 pungency, respectively? If all liquids were trans- 

 parent and no non-liquid were transparent, it 

 would be long before we had separate names for 

 liquidity and transparency. If heat were a func- 



tion of position above the earth 's surface, so that 

 the higher a thing was the hotter it became, one 

 word would serve for hot and high. We have, in 

 fact, a number of sensations whose concomitants 

 are invariably the same, and we find it accord- 

 ingly impossible to analyze them out of the totals 

 in which they are found. 



Now to lift a stone vertically we have to 

 exert an effort, neutralizing the earth's pull 

 upon it, its weight. To throw the same stone 

 horizontally, to accelerate it, we have also to 

 exert effort ; and the harder the stone is to lift, 

 the harder it is to throw. (If we refine this 

 crude observation by experiment, we find an 

 exact proportionality between the weights of 

 objects and the efforts or forces required to 

 accelerate them equally.) Hastily general- 

 izing, but most naturally, we say that stones 

 are hard to throw, gates hard to swing, not in 

 proportion as, but "because they are heavy. To 

 ordinary observation the accelerating and the 

 gravitational efforts always increase and de- 

 crease exactly together; they do not tend to 

 become discriminated, we do not abstract them 

 separately. 



To exact observation, however, a difference 

 does show itself. The same stone weighed in 

 a spring balance would elongate the spring less 

 in low latitudes than in high (we tell our 

 classes this; did any one ever try it?). The 

 same pendulum vibrates more slowly in low 

 latitudes than in high, as Richer found in 

 1672-3. We can imagine a man lifting and 

 throwing a ball at the bottom and again at the 

 top of a tower four thousand miles high, ob- 

 serving a notable change in the weight of the 

 ball and yet none at all in the difficulty of 

 throwing it. But such observations under ter- 

 restrial conditions have to be accurate to less 

 than ^ per cent., far more accurate than the 

 unaided sense memory can be. To the average 

 man a heavy thing is also hard to throw, be- 

 cause it is heavy; a fact which stands as a 

 formidable obstacle to a clear grasp on the idea 

 of mass ; to most students mass and weight are 

 forever identical, except that the book says to 

 divide weight by g to get mass. 



In an old copy of Wells' " Natural Philos- 

 ophy " I find the following problem and an- 

 swer, which may serve as an illustration : 



