20 



SCIENCE 



[N. S. Vol. XLIV. No. 1123 



dictum about the necessity of force for the 

 maintenance of motion is thus a consequence 

 of common experience, a deduction of " com- 

 mon sense," which is the result of common ex- 

 perience. And while the common experience 

 of boys and young men is changeable from age 

 to age and different from one culture level to 

 another, while men in the age of stone clubs 

 or in the days of the stage coaeh had a range of 

 common experience vastly different from what 

 they have in an era of electricity and gasolene, 

 nevertheless this element of terrestrial experi- 

 ence persists in them all — to maintain motion 

 force must be continuously exerted ; force lack- 

 ing, rest supervenes. 



Galileo's principle of inertia, then, Newton's 

 first law of motion, is not a deduction of com- 

 mon sense, because it contradicts common ex- 

 perience. Only uncommon experience, inter- 

 preted by an uncommon mind, could arrive at 

 it ; and it is a fact that the world waited many 

 ages for a genius to arise, fly in the face of 

 common terrestrial experience, announce that 

 the immediate consequence of force is accelera- 

 tion, and interpret the inevitable extinction of 

 unsupported terrestrial motions by the hypoth- 

 esis of a force of friction, always opposing 

 the existing motion and producing a negative 

 acceleration. And the clear grasp of the 

 inertia principle could only follow the study 

 of a frictionless system. 



Here we have the first difficulty of kinetics; 

 its first law contradicts the student's common 

 sense and all his ingrained mechanical experi- 

 ence. I doubt that many students, seeing the 

 experiment for coefficient of friction, with 

 horizontal slab, pulley and cord, actually inter- 

 pret the slow uniform motion of the block in 

 terms of two equal and opposed horizontal 

 forces, producing each its own acceleration. It 

 seems too far fetched; rather say, if you stop 

 pulling the slab stops — and have done with it. 

 And so with all the movements of wind and 

 water; they go on because somehow they are 

 driven. And so also Kepler interpreted the 

 motion of the planet Mars in its orbit as due to 

 a forward tangential force arising no doubt in 

 the sun; and the schoolmen said that bodies 

 fall with speeds proportional to their weights 



— which is roughly true for snowflakes and 

 raindrops. 



Change of motion, quantitatively called ac- 

 celeration, is an idea rather remote from com- 

 mon experience. Every player of games is 

 familiar with it in a crude way, but that it is a 

 measurable quantity, or worth measuring, 

 never entered any head before Galileo's. This 

 is not at all remarkable, when we consider that 

 speed is not given us by direct measurement, 

 but only by simultaneous direct measurements 

 of distance and time; much less are we given 

 the rate of change of speed. The beginner has 

 no real experience with acceleration as a meas- 

 urable quantity; it is the rate of change of a 

 rate of change, and too abstract for most peo- 

 ple. It does have a connection with effort; to 

 throw a ball fast is harder than to throw it 

 slow; but I doubt if the average beginner ever 

 has gone beyond that — and certainly many a 

 student of- calculus never connects this rough 

 experience with d 2 x/dt 2 . In fact, we can not 

 get differential expressions by measurement; 

 Kepler's planetary laws and Galileo's laws of 

 falling bodies are either integral expressions 

 representing their tables of length 1 and time 

 measurements, or are deduced from these inte- 

 gral expressions. Beginners do not of their 

 own accord take the trouble to construct such 

 tabulations or to differentiate twice the result- 

 ing integral expressions; in fact, few can do 

 this, or at first realize what it all means when 

 they are made to do it. 



Our most continuous effort is to keep our- 

 selves or other objects off the ground ; the next 

 most familiar, to set objects in motion upward, 

 a motion which, unless some obstacle prevents, 

 is sooner or later reversed into a motion down- 

 ward. We say, as if an antagonistic effort were 

 opposing ours, that the earth exerts a down- 

 ward force upon us and all things near it ; it is 

 able to change their forms or to set them in 

 motion downward. 



While our sensations of effort are only quali- 

 tative, telling us of more and less, but not of 

 how much, we assign measure to this earth 

 effort, or force, or weight, by saying that its 



i Angles are measured by ares of graduated cir- 



