Apeil 30j 1915] 



SCIENCE 



647 



course. So it is natural to assume that the 

 inertia of any body is proportional to the force 

 (F) required to give it unit acceleration, or 

 since acceleration is proportional to force and 

 since the acceleration produced by unit force 

 would be 1/F, this is equivalent to assuming 

 that inertia is inversely proportional to the 

 acceleration produced by unit force. 



12. Inertia of Different Volumes of Iron. — 

 (1) Two carriages carrying two or three equal 

 volumes of iron, accelerated toward each other 

 by a stretched rubber band. 



(2) Atwood's machiae, same force, different 

 volumes of iron. 



Conclusion: Acceleration is inversely pro- 

 portional to the volume of iron for the same 

 force; therefore inertia is directly propor- 

 tional to the volume of iron or to the amount 

 of iron. 



13. Inertia of Equal Volumes of Various 

 Substances. — Assume that two bodies have the 

 same inertia when the same force gives them 

 the same acceleration. Using the same appa- 

 ratus as in §12, we find that the ratio of the 

 inertias or masses of any two bodies is equal 

 to the ratio of their weights (at a given point 

 on the earth). 



14. Units of Mass. — ^Kilogram, gm., pound. 



15. Falling Bodies. — Since the force acting 

 is proportional to the mass of each body, the 

 acceleration must be the same for all. This 

 conclusion agrees with experiment. 



G. Fundamental Law of Mechanics 



16. Summary: 



With same mass : - a^-.a^^F^: F,. 



With same force : a^:a^=^m^: m^. 



With same acceleration : m,^:m^^F^: F,. 

 Combining these : m^a^ : mji^ = F^ : F^. 



17. Fundamental Law. — When any body is 

 acted on by an unbalanced force, the accelera- 

 tion produced is in the direction of the force, 

 is proportional to the force and is inversely 

 proportional to the inertia of the body acted 

 upon. 



18. Gravitational Units of Force. — Kg. wt., 

 lb. wt. The units we have been using. If 

 force is measured in kg. wt., mass in kg., and 

 acceleration in cm, per sec. per sec. then 



a ==■ gF/m, 



where g is the acceleration of gravity. The 

 same equation holds for lbs. wt. and lbs. and ft. 

 per sec. per sec. Variation of g with distance 

 from center of earth. Units not absolute. 



19. Absolute Units of Force. — Dyne, poundal. 

 Independent of gravity. Simpler equation 

 F=^ma. 



20. Application to Various Special Gases. — 

 Atwood's machine, inclined plane, etc. 



21. Definition and Discussion of Momentum, 

 Impulse, Work and Energy. 



I shall be very grateful for any suggestions 

 in regard to the above outline, especially from 

 those who are willing to concede that a de- 

 parture from our present dogmatic method of 

 presentation is advisable. 



Gordon S. Fuloher 

 Wisconsin Univeesity 

 April 1, 1915 



GET THE UNITS EIGHT 



Professor A. Gray iu a recent lecture on 

 Kelvin's work in gyrostatics, says: 



It is always a good thing to get down to num- 

 bers and it is a most healthful mental diseiplino 

 to be forced to get the units right. 



The force of this remark is apparent in fol- 

 lowing the discussion in Science relative to 

 the best expression of the fundamental equa- 

 tion in mechanics. Professor Kent criticizes 

 Professors Huntington and Hoskins, objecting 

 to the form of the equation F = ma. He 

 rightly says: 



The equation is not true in the ordinary Eng- 

 lish system (foot-pound-second) until it is hybrid- 

 ized by valuing either ^ or m in some other unit 

 than pounds (poundal or gee-pound) or a in grav- 

 itals (instead of feet) per second per second 

 (1 gravital ^32.174 feet) or else the letter m 

 is explained as not being quantity of matter in 

 pounds but only the quotient or ratio W/g. 

 Neither is it true in the metric kilogram-meter- 

 second system. ... It is of course true in the dyne- 

 centimeter-gram-second system but this system is 

 only used in higher physical theory and it should 

 not be inflicted on joung students.i 



1 Science, Vol. XLI., No. 1055, p. 424. 



