Decembeb 24, 1909] 



SCIENCE 



919 



the subject of dynamics clear and interesting 

 to the student, but to muddle it as much as 

 possible with " poundals," " gee pounds," 

 dynes, etc., and with such statements as 

 "force is the time-rate of acceleration," etc. 

 When the student gets into college he has to 

 forget much that he has been trying to learn 

 before he can get the clear concepts of dy- 

 namics that are necessary to further progress 

 in the subject. 



I have taught elementary djiiamics to some 

 high school students who were floundering 

 with the mysteries of the text-book, and have 

 also taught it to college students who com- 

 bined a parrot-like memory of the words of 

 the book they had used with total inability to 

 make intelligent use of first principles. It 

 may be of interest to some readers to have a 

 short syllabus of my method of beginning the 

 subject. Here it is: 



Matter. — A stone is suspended by an elastic 

 cord from a nail driven into a projecting shelf. 

 The stone is a piece of matter. Define matter. 

 Quantity of matter, determined by measuring 

 (bulk or volume), or by weighing (weight). 

 Bulk is inconstant and inexact, varying with 

 temperature, porosity, etc. Weight (deter- 

 mined by weighing on an even balance scale) 

 is exact and constant. The weight of the 

 stone is W pounds. The unit of weight is the 

 pound. The standard pound is kept in Lon- 

 don and copies are made of it. 



Force.— The cord is stretched when the 

 stone is hung on it. Measure the stretch per 

 foot of length. Why is the cord stretched by 

 the stone? Attraction of the earth's gravita- 

 tion. But the cord may be stretched by pull- 

 ing it between the two hands horizontally. 

 Also the cord with the stone or weight hung 

 from it will return to its unstretched length 

 if the stone be pushed upwards by the hand 

 through a distance equal to the stretch. The 

 pull of the earth upon the stone (gravitation), 

 the opposite pull of the elastic cord on the 

 stone, the pull of the hands, the push upwards 

 by the hand, each is called by the name force. 

 Force is defined as a pull or a push, something 

 that causes or tends to cause either motion, or 

 a change in the velocity or direction of motion. 



As the weight of a body (quantity of matter) 

 is stated in pounds, so the amount of a force 

 is also stated in pounds, a pound of force 

 being defined as equal to the force with which 

 the earth's gravitation attracts a one-pound 

 weight. Force is generally represented by F. 

 The force of the earth's gravitation acting on 

 the stone whose weight is W pounds, is also 

 W pounds, or F =: ^Yj' Force may be meas- 

 ured or weighed by a spring balance graduated 

 in pounds, or by counterpoising it with 

 weighted levers (illustration, the lever safety 

 valve), or in other ways. This force varies 

 somewhat with the latitude of the place, being 

 about 3^000 Psrt greater at London than at 

 Philadelphia, but in ordinary and elementary 

 problems relating to force, this difference is 

 neglected. In advanced studies it will be 

 considered. 



We have thus far considered two different 

 things, matter and force and the method of 

 determining the quantity of each; W and F. 



Space, Time. — Now let the cord be suddenly 

 detached from the stone. The stone falls to 

 the ground. It traverses a certain distance, 

 which we call space, B, measured in feet, 

 during a certain time, T, in seconds. We now 

 have all four of the elements, or concepts, of 

 dynamics, matter, force, space, time, repre- 

 sented by W, F, 8, T. The whole science of 

 dynamics is built on these four elements, and 

 it may be defined as the relations existing 

 between them when force acts on matter 

 through space and in time. 



Velocity, etc., of Falling Bodies. — The sim- 

 plest case of the relation of these elements is 

 that of a falling body, when the force acting 

 in pounds is numerically equal to the pounds 

 weight, or quantity of matter W. By experi- 

 ment it has been found that when a body falls 

 freely in air 



for seconds T = 1 2 .3 4 5 



It will fall in each of the several 



seconds 10. 1 ft. X 1 3 .5 7 9 



And the total fall at the end of 



each second is S = 16.1 ft. X 1 4 9 10 25 

 ^ The term " weight " is correctly used both as 



a measure of a quantity of matter and as a meas- 



ure of the force with which that quantity would 



be attracted by the earth at London. 



