426 



SCIENCE 



[N. S. Vol. XLI. No. 1055 



useful. It is well not to give the student too 

 many of them or he will become confused. 



Here are some conclusions that may be de- 

 rived from the equations, (1) and (2). 



From (1), let F=W, the case of a body 

 falling at latitude 45° at the sea level; then 

 V = gT. If T also = 1, then V = g, that is 

 the velocity at the end of 1 second is g. 



In the equation V = gT substitute for T its 

 value 28 /V and we have V = 2gS/V, whence 

 V^^igS. In the case of falling bodies, the 

 height of fall H is usually substituted for 8, 

 and we obtain Y = \/'iglI (3). 



Equation (2) with i^ = "R^ gives Y = IgT"^. 



From (1), by transposition we may obtain 

 FT=Yf y^Y/g (4). The product ¥T is 

 sometimes called impulse, and to the expression 

 TF X T^/ff is given the term momentum. It 

 is usually written Y^ /gY , but there is no rea- 

 son why, except that it is customary, and it 

 has been found convenient to use the letter M. 

 instead of Yf /g, so that the equation becomes 

 FT = MY (5) 



Impulse = Momentum 



In (4) we may substitute for T its value in 

 terms of 8 and Y above given, viz., T^i8/Y 

 and obtain ViS/Y = MY; whence F8 = iMY^ 

 (6). The product F8 is called work, and the 

 expression iMY^ kinetic energy, whence work 

 expended = kinetic energy. 



Acceleration. — The quotient V/T is called 

 the acceleration. It may be defined at the rate 

 of increase of velocity, the word rate, unless 

 otherwise stated, always meaning the rate with 

 respect to time, or " time-rate." In the prob- 

 lem under consideration, the action of a force 

 in a body free to move, with no retardation by 

 friction, the acceleration is a constant, 

 Y/T=.A. The quantity g is commonly called 

 the acceleration due to gravity, but it also 

 may be considered either as an abstract figure, 

 the constant g in equation (1), or as the 

 velocity acquired at the end of 1 second by a 

 falling body, or as the distance a body would 

 travel in 1 second at that same velocity if the 

 force ceased to act and the velocity remained 

 constant. 



Equation (6) then may be written 



F = MA (Y) 



Force = M times the acceleration. 

 If a given particle [body] is acted on at two 

 different times by two forces F and F', and if A 

 and A' are the corresponding accelerations, then 

 F^MA 

 ff>^MA' ""^^"""^ F/F' = A/A'. (8) 



Equation (Y) is called the fundamental 

 equation by Professor Hoskins, while equation 

 (8) is called fundamental by Professor Hunt- 

 ington, but it is shown above that they are 

 derived from the more fundamental equation 

 Y=.FTg/W. 



8ummary. — Take equation (1), Y = FTg/'W 

 (1). Substitute 28 /T for Y, 8 = FT^g/2W 

 (2). 



Take F=W, then 8^igT^ 



and Y = \/2gH (3) 

 From (1) by transposition FT=WY/g (4) 



Substitute M for W/g, FT = MY (5). 

 In (5) substitute 28 /Y for T, 



F8 = iMY^ (6) 



In (5) substitute A for Y/T, F = MA (Y) 

 Apply (Y) to the case of two forces acting 

 at diiferent times on the same body 



F/F' = A/A' (8) 



In this treatment the ambiguous words 

 " weight " and " mass " have purposely been 

 omitted. 



If there is any easier way of " making the 

 student understand the effect which a force 

 produces when it acts on a material particle " 

 than to have him study the above discussion 

 and solve examples by its aid, it is very im- 

 portant that it should be found and incor- 

 porated in the text-books. 



Wm. Kent 



a course in agriculture for non-technical 

 colleges 

 That there is an interest in agriculture as 

 a subject of study in colleges or higher insti- 

 tutions in addition to that met by the state 

 agricultural colleges, is manifested by the 

 introduction a few years ago into the curric- 

 ulum, in certain institutions (e. g., Syracuse 

 and Miami Universities) of several subjects 

 associated with the work of the land-grant 

 colleges. Further evidence is shown in the 



