[ 420 ] 



XLVIII. Example of the Application of a Graphical Method to 

 the Problem of Rectilinear Motion in a Homogeneous Resisting 

 Medium. By C. W. Meiuufield, F.R.S* 



npHE equation of the motion is in general 



dt=^ v) > 



which, being integrated, leads to 



* = I»-F(» ); 



and this equation has to be solved for v, which is only possible 

 in a few very limited cases. In all other cases it is necessary to 

 have recourse to very tedious arithmetical applications of the 

 method of quadratures, or to graphical methods. The object of 

 this paper is to give an example of the latter. 



In the case which actually occurred, the problem presented 

 itself under the form 



k being a known coefficient of resistance. The process adopted 

 was to tabulate the functions 



1 



(1) 



(2) 



g g + kv 3 

 and 



_1 1 



g-kv 3 g 



from # = (that is to say, taking the point of rest for origin) for 

 equidistant values of v. The tabulated values of each were then 

 laid off on a sheet of squares as ordinates of a curve, which was 

 then integrated, so as to give a new curve, by the following rule. 

 The tabulated ordinates being a, b, c, . . . &c, those of the new 

 curve will be 



±a + b + ±c, 



±a + b + c + ^d, kc. 



These are very quickly obtained by measuring with a strip of 

 paper. 



The integrated curve due to the motion in vacuo is easily seen 



to be a right line making an angle = tan -1 - with the axis of v. 



9 



* Communicated bv the Author. 



