Mr. C. W. Merrifield on the Problem of Rectilinear Motion. 421 



The scale of the ordinates of this line, and of the two curves, 

 must then be made to correspond, and also to fall within conve- 

 nient limits. The ordinates of the curves must then be set off 

 as additive or subtractive to those of the vacuum-line. 



We have hitherto used v as the independent variable. We 

 have now to make t the independent variable in order to inte- 



. ds 

 grate j- ... 



In the accompanying diagram, let 0, at the left-hand lower 

 corner of the sheet of squares, represent the origin, point of rest, 

 or highest point, in the case of a projectile thrown upwards, and 

 let v be reckoned horizontally towards the right. Then we may 



Spaces (cut 

 ' II 



!■■■■■■■■■ 



® H 



1 1 ■■ m 



w'mummwmm 



I 1R iSIB9IH 



ves OU , OUx, 0U 2 ). 



■■■■eppHBiRi 



RBiiiiliiiii 

 BililBEB 



o 



(point of rest). 



Velocities (curves OW , 0W 1( OWo). V 



call the line OW the vacuum-line, the curve W x that belonging 

 to the rise, and 0W 2 that belonging to the fall. 



We must now take the axis of t (the left-hand side of the 

 sheet) as the line of abscissae, and we must integrate all the three 

 curves from upwards, taking v as the ordinate, instead of, as 

 before, the abscissa. We use the same rule as before, dividing 

 any selected value of t into a number of equidistant parts, to suit 



Phil. Mag. S. 4. Vol. 35. No. 239. June 1868. 2 F 



