7 I ANALYTIC QSOMEll: Y [Cii l\ 



these was attained. In this problem the curve gives no 

 new information, hut it presents in u much more concise 

 and forcible form the information given by the tabulated 

 numbers. 



Again, if the distances passed over by a train in successive 

 minuU's during the run between two stations are taken as 

 OK li nates, and the corresponding number of minutes since 

 starting, as abscissas, a smooth curve drawn through the 

 points so determined will show at a glance, to an experi- 

 enced eye, where and when additional steam was turned int<> 

 the cylinders, brakes applied, heavy grades encountered, etc., 

 etc. 



In all such cases the coordinates of the points are taken to 

 represent the numerical values of related quantities, such as 

 time, length, weight, velocity, current, temperature, etc., and 

 the curve through the points so determined usually gives, to 

 an experienced person, all the information concerning th< 

 relations involved that is of practical importance. It is 

 in the study of such curves that much of the value of train- 

 ing in analytic geometry becomes apparent to the physicist 

 and the engineer. The student should early learn to trans- 

 late physical laws into graphic forms, and he should give 

 careful attention to the interpretation of all changes of form, 

 intercepts, intersections, etc., of such cui 



EXERCISES 



1. In simple interest if p= principal, /= time, r=rate, and a = amount, 

 then a -p (1 + rt). If now particular numerical values are given to 

 p and r. and if the values of the variable a be taken as ordinates, and 

 the corresponding values of t as abscissas, then the locus of this equa- 

 Uoii may be drawn. Draw this locus. What lim- in the figure repre- 

 sents the principal? What feature of the curve depends upon the rate 

 per cent? Interpret the intercepts on the axes. 



