48-: IIIK KtjUATlOS OF A LOCUS T.; 



40. The use of curves in applied mathematics.* In Chap- 



Ill it \\.i> H|,,,\\M ih.it whenever the relation between 

 variables, whoee values depend upon each other, can be defi- 

 .it.-.l. i.e., when the variables can be connected by 

 an venation, then the geom< representation of 



tin- 11 is given by means of a curve. Such a cum.- 



n gives at a glance, information which would otherwise 

 considerable computation to secure; and in many 

 cases it brings out facts of peculiar interest ami importance 

 \\hi.h :..-!.! otherwise escape notice. 



use of graphir methods in th- study of physics and 



engineering, as well as i ;< s au<l m.i:. branches 



libation, is already extensive and is rapidly increas- 



I'nder tin- name "graphs mrthods" there arc- in- 



1 uded, however, not only such examples as those already 



the e<p -\\n\f the variables is known, 



lut also those where no such equation can be found ; in 



cases the curves constitute almost the only prac- 



1 way of studying the relations involved. 



As a simple example of this kind, suppose the temperature 



pati.nt t<* Inaccurately observed at intervals of one hour; 



the nuinliers representing the hours, / , 1. J. 3, are 



taken as abscissas, and th<> corresponding numerical values of 



l-raturrs IK- taken as ordinates, then a smooth mrvf 



.vn through the points so determined will express graphs- 



\ the \ariati. .n ,,f th- trnijH-rature of t: ..-lit with 



A ill also show to the physician what 



was the greatest and least temperature during the inter- 



. as well as the time when each ot 



ror most of the suggestions in this article, and ID the 

 It, the authora ure indebted to Mr. J. 3. Shearer of the 

 vice of Cornell University. 



