.1 \ .I 



<.r<>\n 1 i;Y 



[('n. I. 



and 



tlial is, 



Again, 



i.e., 



also 



and 



tem, the pole ami origin therefore 

 being coincident, then simple rela- 

 tions exist between the two set 



dinatefl for any point. For. since 



Z OMM' = 90 and Z OM'1>= !U, 

 therefore OM = OM' cos0 

 = OP sin <f> cos 0. 

 OM'ain0 = 



[1] 



P sine si 



pros4>. 



[2] 



+ y* + z*. 



The above relations give formulas for transformation 

 from the one coordinate system to the other. 



203. Direction angles : direction cosines. 

 method of fixing a point in space 

 is a coinhination of the two 

 methods already considered. 

 The axes of reference are chosen 

 as in rectangular oodrdinates, 

 and any point P of space is fixed 

 liy its distance from the origin, 

 called the radius vector, and the 

 angles , /9, 7, which this radius 



A thin I useful 







Fio. 143 



