32 OUTLINES OF NATURAL PHILOSOPHY. 



three axes ; p 9 /3', p" 9 fl'" 9 &c. the angles which they 

 make with another of the axes, and y, y', y", y'", 

 &c. the angle which they make with the third, 



F cos a + F' cos a' + F" cos a" + F'" cos a!" +, &c. = 

 F cos ft 4- F'cos /3' + F" cos ^s" + F"' cos /3'" +, &c. = 

 P cos y + F' cos y ' + E" cos 7" + F /x/ cos y*" +, & c . = 



When all the forces are in one plane, there are only 

 two axes, and the equations are therefore reduced to 

 the two first. Also as . is in this case the comple- 

 ment of a, cos /3 = sin a, and so of the rest ; there- 

 fore the equations are 



F cos a + F' cos of + F'' cos a" +, &c. = 

 .and F sin a + F' sin a' + F" sin a' +, &c. 



SECT. 



