226.] CONSTRAINTS. 



Each member being a determinant of the second order, we find 

 by squaring and adding the three equations, 



ds .as ds 



The reaction N can now be eliminated between (15) and (16), 

 and we obtain the single condition of equilibrium independent 

 of the reaction : 



_ _ 

 ds ds ds Vi -fyu, 2 



(17) 



The differential coefficients dx/ds, dy/ds, dz/ds must satisfy 

 the differential equations of the curve (10), viz. : 



dx . , dy . , dz 



d-s + *'i + *'^ =0 > 



dx . , dy . , dz 

 - 



If the values of dx/ds, dy/ds, dz/ds be determined from the 

 last three equations and substituted into the relation 



the equation of a surface will result, which cuts out, on the curve 

 (10), the limits between which equilibrium is possible. 



226. Rigid Body with a Fixed Point. A body that is free to 

 turn about a fixed point A can be regarded as free if the reaction 

 A of this point be introduced and combined with the other 

 forces acting on the body. 



Let A x , A yJ A g be the components of A ; then, taking the fixed 

 point A as origin, the six equations of equilibrium (Art. 213) are 



