OF PRESSURE AND EQUILIBRIUM. 103 



252, Corollary 2. For the equilibrium 

 of a point resting on a given surface, we may 

 either comprehend tlie reaction of the surface 

 among the forces S, or, with greater conve- 

 nience, call the direction of the reaction r, and 

 the force E, and we shall have xs^s-^Rdr=0. 



ic) 



253. Corollary 3. For a canal, or a 

 curved line, which may be considered as a 

 combination of two curved surfaces, the re- 

 action of the second surface being called R\ 

 and the perpendicular to it r', we have xs^s + 



mr + R^r' = 0. {d) 



Whatever the direction of the canal may be, its resist- 

 ance may be conceiv-ed to be the result of the reactions R 

 and R' of the two surfaces which determine its form, since 

 the resistance being perpendicular to the curve, it must be 

 in the same plane with the forces, which are perpendicular 

 to the surfaces, of which it is the intersection. 



254. Scholium 1. IfweTjb^pose the arbitrary varia- 

 tions S.r, hjy Sz, to take place in the direction of the surface 

 to which the body is confined, we shall have Zr—O, and the 

 equation l.S^szzO will still be true: but the variations of 5 

 must then be taken so as to be limited to the given surface 

 by means of its equations, and they cannot be all arbitrary. 

 In the same manner we may make Sr and §/ both vanish 

 when the motion is confined to a canal or a single curve, 

 but in that case any one of the variations of s will deter- 

 mine the other two. It is, however, more convenient to 



