TRANSACTIONS OP THE SECTIONS. 7 



Zdz + *dy + *dz = 0, whence ^ + X = 0, ^ + Y = 0, , + Z = 0; that is the 

 magnJude of The force may be arbitrary, but its .directum must be surf t AatX Y ,Z 

 Se negative, since X, ^, * are positive; whence it results, that the direction of the 

 force must be comprised within the angle of the negative coordinates. 

 If there are more than three conditions, " ( * ~ yj* " 8) combinations may he 



made by three, and 3 - M ^~ l) (n ~ ?) inequalities are obtained, some of which may 

 * Z . 3 



b ^ C nr P attmiri\nTknown demonstration, (I have transformed the demonstra- 

 tiono?CaudT2 well as that of Lagrange,) it may be proved that the condition 

 hat a forcTdol not tend to produce displacements, the ^^if^fj^f 

 axes are, for the- first point of the system, fx dy,dz for the ™™*>*?> z fj>j 



ds i & c is expressed by Xdx + Y dy + Z dz 4 X'da +} d V + \ az 



4 X»dV' 4 < 0, the conditions of the system must be of the form hdx 



4 B dy 4 C d z 4 A' dx' + > ; and by proceeding in the same manner, 



that for the point K u, u are found to have the same signs as d L, d M, dN 



. .for the possible displacements, and that the conditions of equilibrium are 



X4xA4i"A 1 4vA 2 4 = ° 



Y4aB4^Bi + »B 3 4 = ° 



Z4xC4^C,4xC 2 4 = ° 



X 1 + xA'4f«B'+ = °- 



The same is demonstrated for the flexible wire. There is still one observation to be 

 Ine same aemo ^, ^ ^ ^.^ rf ^ ^^ . m ^ case ^ t 



Y alone acts on the wire of a constant thickness, an equation of 



A I the following form is obtained for the curve ABC 



j[ e J*+e-» a ' — 2 



-4— [- W -*7 C where 6 is an arbitrary constant, which is determined by a 

 \ i I J transcendent equation 



B e 2 _ e 2 = ?, 



6 



evident that the form of the surface containing the fluid has no influence on 



^WhfrSpect to the principles of 'the curvilinear movement of a point it is first 

 shown that P the space described by a point, during an infinitely small timedt s ex 

 pressed by an infinitely small quantity of the «cond «der,^ft tfc. space £ the 

 chord- no other straight line can give an approximation which goes beyond tms 



^S3TSJ&^ »1SS^ magnitude combined .with the 

 direct Ln o £ movement, but simply to express this ™f^-™£«£ ° h °ave 



s^ab^^ 



for the movement of a system subjected to variable conditions. 



