176 



Journal of Agricultural Research 



Vol. XII, No. 4 



Through point Oj (fig. 18) draw a line oji parallel and equal to line og. 

 With h and as points of suspension describe a catenary with its lowest 

 point at O. Taking the point O (fig. 18) as origin, the equation of the 

 catenary is 



y _ _ /g21z /3ba ^ g-21z y3ba\ ^ 



a = Og. 

 Transferring the origin to the point gives 



yz= — (g21z /3ba ^ g-21z /3ba\ _ ^j 



(91) 



(92) 



as the equation of the catenary oh (fig. 17). The equations of line pm 

 (fig. 17) are 



Fig. 18. 



Any plane parallel to the plane 2 = is given by 2==c, and this plane cuts 

 the line pm at the point 



z^ = c. 

 It also cuts the catenary oh at the point 



^^~2l^ 



J2 = /(C) 

 Z2 = C. 



The equation of the fine in the plane z = c which cuts the line pm and the 



catenary oh (fig. 17) is 



x—h _ y—0 



(93) 



or 



3& , }{c)-0 



(94) 



