256 Mr KELLAND, ON THE MOTION OF 



2 _ * f 3 a;' 3.5 x^ . 1 



'^•'"' (F^-TF^^* " (y^ + «^)* l^ ~ 2 y^T? + 2 .4 (y= + ^')» ''•I ' 



and 2, . 1 = .v, 



of x° 

 2.(.r+ ir=- + -+ ... 



2.(a; + 1)" = =• + TT + ••• 



^ ^ w + 1 2 



Substituting and, for the present, retaining only the first term, 

 which amounts to supposing - very large, we have 



Proceeding with this in like manner for x, we obtain 



s/x^ + y^ + ss"^ — X ^ x^ + y" + X 



X, 



(a;" + y + s'O* ~ 2 °^ \/ir- + y' + a' + a; ' y/x° + y' - a- ' 



' /'».2 



and applying the same process to y, we obtain finally 



2 — ? 



+ ss.cot-'— ^^ ^ 



a;y 



= - {A cot-' ^^ + 2«log-^^^). 



If we further suppose the height of the tube considerable, com- 

 pared with the side of the section, we may omit j^ compared with a : 



