Rev. 0. Fisher — Oblique and Orthogonal Sections. 21 



horizontal round cylinder by a plane, gives rise to an ellipse, the 

 position of Avhqse major axis can be in a vertical plane only in one 

 particular relative position of the two. 



Let us speak no longer of trail furrows, but generally of the 

 section of anj horizontal cj'lindrical surface, or part of such surface, 

 or of a folded stratum, such that its section by any horizontal plane 

 would give a system of parallel straight lines ; for it is obvious that 

 our conclusions are unaffected by the scale on which the phenomena 

 occur. It appears then that no apparent obliquity of trend can be 

 given by a vertical section, e.g. by a vertical cliff, and that if any 

 such obliquity appears in the trend of the trace, it must in that case 

 exist in the folding of the strata themselves. But if the section be 

 made by a plane inclined to the vertical like the side of a railway 

 cutting, then, although there may be great obliquity of trend in the 

 trace of the foldings, there need not necessarily be any in the foldings 

 themselves. 



Note. — The following is a geometrical solution of the problem : 



How to delineate upon a cutting plane the trace of a cylindrical, or any 



other surface, lohich can he formed out of a folded plane. 



Fig. 1. 



Let B'ABh be a horizontal straight line (which, for simplicity, 

 we may consider to be the axis of a prism) parallel to the curved 

 surface, whose trace we wish to delineate upon a given plane which 

 cuts it. 



Let J. C be a horizontal straight line, drawn upon the cutting 

 plane. 



Let the angle B A C=:a, and let the cutting plane be inclined at 

 an angle /S to the horizon. 



Draw the line A E normal to the plane, and let it make with A B 

 the acute angle E A B =z 0. Then the angle between the cutting 

 plane and the axis of the prism will be the complement of 6. 



Describe a spherical surface about A, and let this cut the vertical 

 plane in E D G, the cutting plane in G F, the horizontal plane in 

 BBC, and the plane, in which lie the normal to the cutting plane 

 and the axis of the cylinder, in E B F. 



