Van Nostrand's eclectic engineering magazine . lined to the base, and we shallget a Transformed Catenary, and theshape of the sheet of metal under which itwill be balanced ; for the new curve andsurface cut out by the inclined plane are theparallel projections of the curve CAB andthe surface C Q T B A C (Fig. 10). Letthis inclined plane be so placed that it shallintersect the plane of the base in thestraight line C B (Fig. 10) or in one paral-lel to it. Then all horizontal lines (orthose parallel to C B or d T) will be un-changed in length in the parallel projection,while all vertical lines (t
Van Nostrand's eclectic engineering magazine . lined to the base, and we shallget a Transformed Catenary, and theshape of the sheet of metal under which itwill be balanced ; for the new curve andsurface cut out by the inclined plane are theparallel projections of the curve CAB andthe surface C Q T B A C (Fig. 10). Letthis inclined plane be so placed that it shallintersect the plane of the base in thestraight line C B (Fig. 10) or in one paral-lel to it. Then all horizontal lines (orthose parallel to C B or d T) will be un-changed in length in the parallel projection,while all vertical lines (those parallel toA 0, etc.) will be lengthened in a constantratio whose magnitude will depend upon theinclination of the cutting plane. Make avertical section of the cylinder on the line if the cutting plane passes though0 B we get the triangle 0 U Y (Fig. 13a) cut out of the wedge to which the cylinderreduces in this case. In the triangle U Vis the ordinate of the vertex of the trans-formed catenary corresponding to 0 A in Tig 13 ia).. the common catenary, and all lines parallelto U V are evidently increased over thecorresponding ones of which they are the Fig. 13 (5).
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Keywords: ., bookcentury1800, bookdecade1860, bookpubl, booksubjectengineering
