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Mathematics practically applied to the useful and fine arts / by Charles Dupin; adapted to the state of the arts in England by George Birkbeck
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PARALLEL GUAGEPUMPS.

the sliding tneek D, it forms the common gage, and may be usedto draw lines parallel to the edge of any piece of work. Withthe addition of F and G, two brass arms of equal length, thisinstrument bisects any solid, and draws a line along its cen-tre. One end of each is centered in the two sliding cheeks pa-rallel to A; the other ends are united by the screw H, which itformed into a sharp point beneath, to mark with. It is evidentfrom what has been said of obliques and parallels, that thispoint will always be in the centre, between the two cheeks BD.When the two sides of the solid to be marked are not parallel,unscrew C, and as the gage is drawn along, press the two cheeksB, D, towards each other, so that they may always be in contactwith the sides of the solid, and the point H will pass along thecentre of the solid, as correctly as if its sides were parallel. Be-cause the obliques F, G, are of equal length, the scribing pointalways preserves the same distance from the two cheeks B and D,both of which are always in contact with the two sides. When thecheeks B, D, are brought together, the two arms F G, lodge ingrooves made in the cheeks to receive them.

Application to the movement of pistons in pumps :Theabove explanation gives us to understand how a piston,which fits exactly into the barrel of a pump, the figure ofwhich is represented by parallel right lines, moves in itwith precision, meeting no obstacle, and yet not beingloose, when the barrel of the pump and the piston are madecorrectly. As the piston ascends and descends alter-nately, each point in its outline describes a right line pa-rallel to the axis of the barrel; and all the parallels thusdescribed must be placed exactly on the inner surfaceof the barrel. In making the pistons of steam-engines,in particular, the least defect in parallelism and the leastdeviation, produces serious inconveniences and a great lossof power.

Application of this principle in stretching thi warp andin weaving.To prepare the warp, a certain number otthreads are first of all extended parallel to each other, oneend of each being fastened to a piece of list, and the otherrolled up round a piece of wood. The part unrolled fromti e wood forms a series of right lines parallel to eaeh