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Fig. 1.

We have to make fifty-four such pipes, each of the dimensions proper for the production of its own note, deep in the bass or shrill in the treble.

It is quite clear that we must not work by "rule of thumb," but understand well what we are about from the very first, if we do not wish to cut our wood to waste and cover ourselves with mortification.

Begin thus. Take a sheet of stout paper, and on it, with rule and compasses, draw a scale showing all the requisite measurements.

Here we must be a little arbitrary, and lay down the law without giving lengthy reasons for our ruling. Stopped pipes are half the length of open pipes yielding the same notes. Our CC pipe will therefore be 4 feet long. The four C's of the ascending scale are the halves of each other. Therefore Tenor C will be 2 feet, Middle C 1 foot, Treble C 6 inches, and C in alto 3 inches, in length. The word nearly, or about, must be understood as prefixed in every case to our measurements. Accordingly, the lengths of all the pipes in the stop will be easily obtained by drawing a vertical line 1 foot in length on the paper, and dividing it into twelve equal parts. At the bottom, write Tenor C, 2 feet; at the top, Middle C, 1 foot. Then the length of each of the eleven pipes intervening between these extremes will be at once obtained by easy measurement. By doubling these lengths we shall obtain those of the bass, or 8-feet octave. By halving them, those of the middle octave. By dividing them by four, we get those of the treble octave.