74 UNIVERSITY OF MISSOURI STUDIES 



by making x, successively equal to w, to %w, to 3zv, to <kv, 

 and so forth. If x = nw, we have 



F=— — \ (low -\-nwY— (iow) 3 = 

 30OW 2 L 7 v 'J 



a w 

 300 



(io+w) 3 — 10 3 . 



Let us arbitrarily regard as the unit of displaced 



fluid. We could then easily compute a table which contains 



the number of fluid units displaced by the 



Two tables number n of partition units. If the num- 



possible ber of partition units is, for example, three, 



the quantity of displaced fluid is 

 (13 s — 10 s ) units and so on. 



More useful, however, is a table which progresses in a 

 regular series of units of fluid and tells us — in decimals — the 

 lengths of the initial sections which make room for these quan- 

 tities of fluid ; for our representation of the movement of the 

 partition tells us the quantities of displaced fluid, and the cor- 

 responding section lengths are to be found in order to obtain 

 a more correct idea of the relative tone intensities. In order 

 to compute such a table it is advantageous to use a larger 

 fluid unit than the above. Let us determine the total quan- 

 tity of fluid for which room is made by the partition section 

 from x = to x = 50-^', that is, the whole part of the partition 

 near the windows for which we have assumed a uniform taper- 

 ing or change of width; and let us — arbitrarily — regard one- 

 fiftieth of this quantity as the fluid unit. 



F== aw r y_ 1 = 



300 L J 



_ 215000 a w 

 300 



