74 UNIVERSITY OF MISSOURI STUDIES 



by making a\ successively equal to w, to 2w, to 3u>, to 4k/, 

 and so forth, li x =z nw, we have 



F = \(iow-\-nwY — (10^)^ = 



30OW" L J 



300 L J 



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° — 10°) 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 = 0' to x = 50ii', 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 = ^^ !"(io+so)3— lo^l^ 



300 L J 



215000 a w 



~ 300 



