E.. Loomis on vibrating Water-falls. 359 
A column of air 1017 feet long, and having a very small 
diameter, would make one vibration in (a= 08926. Accord- 
ing to experiments with organ pipes, the length of the column 
in this formula should be increased by some function of the 
breadth, génerally about twice its breadth. If we increase the 
length of the column of air by the sum of the height and thick- 
ness, we shall have for the computed time of one vibration 
1053 ‘ a2, . 
(Foaa= 0-959. Hither of these quantities exceeds the time ac- 
It appears, from experiments 
forms and with different embouchures, that the time of one 
vibrates as one mass, or as two separate portions. e change 
in the number of Vibrations, when the depth of water increases 
i Vibration of air | Time of falli 
ap igs Poa ges 5 | tee computed. | pode Weed 
15°90 13°12 | Os'236 08°232 { 08-261 
25°33 20°90 | 445 -465 H "329 
48°75 40°63 I “139 “959 459 
54°33 45°28 “152 95 484 
In the preceding table, column I shows the depth of water in 
inches according to the gauge; column It shows the dep 
the crest of the dam, determined according to the principles ex- 
plained on page 856; column 11 shows the observed time of one 
vibration; column Iv shows the time of one vibration of a 
column of air 1017 feet long, computed in the manner explained 
above; the air in the first case nee supposed to be divided 
into four vibrating portions, and in the second ease into two 
ortions; and column Y shows the time in which a heavy body 
would fall through the spaces given in column Il, 
It will be noticed that the observed time of vibration in each 
case falls between the times computed by these two methods, 
