364 E. Loomis on vibrating Water-falls. 
observed time is 0081 greater than the computed time of an 
air vibration. 
At Lawrence, (if we suppose there are only two vibrating 
segments,) the time of an air vibration is 0%:383, while the ob- 
served time exceeds this by only 03-026. If we suppose there 
are three vibrating segments, the time of an air vibration is 
0*255, and the observed time exceeds this by 08154. If we 
suppose there are four vibrating segments, the observed time is 
0218 greater than the computed time of an air vibration. If 
we suppose there are six vibrating segments, the observed time 
is 08-281 greater than the computed time of an air vibration. 
we compare the results obtained at these three locali- 
ties, we shall find that we may make such a supposition with 
regard to the number of vibrating segments into which the 
column of air divides itself, that the apparent retarding effect of 
the water shall be nearly proportional to the thickness of the 
sheet. The following table presents a summary of these results, 
Number of ‘ Quotients. | 
Depth of ini hes vibrating = view agi beste ote: § = R 
| se prose Vibeation, wenpeaed: adr waivition. theme a D ee 
; 5-06 inches, 08138 1 05100 08038 ‘0075 
South Natick | 1000 “ | 0-214 1 0-100 | o-114 | “0114 
13-12 « 0 -236 8 0-155 | 0°08 0062 
20:90 « 0 °445 8 0°310 | 0°135 | “0064 
Holyoke 4068 « | 0-739 2 0-480 | 0-259 | -0064 
26° 0 “752 Qe 0 -480 0-272 0060 
48-00 « 0 :409 4 0 ‘191 0-218 
pawretce ts 00 « 0 -409 6 0128 | 0°281 | ‘0059 | 
the small height of the fall, in consequence of which, especially : 
mewhat 
when the water is high, the descending sheet acquires somewha 
of the rigidity of a solid body. 
"he number of vibrating segments of the column of air, is the i | 
principal unknown quantity which renders our sone ae ae ao 
very uncertain. I do not know of any theory which will enab 
_ us to compute the precise influence of a sheet of water of giv 
_ dimensions; but at present, it seems probable that the vibrat 
a originates in the column of air behind the sheet of w: 
