354 E.. Loomis on vibrating Water-falls. 
the descending sheet strikes the sloping boards nearly in the 
middle of their height. The south dam is quite old and its ini 
is rough, so that the vibrations are never very regular or strong 
The north dam is the one upon which Mr, Edwards’ Sec isee 
have all been made. 
In the spring of 1863, Mr. Edwards, at my request, made a 
more extended series of observations, measuring accurately the 
depth of water on the edge of the dam, aris counting the cor- 
responding number of vibrations. The th of water was 
measured by inserting a small rod 4 inches etn the edge of the 
r. Edwards states that, at a distance of 20 rods above 
the ado: the water was 1? inches higher than at the point where 
he measured it. The following table shows the results of Mr. 
Edwards’ observations in 1863, and is deduced from numerous 
trials between April 23 and May 4, 
Depth of Ti f one Ti f falli . 
ainde pieration. _throngh deptie Ratio: | 
9-21 inches. 0s:220 0S-218 1-007 
812 « 0-192 0 +205 937 | 
700. * 0°177 0-190 930 | 
e3l “ 0-164 0-181 -906 
506 “ | 0-188 0-162 “850 
These results differ sensibly from those deduced from Mr. 
Edwards’ “ihat series of bbe Petione: The difference ma 
ascribed in part to the greater accuracy of the last observations, 
since fractions of an inch were disregarded in the first measure- 
ments. Perhaps also something is due to the modification in 
the structure of thedam. Iam 1 however inclined to think that 
the influence of the latter cause is slight, and that the discrepan- 
cies are mainly due to the unavoidable imperfection of such 
observations. Any one who shall attempt to repeat these ob- 
servations, instead of complaining that Mr. Edwards’ results are 
not perfect, will probably be surprised at the precision which he 
has actually attain 
The result, then, which we deduce from these observations at 
South Natick, is that the time “ one vibration is a little less than 
the time in which a heavy body would fall through a space equal to 
th of water on the dam; and this deficiency increases as the 
depth of water diminishes. 
Observations at Holyoke, Mass. 
The dam across the Connecticut river at Holyoke, Mass, is 
1017 feet long and 80 feet high. It is formed of square timbers, 
inclined 22 degrees to the horizon, having one end bolted to viet 
_ rock, and the other resting upon a timber frame-work. From 
the crest of the dam, the oe atl aasce 
about four feet i in length, which sae otek dark at an angh 
