~ 
162 W. P. Trowbridge on Deep Sea Soundings. 
Lieutenant Lee, which in some respects are preferable, (and 
which are sufficiently numerous to give good results,) rather 
than a mean of the results of Lee and Berryman. 
The intervals of descent for one and two thirty-two pound 
shot are given in the table (I); the first column shows the depth 
in fathoms, the second the intervals of descent, in time, for each 
successive 100 fathoms. 
The velocities are determined from these intervals by suppos- 
ing the motion uniform during the running out of each one 
hundred fathoms, and dividing the space, in feet, by the time in 
seconds, which will give, very nearly, the velocity in feet at 50, — 
150, 250, &c. fathoms. The velocities at these points are given 
in the third columns under their respective heads. se 
It will be observed that the velocities of descent diminish, in 
the case of one 32-pound shot, from 8°83 feet per second at 50 
fathoms, to 2°84 feet at 1000, and 2°09 feet at 2000 fathoms, and 
soon. And in the case of two 82-pound shot, from 12°50 feet 
per second at 50 fathoms, to 3°48 feet at 1000, and 2°99 feet at 
2000. 
The curves representing these circumstances of motion are 
given in diagrams marked (A), the vertical distances represent- 
ing the spaces in fathoms and the horizontal distances for curves 
(1) and (2) representing intervals of time, and for curves (8) and 
(4) velocities in feet. Curves (1) and (2) therefore show the re 
lation of the spaces and times, and curves (8) and (4) the rela- 
tion of spaces and velocities. The curves in full lines are for one 
32-pound shot, and those in broken lines for two 32-pound shot; 
the sounding line being the same in both cases. these bodies 
have no initial velocity but start from rest at the surface, 1t 18 
evident that the curves of velocity must pass through the origi2 
heavy nen falling in water, the velocity ss in terms 
time, weight, density of medium, and form o 
mish 29 Ww N—1 
v= s5 mtn (FA) — 
the weig: 
body in water, (S) the area of the greatest cross section of 
dy, (D) the density of water, and (m+q) a ¢ 
yy experiment; and, (th bolic logarithm N) 
body, is given by 
eS 
eee ee. eae 
