W. P. Trowbridge on Deep Sea Soundings. 167 
in which ( W’z) is the weight of that part of the line immersed ; 
the plus sign being used when the line is heavier than wa r, 
and the minus sign when it is lighter; and ( W’) being the weight 
in water of one foot of line. 
In the experiments with one and two 32-pound shot the spe- 
cific oe of the line is supposed to be the same as that of 
water, and itis only in case of a wire being used, or a hemp 
line of large ond that it is necessary to take the specific 
gravity into account. As we wish to determine the Jaws of the 
sistances and not their absolute quantities in pounds, except 
in general ee these very small quantities may with propriety 
be neglected. 
We may now find the values of F' at different depths in the 
cases under consideration, viz., the fall of one and two 82- -pound 
shot attached to a sma 
ats one 32- ate shot W=27:36 pounds, and the values of 
D(m+q)jh. for the different velocities in the third column of 
the table may a calculated. At the maximum velocity there 
is practically no line attached, as the action of a few feet may 
be neglected, and the whole resistance will be equal to 27°36 
pounds, or exul to the weight of the shot in water, which is 
determined also from the . 
Lf nk eee 
451 S.D(m-+9) 
from which R=S. D(m+9) = W=27'36 pounds. 
The resistances to the a are given in the fifth ore | 
of the table, and the curye representing these es 
pounds, is given in diagrams marked (B) curve No. 1. 
The values of R’= W—S.D.(m+q)h. are given in the xh 
column of table I. 
It will be seen that the resistance to the shot diminishes very 
Tapidly at a and at the depth of 2000 pn it becomes 
only 6-5 of a pound, while the resistance upon the line increases 
with ae depih; becoming at 2000 fathoms oT 36-—05=26'8 
fe bs pea Se eats eal #000 Sa 
e unds, and a : 
maximum velocity wil the i a this cae ‘e at 2000 
fatho ly equal to its bearing weight, which was only 60 
poun fe ‘Flow coch fat —— would ib have gone without break- 
vie agra conan botto 
Tines to two 82-pound shot. Curves (1) and (2) reo the 
‘Tesistance to the shot, in pounds, at depths 50, 150, 250, etc. 
