W. P. Trowbridge on Deep Sea Soundings. 165 
(h) being the height due to the velocity; and if at any point of 
the path described the motion be supposed uniform, for one sec- 
ond, we shall have, calling (W) the weight of the shot and line 
in water, (2’) the resistance upon the line, and (/2) the resistance 
j upon the shot or sinker 
r W—(R+R)=0, 
that is, the resistance is equal to the weight. This is the sim- 
plest mode of considering the subject. If the inertia of the 
masses be taken into account, we must employ the expression 
Jf wae—[ Raf, Ride=4M(v—v") 
_ The expression W—(R+2)=0 or W—(S. D(m+g)h—R)=0 
involves two variable quantities (g) the force of gravity and (D) 
; aS earth, and if ( he f f vit rat the surface. 
, ie g) represent the foree of gravity. ’ 
(g’) the same bale s the depth z, and (r) the radius of the earth, 
we shall have ; 
natorjal radius in fathoms is equal to 3487266, and at 
e 
ee ae A 
| g =p (=) =9-9; 
-_, The eq ms i 
the equator for a depth of 3000 fathoms we shall hay 
Ne eee eo 
I=I-I 3487266 
__ the depth, but in 
at Ss goede will be less than “0004 of the force; we may 
_ SECOND SERIES, Vou. XXVI, No. 77.—SEPT., 1858. 
