352 MESSRS. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND: 
Fig. 13. The determination of the coefficient of the force acting normal to the shell. 
The plotted points show the observed values of the couple coefficient plotted against the distance of 
the centre of gravity from the base. 
The slopes of the lines drawn determine the coefficient of the normal force. 
The numbers against the points for the Type II. shells give the number of observations whose mean 
is represented by the plotted point. 
4.12. The Damping Factors. —It now only remains to derive as much information 
as possible as to the damping factors k, h , and y from the observed values of ai and 
A- The factor k is known in terms of the value of f h , since, by § 3.1, 
(4.121) k = pvFfJm. 
Squaring and subtracting equations (4.041) and (4.042), we obtain 
rr 0 J J e~ 2gi = (T (a 2 — /V), 
q l = — T log {cr (ad —A 2 ).' + const., 
(4.122) 
h + K 
! 
(^2 h) 
log {^(a^-A 2 )} 
In this formula, as well as in those which follow, k, h, and y may be treated as 
sensibly constant over the whole range of one experiment. On dividing (4.041) by 
(4.042), we obtain 
(4.123) 
tanh {j-q 2 ) = A/ a i- 
