F. A. P. Barnard on the Pendulum. 193 
' would issue from a vessel in consequence of the superincumbent 
weight, is determined by ie ie mula 
=2 gh. 
Were the pendulum Fc Pe to move with a velocity equal 
to the square root of 2 x 32 x 1250 doy 80,000), the resistance 
would be equal to its weight. Hence 
k= /80, 6003 
And r (cos p— — C08 #) =F x aie ere 
This being the coefficient of the arable resistance, the total 
soe we - resisting force may be found by integrating the ex- 
ress 
gli(a2—g)? |. 
80,000 4%? 
between the limits « and — loying the symbol 1, instead 
of the fractional coefficient, an abe the value of dt as given 
above, we have, calling the total resistance 
—do 
Ba flee, |e ea ae 
Integrating between the limits « and —e, and putting Eas =-, 
=ol(—>") (= + are sin) +(@+ sma/ma)|- 
Sais m is very minute in comparison with «, we may make 
atm Sal, and also neglect —2ma. The small positive term at 
the end a insensible, when multiplied by the general 
Coefficient, i which &? is a divisor—the term itself being in- 
cant stead with 7, with which it is connected by the 
Sgn+. The errora thus introduced, besides being insensible, 
pre Opposite Ror and nearly’ balanced. The simplified 
€xpression is then 
, g a? g2la? 
2h?” 
This Tesistance extends over ae whole are of vibration; but 
the ant ee power acts ped only between the limits 8 
k= 
‘o main 
eet of & may be pretty nearly necattdiced Se bodies of Fn pagal shape, 
“Snsidering the inclination of their surfaces to the direction of m 
