71. We take derivatives and let dg

≈ ∆g and dT ≈ ∆T . The derivative of Eq. 16-28 is

dT

dg

= 2π

1

2

−L/g

2

L/g

which (after dividing the left side by T and the right side by 2π

L/g) can be written

∆T

T

=

−

1

2

∆g

g

where both sides have also been multiplied by dg

→ ∆g. To make the units consistent, we write

∆T

T

=

2.5 min

1 day

=

2.5 min

1440 min

= 0.00174 .

Therefore, with g = 9.81 m/s

2

, we ob tain

0.00174 =

−

1

2

∆g

9.81 m/s

2

=

⇒ ∆g = −0.034 m/s

2

which yields g

= g + ∆g = 9.78 m/s

2

.