#### Answer

Using Adams's method, each clinic is apportioned the following number of doctors:
Clinic A is apportioned 6 doctors.
Clinic B is apportioned 8 doctors.
Clinic C is apportioned 12 doctors.
Clinic D is apportioned 14 doctors.

#### Work Step by Step

Let's use a modified divisor of $d = 52$ to find the modified quota for each clinic.
Clinic A:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{275}{52}$
$modified~quota = 5.29$
Clinic B:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{392}{52}$
$modified~quota = 7.54$
Clinic C:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{611}{52}$
$modified~quota = 11.75$
Clinic D:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{724}{52}$
$modified~quota = 13.92$
Using Adams's method, the modified quota is rounded up to the nearest whole number. Each clinic is apportioned the following number of doctors:
Clinic A is apportioned 6 doctors.
Clinic B is apportioned 8 doctors.
Clinic C is apportioned 12 doctors.
Clinic D is apportioned 14 doctors.
Note that the total number of doctors apportioned is 40, so using a modified divisor of 52 is acceptable.