The next part of positioning to avoid car sickness is to have the Beagle facing forward. You may think that restraining your Beagle would be counterproductive to his panicked feelings; however the correct canine seat restraint will actually help quite a bit.
Once a Beagle is secured, he will remain facing forward, which allows him to view the road and see that he is actually moving which often can cure car sickness for many dogs.
Stability - Another reason why a car restraint or seat works so well to cut down on motion sickness is that it keeps the dog secure. If a dog is unrestrained, he is moving in a way that that does not match the forward or turning motions of the car, and his body sways with turns and stops; this all leads to more nausea.
Puppies under the age of one year old do best with bolstered car seats that rise them up high enough to look out. Dogs can be secured to these via either the collar or harness which connects to a safety loop; it is dangerous to use the collar since this can cause strain on the neck, so do be sure to use a harness.
For older Beagles that are large enough to clearly see the road without being in a car seat, a simple canine safety belt strap is best. Do be sure that this is properly secured and sized appropriately so that the Beagle is safe and cannot turn around.
And this isn't even to yet mention the very important fact that buckling up your Beagle is a huge step in prevention injury or even death. There are 16,000 car accidents per day in the U.S. and a 25 lb. unrestrained dog will be thrown with the force of a 875 lb. object in a crash going 35 MPH.