What is the falling action in Anna Sewell's "Black Beauty"?

The falling action of a plot follows the conflict.  So, in "Black Beauty" by Anna Sewell, in Chapter 47 after Black Beauty endures many hardships at the hands of callous or uncaring owners, Beauty collapses.  But, a farrier realizes that Beauty can heal, so the horse is taken to an auction in Chapter 48 where he is purchased by Squire Thoroughgood and his compassionate grandson who believe that they can restore the black horse to health in their meadow in the country.  The fresh air and good grass heal the horse and he is sold to Ellen and Lavinia Blomfield.  Their groom Joe Green recognizes Beauty and cares for him for the rest of his life, and the horse is at peace.

What is the rising action in Anna Sewell's Black Beauty?

Rising action is defined as all action leading up to the climax. The climax is the turning point in the story, the moment rising action becomes falling action leading to the resolution; it is often the most emotionally intense moment in the story.

The conflict of Anna Sewell's Black Beauty concerns the title character's struggles against his harsh and cruel environment, and the resolution occurs the moment Beauty finds himself once again in a happy home in which he knows he'll spend the rest of his life. The climax occurs when Beauty reaches the peak of his physical exhaustion, nearly dying. Therefore, all action leading up to his near-death moment counts as rising action. The rising action grows more intense as Beauty finds himself under the care of crueler masters.

One moment of rising action occurs after Beauty and Ginger are sold by Squire Gordon to the Earl of W-- at Earlshall Park. It is here that Beauty first experiences having to wear the check-rein, and he explains how much it strained his back, legs, and breathing not to be able to move his head freely, especially when pulling a load uphill. Another moment of rising action concerns when has an accident with the drunken groom Reuben Smith that kills Smith and scars Beauty's knees, making him no longer suitable for carriage work but only suitable for heavy labor instead.

Rising action grows more intense as he continues in his story to describe being poorly treated as a hired horse and working in torturous conditions as a carthorse and cab horse until he finally collapses; it is the moment of his collapse that is considered the climax, the same moment Beauty thinks his life is over:

... [I]n a single moment--I cannot tell how--my feet slipped from under me, and I fell heavily to the ground on my side; the suddenness and the force with which I feel seemed to beat all the breath out of my body. I lay perfectly still; indeed, I had no power to move, and I thought now I was going to die. (Ch. 47)

However, he is luckily given rest and purchased by an elderly man and his grandson who revive him and sell him one last time to kindly ladies.

What is the rising action (include conflict) in Black Beauty?

Since the rising action of the plot of a narrative involves the onset of a problem, in "Black Beauty" by Anna Sewell this problem occurs after Beauty has been purchased by the Gordons of Birtwick Hall.  There Beauty experiences an idyllic existence, but when Mrs. Gordon's poor health forces her and her husband to move, Beauty and Ginger are sold to Earshall Park where the mistress insists upon using the bearing rein, a painful device that forces the horses' head up while they pull her carriage.  Of course, this conflict is an external one as the horses are victimized by the owner.  When the Earl of Earshall and his family go to London, the Lady Anne rides Beauty, but on another ride she tries another horse.  This time she is thrown, but Beauty races for help and is lauded as a hero.  The horse feels that it has settled back to a comfortable life, but on one night the drunken stable hand takes him on a dangerous route and Beauty falls, scarring his knees.  Because his appearance is marred, the horse is sold as a livery animal and is subjected to much misuse.  Beauty suffers several turns of fortune as he is overworked and mistreated.  But, finally, he is bought at an auction where the horse is recognized by Joe Green and put out to pasture to live out his life in contentment.