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.