In "The Adventure of the Speckled Band" story and BBC film adaptation, what would you say were some of Sherlock Holmes' motivations?

Sherlock Holmes has at least three principal motives for getting involved in Helen's Stoner's case. In the first place, he frequently helps young ladies in distress out of sympathy and chivalry. This motivation can be seen in such stories as "The Adventure of the Speckled Band," "The Adventure of the Solitary Cyclist," "The Adventure of the Copper Beeches," "A Case of Identity," and "The Adventure of the Dancing Men."

Another motive is professional curiosity. Watson...

Sherlock Holmes has at least three principal motives for getting involved in Helen's Stoner's case. In the first place, he frequently helps young ladies in distress out of sympathy and chivalry. This motivation can be seen in such stories as "The Adventure of the Speckled Band," "The Adventure of the Solitary Cyclist," "The Adventure of the Copper Beeches," "A Case of Identity," and "The Adventure of the Dancing Men."

Another motive is professional curiosity. Watson repeatedly informs the reader that Sherlock Holmes has a compulsion to use his analytical powers and that he will only take cases that interest him. He is not particularly concerned about money because he has become so famous that wealthy people pay him large sums for his help. An example is "The Adventure of the Priory School" in which the Duke of Holdernesse writes Holmes a check for six thousand pounds, which would be the equivalent in buying power of at least a million dollars today.

A third motive in "The Adventure of the Speckled Band" is the challenge presented by Dr. Grimesby Roylott, who bursts into Holmes rooms shortly after his stepdaughter Helen Stoner has left and issues the following threat.

“I will go when I have said my say. Don't you dare to meddle with my affairs. I know that Miss Stoner has been here. I traced her! I am a dangerous man to fall foul of! See here.” He stepped swiftly forward, seized the poker, and bent it into a curve with his huge brown hands.

“See that you keep yourself out of my grip,” he snarled, and hurling the twisted poker into the fireplace he strode out of the room.

This is the only time Dr. Roylott is seen alive, but he seems to haunt the remainder of the story, making it, as the author intended, a conflict of man against man, Holmes against Roylott. Holmes is doubly motivated to interfere in this half-mad bully's affairs just because Roylott has warned him not to do it. 

So in "The Adventure of the Speckled Band," Sherlock Holmes has three strong motives for solving the problems brought to him by Helen Stoner. The great detective not only saves Helen's life but clears up the two-year-old "locked room" mystery of the death of her sister Julia--all in less than twenty-four hours. His conflict with Dr. Roylott is resolved when the villain is killed by his own poisonous snake.