What's sedulous mean?

Sedulous means persistent and steady, or diligent. In The Strange Case of Dr. Jekyll and Mr. Hyde, Mr. Utterson's clerk, Mr. Guest, is "a great student and critic of handwriting." He finds something amazingly similar between Dr. Jekyll's and Mr. Hyde's handwriting:
"Is that from Dr. Jekyll, sir?" inquired the clerk. "I thought I knew the writing. Anything private, Mr. Utterson?"
  "Only an invitation to dinner. Why? Do you want to see it?"
  "One moment. I thank you, sir"; and the clerk laid the two sheets of paper alongside and sedulously compared their contents. "Thank you, sir," he said at last, returning both; "it's a very interesting autograph. . . . there's a rather singular resemblance; the two hands are in many points identical; only differently sloped."