The passage on the previous page is from J.M. Barrie (1860-1937), The Little White Bird (1902), an early version of Peter Pan in Kensington Gardens, which Barrie later wrote into his famous play, Peter Pan. Barrie and Conan Doyle were close friends.

"'I have reason to think that they are hot upon our trail. Ah, there is Moriarty himself.'"

...clambering over the wall which leads into Mortimer Street....
If Watson's rooms backed on Mortimer Street, then he lived in an area near several hospitals, located quite close to the place where Holmes was attacked.

"It was my brother Mycroft."
Mycroft Holmes, known both for his brilliant mind and his sedentary habits, apparently made an exception to his usual aversion to action in order to accommodate Watson. Besides this story, he appears in two others, "The Greek Interpreter" and "The Bruce-Partington Plans," and is mentioned in two more. Mycroft is deeply involved behind the scenes in the British government.

"This train stops at Canterbury; and there is always at least a quarter of an hour's delay at the boat."
Canterbury is located on the way to Dover, a port at the end of a rail line on the south coast of England. From Dover, one could take the steamboat (today the ferry or hovercraft) across the English Channel to Calais, France.

"Well, then we must make a cross-country journey to Newhaven, and so over to Dieppe."
Instead of boarding the steamboat across the English Channel to France at Dover, they will travel overland to Newhaven and from there take the ferry to Dieppe, France. Today, although a train tunnel has been bored underneath the English Channel, several different ferry routes are available to France, some longer than others. Newhaven-Dieppe is one of the longest.

"…a coup-de-maître…."
A master stroke.

We sat in the Strasburg salle-à-manger arguing the question for half an hour....
Strasburg (or Strasbourg) is a city on the border between France and Germany. After enjoying a century of independence, it passed back and forth between France and Germany until the end of World War II. In Holmes's time it belonged to Germany, but was returned to France after World War I. During World War II, it reverted to German control, but today is part of France.

The salle-à-manger is the dining room at the train station.