Clouds of Witness continued

“Yes. Who's on the case, by the way?”
“Mr. Parker, my lord.”

Parker is a police inspector whom we first met in Whose Body?

“Parker? That's good. Splendid old Parker! Wonder how he managed to get put on to it. How do things look, Bunter?”
“If I may say so, my lord, I fancy the investigation will prove very interesting. There are several extremely suggestive points in the evidence, my lord.”
“From a criminological point of view I daresay it is interesting,” replied his lordship, sitting down cheerfully to his café au lait, “but it's deuced awkward for my brother, all the same, havin' no turn for criminology, what?”

Café au lait is a French coffee drink. The meaning of the term differs between Europe and the United States; in both cases it means some kind of coffee with hot milk added, in contrast to white coffee, which is coffee with room temperature milk or other whitener added.

“Ah, well!” said Mr. Bunter, “they say, my lord, there's nothing like having a personal interest.”
“The inquest was held to-day at Riddlesdale, in the North Riding of Yorkshire, on the body of Captain Denis Cathcart, which was found at three o'clock on Thursday morning lying just outside the conservatory door of the Duke of Denver's shooting-box, Riddlesdale Lodge.

The North Riding of Yorkshire was one of the three historic subdivisions of the English county of Yorkshire, alongside the East and West Ridings. From the Restoration it was used as a Lieutenancy area. The three ridings were treated as three counties for many purposes, such as having separate Quarter Sessions. An administrative county was created with a county council in 1889 under the Local Government Act 1888 on the historic boundaries. In 1974 both the administrative county and the Lieutenancy of the North Riding of Yorkshire were abolished, being succeeded in most of the Riding by the new non-metropolitan county of North Yorkshire.

Evidence was given to show that deceased had quarreled with the Duke of Denver on the preceding evening, and was subsequently shot in a small thicket adjoining the house. A pistol belonging to the Duke was found near the scene of the crime. A verdict of murder was returned against the Duke of Denver. Lady Mary Wimsey, sister of the Duke, who was engaged to be married to the deceased, collapsed after giving evidence, and is now lying seriously ill at the Lodge. The Duchess of Denver hastened from town yesterday and was present at the inquest. Full report on p. 12.”
“Poor old Gerald!” thought Lord Peter, as he turned to page 12; “and poor old Mary! I wonder if she really was fond of the fellow. Mother always said not, but Mary never would let on about herself.”
The full report began by describing the little village of Riddlesdale, where the Duke of Denver had recently taken a small shooting-box for the season.

A shooting box is a term used for a (usually) small country property in the UK popular with the upper classes which was or is used for organising hunting parties, the pastime of shooting wild or semi-wild creatures a favoured pastime of a leisured, moneyed or propertied class. It can also be called a Hunting Box, Royal Hunting Lodge, or a Shooting Lodge. Such places might be quite separate or detached from the main property, or in a different and more remote part of the country.