“How can you do that if you don’t know the exact scale of the chart?”

“I will show you,” said Thorndyke.  “We shall establish the true scale and that will form part of the proof.”

He rapidly constructed on the upper blank part of the paper, a proportional diagram consisting of two intersecting lines with a single cross-line.

“This long line,” he explained, “is the distance from Stillbury’s house to the Vauxhall railway bridge as it appears on the chart; the shorter cross-line is the same distance taken from the ordnance map.  If our inference is correct and the chart is reasonably accurate, all the other distances will show a similar proportion.  Let us try some of them.  Take the distance from Vauxhall bridge to the Glasshouse Street bridge.”

[Illustration:  The Track Chart, showing the route followed by Weiss’s carriage.

A.—­Starting-point in Lower Kennington Lane.

B.—­Position of Mr. Weiss’s house.  The dotted lines connecting the bridges indicate probable railway lines.]

He made the two measurements carefully, and, as the point of the dividers came down almost precisely in the correct place on the diagram, he looked up at me.

“Considering the roughness of the method by which the chart was made, I think that is pretty conclusive, though, if you look at the various arches that you passed under and see how nearly they appear to follow the position of the South-Western Railway line, you hardly need further proof.  But I will take a few more proportional measurements for the satisfaction of proving the case by scientific methods before we proceed to verify our conclusions by a visit to the spot.”

He took off one or two more distances, and on comparing them with the proportional distances on the ordnance map, found them in every case as nearly correct as could be expected.

“Yes,” said Thorndyke, laying down the dividers, “I think we have narrowed down the locality of Mr. Weiss’s house to a few yards in a known street.  We shall get further help from your note of nine twenty-three thirty, when records a patch of newly laid macadam extending up to the house.”

“That new macadam will be pretty well smoothed down by now,” I objected.

“Not so very completely,” answered Thorndyke.  “It is only a little over a month ago, and there has been very little wet weather since.  It may be smooth, but it will be easily distinguishable from the old.”

“And do I understand that you propose to go and explore the neighbourhood?”

“Undoubtedly I do.  That is to say, I intend to convert the locality of this house into a definite address; which, I think, will now be perfectly easy, unless we should have the bad luck to find more than one covered way.  Even then, the difficulty would be trifling.”

“And when you have ascertained where Mr. Weiss lives?  What then?”

“That will depend on circumstances.  I think we shall probably call at Scotland Yard and have a little talk with our friend Mr. Superintendent Miller; unless, for any reason, it seems better to look into the case ourselves.”