"As I Have Repeatedly Told You, My Interest in These Matters is Purely Theoretical, and Confined to the Processes of Deduction"

HERE WE HAVE another in our intermittent series of mysteries, sometimes tenuously and sometimes unmistakably, tied into railways, this one featuring a detective character with a successful track record spanning thirty-six years:

   "Dr. Lancelot Priestley was created by John Rhode and appeared in, oh, at least three dozen novels beginning with The Paddington Mystery (1925) and continuing through 1961. Priestley is an English mathematician and former professor who was forced to resign his position after an ugly argument with the university authorities. Because of his personal income and intelligence he was able to spend his time writing books on math and popular myths, which he would debunk through the application of logic. For fun he spends his time solving crime problems, upon which he brings his considerable intellect and abilities and logic to bear. Priestley is a somewhat cold person, although he can be a friendly host; he has a marked disappreciation for the human element of the crimes he solves. He lives and works in his house in Westbourne Terrace in London."
   — Jess Nevins, Pulp Adventure Heroes

"The Elusive Bullet."
By John Rhode (Cecil John Charles Street, 1884-1964).
First appearance: Unknown.
Reprinted in The Second Omnibus of Crime (1932) and 
World's Great Detective Stories: American and English Masterpieces (1943).
Short story (15 pages).
Online at UNZ (HERE).

"Poor girl! To lose her father so tragically, and then to see the man she loves accused of his murder!"

A man is shot through the head on the 2.15 from Fenchurch, a moving train, and the prime suspect, the victim's young business partner, can't provide a reasonable alibi, with every piece of circumstantial evidence pointing straight at him. Only incidentally does Professor Priestley become involved in the case, but once he does his unwavering commitment to the facts, his superior mathematical skills, and a fact-finding field trip will combine to completely explode the murder scenario the police have constructed against the young man and pave the way for wedding bells.

The characters:
~ Dr. (or Professor) Priestley:
  His hobby: "the mathematical detection of crime."
~ Harold Merefield:
  Dr. Priestley's secretary.
~ Inspector Hanslet:
  With the C.I.D.: "an old friend of ours, who availed himself of the Professor's hobby."
~ Mr. Farquharson:
  The victim: a "Prominent City Merchant," according to the newspaper headline.
~ Robert (Bob) Halliday:
  The prime suspect: the victim's nephew, "a rather wild young fellow."
~ Miss Mary Farquharson:
  Halliday's fiancée: "the daughter of the fellow who was murdered the other day."
~ The firing range-wardens at Purfleet and Rainham and a young officer at the 
Arsenal at Woolwich.

Priestleyisms:

   "You know perfectly well, Inspector, that I most strongly deprecate all conjecture. Conjecture, unsupported by a thorough examination of facts, has been responsible 
for more than half the errors made by mankind throughout the ages."

   "I have always remarked that Hanslet's difficulties are comparatively easy of 
solution, but that what he calls simple problems completely baffle his powers 
of reasoning."

   "Well, if you can spare the time, I should like to introduce you to the murderer 
of Mr. Farquharson."

   "Speaking without a full knowledge of the facts, I should say that this rather 
tended to establish his innocence."

   "Well, guesses must hit the truth sometimes, I suppose."

Dr. Priestley

   "You cannot expect the average juryman to have an intelligence superior to yours, you know."

   "How often am I to tell you that facts are all that matter? Our journey to-morrow will be for the purpose of ascertaining facts. Until we know these, it would be waste of time to indulge in conjecture."

   "Very puzzling, very! There must of course be some explanation. A mathematical deduction from facts can never be false."

   "At this point it occurred to me that my theory was incapable of proof, although I still adhered to my view that it was correct."
   
   "There you see the murderer of Mr. Farquharson."

Resources:
- The basic facts about John Rhode are on Wikipedia (HERE) and the GAD Wiki (HERE), but Mike Grost's page at his Guide to Classic Mystery and Detection website (HERE) has much, much more.