526 THE ROYAL SOCIETY OF CANADA 



Case 10. 



Narration. 



(Part 1) : "An east-bound passenger train travelling at the rate of 



36 miles an hour, which was due at Port Huron at 12:15 a.m., left 



Sarnia the same morning at about 2:30." 



(No. 1): "Probably the ordinary time between these points is about two 

 hours and a quarter, and the distance about 81 miles." (5/6 or 5:1). 



(Part 2) : "The train was travelling on Standard Time, and Port 



Huron is in the Central Time division while Sarnia is in the Eastern 



rime division." 



(No. 2): "In that case the ordinary time between these points is probably 

 only one hour and a quarter, and the distance about 45 miles." (5/6 or 5:1). 



(Part 3): "The train was a half an hour late at Port Huron." 



(No. 3): "Then the ordinary time between the two points is probably 

 three-quarters of an hour, and the distance about 27 miles. (5/6 or 5:1). 



(Part 4): "The train stops at Port Huron for 15 minutes." 



(No. 4): "Accordingly it is probable that the ordinary time between the 

 points is about a half an hour, and the distance about 18 miles." (5/6 or 5:1). 



(Part 5): "Sarnia is a border point where the train made its 



usual stop of some 15 minutes for custom's inspection, etc." 



(No. 5): "In view of this circumstance the ordinan,' time between the 

 points would probably be but 15 minutes, and the distance about 9 miles." 

 (5/6 or 5:1). 



(Part 6): "The distance between Port Huron and Sarnia is 



about 3 miles." 



(No. 6) : "In that case the train, already a half an hour late at Port Huron, 

 probably had an additional delay either at that place or at Sarnia." . (10/11 

 or 10:1). 



(Part 7): "Between Port Huron and Sarnia the railway passes 

 the St. Clair river by a lengthy tunnel through which the train travelled 

 at the usual much reduced speed." 



In this case the narrative of necessary conclusions, formed mostly 

 by successive brief insertions, will finally read thus: 



"An east-bound passenger train, travelling on Standard Time 

 at the rate of 36 miles an hour, was a half an hour late at Port Huron, 

 where it is due at 12:15 a.m. {Central Time) and stops for 15 minutes. 

 It left Sarnia, a border point three miles beyond, after the usual pas- 

 sage at much reduced speed through the lengthy St. Clair river tunnel 

 and after the usual stop of some 15 minutes for custom's inspection, 

 etc., at about 2:30 a.m. {Eastern Time)." 



In conclusions 1 to 5 in this case the probability of 5/6 or 5:1 

 depends on the chances that a train is run substantially on time, so 

 that, if it is due at any one station at a certain hour and leaves another 



