What is the test for proving a claim by a preponderance of evidence?

I believe the learned author of The Law of Evidence in Canada, supra, had in mind the precise situation confronting me. I quote again from page 155: Cartwright J. in Smith v. Smith, [1952 CanLII 3 (SCC), [1952] 2 S.C.R. 312, [1952] 3 D.L.R. 449] articulated the test as follows: . . .that civil cases may be proved by a preponderance of evidence or that a finding in such cases may be made upon the basis of a preponderance of probability and I do not propose to attempt a more precise statement of the rule. I wish, however, to emphasize that in every civil action before the tribunal can safely find the affirmative of an issue of fact required to be proved it must be reasonably satisfied, and that whether or not it will be so satisfied must depend upon the totality of the circumstances on which its judgment is formed including the gravity of the consequences of the finding. Simply put, the trier of fact must find that “the existence of the contested fact is more probable than its nonexistence.” Conversely, where a party must prove the negative of an issue, the proponent must prove its absence is more probable than its existence. [Emphasis added]