delivered the Opinion of the Court.
*532This is an appeal from a judgment in the amount of $1,401.47 rendered by the District Court in favor of the plaintiffs. Plaintiffs alleged in their complaint that between November 29, 1952, and November 30, 1953, they delivered to the defendant 67,570 board feet of white pine lumber.' They further alleged that the lumber was worth the reasonable value of $4,392.05 and that defendant had failed to pay any of this amount except the sum of $492.05, leaving a balance owing of $3,900. The defendant’s answer amounted to a general denial.
Upon issue being joined, the case was tried before the District Court sitting without a jury. The court found that the plaintiffs had sold and delivered to the defendant 38,153 board feet of white pine lumber at the agreed and reasonable price of $65 per 1,000 board feet; that the defendant paid plaintiffs the sum of $1,078.48, leaving a balance due and owing of $1,401.47.
There is no dispute regarding the agreement which the parties entered into. The plaintiffs agreed to sell and defendant to buy certain logs and lumber which plaintiffs cut and in some instances sawed into rough lumber. It is agreed that the white pine lumber in dispute was cut in the Harris Creek area of the Flathead National Forest pursuant to a timber sales agreement between the United States Forest Service and the plaintiffs.
At the conclusion of plaintiffs’ operations in the Harris Creek area the Forest Service log scale showed that 117,430 feet of white pine logs had been cut in that area. It is admitted that plaintiffs sold some of this white pine to mills other than to defendant. Some of this was sold in the form of logs and some in the form of rough cut lumber which the plaintiffs cut at their small mill.
Plaintiffs’ original claim was for 67,570 board feet of white pine lumber. At the trial, they introduced a tally slip which they had misplaced. This slip showed that they had been paid for more white pine than they had originally believed and re *533duced their claim by 32,280 feet. The defendant subsequently proved that plaintiffs had misplaced four other tally slips which showed payment by the defendant for 10,210 feet, thus further reducing plaintiffs’ claim.
Plaintiffs kept no records of the various deliveries, relying completely upon the tally records which were kept by the mills that bought the lumber and logs. The broad basis upon which plaintiffs based their case was that the Forest Service report showed that 117,430 feet of white pine had been cut by plaintiffs in the Harris Creek area; only a certain portion of which could be accounted for and the balance which could not be accounted for must have been delivered to the defendant in spite of the fact that plaintiffs sold white pine to other mills.
During the course of the Harris Creek operation, the plaintiffs sold defendant large quantities of fir, larch and spruce, in both lumber and log form. It is admitted that they were paid in full for this timber. It is also admitted that they were paid in full for all of the white pine logs, as distinguished from lumber, which were delivered to defendant.
Plaintiffs’ mill was set up in November of 1952 and the agreement with defendant was made the same month. According to plaintiffs’ testimony, the mill operated continuously through the winter, closing in March of 1953 due to the spring-breakup. Plaintiffs attempted to show that while the min was in operation they delivered white pine lumber to the defendant and that the defendant neither tallied nor paid them for this lumber. Defendant’s proof was to the effect that no white pine lumber had been delivered during this period. We will present the proof adduced more fully during our discussion of the case.
Six specifications of error are relied on by the defendant, appellant herein, however they all go to one proposition — that the evidence was insufficient to justify the court’s judgment.
There is a definite conflict in the testimony concerning the plaintiff’s delivery of the white pine lumber to the defendant. *534Plaintiffs’ witnesses testified that lumber had been delivered during* the period from November of 1952 to March of 1953. Their estimates of the amount are mere guesses due to the fact that they kept no records whatsoever. Defendant contradicted this testimony by setting up its entire system for processing logs and lumber and detailing its accounting system by which every piece of lumber processed was accounted for on a tally sheet and figures taken from this tally sheet and put into a sales book. This sales book showed the footage and species of all the timber which defendant processed.
It is undisputed that the manner in which the plaintiffs ascertained the amount for which they sued is the aforementioned system of deducting the amount which could be accounted for from the total cut as shown on the Forest Service report.
In an action at law, this court will not disturb the findings and judgment of the court below where there is substantial evidence to support them. State ex rel. Olsen v. Sundling, 128 Mont. 596, 281 Pac. (2d) 499.
The District Court found that between November 29, 1952, and November 30, 1953, plaintiffs sold and delivered to the defendant 38,153 board feet of white pine lumber. The finding that defendant had paid $1,078.48 amounted to a finding that plaintiffs had been paid for 16,592 board feet of tvhite pine lumber at the agreed price of $65 per thousand board feet. The finding* that the balance due was $1,401.47 amounted to a finding* that the plaintiffs had delivered 21,561 board feet of white pine lumber for which they had received no payment.
There is substantial evidence to support a finding that the plaintiffs delivered some white pine lumber to the defendant during the period encompassed by the complaint. But, the question remains, how much? All of plaintiffs’ direct evidence goes to the period from the fall of 1952 until their mill closed in March of 1953. In order to make a finding that the plaintiffs had delivered 21,561 feet of white pine lumber for which they had not received payment, the court must have *535adopted plaintiffs’ deductive reasoning theory. This is substantiated by the record which shows that from the beginning of the Harris Creek operations until July 15, 1953, the plaintiffs sold and were paid for 73,800 board feet of white pine. The Forest Service report showed that as of July 25, 1953, 83,250 board feet of white pine logs had been cut by plaintiffs in Harris Creek. This left a balance unaccounted for of 9,450 board feet, less than half of what the court found was delivered and not paid for.
The question for our decision then is whether plaintiffs’ deductive reasoning theory constitutes the substantial evidence which is required to support the court’s judgment. Substantial evidence has been defined by this court as such evidence “as will convince reasonable men and on which such men may not reasonably differ as to whether it establishes the plaintiffs’ case, and, if all reasonable men must conclude that the evidence does not establish such case, then it is not substantial evidence.” Adami v. Murphy, 118 Mont. 172, 179, 164 Pac. (2d) 150, 153, and cases cited therein.
In the instant case, plaintiffs made no real demand for payment until this suit was instituted almost three years after they allegedly delivered the lumber. The dates on which they questioned the failure to tally the white pine lumber are indefinite. Mrs. Sands testified that it was in the spring and it was warm so it must have been in April. Mr. Sands stated that he questioned defendant’s failure to tally this lumber in January of 1953 but his other testimony regarding specific dates was very uncertain and weakened his testimony on this point. The trial was held four years after the period in question. Plaintiffs kept no written records, relying solely upon their recollection of events which had transpired four years before. They delivered white pine to several mills. It is undisputed that white pine, in lumber form, is difficult to distinguish from spruce lumber, even for an experienced lumber grader. It is also undisputed that plaintiffs were paid for *536309,456 board feet of fir and lareh lumber, 4,226 board feet of spruce lumber, 443,910 board feet of fir and larch logs and 95,530 board feet of spruce logs. In addition to Mr. and Mrs. Sands, the only other witnesses who testified for the plaintiffs were Mr. Sands’ brother and Mrs. Sands’ brother, both of whom were also interested parties.
Plaintiffs’ entire suit was premised upon the discrepancy between the amount of board feet which the Forest Service report showed they cut in logs and the amount for which they could account by using* the tally slips given them by the various mills to which they delivered logs and lumber.
Looking to the entire record in the case, we do not feel there is substantial evidence to show that the plaintiffs delivered 21,561 board feet of white pine lumber to the defendant for which plaintiffs were not paid. The facts which we have set out above militate against such a conclusion. These facts are taken from the plaintiffs’ own proofs. Accepting these proofs, they demonstrate an impossbiility of the court’s findings. As related before, an unaccounted balance of only 9,450 board feet of logs cut from the Forest Service sale, during any possible time involved in the suit, remains. The burden of proof is not on the defendant to account for this. The plaintiffs did not prove by any substantial evidence that the defendant received that amount of white pine lumber.
The plaintiffs, seemingly recognizing their lack of proof, attempt to explain the difference by applying a fifteen percent overrun figure that was testified to as being usual for white pine. However, even accepting this disputed overrun in favor of plaintiffs, it does not explain the impossibility of the trial court’s findings.
For the reasons given, the judgment of the District Court is reversed.
MR. CHIEF JUSTICE HARRISON and MR. JUSTICES ADAIR, ANGSTMAN, and THE HONORABLE JAMES T, *537SHEA, District Judge, sitting in place of MR. JUSTICE BOTTOMRY, concur.