Appellant corporation sued appellee (its stockholder, officer and director), upon various theories, charging he had competed with it in the production and sale of phonograph records and accompanying booklets which presumably aided in teaching children arithmetic in various schools, public and private.

The court below (a) found the appellee-defendant not guilty of copyright infringement by publishing a book allegedly copied from a book appellant had copyrighted; (b) held appellant had no trademark rights or secondary meaning rights in the phrase “The 390 Basic Arithmetic Facts”; and that appellee did not infringe any trade-mark rights of appellant by using that term in appellee’s books and records; (c) held appellee did not violate any rights of appellant in the use of customers’ lists; and (d) found appellant damaged in the sum of $50 by appellee’s unfair competition.

All such findings and holdings are alleged as errors on this appeal, as well as (e) error in denying appellant’s motion to amend the pleadings to conform to proof by alleging a breach by appellee of an express contract to transfer to appellant “his entire right, title and interest” (emphasis added) to and in a set of records and books entitled “The 390 Basic Arithmetic Facts” and the idea behind them; (f) the same error with respect to an amendment alleging a contract implied in law to the same effect; (g) error in refusing to grant a permanent injunction against appellee preventing the sale of his records and books.

Jurisdiction below rested on 28 U.S.C. § 1338 (a) and (b), and § 1332(a) (1), and lies here under 28 U.S.C. § 1291 .

It would serve little purpose to describe and recite all the peculiar factual circumstances existing in this particular case. We doubt if any concise recital would at any time in the future aid lawyers, other than the two here involved, to understand the situation created by the parties, and each of the parties, and their respective counsel, are thoroughly familiar with the facts. We think this opinion will have little, if any, precedential usefulness.

I

Was the copyright infringed?

As the trial court pointed out, and as appellant admits, a copyright protects against a copying, but gives no exclusive right to an idea. Despite this basic assertion, appellant urges a comparison of the two treatises (compared in twenty-one instances in Appendix I attached to appellant’s brief) “will establish that appellee’s book is basically derived from, paraphrased from, and in many instances, copied from the book published by appellant.”

We know not what appellant means by the phrase “derived from” as distinguished from “copied.”

Of the twenty-one instances cited (in the twelve printed pages of appellant’s “book” and the nineteen printed pages of appellee’s “book”) there are many obvious words paraphrased. Only two of the twenty-one sentences are precisely similar — examples, C and I. These read, respectively: “Many combinations are reversible and may be stated two ways”; and “Take out a sheet of paper.” About ten other examples use similar phrases. About fifty per cent of the stressed examples are therefore, in the opinion of this court, substantially dissimilar.

“ ‘Since one work may be similar to another without having been derived from, or based on, it, mere resemblance between two works does not necessarily show that the one is a piracy of the other. It is merely evidence of copying and is more or less strong according to circumstances. In the case of works of imaginative literature, or of a strikingly original character, any considerable amount of close similarity raises a strong inference of copying. * * * In all cases, the weight of mere similarity or identity as evidence of copying depends on the likelihood of its existing in the absence of copying. * * * ’ ” Harold Lloyd Corporation v. Witwer, supra, at 16-17 , quoting 13 C.J. § 426, p. 1213.

Citation by appellant of other cases where a sufficient similarity was found by the trier of fact to justify a conclusion of copyright infringement, aids us not at all here. In Harold Lloyd Corporation v. Witwer, supra, the lower court’s finding of infringement was reversed. In American Visuals Corporation v. Holland, 2 Cir. 1958, 261 F.2d 652 , Judge Murphy found infringement based on actual and precise similarities. “Almost every idea and means of expression has been copied in its essence.” (Emphasis added.) Id. at 655 .

We agree that the test for infringement of a copyright is of necessity vague. Peter Pan Fabrics, Inc., v. Martin Weiner Corp., 2 Cir. 1960, 274 F.2d 487. That this is true is more a reason we cannot say the trial court erred, as a matter of law, in finding no infringement. Appellant concludes “in the present case, there has been extensive reproduction of the exact terminology.” We respectfully disagree. As stated above, two precisely similar sentences out of many hundreds, is not, in our view, an “extensive reproduction of the exact terminology.” We concede the two compared booklets show a general similarity, but (with the two previously noted exceptions) no precise duplication. A “copyright is not infringed by an expression of the idea which is substantially similar where such similarity is necessary because the idea or system being described is the same.” Baker v. Selden, 1879, 101 U.S. 99 , 25 L.Ed. 841 . Nor can we term or classify such sentences so reproduced as “important and vital part[s] of the two compositions,” as were the two lines from the copyrighted lyrics in Whitney v. Ross Jungnickel, Inc., S.D. N.Y.1960, 179 F.Supp. 751 ; nor can we conclude the alleged infringing matter “gets so close to the copyrighted] matter that it is practically the same.” Cash Dividend Check Corporation v. Davis, 9 Cir. 1957, 247 F.2d 458 .

We affirm the finding of the court below of no infringement, holding it committed no clear error in so finding.

II

We must first keep in mind that the only trade-mark obtained by appellant contains the words “Caddy-Imler Creations” placed in a circular design containing a likeness of the “lamp of knowledge” (Ex. 2a). It does not bear the words “The 390 Basic Arithmetic Facts.”

There was evidence that that phrase was known to the teaching profession long prior to its use by appellant. It is based on the three hundred and ninety possible combinations into which the numbers zero to nine, inclusive, can be arranged. According to the witness Dale Carpenter, Mathematical Supervisor of the Los Angeles City Schools, the phrase is a “common working phrase” known to him for at least twenty years. The three hundred and ninety facts are contained in many basic arithmetic books, including Mr. Carpenter’s series “The World of Numbers”, and Exhibits B and C in evidence.

Appellant protests that the trial court relied upon the testimony of a single witness (Mr. Carpenter) in its determination that the phrase in question had no secondary meaning, despite other testimony to the contrary. That is the trial court’s privilege, and we are not privileged to overrule the trial court. Dierks Lumber & Coal Company v. Barnett, 8 Cir. 1955, 221 F.2d 695, 696 ; Simmonds v. United States, 9 Cir. 1952, 199 F.2d 305, 307 . See also, Riddell v. California Portland Cement Company, 9 Cir. 1962, 297 F.2d 345 (No. 16438, amended and revised January 2, 1962). The court relied on the testimony of witness Carpenter, because it found him “the best expert we have had.” That was, and is, an excellent reason for such reliance. Tuck v. United States, 9 Cir. 1960, 282 F.2d 405, 410 ; Hamilan Corporation v. O’Neill, 1959, 106 U.S.App.D.C. 354 , 273 F,2d 89, 92; Padgett v. Buxton-Smith Mercantile Company, 10 Cir. 1958, 262 F.2d 39, 41 .

Ill

Appellee had made up for appellant’s use (during the time his association with it had been friendly) a list of potential customers taken from publicly available school directories published by school authorities in various states and large cities. He made up his own list, from the same sources, after he terminated his association with appellant corporation, using, in addition, subsequently published publicly available directories from the three largest states (Ex.’s D, I and J).

Thus, if appellee is to be believed, he received no confidential information from his corporate employer other than perhaps thirty invoices (Ex. 60) of appellant’s sales. Appellee says he had possession of the invoices, but used only publicly available material for his lists. Appellant says appellee had the opportunity to use more than that, but offers no proof he did, other than using names from invoices that were also on publicly available lists. The court found only published directories were used to make up the list. (Finding XV.) On the record before us, that finding is not clearly erroneous.

Appellee sold all together about two hundred and fifty sets of records — some of them to customers of appellant. But how many of such customers were not named in publicly available school directories does not appear in the record. We do not find either Sketchley v. Lipkin, 1950, 99 Cal.App.2d 849 , 222 P.2d 927 , or Audio Fidelity, Inc. v. High Fidelity Recordings, Inc., 9 Cir. 1960, 283 F.2d 551 (or the remaining California cases cited by appellant) apposite to the facts contained in this record. This record supports the court’s finding “that there is no evidence that the defendant at any time used a confidential customers’ list.” (Emphasis added.)

IV

This brings us to the question of damages for unfair competition in which the court found appellee engaged in setting up a rival organization for the manufacture and sale of phonograph records and an accompanying booklet to aid in the teaching of arithmetic, during the time he remained an officer, director and employee of appellant corporation, although he had purportedly endeavored to sever his connections with appellant.

The court below confessed he was hard put to find that appellant had suffered any damage by appellee’s actions. Appellant testified to none. Appellant had a bigger sales year in 1960, after appellee’s competitive acts commencing in December of 1959, than it had had in any year before. “It is true,” said the court, “that defendant [appellee; during a certain period] sold 135 to 150 sets. But that doesn’t necessarily mean that the plaintiff corporation could have sold 135 to 150 sets * * * ”, or 175 sets, or any other number of sets more than it did.

Appellant urges the rule that “nominal damages are deemed inadequate where the plaintiff has sustained actual damage that is susceptible of measurement.” That, of course, is good law, but does not solve any problems where there is no proof of actual damage susceptible of measurement. That was precisely the state of the evidence, as the trial judge found it.

Further, the trial judge was troubled by the fact that “If I render a judgment, one-half of the judgment will belong to the defendant because he is owner of one-half of the [plaintiff] corporation.” And so, in an attempt to render an equitable decision and accomplish rough-hewn justice between the parties, the trial judge suggested that the Imler’s buy out Caddy’s stock interest in Caddy-Imler Creations, Inc. This was done after the trial, and before judgment. (Finding XIX.)

Appellant presumes that this influenced the award of damages by reducing the amount. We do not presume it influenced the trial judge any more than we would presume the trial judge would have been influenced by the fact that appellee, as a fifty per cent stockholder, would be entitled to one-half of any damages awarded against him if he did not sell his stock.

This court might not have awarded so small a judgment. But the trial court here did award a small judgment and had reason to do so. We cannot “second-guess,” and find no error.

V

The motions to amend.

The testimony is conflicting as to whether there was any agreement, express or implied, that Caddy would transfer his entire right, title and interest in and to the books and record sets to appellant, including therein all rights to Caddy’s idea of the existence of “The 390 Basic Arithmetic Facts.” (We doubt if Mr. Caddy had any title to such an idea that he could have transferred.) There was no reference in the written agreement made by the parties that Caddy purported to sell his idea; nor was there any attempt to incorporate a provision prohibiting competition by Caddy with his assignee. But we need not decide whether Caddy had the right to assign his idea. A motion for leave to amend is addressed to the sound discretion of the court, and must be decided upon the facts and circumstances of each particular case. Under the facts of this case, there was no clear abuse of discretion in the trial court’s refusal to change the entire legal theory of the case after the introduction of all evidence was complete. Fed.R.Civ. P. 15(a), 28 U.S.C. See Shubin v. United States District Court, 9 Cir. 1961, 299 F.2d 47 (No. 17590, decided December 29, 1961); County of Marin v. United States, N.D.Calif.1957, 150 F.Supp. 619 .

VI

Neither is there any basis for urging that the trial court was required to issue a permanent injunction against appellee. That trade-mark infringement should be permanently enjoined rests upon proof of the validity of the trade-mark and the fact of infringement, plus acts which make damages unascertainable or inadequate as a remedy. Only the first was here proved. That unfair competition, once established and for which damages have been awarded, must be forever enjoined violates the fundamental theory underlying the limited use of the injunctive process — i. e., that it should issue only when irreparable damage occurs, or is likely to occur, or where the ascertainment thereof is impossible, or nearly so. Beacon Theatres v. Westover, 9 Cir. 1958, 252 F.2d 864 , 873; Ogden River Water Users’ Ass’n v. Weber Basin Water Conservancy, 10 Cir. 1956, 238 F.2d 936, 942 . We think the trial judge wise in concluding he should, on this aspect of the case, permit the future to develop as it might.

Finding no error, we affirm the judgment rendered below.

. Exhibit B is entitled: “Refresher Arithmetic, With Practical Applications,” by Edwin D. Stein, published 1947, by Allyn & Bacon. Exhibit C is entitled: “The Number Combinations. Their Respective Difficulty and the Frequency of Their Appearances in Text Books,” by Frank L. Olapp, published in 1924 by School of Education, University of Wisconsin. . For example, Defendant’s Exhibit N is a “Guide to Schools and Offices” of the Los Angeles City School Districts, 1958-1959, lists all principals and vice principals, and the addresses of all elementary, handicapped, junior high, senior high and adult schools and junior colleges in the city — some 250 in number.