OPINION
Posner, Circuit Judge.
Abbott Laboratories filed suit for patent infringement in 1997 against TorPharm, a manufacturer of generic pharmaceutical drugs, and affiliates of TorPharm unnecessary to discuss separately. 35 U.S.C. § 271(e)(2)(A). The district court granted summary judgment in favor of Abbott on both validity and infringement. 156 F.Supp.2d 738 (N.D.Ill.2001). The Federal Circuit affirmed the validity of Abbott’s patent but remanded for a trial on infringement. 300 F.3d 1367 (Fed.Cir.2002). I was designated to conduct the trial pursuant to 28 U.S.C. § 291(b)—a bench trial, because Abbott is seeking only equitable relief. Indeed, it could not seek damages, because TorPharm has not yet begun to market its generic substitute for Abbott’s product. The trial was conducted between February 23 and February 27 of this year, and I now set forth my findings of fact and conclusions of law.
The patent (actually two patents, U.S. Patent Nos. 4,988,731 and 5,212,326, but they differ in only one material respect, discussed later, so in most of the opinion I shall treat them as one) is on a chemical called divalproex sodium, which Abbott sells under the trade name Depakote for the treatment of epilepsy and other ailments. The chemical formula is (C16H31 Na04)n, with the “n” signifying that the chemical unit is repeated n times. Dival-proex sodium, the unit, is a combination, of a type commonly called a “complex,” of two molecules, one of sodium valproate and the other of valproic acid. Each molecule contains valproate, an organic compound composed of carbon, oxygen, and hydrogen atoms, and it is the valproate that is responsible for the therapeutic properties of the drug. The other constituents of the complex — a sodium ion in the sodium valproate molecule and an extra hydrogen atom in the valproic acid molecule — do no therapeutic work. The chart at the end of this opinion (“Atwood 1” — a demonstrative exhibit used by Abbott’s expert witness at the trial) contains a diagram of divalproex sodium and its constituent molecules (with the valproate itself
designated “V”) together with some of the other data referred to in this opinion.
Although either sodium valproate or val-proic acid would have all the therapeutic properties of divalproex sodium, neither is as easy to manufacture into pills — valproic acid because it is a liquid and sodium valproate because it is hygroscopic, that is, attracts moisture from the atmosphere, which makes it semi-liquid unless costly efforts are undertaken to remove the moisture from the atmosphere of the manufacturing plant. When sodium valproate and valproic acid combine to form divalproex sodium, however, the result is a nonhygro-scopic, crystalline solid (powder or flakes) better suited for manufacturing into pills than either of its constituents.
What holds the sodium valproate molecule to the valproic acid molecule? A normal atom has a neutral charge because it has the same number of protons and electrons and because the other atomic particle, the neutron, has no charge. An ion is an atom that has a different number of protons and electrons and therefore carries a positive charge (if it has more of the former) or a negative charge (if it has more of the latter). The sodium atom in the sodium valproate molecule is a positively charged ion, because the oxygen in the valproate “steals” an electron from that atom. The ion is attracted to the (negatively charged) electrons in the oxygen atoms of the valproic acid molecule (see Atwood 1), bonding the two molecules.
For reasons that have never been adequately explained, the patent examiner before whom Abbott prosecuted its patent application insisted that the patent claims include a specification of the chemical structure of divalproex sodium beyond what I have just described. Abbott obliged by claiming that divalproex sodium is an oligomer consisting of about 4 to 6 units of the divalproex sodium. In one of the patents, the number of units is not specified, but the parties make nothing of this; in effect they have agreed that if TorPharm’s product contains no fewer than 4 and no more than 6 or 7 units, it infringes both patents.
Just as the' two molecules combine to form the divalproex sodium complex, ‘ so two or more of these complexes might join together to form a larger structure, such as a crystal, which might consist of millions or billions of identical units, whether atoms, molecules, or looser complexes. A polymer, usually a “soft” structure (many proteins are polymers) compared to a crystal, and usually classified as a molecule— although a very loosely bound polymer might instead be described as a “coordination polymer” — is an assemblage of a large number of smaller molecules. It is like a crystal (indeed sodium valproate, which
is
a crystal, was also described by one of the expert witnesses as a coordination polymer), but it needn’t be solid and it will usually not be as extensive, although some proteins consist of thousands of lesser molecules.
At the opposite extreme is a monomer. If the divalproex sodium complex — this bound pair of valproate molecules — does not have any discernible linkage with neighboring divalproex sodium complexes, so that a batch of divalproex sodium would be a loose mixture, like the grains of sugar in a teaspoonful of sugar (which is a mixture of sugar crystals — the mixture itself having no structure, whether crystalline or otherwise), then divalproex sodium is a monomer.
An oligomer, as the name implies, is an assemblage of several rather than, as in the case of .a polymer, many identical units, in this case divalproex sodium complexes. In other words, it is a small polymer. TorPharm’s product must be an oli-gomer of about 4 to 6 units to infringe Abbott’s product. Divalproex sodium in
the solid state is a crystal, and a crystal is a structure of many repeating units, but it could be composed of oligomers loosely connected to each other to form the crystal. Alternatively, it could be composed of monomers, as I have already noted, or it could be a polymer; in either event it would not be infringing.
TorPharm insists that to count as an oligomer the units constituting the aggregate in question must be connected “end to end” in the special sense of forming a row, rather than a circle or sphere or any other shape other than simple horizontality. There is no basis in the scientific literature, the patent itself, the proceedings before the patent office, or the Federal Circuit’s opinion for so restrictive a definition.
Although the exact structure of the divalproex sodium complex is, as I’ll explain, unknown, the expert testimony indicates that each of the two molecules composing it has a “head” and a “tail.” The tail is a chain of carbon and hydrogen atoms constituting part of the valproate; in the diagram at the end of this opinion, the tail is shown as the top layer of the upper molecule, the sodium valproate molecule, and the lower layer of the lower molecule, the valproic acid molecule. The “head” is mainly sodium and oxygen in the case of sodium valproate and oxygen and hydrogen in the case of the valproic acid molecule. Because sodium “loves” oxygen (chemists actually talk this way), and its affection is reciprocated, the heads of the two molecules want to nestle together. The carbon and hydrogen atoms in the tails are less passionately attracted to each other, but likes do sometimes attract (though sometimes repel, as when two particles have either a positive or a negative electrical charge), and so they want to be touching each other too. The tails of the two molecules composing the divalproex sodium complex cannot touch each other, but each tail can touch a tail of an adjacent divalproex sodium complex. The affinities of the heads for one another and, perhaps as well (though the record is unclear on this point), the weaker affinities of the tails for one another bind the divalproex sodium complexes into an oligomeric structure. The heads and the tails are the ends of the divalproex sodium complexes, and so the complexes are connected “end to end,” just not horizontally, and so satisfy the legal (patent office and Federal Circuit) and scientific definition of oligomer.
The tails of the divalproex sodium complexes are larger than the heads. There are 44 atoms in the two tails (which incidentally are forked, as shown in the diagram), compared to only 8 atoms in the two heads. After the divalproex sodium complex has repeated itself four to seven times, the tails become as it were entangled and lose most of their ability to attract neighboring complexes, while after a certain point the crowding of sodium ions in the heads creates a repulsive force, since like-charged particles repel each other. Hence the oligomeric structure: a structure that peters out after a few repetitions of its constituent units. But remember that divalproex sodium is a crystal. Each tiny crystal (and the crystals are tiny, as we’ll see, unlike a diamond, for example, which is a crystal of carbon) contains a large number of oligomers. Since a crystal has a definite and uniform structure, there must be some attractive force holding the oligomers in that structure, but it is weaker than the forces holding the units within each oligomer together.
Such at least is Abbott’s theory of why divalproex sodium is an oligomer rather than a polymer or a monomer. At the first round in the district court and before the Federal Circuit on appeal, TorPharm vigorously contested the validity of Abbott’s patent, contending that divalproex sodium is not, as the patent claimed, an
oligomer. But the Federal Circuit held unequivocally that divalproex sodium, or more precisely Abbott’s divalproex sodium, is an oligomer. 300 F.3d at 1372, 1378. That is the law of the case, and it binds me. E.g.,
United States v. Husband,
312 F.3d 247, 250 (7th Cir.2002).
But the qualification
(Abbott’s
divalproex sodium) is vital. Only if TorPharm’s product, which is also divalproex sodium, is an oligomer is TorPharm infringing. Now one way in which TorPharm’s product might not be an oligomer, even though it has the same chemical constituents as Abbott’s, is that it might not consist of a 1:1 ratio of sodium valproate to valproic acid at the molecular level, that is, might not consist of paired molecules of sodium valp-roate and valproic acid. If its product consisted, say, of two sodium valproate molecules bound to one valproic acid molecule, it might not form up into an oligomer. But this issue too is foreclosed by the Federal Circuit’s decision, which states that TorPharm’s product, like Abbott’s, has a 1:1 ratio of sodium valproate to valproic acid at the molecular level. 300 F.3d at 1374-75.
“At the molecular level” is another important qualification. A given quantity of TorPharm’s divalproex sodium might contain the same number of sodium valproate and valproic acid molecules, yet they might not be paired — one sodium valproate molecule with one valproic acid molecule in a divalproex sodium complex. But as I have noted, the Federal Circuit held that they are paired.
If, then, TorPharm’s product like Abbott’s is a divalproex sodium complex consisting of a pair of sodium valproate and valproic acid molecules, and if as the Federal Circuit also held Abbott’s product is an oligomer, it is difficult to see how TorPharm’s product could be anything else. For these findings imply that the two. products are identical. And in fact TorPharm’s major, contention throughout the trial before me and ever since the case began seven years ago is that neither firm’s product is an oligomer. See, e.g., 2003 WL 22462614, at *15 (N.D.Ill. Oct.29, 2003) (opinion of Magistrate Judge Nolan). TorPharm argues that its failure to convince the Federal Circuit by clear and convincing evidence — which is what you need to invalidate a patent — that Abbott’s product is not an oligomer should not prevent it from showing at the infringement stage of the litigation, where the burden of persuasion is on Abbott, .that Abbott’s product is not an oligomer and therefore TorPharm, whatever the structure of its product, cannot have infringed Abbott’s patent because the patent is invalid. But this collateral attack on validity is impermissible. Cf.
Heck v. Humphrey,
512 U.S. 477, 483-87, 114 S.Ct. 2364, 129 L.Ed.2d 383 (1994). It would mean that .every infringement case in which- validity was questioned would require two trials of validity, the first with the infringer having the burden of proof (to prove invalidity) and the second with the patentee having the burden (to prove infringement and in the course of doing so to prove validity). That doesn’t make sense. I must take for granted that Abbott’s product is an oli-gomer.
Because the Federal Circuit remanded the case for a trial on infringement, however, I cannot take the position that since Abbott’s product is an oligomer and TorP-harm’s product is chemically identical, consisting of the identical molecules in the identical ratio, TorPharm’s product must be an oligomer. I imagine that that is the case. But it is conceivable, or at least must have seemed so to the Federal Circuit — otherwise it would not have remanded the case for a trial on infringement— that differences in the production process (Abbott uses a solvent in manufacturing divalproex sodium and TorPharm does
not — TorPharra just mixes the sodium valproate and the valproic acid and heat's the mixture, producing the crystalline divalproex sodium) may somehow prevent the oligomeric structure from forming. In effect, the Federal Circuit’s decision can be interpreted as an acknowledgment that as. a matter of- theory, indeed of logic, TorPharm’s product must be oligomeric, but as insisting that this be shown empirically. And so that is what Abbott tried to do at the trial before me.
Its principal witness was an eminent supramolecular chemist, Dr. Jerry Atwood. Atwood conducted a series of tests on a batch of TorPharm’s product. I shall summarize his testimony but interrupt the summary from time to time to consider the criticisms by TorPharm’s legal team and by its testifying experts (who conducted no tests themselves). The first thing he looked at was the melting point of the batch. He found that it is much lower than the melting point- of sodium valproate alone, roughly 100 degrees Centigrade versus more than 400 degrees. Sodium valp-roate like divalproex sodium is a crystal, but its high melting point suggested to Atwood that the molecules are held together in the crystalline structure by strong bonds. The much lower melting point of divalproex sodium suggests that it is held together by weaker bonds. Think of the sodium valproate as a single long sausage and the divalproex sodium as a series of sausage links that can be broken just by cutting the links without having to. cut through an entire sausage. Atwood found, consistent with this analogy, that dival-proex sodium dissolves more easily, in a weak (nonpolar) solvent, namely cyclohex-ane — -that is, is broken up more easily— than sodium valproate is, because of the weak link constituted by the bonds that join oligomers to one another.
He also found that sodium valproate dissolves more easily than divalproex sodium in water. And recall that. sodium valp-roate is hygroscopic while divalproex sodium is not. These, too, are clues to a structural difference. The fact that sodium valproate dissolves easily in water and is hygroscopic and that divalproex sodium is neither suggests that the sodium atom in sodium valproate is on the outside of the molecule but that the sodium atom in the divalproex sodium complex is inside and so is shielded by the carbon-hydrogen tails from combining with the oxygen in the moisture. (As a detail, I note that the reason that sodium ions pull oxygen out of water but not out of air is that the (negatively charged) electrons of the two oxygen atoms in 02 (the form in which oxygen exists in the air) are between the oxygen nuclei, which “hides” them from the positively charged sodium ion.) This is further support for the model of divalproex sodium as an oligomer held together by the attraction of the sodium ions and the oxygen in the molecules’ heads and (possibly) by the weak attraction of the carbon-hydrogen tails.
Atwood then conducted a freezing-point depression test on TorPharm’s product. This is called a “colligative property” test because it tests for the number of molecules or other particles rather than the kind of molecule or particle. If a solid is dissolved in water or some other-solvent, the freezing point of the solution will be lower than the freezing point of water alone, because the solid interferes with the “desire” (I continue in the anthropomorphizing vein) of the water molecules to crystallize. That is the theory behind salting the roads in winter. And so the more molecules of the solvate (the substance dissolved in the solvent) there are, the lower the solution’s freezing point will be. This relation enables molecular weights to be determined. If we know how many solvate molecules the solution must contain to make its temperature fall
x
degrees
below the freezing point of the solvent, then, since we know the weight of the solvate, by dividing that weight by the number of molecules in the solvate we will come up with the weight of each of those molecules, assuming it is a uniform compound.
Molecules are not the only particles that can be weighed in this fashion. The weights of each of the atoms in an individual divalproex sodium complex being known, Atwood could calculate before he performed the test that each complex weighs 310 molecular weight units. Hence if a solvent were used that would break up a batch of divalproex sodium into its constituent complexes and the freezing point of the solution relative to that of the solvent was calculated and from that calculation was derived the number of complexes in the solution, division of the weight of the solvate by the number of complexes would be expected to yield the number 310 — if the complexes were monomers. The number Atwood actually came up with when he performed a series of freezing-point depression tests on a batch of TorPharm’s product was six to seven times as large. He inferred that what he was weighing was an oligomer of divalproex sodium.
Atwood had used a gentle (low-polarity) solvent, cyclohexane, which he believed was strong enough to break apart the batch into its constituent oligomers but not strong enough to break up the oligomers themselves. Had he used water as the solvent, it would have broken them up. Because water contains oxygen in a form that makes it irresistible to any sodium ions in the vicinity, if you place divalproex sodium in water the oxygen in the water rips the sodium out of the divalproex sodium, destroying its structure. Cyclohex-ane, a compound of carbon and hydrogen very similar to the tails of the divalproex sodium complex, does not have that disruptive effect. It contains no oxygen and so does not lure the sodium ions out of the divalproex sodium complexes.
Atwood performed a very similar — really a mirror-image — eolligative-property test called vapor phase osmometry, with similar results, except that the weight found was only five to six, rather than six to seven, times the weight of a single divalproex sodium complex. Just as dissolved solids interfere with the solvent’s desire to crystallize, so they interfere with the solvent’s desire to evaporate if it is heated or otherwise pressured, and from the rate of evaporation and the cooling effect that varies with that rate molecular weights can again be determined. The discrepancy in the test results appears to be due to the fact that the vapor phase osmometry test is less accurate than the freezing-point depression test.
TorPharm makes two very bad arguments against Atwood’s interpretation of the test results. The first is that all Atwood was doing was weighing things, and an oligomer is not a weight measure. What Atwood was doing of course was inferring structure from weight. If you weigh particles of divalproex sodium and instead of weighing what a single dival-proex sodium complex weighs the complex weighs six times that, it is inferable— though not with certainty, as I am about to point out — that what is being weighed is an oligomer. As the Federal Circuit pointed out, “a trier of fact might well infer the existence of the claimed oligomeric species from Abbott’s [i.e., Atwood’s] molecular weight data.” 300 F.3d at 1377; see also 2003 WL 22462614, at *25.
TorPharm’s second very bad argument is that the only way to determine the structure of a crystal is to perform a single crystal x-ray diffraction test on it. What is true is that the only
certain
way to determine whether a crystal is oligomeric is to perform such a test. But Atwood
testified without contradiction that when he examined divalproex sodium under the microscope, he saw that the facets of the crystals were too small to allow such a test to be performed. And in fact no such test has, so far as anyone knows, ever been performed successfully on divalproex sodium. To argue that therefore Abbott must lose is absurd, quite apart from the fact that the patent office and the Federal Circuit found that divalproex sodium is an oligomer on the basis of tests similar to those performed by Atwood, and, as I just noted, the Federal Circuit was explicit that oligomeric structure could be inferred from such tests. And Atwood testified without contradiction that when a single-crystal x-ray diffraction test can be performed on a crystal, it usually confirms rather than contradicts the results of the colligative property tests. The burden of proving infringement is the typical civil burden of a preponderance of the evidence, meaning that the plaintiff has merely to convince the trier of fact (me) that his position is more probably true than the defendant’s. If I find that it is more likely that TorPharm’s product is an oligomer than that it is not an oligomer, Abbott wins.
TorPharm’s only good argument against the evidence of the freezing-point depression test, though not good enough, is that the inference of oligomeric structure is an artifact of the test. Another way to put this is that divalproex sodium may be an oligomer when it is in liquid form, but not when it is in solid form, and it is the solid form that is TorPharm’s product. If it is not oligomeric in the solid form, the fact that it may be oligomeric in the liquid form is irrelevant. One of TorPharm’s two expert witnesses, Dr. Thomas Barton, testified that he believes that the solvent caused the divalproex sodium complexes, which he believes are monomers, to rearrange themselves into loose oligomeric clusters called inverse micelles because the carbon-hydrogen tails of the divalproex sodium complexes are attracted to cyclohex-ane, which is also a compound of carbon and hydrogen.
The disagreement between him and Atwood, both of whom agree that the divalproex sodium tails are attracted to cy-clohexane, is that Barton thinks that the cyclohexane caused the divalproex sodium complexes to form an oligomeric structure, whereas Atwood thinks that the oli-gomeric structure preexisted and was unaffected by the solvent. He testified that if the solvent he used, the cyclohex-ane, had created inverse micelles, as Barton believed, then the greater the concentration of the solvate (that is, of the divalproex sodium), the larger the inverse micelles would be. More of them would be bumping up against each other, and when they bumped their tails would bond and the inverse micelle would grow. If the inverse micelles didn’t bond when they bumped, this would show that the clusters were oligomers, that is, that they had a structure that collapsed after reaching only a modest size. Since the molecular weights found by Atwood were independent of the concentration of dival-proex sodium in the cyclohexane, this suggested a more stable structure than an inverse micelle — namely an oligomer, in which the clumping of complexes quickly reaches a limit.
Atwood was the more credible witness, in part because Barton, when asked for an example of a similar compound that would behave in this fashion though it was not an oliogomer, gave as his only example ben-zoic acid, which, unbeknownst to him, is in fact an oligomer, as established without contradiction on rebuttal. In addition, Barton admitted that he didn’t know that sodium valproate is practically insoluble in cyclohexane and that divalproex sodium is soluble in water, which suggests a general
lack of familiarity with the relevant chemistry. He conceded, moreover, that Atwood could be right that divalproex sodium in the solid state is an oligomer. He also said that Atwood had performed the freezing-point depression and vapor phase os-mometry tests correctly. He did not testify about the fast atom bombardment (FAB) mass spectrometry test performed by Atwood and discussed next.
In that test, a batch of TorPharm’s product was mixed with glycerol to form a paste that was then bombarded by atoms accelerated to about 20,000 miles per hour. When the atoms hit the paste, they caused its constituents, including the divalproex sodium, to vaporize and fly up, often in badly broken or shattered form, into a tube equipped with a detector. The mangling of the constituent particles is important, because the detector will record only positive ions. Those ions are then channeled through an analyzer that generates a spectrum from which their weight can be determined. Most of the ions, having been badly shattered by the atom bombardment, are quite small. Some of them, however, were found to have molecular weights indicative of oligomeric structure, as in the freezing-point depression and vapor phase osmometry tests, although the largest had only four units, the minimum.
Again TorPharm makes the bad argument that all Atwood was doing was measuring weight, and not structure. It also arg-ues that Atwood should have used similar but newer tests, namely MALDI and ElectroSpray. But Atwood explained that those tests are designed for measuring much larger masses and that for the masses (no greater than 2000 molecular weight-units) relevant to determining the oligomeric structure of divalproex sodium the FAB mass spectrometry test does fine. TorPharm itself did not attempt to use these other tests to determine the structure of its product.
TorPharm’s second expert witness, Dr. David Hercules, pointed out that all the weights found by Atwood were consistent with the ions all being ions of sodium valproate rather than of divalproex sodium, and indeed the spectrum that Atwood derived is almost identical to the spectrum of sodium valproate. So what is going on? What happened to the valproic acid? Atwood thought that it must have been converted either by interaction with the glycerol or by the violence of the atom bombardment to sodium valproate, so that the oligomer, instead of consisting of, say, four molecules of sodium valp-roate and four molecules of valproic acid (in a four-unit oligomer — six and six in a six-unit oligomer), when it reached the detector consisted of eight molecules of sodium valproate.' That would still signify that TorPharm’s divalproex sodium is an oligomer.
The conversion of a molecule of valproic acid into a molecule of sodium valproate would occur if a hydrogen ion in the val-proic acid was replaced by a sodium ion. Atwood conjectured that the bombardment of the divalproex sodium-glycerol paste had wrenched a number of sodium ions free from the sodium valproate molecules. (There is also “free” sodium in the atmosphere of the tube.) Remember that sodium ions have a passion for oxygen, and this might impel them to shove a hydrogen ion out of the valproic acid molecule and take its place, forming a sodium valproate molecule.
Hercules pointed out that it would be unlikely that four sodium ions would knock out the identical number of hydrogen ions in a divalproex sodium oligomer all at once, and if instead they.did it in intervals some valproic acid, which has a different spectrum from sodium valproate, should have been recorded by the analyzer. His theory was that all that Atwood had re
corded was a bunch of sodium valproate molecules, rather than an oligomer in which the valproic acid molecules had been converted into sodium valproate molecules without destroying the oligomeric structure. The problem is that his theory is even less probable than Atwood’s, and as readers of Hume’s critique of miracles will recall, if there are only two theories offered to explain some phenomenon (such as the FAB spectrum of TorPharm’s product), then it is sensible to believe the more probable even if neither theory is highly probable. Hume reasoned that either the Christian miracles had occurred, that is, that there was a supernatural explanation for them, or that the witnesses who had testified to them were lying or mistaken, in which event the so-called miracles had a purely naturalistic explanation. He argued that even if the naturalistic theory seemed improbable, it should not be rejected if the supernatural explanation seemed even less probable. See David Hume,
Enquiries Concerning the Human Understanding and Concerning the Principles of Morals
114-16 (L.A. Selby Bigge ed., 2d ed.1902), and for the application of Hume’s theory to problems of legal proof,
Sandoval v. Acevedo,
996 F.2d 145, 150 (7th Cir.1993);
Spitz v. Commissioner,
954 F.2d 1382, 1384 (7th Cir.1992); Ronald J. Allen, “Factual Ambiguity and a Theory of Evidence,” 88
Nw. L.Rev.
604, 611 (1994); Allen, “The Nature of Juridical Proof,” 13
Cardozo L.Rev.
373, 409-40 (1991); Allen, “A Reconceptualization of Civil Trials,” 66
B.U.L.Rev.
401 (1986).
Similarly here, while Atwood admitted that his explanation of the FAB results was improbable (though Abbott did submit scientific literature suggesting that such ion exchanges do sometimes occur), Hercules’ explanation was even more improbable, because he had no explanation for the disappearance of the valproic acid. That is, no explanation until, either right before or maybe even during the trial, he came up with the idea that maybe TorPharm’s product contains microcrystals of sodium valproate in a spherical shape, with a coating of valproic acid. Because of the shape of the crystals, some of the sodium valp-roate' 'molecules — the ones at the center of the sphere — -would not be interacting with the valproic acid. But that would make TorPharm’s product a mixture of dival-proex sodium and sodium valproate, which would be inconsistent with the Federal Circuit’s determination that the product is a 1:1 combination of sodium valproate and valproic acid at the molecular level — that is, that
every
molecule of sodium valproate in the batch Atwood tested was bonded to a molecule of valproic acid, with no remainder. I am also uncertain how Hercules’ theory squares with the failure of the FAB spectrum to reveal any valproic acid; he seems to have thought that the analyzer would somehow just record the unbonded sodium valproate in the core of the micro-crystals. One possibility might be that the test would not produce any positive ions of valproic acid (the test only registers positive ions), but he did not suggest this.
I find that Hercules’ theory was belated, unsubstantiated, and unconvincing. It was also inconsistent with the explanation that he offered in his expert report for the spectrum generated by the FAB mass spectrometry test: that TorPharm’s product does not have a 1:1 ratio of sodium valproate to valproic acid at
any
level, molecular or otherwise. His testimony was that it did have that ratio, albeit not at the molecular level.
I make two final observations about the evidence that TorPharm’s product is an oligomer. First, the concordance of all five tests that Atwood performed (melting point, solubility, freezing-point depression, vapor phase osmometry, and FAB mass spectrometry) strengthens the inference of oligomeric structure that he drew from
them. This is a simple statistical point. If the probability that the result of one test is erroneous is .1, and the probability that the result of another test is erroneous is also .1, the probability (if the two probabilities are independent of each other) that both tests are erroneous is only .01.
Second, Atwood conducted his five tests not only on TorPharm’s product but also on a batch of divalproex sodium that he made himself following directions in Abbott’s patent. And the results of the tests were virtually identical. As I said earlier, I am constrained by the doctrine of the law of the case to assume that Abbott’s patent describes an oligomer. If all the tests that Atwood ran on TorPharm’s product yielded the same results as the tests on the product that he made according to Abbott’s patent recipe, the inference is strengthened that TorPharm’s product is also an oligomer. This is not to say that TorPharm is guilty of infringement because it made the same product as Abbott. You infringe a claim, not a product,
Zenith Laboratories, Inc. v. Bristol-Myers Squibb Co.,
19 F.3d 1418, 1423 (Fed.Cir.1994), as otherwise a patentee could obtain greater protection than its patent conferred, simply by making a product that did not conform to the claim. But Atwood wasn’t testing the product that Abbott makes and sells, but the product that
he
made in accordance with the claims of the patent. The fact that
that
product tested the same as TorPharm’s is evidence that TorP-harm’s product infringes the patent.
I am clearly entitled to draw a negative inference from TorPharm’s failure to present in the form of admissible evidence any results of tests that it performed on its product, especially since it is known that employees of TorPharm did perform a number of such tests. TorPharm sought to introduce the results of those tests through testimony by the CEO of TorP-harm’s corporate parent (Apotex, Inc.), Bernard Sherman. Dr. Sherman is a systems engineer, not a chemist. He is qualified to testify about the production of TorPharm’s products, but not about their chemical structure or about the accuracy or meaning of tests performed by TorP-harm’s employees. The chemistry of su-pramolecular entities is highly complex, technical, and specialized. It is not a field in which an amateur can be allowed to testify.
If the tests that TorPharm’s chemists conducted yielded results that a competent chemist would attest showed that TorP-harm’s product is not an oligomer, I am sure that Dr. Barton or Dr. Hercules would have presented the test results. Or had TorPharm any confidence that it could conduct tests on its product that would contradict Atwood’s test results, I imagine it would have asked Barton or Hercules to conduct them; they are both eminently qualified to do so. Apotex’s vice president for R & D, another individual competent to testify about the results of chemical tests on TorPharm’s product, was authorized to testify in this case, 2003 WL 22462614, at *15, but TorPharm didn’t call him. TorP-harm’s implicit position, impossible to take seriously and in any event without any foundation in the law of proof, is that Abbott’s burden was to. prove
to a certainty
that TorPharm’s product is an oligomer, so that
any
doubt concerning Atwood’s findings requires the dismissal of Abbott’s suit.
I also excluded evidence by which TorP-harm hoped to show, mainly through testimony by Dr. Sherman, that the tests that convinced the patent office and the Federal Circuit that Abbott’s product was an
oligomer were fatally flawed. TorPharm submitted offers of proof, indicating the evidence it would have liked to present at the trial about those tests, and if everything in those offers of proof is true, this would not affect my conclusions. Sherman is no more qualified to testify about Abbott’s tests than about TorPharm’s tests. And not only is the oligomeric structure of Abbott’s product an issue that the Federal Circuit’s decision precludes me from considering, but the evidence that Dr. Sherman wanted to present, consisting as it largely did of carping criticisms of much earlier tests performed by Abbott, was greatly outweighed by Atwood’s evidence. Sherman also wanted to testify that dival-proex sodium does not consist of a 1:1 ratio of sodium valproate to valproic acid at the molecular level, another issue excluded by the Federal Circuit’s decision.
I did permit TorPharm to call, as an adverse witness, Dr. John Bauer of Abbott, who had conducted the tests that persuaded the patent office to issue Abbott’s patent. But after hearing a portion of his testimony and considering his offer of proof, I excluded all his testimony. TorPharm wanted to show through him that the tests had been flawed. Suppose they had been. This would be evidence of negligible weight concerning the composition of TorPharm’s product. Bauer did not test TorPharm’s product; Atwood did; and while TorPharm’s experts quarreled with the inferences that Atwood drew from the test results, neither of them suggested that the tests had been performed improperly.
Abbott has proved by a preponderance of the evidence that TorPharm’s product is an oligomer of 4 to 7 units of divalproex sodium and therefore infringes Abbott’s patent. Abbott is directed to submit a draft injunction for my consideration within seven days; TorPharm shall then have seven days to suggest changes in Abbott’s draft.
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