
    Application of Dean M. CHRISTENSEN.
    Patent Appeal No. 8558.
    United States Court of Customs and Patent Appeals.
    May 31, 1973.
    Homer J. Schneider, Phillip H. Mayer, Wolfe, Hubbard, Leydig, Voit & Os-ann, Chicago, 111., attorneys of record, for appellants. William A. Smith, Jr., Washington, D. C., of counsel.
    S. Wm. Cochran, Washington, D. C., for the Commissioner of Patents. Jere W. Sears, Washington, D. C., of counsel.
    Before MARKEY, Chief Judge, RICH, BALDWIN and LANE, Judges, and ALMOND, Senior Judge.
   LANE, Judge.

This is an appeal from the decision of the Patent Office Board of Appeals, adhered to on reconsideration, affirming the rejection of claims 4 and 5 of appellant’s application entitled “Method of Determining Subsurface Porosity.” No claims were allowed. Subsequent to the oral argument of this appeal, the Supreme Court of the United States handed down its opinion in Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972) (hereafter Benson). We allowed appellant and appellee here to file supplemental briefs directed to that Supreme Court opinion and both have done so. We affirm the decision of the board.

The invention relates to a method of determining the porosity of subsurface formations. Porosity is one of the subsurface parameters which are of value to geologists, petroleum engineers and others interested in analyzing lithologic formations. In accordance with the present invention, it is possible to obtain a continuous plot of the porosity of the substances penetrated by a bore hole. The claimed method of determinng the porosity of lithologic substances from collected well logging data is set forth in claims 4 and 5:

4. The method of determining the porosity of a subsurface formation in situ comprising the steps of forming a fluid filled hole through said formation, measuring the density of said formation, generating both compression and shear waves in said formation, computing compression and shear wave velocity from said waves, determining the bulk modulus of said fluid, and computing the porosity of the formation from the relation:

wherein 0 is the porosity, X*is said density, Vp is said compression wave velocity, Vs is said shear wave velocity and K is the bulk modulus of said fluid. CA7561]

5. The method of claim 4 in which the value of K is taken to be 0.235 x 1011 dynes/cm2.

The examiner rejected method claims 4 and 5 under 35 U.S.C. § 103 as unpat-entable over Itria and Blizard since, in his opinion, the alleged advance over the art resides in nonstatutory subject matter. The examiner explained the reasoning behind the rejection in his Answer stating:

* * * the prior art teaches all the claimed steps except that drawn to computing the porosity of a formation. The essence of the appellant’s invention lies in using data already available to one of ordinary skill in the art to compute the values of a parameter known to be of value in determining the geophysical properties of a formation * * * according to a novel quadratic equation. Stated otherwise, the appellant’s point of departure from the teachings of the prior art lies in applying his new formula to old data to calculate values of a known parameter. While this discovery of the appellant may constitute an important contribution to' the art of geophysical prospecting, unless it falls within the four statutory subjects matter of 35 U.S.C-. 101 it cannot be protected by the patent laws.

The 'board, agreeing with the examiner’s reasoning, affirmed. On request for reconsideration, the board went on to explain:

* * * the present case, which * * * depends for patentability on non-statutory matter, comes primarily under the provisions of 35 U.S.C. 101.
The Examiner referred to 35 U.S.C. 103 in the final rejection since no single reference showed each of the physical steps of collecting data as defined by the claims, even though these steps were admitted to be old in the specification.

From this, we conclude that the only real issue before us is whether the method claims, which recite a mathematical formula at the point of novelty, define a statutory process within the meaning of 35 U.S.C. § 101.

OPINION

It is well established that under the present statutory scheme, patent property rights may not be secured on mathematical equations. As this court recently said in In re Bemhart, 417 F.2d 1395, 1399, 57 CCPA 737, 743 (1969):

We think it is clear that in enacting section 101 Congress meant to exclude principles or laws of nature and mathematics, of which equations are an example, from even temporary monopolization * * *.

The Supreme Court in Benson, supra, more recently said:

It is conceded that one may not patent an idea. But in practical effect that would be the result if the formula for converting * * * [BCD numerals to pure binary numerals] were patented in this case. The mathematical formula involved here has no substantial practical application except in connection with a digital computer, which means that if the judgment below is affirmed, the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself.
It may be that the patent laws should be extended to cover these programs, a policy matter to which we are not competent to speak. [409 U.S. at 71, 93 S.Ct. at 257.]

The Benson application claims, which the Supreme Court held do not constitute a patentable process within the meaning of 35 U.S.C. § 100(b), recite a method of converting signals or representations from binary coded decimal form into binary form by a series of steps. The steps include shifting, masking, adding, and repeating. The Benson claims are set forth in the appendix to the Supreme Court opinion, 409 U.S. at 73-74, 93 S.Ct. 253.

The Supreme Court concluded that the Benson method varies the ordinary arithmetic steps á human would use by changing the order of the steps, changing the symbolism for writing the multiplier used in some steps, and by taking subtotals after each successive operation. The Court found that the claimed mathematical procedures may be carried out in existing digital computers long in use, no new machinery being necessary, and that the mathematical procedures may also be performed without a computer.

Appellant here, in his supplemental brief, contends that Benson did not decide the issues of this case. Appellant states that his claims are drawn explicitly to a method of determining subsurface porosity in situ, and that his invention is not a computer program. It is clear that the term, in situ, as used in appellant’s application and claims merely means that formation porosity is determined without removing core samples for direct measurement. The actual computation of subsurface porosity is not made in the ground. The measurement of density, compression wave velocity, shear wave velocity and bulk modulus of the subsurface formation, all known steps, merely precede the mathematical computation of formation porosity by solution of appellant’s novel equation. The in situ limitation in appellant’s claims does not render Benson inapplicable. We believe that Benson must influence our decision in the instant case. Appellant’s arguments, that Benson does not fully deal with the breadth of ’§ 101 and does not suggest what view the Congress should take, do not render inapplicable what the Supreme Court said in the quotation reproduced above.

Appellant further states that Benson does not mention the mental step issue and that it does not refer to the prior decisions of this court except the specific one before it. The issue considered by the Supreme Court in Benson was a narrow one, namely, is a formula for converting binary coded decimal numerals into pure binary numerals by a series of mathematical calculations a patentable process? The issue before us in the instant case is also a narrow one, namely, is a method claim in which the point of novelty is a mathematical equation to be solved as the final step of the method, a statutory method? We follow the Supreme Court'in concluding that the answer is in the negative. Given that the method of solving a mathematical equation may not be the subject of patent protection, it follows that the addition of the old and necessary antecedent steps of establishing values for the variables in the equation cannot convert the unpatentable method to patentable subject matter.

In reaching our conclusion in the light of Benson, we find it unnecessary to discuss the correctness or the rationale of any of our prior decisions in a line of cases starting with In re Abrams, 188 F.2d 165, 38 CCPA 945 (1951). Each new appeal must be decided on its own facts and in view of interpretations of the patent law as handed down by the Supreme Court of the United States.

We conclude that in the instant case, the nonstatutory subject matter rejection made toy the Patent Office calls only for a treatment of this aspect of patentability with respect to the particular claims here involved. The decision of the board is affirmed.

Affirmed.

RICH, Judge

(concurring).

I agree, reluctantly, with the result reached in Judge Lane’s opinion because, in view of Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972), we have no alternative but to affirm the rejection of claims 4 and 5. However, I wish to state my own views as to the bearing on this ease of the Supreme Court’s Benson decision.

This ease is quite unlike Benson, which we decided in 1971, 441 F.2d 682, 58 CCPA 1134, and which the Supreme Court reversed. The rejection by the examiner in the present case was based on a combination of a holding of obviousness under 35 U.S.C. § 103, using two prior art references, and application of the old “mental steps” doctrine. He found the only advance over the prior art to be the computation step, recited in the claims, which he said was “purely mental” and, in itself, therefore “non-statutory.” He relied primarily, for legal support, on this court's old opinions in In re Abrams, 188 F.2d 165, 38 CCPA 945 (1951), and in the companion case of In re Yuan, 188 F.2d 377, 38 CCPA 967 (1951), containing ideas which we have partially rejected and considerably refined in recent years. The board, in a two-paragraph opinion, added nothing and affirmed the section 103 obviousness rejection. In a second opinion, in response to a request for reconsideration, the board added a short discussion of the mental step aspect of the case, Abrams, and Yuan and said 35 U.S.C. § 101 had applicability to the decision. The implication in that observation, which was not explained, is that under section 101 a mental step is not patentable subject matter.

In Benson, on the other hand, the sole rejection was purely and simply that the rejected method or process claims, as a whole, were directed to non-statutory subject matter in that they were not “processes” within the meaning of 35 U.S.C. § 101. Stated another way, Benson’s process was said not to be the kind of process the statute contemplates. That was the only question we decided in Benson. That was the only question presented to the Supreme Court. As its opinion states at the outset,

The question is whether the method described and claimed is a “process” within the meaning of the Patent Act [quoting 35 USC 101 and the section 100(b) definition of “process” in a footnote].

Unfortunately, after stating that to be the question, the Supreme Court opinion does not again advert to it and never decides it, except inferentially by reversing our decision that the claims were directed to statutory processes. Since the Court’s opinion does not discuss the meaning of “process” in the statute, it sheds no light on that subject. It ends up discussing the patentability of programs for digital computers but no program was before us in Benson. Nor is a program before us in this case.

Since the issue in Benson was not the same as the issue in this case, one must ask what bearing the Supreme Court’s Benson decision has here. The answer for me is that, notwithstanding the fact that the Supreme Court never discussed the issue presented to it, its opinion went on at some length about the “abstract and sweeping” scope of the claims, making that the pivot on which its decision turned, proceeding on the assumption — of doubtful validity — that the processes they defined could be carried out “through any existing machinery or future-devised machinery or without any apparatus.” Having set up these hypothetical abstract and sweeping claims as the subject of its consideration, it treated them as for a “mathematical formula” or “the algorithm itself,” because of their breadth, and as such, held them unpatentable.

Thus the reasoning of the Supreme Court’s opinion has more bearing on the facts in this case than it had on the facts before it in Benson. The claims in this case do contain a mathematical formula; in Benson they did not. I therefore agree with Judge Lane that the Benson opinion “must influence our decision in the instant case.”

It was made quite clear in the “nutshell” summation in the Benson opinion that patents are not to issue where their effect would be to enable the patentee to prevent others from making use of a mathematical formula. That would be the effect here. I think it matters not, under the Supreme Court’s rationalization, that appellant’s claims are limited to porosity-determination application of the novel formula, characterized by the examiner as a possible “important contribution to the [useful] art of geophysical prospecting.” In Benson, the Supreme Court specifically assumed that the “mathematical formula involved here has no substantial practical application except in connection with a digital computer” yet it went on in the same sentence to say that “the patent would wholly pre-empt the mathematical formula * * Whether or not that statement conforms to fact, it expresses the view of the Supreme Court which we must follow in administering the patent law, at least until such time as it may clarify the situation.

If the process claimed in Benson, having no practical application other than in operating a digital computer, constituted pre-emption of a formula, it follows that the processes claimed here pre-empt a formula notwithstanding they have application only to subsoil porosity determinations. According to the reasoning of the Supreme Court, this appears to be a question of scope, or at least the abstract nature of the claims, not a question of what the Patent Act means by “process.” I can read the opinion only as saying that the abstraction or undue scope of the claims is the result of their assumed pre-emption or exclusion from the use of a formula, algorithm, or “generalized formulation,” though for a specific application in a useful art. “Algorithm” has been used in the sense of a “procedure for solving a given type of mathematical problem” and “formula” is used in the sense of a mathematical formula. The Supreme Court in Benson appears to have held that claims drafted in such terms are not patentable — for what reason remaining a mystery. Under the rules of the legal game, we are obliged to follow its lead as best we can.

But for the Benson decision, I would reverse the rejection here because I see no reason why such a specific, useful, technological process as a process for determining subsurface porosity, concededly a contribution to the useful arts, cannot be defined in the language of mathematics which is widely used as a medium of communication in that field. I have no more doubt it is a “process” within the meaning of § 101 than I had about Benson’s process; but on that point I seem to have been reversed. 
      
      . Serial No. 450,503 filed April 23, 1965.
     
      
      . U. S. Patent 3,127,950 issued April 7, 1964.
     
      
      . U. S. Patent 3,181,645 issued May 4, 1965 on an application originally filed August 6, 1959,
     