CITE:  478 F.2d 1392
CMON:  May 1973
DEFND: United States Patent and Trademark Office
COURT: Court of Customs and Patent Appeals
DATE:  May 31, 1973

Appeal from a decision of the Patent Office Board of Appeals, Serial No.
450,503, adhered to on reconsideration, affirming the rejection of claims
4 and 5 of patent application for an invention relating to a method of
determining the porosity of subsurface formations.  The method claims
were rejected on ground that the alleged advance over the art resided in
nonstatutory subject matter.  The Court of Customs and Patent Appeals,
Lane, Judge, held that the method claim in which the point of novelty was
a mathematical equation to be solved as the final step of the method was
not a statutory method.

Rich, Judge, concurring with opinion.

  Method where final step is a solution to a mathematical equation is not

Before MARKEY, Chief Judge, RICH, BALDWIN, and LANE, Associate Judges,
and ALMOND, Senior 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." {1}  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 (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 determining 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:

       [.... mathematical equation ....]

  wherein phi is the porosity, rho is said density, Vp is said compression
  wave velocity, Vs is said shear wave velocity and K is the bulk modulus
  of said fluid.

  5. The method of claim 4 in which the value of K is taken to be
  0.235 x 10^11 dynes/ cm^2.

The examiner rejected method claims 4 and 5 under 35 U.S.C. 103 as
unpatentable over Itria {2} and Blizard {3} 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,

  * * * 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 he 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.


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 Bernhart, 57 CCPA 739, 743, 417 F.2d 1395,
1399,  (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, St. Ct. 253.

The Supreme Court concluded that the Benson method varies the ordinary
arithmetic steps a 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 he 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 by 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.

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 (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 case of
the Supreme Court's Benson decision.

This case is quite unlike Benson, which we decided in 1971, 58 CCPA 1134,
441 F.2d 682 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, 38 CCPA 945, 188 F.2d 165 (1951), and in the
companion case of In re Yuan, 38 CCPA 967, 188 F.2d 377 (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 U.S.C. 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 Section 101 than I had about
Benson's process; but on that point I seem to have been reversed.


{1} Serial No. 450,503 filed April 23, 1965.

{2} U.S. Patent 3,127,950 issued April 7, 1964.

{3} U.S. Patent 3,181,645 issued May 4, 1965 on an application originally
filed August 6, 1959.