CITE:  186 F.2d 377
CMON:  April 1951
PLAIN: Application of Shao Wen Yuan
DEFND: United States Patent and Trademark Office
COURT: United States Court of Customs and Patent Appeals
DATE:  April 3, 1951

Proceeding in the matter of the application of Shao Wen Yuan for a patent
relating to the mathematical procedure of the construction of an airfoil.
The Board of Appeals of the United States Patent Office, Serial No. 539,056,
affirmed, the decision of the Primary Examiner rejecting two of the claims,
and the applicant appealed. The Court of Customs and Patent Appeals,
Garrett, Chief Judge, held that the claims were properly rejected as
purely mental steps in the construction of an airfoil, which did not fall
within the scope of patentability.


  Pure mental steps are not patentable.  Process steps must be performed
  on physical objects.  Process based on mathematical procedure not


By this appeal reversal is sought of the decision of the Board of Appeals
of the United States Patent Office affirming the rejection by the Primary
Examiner, hereinafter referred to as the examiner, of the two claims,
numbered respectively 8 and 9, remaining in the application after it,
during a protracted prosecution in the Patent Office, had been amended
in various particulars, including the withdrawal of many claims. It appears
that The Glenn L. Martin Company of Baltimore, Maryland, as assignee of
the application, is the actual party in interest.

The application relates to the alleged "new and useful improvements in
Low Drag Airfoil", claim 8 being for the article. The claims read:

    "8.  A high speed airfoil having low drag characteristics at both
    high and low lift coefficients having a profile including a curve
    representing a substantial portion of the airfoil profile, which
    curve is obtained by computing the exact pressure distribution
    along the chord of the airfoil for said aerodynamic characteristics,
    which can be converted into velocity distribution along said chord,
    and from said pressure distribution and the airfoil attitude
    corresponding to a known optimum lift coefficient, computing the
    value of the rectangular coordinates on points of the curve from
    the equations:
        "X = 2 cosh psi cos theta
        "Y = 2 sinh psi cos theta
    wherein theta varies from pi/16 to 1.94, the remainder of the curve in
    the area of the leading edge of the airfoil profile being completed by
    a sector of a circle tangent to the curves forming the upper and
    lower surfaces of the airfoil profile.

    "9.  A method of determining the exact airfoil profile for certain
    desired aerodynamic characteristics comprising computing the pressure
    distribution along the chord of the airfoil profile for the said
    aerodynamic characteristics, converting the pressure distribution
    along the chord into velocity distribution along the chord, from
    the pressure distribution, determining the airfoil attitude 
    corresponding to the known optimum lift coefficient, and from said
    value of attitude and velocity distribution, determining values of
    necessary for parameters, converting said form parameters into the
    rectangular coordinates of a series of points from which substantial
    portions of the upper and lower curves of the airfoil profile can be
    obtained by means of the expression:
        "X = 2 cosh psi cos theta
        "Y = 2 sinh psi cos theta
    wherein theta varies from pi/16 to 1.94, and completing the leading
    edge of the profile by a sector of a circle tangent to the curves
    for the upper and lower surfaces."

The examiner rejected both claims on several distinct grounds, all of
which were specifically approved by the Board of Appeals.

In the reasons of appeal accompanying the appeal to us there are twenty-one
allegations of error. Sixteen of these are limited to allegations of error
on the part of the examiner only. Three of the sixteen allege error with
respect to a claim, numbered 7, which is not before us, and reference is
made to a document which does not appear in the record. Three others allege
error on the part of the examiner in "failing to understand" appellant's
claimed invention, and one of these three says, in substance, that such
failure was demonstrated by the rejection of claims 1 to 6, inclusive,
in a paper wherein he discussed features not present in appellant's
application. Claims 1 to 6, inclusive, are not before us.

Of the five allegations of error on the part of the board at least two --
Nos. 17 and 21 -- are so general in character that they are virtually
worthless as assignments of error, and that is true of many of the sixteen
assignments relating to the decision of the examiner only.

We note that the brief for appellant states: "This Court is asked to find
that the Board of Appeals erred in not fully considering the points of
error on the part of Examiner, pointed out above, particularly the
Examiner's failure to understand the invention and his rejection of the 

This appeal is from the decision of the Board of Appeals -- not from that
of the examiner -- and there is no allegation that the board did not fully
understand the application. It is noted from its decision that the
allegation that the examiner did not understand the questions involved was 
made before it and that the board expressed its view as follows:
"* * * Appellant states on page 7 of his brief that the prosecution of
this application clearly demonstrates that the Patent Office has not
understood either the appellant's concept or the claims thereto. From a
study of appellant's own description in the specification and the
description thereof as set forth in the Examiner's appeal Statement,
it seems to us that the Examiner has exhibited an adequate understanding
of what it is that appellant is attempting to cover by his claims. In any
event, if appellant believed that the Examiner's description of the
appealed subject matter was inadequate or erroneous, he should have pointed
out the errors in his brief. This he has not done."

From our study of the record in its entirety, and in the light of the brief
for appellant, we are of opinion that the examiner demonstrated a
comprehension of the subject matter as fully and completely as its nature
admits and that the board did also.

Appellant's difficulty, we think is due to the character of the claims
rather than to any lack of understanding on the part of the tribunals of
the Patent Office concerning them. To state it differently, the claims seem
to us to have been rejected because they were understood by the tribunals
of the Patent Office, not because of any failure to comprehend them.

We take the following descriptive matter, which is a paraphrase of
appellant's own description, from the decision of the board:

    "Appealed claim 9 relates to a method of determining an airfoil
    profile having certain desired aerodynamic characteristics by
    mathematical procedures. Claim 8 purports to be a claim to the airfoil
    as an article of manufacture, and the airfoil is defined in terms of
    the mathematical computations involved in determining the profile
    which will meet the specified requirements. Appellant points out that
    it has previously been the custom in designing airfoil profiles to
    select a known one having characteristics approaching those desired
    and to modify it in the light of experience to produce a trial profile.
    A model employing this trial profile is built and tested in a wind
    tunnel and further modified as indicated by the results of the test.
    This testing and modifying [referred to in appellant's specification
    as 'cut and try' steps] may continue through several stages until a
    profile sufficiently satisfactory to justify building an actual phase
    is obtained. After the actual plane is built and tested it may be
    further modified before the final profile is decided upon. This
    procedure is expensive and time-consuming.

    "Appellant's contribution as stated in his brief lies in a mathematical
    procedure by which the aircraft designer can start with a pressure
    distribution curve of the required characteristics and convert it into
    a velocity distribution curve and by introducing into the calculations
    parameters for airfoil attitude corresponding to the known optimum lift
    coefficient, he can arrive at mathematical values which can be converted
    into rectangular coordinates which can be plotted to produce the exact
    airfoil profile that would in turn produce the desired pressure
    distribution curve. This procedure is used for the major part of the
    upper and lower curves of the profile. Because of the large number of
    points that would have to be calculated and plotted at the leading edge,
    appellant proposes to complete the leading edge of the airfoil profile
    by a sector of a circle tangent to the open ends of the upper and lower
    curves of the airfoil profile. Appellant states that by using his 
    mathematical approach the final or near final form can be calculated
    in one operation so that much of the 'cut and try' procedure is
    eliminated. That appellant's mathematical approach can produce a
    practical embodiment is indicated by an affidavit of one George S.
    Trimble, of record in this case."

In his statement following the appeal to the board the examiner gave a
detailed explanation of the mathematical steps involved in the calculation
of coordinates of the points on the profile curve. This was approved by
the board, and appellant before us has not challenged the correctness of
the explanation. It should not expected of an appellate court that it
find error where no error is alleged.

Unless we are wholly mistaken, appellant's challenge here is leveled
primarily at the rejection of the claims on the ground that they are drawn
to non-statutory subject matter; that is, to subject matter for which
section 4886, R.S. 35 U.S.C.A. Section 31, provides no patent protection.
The allegations of error in reasons of appeal 18, 19, and 20 seem sufficient
to cover this ground which is discussed in the brief for appellant as
follows: "Claim 9 is a method claim and defines a series of steps which,
if the aircraft designer follows, after having read the specification upon
which the claims to the method depend, he will be able to produce the
exact contour of the new high speed airfoil that will have the performance
characteristics that he requires for a specific airplane. It should be
pointed out that claim 8 defines a specific article or a particular type
of novel high speed airfoil, whereas claim 9 defines a method of achieving
that airfoil, as well as similar airfoils, of which claim 8 is
representative. None of the references cited states that an airfoil of
specified performance characteristics can be achieved exactly, nor that 
any method is available other than the 'cut and try' method, well known
and practiced in the prior art. None of the methods suggests anything
that would eliminate the laborious 'cut and try' method. It is for this
advance that appellant is now well known throughout the aircraft industry
and should be entitled to a patent for his contribution."

In considering the foregoing statement it must be borne in mind that all
the so-called steps (viz, (a) "computing the pressure distribution * * *";
(b) "converting the pressure distribution * * *"; (c) "determining the
airfoil attitude * * *"; (d) "determining values of necessary form
parameters" from the value of attitude and velocity distribution; and
(e) "converting said form parameters into the rectangular coordinates * * *")
are purely mental steps dependent upon the mathematical formula which is
recited in, and constitutes the heart of, the claims.

This court has deemed it to have been thoroughly established by decision
of various courts that purely mental steps do not form a process which
falls within the scope of patentability as defined by statute.

The eighth clause of the eighth section of the first article of the
Constitution of the United States empowers the Congress to secure for
limited times to authors and inventors the exclusive right to their
respective writings and discoveries, and it states that the reason for the 
grant of such power is: "To promote the Progress of Science and useful Arts".

It is interesting to note that this particular grant is the only one of
the several powers conferred upon the Congress which is accompanied by
a specific statement of the reason for it. Its inclusion doubtlessly was
due to the fact that those who formulated the Constitution were familiar
with the long struggle over monopolies so prominent in English history,
where exclusive rights to engage even in ordinary business activities
were granted so frequently by the Crown for the financial benefits accruing
to the Crown only. It was desired that in this country any Government grant
of a monopoly for even a limited time should be limited to those things
which serve in the promotion of science and the useful arts.

It was not made mandatory upon the Congress to enact legislation for
carrying out the constitutional provision, but its importance to the
people led to the enactment, during the Second Session of the First
Congress -- specifically on April 10, 1790, 1 Stat. 109, -- of an act
embracing a patent system whereby patents should be issued, upon
application made therefor, to any who "hath or have invented or discovered
any useful art, manufacture, engine, machine, or device, or any improvement
therein not before known or used."

The 1790 act was repealed by the Second Congress, Second Session, being
supplanted by an act of February 21, 1793, 1 Stat. 318, in which patentable
subject matter was defined as "any new and useful art, machine, manufacture
or composition of matter, or any new and useful improvement on any art,
machine, manufacture or composition of matter".

The subject matter so defined has been continued in all patent legislation
since enacted, and has been the subject of administrative and judicial
interpretation which interpretation, taken together with the statutes
themselves, constitutes the vast body of patent law, which Robinson in an
introductory note to his Treatise on the Law of Patents (1890 Edition)
refers to as "a department of jurisprudence whose doctrines were derived
by logical processes from established principles * * *." {1}

It is a matter of history well known to those familiar with patent law
that the question of whether what are known as process or method patents
were authorized by the statute occasioned much controversy during the
earlier developments of patent law, but that it was finally definitely
determined that they are so authorized.

The determination so made stemmed from the construction placed upon the
phrase "new and useful art" -- more specifically upon the word "art" --
appearing in the statute, and all the court decisions brought to our
attention, including those obtained by our own researches, sustain the
holding of the Board of Appeals in the instant case that to be patentable
"the steps of an art or method * * * must be performed upon physical
materials and produce some change in their character or condition."

In the case of Cochrane v. Deener, 94 U.S. 780, 788, 24 L.Ed. 139, the
Supreme Court of the United States said: "* * * A process is a mode of
treatment of certain materials to produce a given result. It is an act,
or a series of acts, performed upon the subject-matter to be transformed
and reduced to a different state or thing. It new and useful, it is just
as patentable as is a piece of machinery. In the language of the patent
law, it is an art. The machinery pointed out as suitable to perform the
process may or may not be new or patentable; whilst the process itself 
may be altogether new, and produce an entirely new result. The process
requires that certain things should be done with certain substances, and
in a certain order; but the tools to be used in doing this may be of
secondary consequence."

Robinson on Patents, 1890 Edition, Vol. 1, page 230, citing the Cochrane
v. Deener case, supra, states: "An art or operation is an act or a series
of acts performed by some physical agent upon some physical object, and
producing in such object some change either of character or of condition.
It is also called a 'process,' or a 'mode of treatment;' and is said to
require that 'certain things should be done with certain substances in a
certain order.' It is so far abstract that it is capable of contemplation
by the mind apart from any one of the specific instruments by which it is
performed. It is so far concrete that it consists in the application of
physical force through physical agents to physical objects, and can thus
become apparent to the senses only in connection with some tangible
instrument and object."

Elaborate discussion follows the definition so stated, and at page 249
the author continued: "But though an art embraces so wide a field of
inventive skill, it includes only such operations as are capable of
producing physical effects. Every invention, when applied according to
the design of its inventor, must accomplish some change in the character
or condition of material objects. This is as essential in a patentable art
as in an instrument." {2}

In Patentability and Validity by Rivise and Caesar, 1936 Edition, at
page 35 et seq. (Sec. 20), there is a discussion of mental processes
which have been held unpatentable in which it is said inter alia: "There
are a number of decisions which hold that a process to be patentable must 
produce a change in the condition of matter, and that processes whose
results can be apprehended only through the intellect are not patentable.
 As a result of these decision it is considered to be well settled that
processes involving mental operations  and processes that merely produce
a desired state of mind are not patentable. In this category are included
methods and systems for transacting business, methods of training animals,
methods of solving problems, and rules for playing games." (Italics

Several cases are cited as illustrative of the text, and the authors then
cite decisions of the Supreme Court which they say "have sustained the
validity of patents covering methods whose results can be apprehended
only through the intellect." They state that the most important of these
are Telephone Cases (Dolbear v. American Bel Tel. Co.), 1887, 126 U.S. 1,
8 S.Ct. 778, 31 L.Ed. 863, and say, "It is to be noted that the Supreme
Court did not in these cases directly pass upon the patentability of
mental processes, for the question was not raised by the parties to the

They further say, in section 22, page 39, that: "The authors are of the
firm opinion that there is no logical reason why certain processes which
involve mental effects should not be patentable", but, after some
argumentative statements, say further: "* * The question of mental
processes has not as yet been presented to the Supreme Court in such
a manner as to call for a direct decision, and it is very doubtful
whether even our highest tribunal would go so far at this late date to
overturn the long line of adverse decisions."

We, of course, do not know what the Supreme Court might hold in a given
case. We know, however, what it did in the case of Cochrane v. Deener,
supra, and until the rule there enunciated is abrogated by another
decision we feel ourselves bound by it.

Many decisions of courts other than the Supreme Court are regarded as
being directly in point here. Among them are the following:

Don Lee, Inc. v. Walker, 61 F.2d 58, a decision by the United States
Circuit Court of Appeals of the Ninth Circuit, which held, as expressed
in a U.S. Patent Quarterly headnote: "Patent is invalid if for mathematical
formula for solution of problem in dynamics; special application of general
formula known to engineering world cannot be patented; nor can formula
for determining dynamic forces in motor shaft when the forces were fully
recognized and considered by engineers in prior publications."

Halliburton Oil Well Cementing Co. v. Walker, 146 F.2d 817, also decided
by the United States Circuit Court of Appeals of the Ninth Circuit, in
which an appeal was taken to the Supreme Court but not upon the "mental"
process phase of the case, 329 U.S. 1, 67 S.Ct. 6, 91 L.Ed. 3.

In re Bolongaro, 62 F.2d 1059, 20 C.C.P.A., Patents, 845, where we held
claims for a method of producing a printed publication not patentable
because directed to a subject matter not within section 4886, R.S.

In re Cooper, 134 F.2d 630, 632, 30 C.C.P.A., Patents, 946, 949, in which
we said: "The appellants have set out a formula determination of the
carbon content of steel corresponding to given quantities of the alloying
elements. This, however, is not patentable per se as it does not fall
within any of the statutory classes of invention as set out in section
4886, R.S., 35 U.S.C.A. Section 31. Patentability of the claims may not
rest solely on the fact that the carbon contents specified therein a
calculated from the formula."

In re Heritage, 150 F.2d 554, 556, 32 C.C.P.A., Patents, 1170, 1174, where
we said: "The feature of appealed claims 1 and 2 which is relied on for
patentable novelty is the mental process of making a selection of the
amount of coating material to be used in accordance with a predetermined
system. Such purely mental acts are not proper subject matter for protection
under the patent statutes, as held by the tribunals of the Patent Office.
See In re Cooper, 134 F.2d 630, 30 C.C.P.A., Patents, 946; Don Lee, Inc.
v. Walker, 9 Cir., 61 F.2d 58; In re Bolongare, 62 F.2d 1059, 20 C.C.P.A.,
Patents, 845."

*   *   *   *   *   *

"Owing to the fact that claims 1 and 2 are essentially directed to a
purely mental process of making a selection of the amount of coating
material to be used in coating a porous fiber board in accordance with
a predetermined system they do not define patentable subject matter."

Our most recent decision respecting mental processes was rendered
March 6, 1951, in the case of In re Abrams, 188 F.2d 165, 38 C.C.P.A.,
Patents, ----. It is deemed apposite here.

In appellant's reason of appeal No. 12, the examiner is alleged to have
erred in failing to take cognizance of certain patents cited by appellant
"in an effort to clarify the issue."

A similar allegation of error on the part of the examiner apparently was
made in the appeal taken to the board and the latter discussed it as
follows: "As bearing on the question of the form of the claim[s],
appellant has referred in his brief to three Stalker patents and a patent
to Davis which include mathematical formulae in their claims, and he
argues that these patents constitute a precedent for allowance of claims
in the form of claims 8 and 9. We do not consider that these claims
support appellant's contention since they do not recite calculations
as positive method steps as in the appealed claims." {3}

No error is specifically assigned as to this holding of the board, and all
the argument relating to it in the brief for appellant before us is
limited to alleged error on the part of the examiner.

Consideration of that point by us, therefore, is not required, but it
may be said that even if it should be found that patents covering purely
mental steps have been issued, such action could not be regarded as
controlling here in view of the court decisions hereinbefore cited. {4}

So far, our discussion has been largely confined to claim 9 -- the method

In affirming the examiner's rejection of the article claim, 8, the board
said inter alia: "Apparatus claim 8, like claim 9, stands rejected as not
defining subject matter of a character which is patentable under the
Statutes. This claim purports to be drawn to an airfoil as an article of
manufacture. The sole novelty in the claim, however, resides in the method
of mathematical computation by which the profile of the airfoil is
determined. The mathematical procedures recited in his claim are the same
as those recited in claim to non-statutory subject matter, and this 
rejection of claim 8 will be sustained."

We think this holding was logical and proper, but there may be added the
board's affirmance of the further rejection on the ground that the article
defined in claim 8 does not appear to be new or novel. Even if the method
claim were held to be patentable as a new and novel  process , the
 article mode by the process  is not new. No distinction in shape,
or otherwise, is made in the claim between an airfoil formed according to
the method set forth in claim 9 and the airfoil which the specification
of appellant's application recites as being manufactured by practicing
the preexisting "cut and try" method.

We deem it unnecessary to discuss at any length the rejection based upon
the fact that in claim 8 the article is not described otherwise than by
the method of making it. The general rule, of course, is than an article
may not be claimed by the process of making it, even though the process
itself be patentable, but there are exceptions to this rule, and the brief
for appellant has cited numerous cases which fall with the exception. We do
not think appellant's case falls within the exception, but, even if it
did, the fact remains that the airfoil claimed as an article is neither 
new nor novel.

Other grounds of rejection -- one as to claim 8 being based upon cited prior
art {5} - were applied by the tribunals of the Patent Office, discussion of
which we regard as unnecessary.

For the reasons stated the decision of the Board of Appeals is affirmed.



{1} Design patents and patents for certain asexually reproduced plants
provided for in subsequently enacted statutes have no pertinency to the
issues here involved.

{2} In connection with the last statement there is cited the decision of the
Supreme Court of the United States in the case of Jacobs v. Baker, 7 Wall.
295, 74 U.S. 295, 19 L.Ed. 200, where it was held, in effect, that an
architectural plan for the building of a house, though new and original,
is not an art or any other form of invention.

{3} It is proper to say that in the examiner's reply to appellant's brief
filed with the board, the patents were referred to and discussed as
follows: "Appellant overlooks the fact that these patents do not define
the  structure  therein disclosed  by the method steps 
involved in their  calculation  as in this application. Furthermore,
the patents to Davis and Stalker were granted prior to the decision in
Ex parte Holley B. Dickinson et al, Ex parte Hobbs et al, and Ex parte
Pappas et al. In fact, as the record in Ex parte Dickinson et al shows,
two of the patents to Stalker 2,041,790 and 2,041,794 were relied upon
by the Examiner in this appeal." (Italics quoted.)

{4} It is possible that the Davis and Stalker patents might furnish an
opportunity of presenting to the Supreme Court the question of the
patentability of "mental process" claims.

{5} The art so cited consists of five patents and one publication listed
in the decision of the board as follows:

Stalker, 2,041,792, May 26, 1936; Klemm, 2,123,429, July 12, 1938;
Herrick (British), 375,327, June 14, 1932; Taylor (British), 525,666,
Sept. 2, 1940; Mitsubishi (French), 643,308, May 15, 1928.

Aerodynamics of the Airplane, by Clark Millikan, pages 24, 66, 67, 68,
69, 70, 71, 72 and 73. Copy in Division 22 of the Patent Office.