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 alleged "new and useful improvements in Low Drag Airfoil," claim 8 being for the article and claim 9 for the method of making 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 ψ cos θ

"Y = 2 sinh ψ cos θ wherein θ varies from π/16 to 1.94 π, 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 values of attitude and velocity distribution, determining values of necessary form 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 ψ cos θ

"Y = 2 sinh ψ cos θ wherein θ varies from π/16 to 1.94 π, 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 claims."

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 plane 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 be 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. § 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 values 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 decisions 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. If 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 decisions 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 supplied.)

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 litigation."

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 operations or which produce 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. Pat. Q. 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 for 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. § 31. Patentability of the claims may not rest solely on the fact that the carbon contents specified therein are 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 claim.

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 made 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 that 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 within 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 art5 — 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.

Affirmed.