659 F.2d 750
8 Fed. R. Evid. Serv. 1297
UNITED STATES of America, Plaintiff-Appellee,v.Walter TRANOWSKI, Defendant-Appellant.
No. 80-1413.
United States Court of Appeals,Seventh Circuit.
Argued Dec. 5, 1980.Decided Aug. 31, 1981.

1
Julius Lucius Echeles, Chicago, Ill., for defendant-appellant.


2
Joseph J. Duffy, Asst. U. S. Atty., Chicago, Ill., Robert Walter Farun, U.S. Atty., Dept. of Justice, Chicago, Ill, of Counsel, for plaintiff-appellee.


3
Before FAIRCHILD and SWYGERT, Circuit Judges, and BARTELS*, Senior District Judge.


4
BARTELS, District Judge.


5
This appeal involves the admission of a novel application of untested mathematical and astronomical theories at appellant's perjury trial.  Appellant was convicted of perjury in violation of 18 U.S.C. § 1623 following a bench trial.  The indictment of Walter Tranowski (Walter) stemmed from testimony he had given at the earlier trial of his brother Stanley Tranowski (Stanley) for uttering a counterfeit $5 bill at a Burger King restaurant on the afternoon of May 12, 1974.  In addition to his evidentiary challenge, Walter further alleges that the trial judge was improperly exposed to his past record of arrests and convictions.

I. Stanley's Trial: The Alibi Defense

6
In order to focus upon the materiality of the issues at Walter's trial, it is appropriate, if not necessary, to relate the pertinent evidence at Stanley's trial.  At that trial Michelle Bonsanto, an employee of the Burger King restaurant at Cicero and North Avenue in Chicago, testified that on May 12, 1974, a little after 4 p. m., a person subsequently identified as Stanley made a purchase of two so-called Burger King "Whoppers" for which he paid $5 with a counterfeit bill.  She described the purchaser to the assistant manager David Jochum as being white, of average height, in his 40's, with dark hair, wearing an overcoat and carrying a newspaper under one arm.  Jochum then conferred with Burger King manager Ed Peterson about the bill.  Immediately thereafter both gave chase; within minutes Jochum and Peterson spotted the individual described by Bonsanto heading west on the opposite side of the street.  After Jochum and Peterson crossed the street, the individual started running.  Neither Peterson nor Jochum was able to keep abreast after running through alleys and yards.


7
It so happened that at the time one Peter McGhee and a number of friends with whom he had been playing soccer saw the chase and joined the pursuit.  Although they reached a point where they were able to confront the fleeing individual, he quickly ran off again and the chase was abandoned. Soon afterwards, McGhee found a Burger King bag containing two uneaten "Whoppers" in a garbage can in a yard through which the individual had run.  McGhee had been an employee at the NorClaire Drug Store for several years, and recognized the individual he had been chasing as a regular customer of the drug store.  From McGhee's description, the store manager recalled that the individual had purchased a newspaper at the store on May 12, 1974 between 6:30 and 7 p. m. He testified at the trial that this individual, accompanied by another person later identified as his brother Walter, had purchased a newspaper on the average of four or five times a week since May 1973.  Both McGhee and the store manager were able to make in-court identifications of Walter and Stanley Tranowski.


8
Walter took the stand in Stanley's defense.  He testified the government alleges perjuriously that he took a photograph (Gov't Ex. 4-A, of which an enlargement, introduced as Gov't Ex. 8, is attached) of Stanley, their mother Mrs. Cecelia Kniebusch, and a dog named Jerry in the backyard of the Kniebusch-Tranowski home on May 12, 1974 (Mother's Day), between the hours of 2:00 and 3:00 p. m. Walter further testified that he and Stanley went afterwards to the Diplomat Steak House, and then to a wake.  He stated that he was in his brother's company until 7:25 that evening.  If true, Walter's testimony gave Stanley an alibi to the charge that he passed a counterfeit bill at the Burger King that day.  The jury, however, rejected Stanley's alibi defense and returned a verdict of guilty on December 16, 1977.  Walter was not indicted for perjury until June 29, 1979.1


9
II. Walter's Trial: Evidence of Walter's Perjury

Ciupik's Testimony

10
The burden rested on the government to prove beyond a reasonable doubt that Walter knew he was giving false testimony when he stated that Stanley was in his company throughout the afternoon of May 12, 1974.  Since there was no testimony directly rebutting Walter's statements as to his whereabouts in the late afternoon of that day, the government's case rested on a rebuttal of the testimony surrounding the picture-taking in the family backyard.  To establish the falsity of Walter's statements, the government offered the testimony of an astronomer, Larry Ciupik, that the photograph alleged to have been taken on May 12 could not have been taken on that day.  Instead of May 12, Ciupik testified that the photo could have been taken on the morning of one of two other days April 13 or August 31, 1974.


11
Ciupik testified that he was an associate astronomer at the Adler Planetarium in Chicago, working chiefly as the Observatory Director; he had authored two children's books on astronomy, worked as a consultant for Rand, McNally, and written articles for McGraw-Hill's Yearbook of Science and Technology.  He had taught astronomy to gifted high school students, and was a member of a local professional organization.  He was accepted by the court, without objection, as an expert capable of making astronomical calculations.  Ciupik testified that as it revolves around the sun, the earth is fixed in its orientation towards the North Star.  The sun's path as we perceive it in the daytime sky therefore repeats itself from year to year.  Twice a year, on dates equidistant from the summer or winter solstices, the sun will be in precisely the same location with respect to both the horizon and the North Star.  Ciupik then expounded the theory that if one knew the compass orientation of an object in a photograph, it would be possible to date that photograph by: 1) measuring the directional angle of the shadow cast by that object to determine the azimuth of the sun;2 and 2) measuring the angle of elevation of a complete shadow cast by another object in the photograph to determine the altitude of the sun.3 Ciupik stated that the intersection point of the altitude and the azimuth, defining the sun's position in the sky, corresponds to the only two dates of the year on which the photo could have been taken.4


12
Ciupik further testified that he could determine those two dates by entering his findings for altitude and azimuth on a "sun chart" (Gov't Ex. 7A, attached).  Although Ciupik could not ascertain who prepared the chart, or even under whose supervision it had been prepared some fifteen years ago, he testified that he had verified its accuracy with an Analog Computer and through continued usage.  He stated, however, that the lines on the chart corresponding to the sun's path in the daytime sky were based on the sun's path on the 22nd day of each month, and that one would be compelled to interpolate the data obtained through his reverse calculations in order to determine the sun's position on any other day.  Moreover, the only purpose for which the chart had been used in the past was to measure the height of lunar mountains.5 The chart, a pivotal piece of evidence, was nevertheless admitted over Tranowski's objection that it was unverified, hearsay, and therefore formed an inadequate basis for Ciupik's calculations. On cross-examination, Ciupik admitted that although he had made numerous measurements of lunar mountains with the aid of the chart, neither he nor anyone else as far as he knew had ever used it prior to this trial for the purpose of dating a photograph.  Nor could he point to any published text suggesting or detailing the method one would use for such calculations.  Finally, there was no evidence that Ciupik's skill in measuring lunar mountains had ever been verified or corroborated.

Neighbors' Testimony

13
While Ciupik's testimony was the most telling evidence of Walter's guilt, the government also called two next-door neighbors of the Kniebusch-Tranowski household, Mrs. Florence Lojkutz and Mrs. Johanna Dressel.6 Mrs. Lojkutz testified that she had known both Walter and Stanley for over twenty years; she recognized certain photographs (Gov't Exs. 4B-4E) as having been taken by Walter and Stanley in the front of their mother's house sometime after July 3, 1974.  She insisted that the photos could not have been taken any earlier than that date, because she only witnessed the picture-taking session after being summoned to the window by her dog Fonzie's bark, a dog she first acquired the day before July 4, 1974.  Moreover, Mrs. Lojkutz recalled the date clearly because she had only recently purchased a peach-colored gown, and noticed that Mrs. Kniebusch was wearing a similarly-colored gown at the time the pictures were taken.  She testified that she did not, however, see the photograph on which Ciupik based his calculations being taken in the backyard of the house, and was of course therefore unable to express any opinion as to when it had been taken.


14
Mrs. Dressel, also a long-time neighbor, recalled that on April 29, 1974 she had had certain plumbing work done, and was sure that the photograph in question had been taken some three or four months after that date.7 She further testified that the Kniebusch-Tranowskis were often taking pictures, but although she was shown several others in addition to the photo in question, she was unable to state when they had been taken.

III. Discussion

15
Appellant claims that his conviction was irreparably tainted by the admission of the "scientific evidence" of the astronomer because the "chart" on the basis of which the witness made his calculations was of unknown origin and unknown accuracy, and the method by which the witness made such calculations had no indicia of reliability and no acceptance in the scientific community.  Since the indictment was expressly predicated on Walter's statements that the photograph (Ex. 4A) was taken between 2 and 3 p. m. on May 12, 1974, the conviction depended upon the admissibility of the astronomer's testimony and the acceptability of the chart upon which his testimony rested.


16
The applicable Federal Rules of Evidence are Rules 702 and 703, which deal with testimony by experts8 and the acceptable bases for their opinions.9 There is no question that Ciupik was qualified as an expert in astronomy by knowledge, skill, experience and education and, as such, was eligible to express an opinion on the subject which was "beyond the ken of the ordinary layman."  United States v. Cyphers, 553 F.2d 1064, 1072 (7th Cir.), cert. denied, 434 U.S. 834, 98 S.Ct. 142, 54 L.Ed.2d 107 (1977).  It was thereafter up to the trial judge within his broad discretion to decide whether the admission of the expert's testimony might assist him in his determination.  Hamling v. United States, 418 U.S. 87, 108, 94 S.Ct. 2887, 2902, 41 L.Ed.2d 590 (1974); United States v. Dellinger, 472 F.2d 340, 382-83 (7th Cir. 1972), cert. denied, 410 U.S. 970, 93 S.Ct. 1443, 35 L.Ed.2d 706 (1973).  Unless manifestly erroneous, his ruling will not be disturbed.  Cyphers; United States v. Stifel, 433 F.2d 431 (6th Cir. 1970), cert. denied, 401 U.S. 994, 91 S.Ct. 1232, 28 L.Ed.2d 531 (1971).


17
Ciupik's qualification as an expert is only the beginning of the case.  The admissibility of his testimony was intertwined with the quality of the data on which it was based.  The court decided to admit both the data, F.R.E. 104(a), and Ciupik's opinion testimony in the form of calculations based on that data, F.R.E. 702.  The underlying data in this case consisted of the photograph and the sun chart.  Since Tranowski originally introduced the photograph in support of his own testimony at Stanley's trial he, of course, has not objected here to its admission, but only to the method used to date it.  The chart, however, is in a different category.  He claims that it was inadmissible as hearsay, and in violation of his Sixth Amendment right to confront his accusers.  Even though its origin was unknown, according to the testimony the chart had been used for some time to delineate the sun's path as viewed from Chicago on the 22th day of each month.  In admitting the chart over Tranowski's objection, the trial court said:


18
Based upon the witness' testimony that the chart is verified in usage, and its continuing use is a continuing verification of it, I'll overrule the objection and it may be admitted.


19
In essence, the trial court deemed the chart to be admissible because it had "circumstantial guarantees of trustworthiness."  F.R.E. 804(b)(5).  The difficulty we have with this ruling is that while the chart might have been admissible for the purpose of assisting Ciupik to measure the height of lunar mountains, the chart had never been verified in usage for the particular purpose for which it was offered at trial, viz., the dating of photographs.  It is true that under Rule 703 Ciupik's opinion evidence might have been admitted without the chart itself, if it had been shown that astronomers who engaged in the field of analyzing and dating photographs would rely on such a chart in making their calculations.10 But this was never shown, either by Ciupik's testimony, or by evidence of published reports, or by earlier experiments.  The chart being unverified for its accuracy in dating photographs, and not being relied on by experts in the field other than Ciupik, lacked any "circumstantial guarantees of trustworthiness."  Since there remains no other theory upon which it could have been admitted, it was error to have ruled otherwise.


20
Aside from the untrustworthiness of the chart, and in spite of the particularly wide discretion of a trial judge in admitting or not admitting expert testimony, Hamling v. United States, 418 U.S. at 108, 94 S.Ct. at 2902, we believe that the technology Ciupik relied on was not "sufficiently established to have gained general acceptance in the particular field to which it belongs."  Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923); United States v. Brown, 557 F.2d 541, 556 (6th Cir. 1977).  This is not because Ciupik invoked a new test or theory, for "(e)very new development must have its first day in court," Stifel, 433 F.2d at 438, nor is it because Ciupik was not absolutely certain of his conclusions, since his lack of certainty goes to the weight, not the admissibility of the evidence.  Cyphers, 553 F.2d at 1072-73.


21
In reaching our conclusion it is unnecessary to question the soundness, as a theoretical proposition, of dating a photograph by means of measuring the lengths of shadows on the photo and then trigonometrically calculating the altitude and azimuth of the sun.  Our rejection is addressed to Ciupik's application of that theory to the photograph in question.  This should not be surprising, since neither Ciupik nor anyone else to his knowledge had ever attempted this procedure before.  But despite the year and a half that the government had to prepare its case against Tranowski with the photograph in its possession Ciupik was never requested to perform any control experiments to verify the accuracy of his techniques.11


22
Under F.R.E. 201 this court may take judicial notice of facts "not subject to reasonable dispute," among which are "things which must happen according to the laws of nature."  Brown v. Piper, 91 U.S. 37, 42, 23 L.Ed. 200 (1875).  For example, in making comparisons of the image with the actual subject of the photograph one would have to take into account possible "distortion(s) caused by the perspective of the picture and other technical factors."  United States v. Sellers, 566 F.2d 884, 886 (4th Cir. 1977).  In Sellers an expert witness was used "to explain the difficulties of making photographic comparisons because of variations in lenses, perspective, light, and development paper."  Id.


23
It was critical to Ciupik's calculations that the measurements he took of the shadows on the photograph accurately reflected the actual lengths of the shadows cast at the time the photograph was taken.12 Yet no evidence was offered to substantiate these measurements by testimony as to the type of lens used, and the probable position and angle of the camera when the photograph was taken.  Thus it is impossible to determine whether or not the photograph in question distorts the heights and lengths of the subjects in the Kniebusch-Tranowski family's backyard, although it was the government's obligation to establish that Ciupik's calculations were not based on distortions.  As it now appears, these calculations are unreliable.


24
Even without these variables, Ciupik's measurements from the photograph do not demonstrate the necessary indicia of reliability.  First, he failed to take into account any possible slope in the ground when he constructed the right triangle of the dog's shadow.  Uncontradicted testimony was admitted to the effect that the backyard did in fact slope somewhat.  Second, the orientation of the back wall of the house in an east-west directional plane was never verified, even though it was essential to the determination of the sun's azimuth that a precise compass orientation be obtained. Third, an examination of the photograph convinces us that it is impossible to locate with any degree of accuracy the intersection line of the chimney with the back wall.  Cf. United States v. Brown, 501 F.2d 146, 150 n.1 (9th Cir. 1974), rev'd on other grounds, 422 U.S. 225, 95 S.Ct. 2160, 45 L.Ed.2d 141 (1975), where the court rejected the admission of expert testimony concerning defendant's likeness in certain photos on the ground that the pictures were "of poor resolution and quality."


25
Ciupik's shadow measurements were the data base for his trigonometric calculations.  It is not necessary to question the accuracy of those calculations; it is sufficient to note that they were predicated on unreliable premises.  The resulting angles were no more than another form of the same information we have already rejected.  Again, when the two angles were entered onto the sun chart, the dates and times that Ciupik arrived at could be no more accurate than his original measurements from the photograph.  We believe, in fact, that they were less so.  The chart itself was drawn for the 22nd day of each month; any errors in the shadow measurements would only have been compounded by the roughness of Ciupik's interpolations on the chart.  In light of Walter's testimony that the photograph was taken on May 12, 1974, these incremental variations become significant since one of the possible dates Ciupik arrived at in spite of the variations was April 13, 1974, plus or minus two to three days a margin of error which could have been much greater.


26
The trial court should not be used as a testing ground for theories supported neither by prior control experiments nor by calculations with indicia of reliability.  In United States v. Kilgus, 571 F.2d 508 (9th Cir. 1978), the court held that opinion testimony based on the "forward looking infrared system", a technique used for generic identification of objects, was inadmissible because the technique was not yet generally accepted for unique identification of remote objects, and the testimony failed to show that barometric pressures, temperature, humidity, and other critical atmospheric conditions had been held constant.  We accordingly endorse the conclusion of the Sixth Circuit in United States v. Brown, 557 F.2d at 556 that:


27
A courtroom is not a research laboratory.  The fate of a defendant in a criminal prosecution should not hang on his ability to successfully rebut scientific evidence which bears an "aura of special reliability and trustworthiness," although, in reality the witness is testifying on the basis of an unproved hypothesis in an isolated experiment which has yet to gain general acceptance in its field.


28
Having rejected the expert's testimony, the critical inquiry remains whether the testimony of the neighbors and of the Burger King and drug store employees is sufficient to support a conviction beyond a reasonable doubt.  Upon this evidence we do not believe that "any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt."  Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979).  "Guilt in a criminal case must be proved beyond a reasonable doubt and by evidence confined to that which long experience in the common-law tradition, to some extent embodied in the Constitution, has crystallized into rules of evidence consistent with that standard."  Brinegar v. United States, 338 U.S. 160, 174, 69 S.Ct. 1302, 1310, 93 L.Ed. 1879 (1949); In re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970).  Consequently, we need not reach appellant's further contention that the trial court was prejudiced by exposure to Walter Tranowski's prior arrest and conviction record.  The judgment of conviction must be and hereby is Reversed.APPENDIX A

Government Exhibit 4-A

29
NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLEAPPENDIX B


30
NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLEFAIRCHILD, Circuit Judge, dissenting.


31
The critical question is whether the district judge abused his discretion in admitting Ciupik's expert testimony, which was based on calculations made from a photograph originally used by defendant in support of his allegedly perjurious alibi testimony and a chart marking the sun's path as viewed from Chicago on the twenty-second day of each month.  See United States v. Cyphers, 553 F.2d 1064, 1072 (7th Cir. 1977), cert. denied, 434 U.S. 834, 98 S.Ct. 142, 54 L.Ed.2d 107 (1977).  Because I would hold that he did not abuse his discretion in admitting this evidence, I respectfully dissent.


32
I disagree with the majority's conclusion that the chart lacked "circumstantial guarantees of trustworthiness."  The chart represents easily verifiable data regarding the position of the sun at one hour intervals on the twenty-second day of each month as observed from 42o North, the latitude of Chicago.  As Ciupik testified, the chart has been verified by tables giving the azimuth of the sun for various times and dates for various locations, and by the analogue computer at the Planetarium, which marks the way the sun crosses the sky day by day.  Ciupik testified that he had used the chart hundreds of times and found it accurate.  Surely it was reasonable for the district judge to conclude that any possible inaccuracies in the chart would have been discovered during the fifteen years the chart has been in use.


33
The majority finds no real fault with the theory explained by the expert that the altitude and azimuth of the sun can be computed from right triangles as described by Ciupik.  That the method is not known to have been applied to a photograph before scarcely establishes that it is unsound.


34
Ciupik did not claim perfect accuracy in concluding that the picture was taken April 13 or August 31.  He suggested a margin of error of several days.  As noted by the majority, the lines on the chart correspond to the altitude and azimuth of the sun only on the twenty-second day of each month.  Ciupik felt that he could interpolate between these days.  In any event, his calculations, made on the chart, put the date well before April 22 or after August 22, a very substantial difference from May 12.


35
The majority questions the application of this theory to the photograph in question, stating that Ciupik failed to take into account any possible slope in the ground when he constructed the right triangle of the dog's shadow.  Yet Ms. Kniebusch testified that her yard was only slightly sloped, if at all, because she had rolled it with an iron roller.


36
The majority also expresses concern over the accuracy of the assumed east-west bearing of the south wall of the house.  It is evident from cross-examination of Mr. Ciupik that his testimony came as no surprise.  Defense counsel had interviewed him concerning his calculations several days before he testified.  It follows that if defense counsel had any concern about the slope of the ground or the true bearing of the wall, he had an opportunity to obtain evidence on those facts.


37
Judge Bartels has very meticulously suggested several other problems in obtaining precise measurements.  Any inaccuracies would then have to account for a difference of twenty-nine days if the picture was actually taken on May 12.  It seems to me these possibilities of inaccuracies are insufficient to demonstrate an abuse of discretion in admitting the evidence.


38
Regardless of Ciupik's testimony, there was ample evidence that Walter's testimony that he spent the afternoon and evening of May 12, 1974 with Stanley was untrue.  The witnesses whose testimony convicted Stanley of passing counterfeit money at the Burger King that afternoon testified again at Walter's trial.  These included Peter McGhee, who identified Stanley as the man he chased after the Burger King incident, and Robert Fusello, who saw Stanley at his drugstore between 6:00 and 7:30 p. m.


39
Walter had also testified at Stanley's trial that other pictures were taken the same afternoon in front of his mother's home.  Two neighbors testified that these pictures were taken long after May 12.


40
Moreover, the photograph examined by Ciupik was taken south, or back of the house looking toward the south wall.  No expert is needed to demonstrate that it was taken well before noon.  The direction of the shadows make that plain to all.  Again, Walter's testimony that it was taken in the afternoon is untrue.


41
Of course, to convict of perjury, the government must convince the trier of fact not only that the testimony was untrue, but that defendant knew it was false.  Ciupik's testimony was significant in the process of persuasion because the more palpably untrue a defendant's testimony can be shown to be, the more readily his knowledge of falsity can properly be inferred.  Hence, the importance of the question whether the expert's opinion and the chart on which he based it were properly admitted.  I would hold that the district judge did not abuse his discretion in admitting them and would affirm.



*
 The Honorable John R. Bartels, Senior United States District Judge for the Eastern District of New York, sitting by designation


1
 The indictment charges, in pertinent part:


4
 On or about December 13, 1977, at Chicago, in the Northern District of Illinois, Eastern Division, defendant herein, while under oath as a witness in the United States District Court for the Northern District of Illinois in case number 76 CR 803, knowingly made false declarations with respect to the aforesaid material matter by stating in substance that on May 12, 1974 he was with his brother, Stanley Tranowski, at all times during the period from approximately 2:00 p. m. until 7:25 p. m., including but not limited to the statements that:
(a) between 2:00 and 3:00 p. m. on May 12, 1974, defendant Walter Tranowski, his mother, Cecelia Kniebusch and Stanley Tranowski, were taking photographs in front of his mother's house.  The defendant Walter Tranowski identified six photographs, Defendant's Exhibit Numbers 2 through 7, as the photographs so taken on that occasion;
(b) later during the afternoon of May 12, 1974, defendant Walter Tranowski, Cecelia Kniebusch and Stanley Tranowski were at the Diplomat Steak House, Chicago, Illinois, where a photograph was taken.  The defendant Walter Tranowski identified said photograph, Defendant's Exhibit Number 7 as the photograph so taken on that occasion.
(c) defendant Walter Tranowski and Stanley Tranowski after leaving the Diplomat Steak House, dropped their mother off at 5171 West St. Paul, Chicago, Illinois, and drove together to the Matz Funeral Parlor, Chicago, Illinois, where they remained until approximately 7:25 p. m. when they left together.


2
 The azimuth of the sun is its angle from true south


3
 The altitude of the sun is the angle formed by its elevation above the horizon


4
 In order to date the photograph in question, Ciupik made the following calculations on the enlarged photograph of Stanley, his mother, and Jerry the dog:
Altitude.  Ciupik used Jerry's shadow as the only complete shadow cast by an object in the photo.  With a ruler, he measured the dog's height to be 10.4 centimeters, and the length of its shadow 16.1 centimeters.  Assuming the ground to be level (but see the discussion infra at p. 756), Ciupik used these two lengths as the legs of a right triangle.  By means of basic trigonometry (tangent of an acute angle of a right triangle equals the ratio of the side opposite to the side adjacent that angle), Ciupik found the angle of the sun's elevation to be 32.86, or 33 degrees.
Azimuth. Ciupik used the shadow cast by the chimney at the back of the house, on the assumption (again, see the discussion infra at p. 756) that the back wall of the house lay in an east-west plane.  Using an hypothetical bird's-eye view photograph of the chimney as it projects from the wall, Ciupik again measured two legs of a right triangle in order to determine the unknown acute angle, here the direction of the sun away from true south (after correcting for the ninety degrees east angle of the house).  He found the length of the shadow cast from the intersection of the chimney and the wall to be 17.4 centimeters, and the length of the shadow cast from the outermost part of the chimney to be 18.9 centimeters.  Using trigonometric calculation (cosine of the acute angle of a right triangle equals the ratio of the side adjacent to that angle to the hypotenuse), Ciupik ultimately found the angle from true south to be 67 degrees.


5
 In making such a measurement, an astronomer knows the position of the sun, since he takes a sighting through a telescope of known directional orientation at a precise time on a specific day.  He then solves for the unknown variable in a trigonometric equation, i. e., the vertical leg of a right triangle formed by a mountain and its shadow on the moon's surface.  Here Ciupik measured the legs of the triangles formed by the shadows of the dog and the chimney as shown in the photograph.  The unknown variable was therefore the position of the sun set forth in the sun chart


6
 Much of the testimony adduced at Stanley's counterfeiting trial was also repeated at Walter's trial.  That testimony only established that Stanley was not with his brother Walter at the time the bill was passed; it could not, without more, prove that Walter lied on the witness stand


7
 Mrs. Dressel never spoke to Mrs. Kniebusch after April 29, 1974, since Mrs. Kniebusch had refused to let her use her bathroom facilities while Mrs. Dressel's were being repaired


8
 "Rule 702 Testimony by Experts
If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise."


9
 "Rule 703 Bases of Opinion Testimony by Experts
The facts or data in the particular case upon which an expert bases an opinion or inference may be those perceived by or made known to him at or before the hearing.  If of a type reasonably relied upon by experts in the particular field in forming opinions or inferences upon the subject, the facts or data need not be admissible in evidence."


10
 Even though the chart would arguably be hearsay evidence in such circumstances, Rule 703 permits a court to admit an expert opinion based on hearsay, if reliance on such factual bases is the normal practice of experts in the field in reaching their conclusions.  To that extent the rule is in derogation of the common law.  See 3 Weinstein's Evidence, P 703(03).  There is no merit in Tranowski's contention that he was deprived of confrontation with his accusers, since his confrontation was in reality with Ciupik, whom he had ample opportunity to cross-examine.  See, e. g., United States v. Genser, 582 F.2d 292, 299 (3d Cir. 1978), cert. denied, 444 U.S. 928, 100 S.Ct. 269, 62 L.Ed.2d 185 (1979)


11
 For example, Ciupik might have had a series of photographs taken at times and dates known to a neutral party, and then worked independently to see whether he would arrive at the same date.  At the very least, he would have been able to establish his margin of error when dealing with photographs taken through a camera of unknown characteristics and position.  The absence of any published work outlining the necessary methodology for dating photographs by reference to the position of the sun raises further doubts.  See United States v. Brown, 557 F.2d 541, 557 (6th Cir. 1977) (rejecting ion microprobic analysis of hair samples where, among other weaknesses in the government's case, it failed to adduce any published authority in support of the theory)


12
 See n. 4 supra


