In the spring of 1975 I was able to locate, with the incidental help of Mr. Klass, the original negatives. (They were in the possession of Philip Bladine, the editor of the newspaper.) Consequently, all density values given in this paper are from those negatives. They were measured on a Joyce-Loeble densitometer that was repeatedly calibrated with a Kodak standard diffuse neutral density "wedge." Although many areas of both photos have been scanned to establish consistency between the exposures, etc., only the density values pertinent to the range calculation will be listed here. These values along with other pertinent photographic data are listed in Table I. The analysis is based on Hartmann's method with the following modifications:
(1) I have used an exposure curve relation for the negatives based on a published D-LogE' curve for Verichrome film whereas, Hartmann implicitly assumed "gamma" = 1 (Film "gamma" relates exposure level or image density to illumination of the film or image brightness. See illustrations labelled "TrntGamma6Curve.gif" and TrntGAMACurves.gif.) Other possible film types are Plus-X and Plus-XX, both Kodak films, but the exposure curves of these are similar to that of Verichrome; measures of the fog density suggest that only Plus-XX and Verichrome are compatible with densities found in unexposed regions; Verichrome was the least expensive, hence most likely to have been used; Verichrome has low sensitivity to red light.);
(2) Since the negatives are pale (1,4), that is, the density range starting from the fog level is not as large as expected for a sunlit day, I have assumed that the negatives were slightly underdeveloped and have, therefore, used an exposure curve for gamma = 0.6, even though it was standard procedure to develop to a gamma of about 1 (4);
(3) I have used a photographic formula to relate image illuminance to object brightness;
(4) I have incorporated laboratory derived estimates of veiling glare; and
(5) I have incorporated the brightness ratio of a shaded vertical surface to a horizontal surface seen from below. The ratio was obtained from field measurements. This brightness ratio was ignored by both Sheaffer and Hartmann.
The first step in the analysis is to determine the relative illuminance on the film plane which produced the image densities. Simple photographic theory corrected for the effects of veiling glare predicts that

E' = image illuminance = K(B + G) cos^4(A) (1)

where K is a constant for a particular picture (and is assumed to be the same for both photos here; this involves f-number and shutter time), B is the brightness in the absence of glare of the object being photographed, G is the amount of veiling glare added to the image, cos^4 is the cosine raised to the fourth power and A is the angle between the lens axis and the direction to the object. Defining Ei = E'/[Kcos^4(A)], and substituting the empirical exposure curve relation between measured image densities and their causative illuminances, yields the total image "brightness" given in Eq. 2 (see Table I). The brightness in the absence of glare is then found by subtracting the glare on the image, as in Eq. 3 (see Table I).

TABLE I

IMAGE OF:	DENSITY, D	ANGLE,A,FROM LENS AXIS
Shadow on wall of distant white house,ph#1	0.025 +/- 0.03 (weighting factor= 1)	A = 17.6 deg.
Same as above,ph#2	0.024 +/- 0.01	12.5 deg
Sky near and above U0	0.061 +/- 0.01	0 deg
Horizon in each photo	0.43 to 0.46 (use 0.45 as avg)	10 deg
Bottom of UO in photo 1	0.315 +/- 0.001	-

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The atmospheric Extinction Coefficient (12 mile visibility from weather report), b = O.2/km.
The distance to white house across the Salmon River Parkway is about 360 meters
The focal length of the lens = 103 (+/-) 5 mm
The f# was probably about f/ll
The shutter time was probably 1/125
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Relative exposures or "total image brightnesses" have been calculated from

Ei = Eo {exp[2.303(Di/gamma - k/Di^3)]}/{Kcos^4(A)}  (2)

where Ei is the image exposure, Di, is the measured density for Di>0.1, Eo and k are constants that depend upon the film development "constant," gamma. Table IV contains a listing of values of E, and k for various values of gamma.
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The relation between image brightness, B, image exposure, Ei, and veiling glare on the image, Gi is

B = Ei - Gi  (3)

The amount of veiling glare added to an image is proportional to the brightness, Bs, surrounding the image: Gi = gi x Bs, where values of gi for particular sizes and shapes of images in particular surrounding brightness distributions have been measured in the laboratory. With a brightness distribution similar to that of the photos (bright above the horizon, dark below the horizon), a laboratory simulation has shown that, when a lens is sufficiently dirty to produce guo ~ 0.12, i.e., glare in the UO image is abou 12% of the surrounding brightness, then g(distant house)~ 0·035 and g(horizon) ~ 0·05.
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Let the ratio of the brightness of a vertical, white, shaded surface (the wall of a white house)to the brightness of a horizontal white surface viewed from below(hypothetical UFO model with a white paper bottom) be called Rb.

Field measurements show that 2.4 < Rb < 4.7. In the calculations done here I have used Rg = 2.4 to be conservative. Use of a larger Rb would result in calculated distances greater than reported here.

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Atmospheric brightening formulas for range r (the formulas first used by Hartmann) are:

(a) B(r=0) = intrinsic brightness = Bh + (B(r)-Bh) e^(br)  (4)

(b) r = range = (1/b)Ln{[B(r=0)- Bh]/[B(r) - Bh]}  (5)

where B(r) is the measured brightness at range r, Bh is the horizon brightness and b is the atmospheric extinction coefficient.

To illustrate the photometric method I shall first summarize Hartmann's analysis, and then I shall present a range calculation based upon the simplified analysis. Hartmann pointed out that the upper bright side of the object appears brighter than the side of the nearby tank and that the elliptical shaded bottom is the brightest shadow in either photo. He attributed the excessive brightness of the bottom of the UO to atmospheric brightening. (NOTE: the contrast between the brightness of an object and that of the sky, assumed to be brighter than the object, approaches zero as the distance to the object increases, i.e., the apparent brightness of the object increases until it matches that of the sky at a great distance.) By definition the intrinsic brightness of an object is the brightness measured from a very short distance. By assuming the intrinsic brightness of the bottom of the UO was the same as that of the shaded bottom of the tank, and using the formula which attributes increased brightness to atmospheric effects over a long distance (Equation 5 in Table 1), he estimated that the range to the object was about 1.3 km, based on his estimate of b (0.289/km.). (NOTE: all his brightnesses were normalized to the horizon brightness so Bh = 1 in his version of Eq. 5). He then pointed out that if the UO were nearby under the wires, the bottom must have been very white, even brighter than the shaded white surface of the distant house which appears near the bottom of the photos.

I have modified Hartmann's analysis by assuming at the outset that the bottom is as bright a surface as would have been available to the photographers (white paper) without being itself a source of light. (Note: the witnesses described the bottom as being copper colored or darker than white. Use of a darker bottom in the following analysis would result in a greater calculated distance.) This assumption has led me to compare the relative brightness of the bottom of the UO with the relative brightness of a hypothetical nearby horizontal shaded white surface as seen from below. The brightness that a horizontal white surface seen from below would have had under the circumstances of the photo has been estimated from the relative brightness of the vertical shaded white surface of the distant house (and also from the shaded white surface of the wall nearby Trent house) and from the brightness ratio Rb in table 1.

If, in a naive way, the intrinsic brightness of a vertical white shaded surface (house wall) is equated to the intrinsic brightness of a horizontal white surface as seen from below (whereas the horizontal surface actually may be somewhat less than half as bright), that is, if Rb is set equal to 1 , and if the effects of veiling glare are ignored (G in Eq. 3 is set equal to zero), then the range of the UO can be calculated from Eq. 5 using as B(r=O) the brightness of a nearby vertical shaded white surface (the Hartmann method). The shaded wall of the distant house was used by Hartmann to estimate the relative brightness of a hypothetical nearby vertical surface (see the illustration labelled "TrntWhteHouse.gif) by correcting the relative brightness of the wall for atmospheric brightening using Eq. 4 (Table I). If the object were hanging under the wires then, by this (naive) reasoning, the brightness of the hypothetical nearby vertical surface should equal the brightness of the bottom of the UO, and Eq. 5 would yield r = 0. Such a result would be consistent with the hoax hypothesis.

However, Hartmann found that the brightness of the image of the bottom of the UO was actually greater than the brightness of his hypothetical neaby vertical surface. Hartmann's calculation is duplicated in Table II except that I have used b = 0.2/km rather than 0.289/km. The table lists the pertinent relative "brightnesses," Ei (uncorrected for glare), the correction of the distant house wall "brightness" for atmospheric brightening, and the range calculated from Eq. 5. The calculated range, 1.4 km., agrees with Hartmann's result and is clearly inconsistent with the nearby UO hypothesis.

TABLE II

Modified Hartmann method
Assume the bottom is white and use gamma = 0.6
Ehorizon = 0·039 (+/-) 0.002;
Edistant house shadow = 0.018 (+/-) 0.001;
Euo = 0.022 (+/-) 0.001 ;
Esky = 0.070 (+/-) 0.001.
Atmospheric Extinction Coefficient (based on visibiliy range): b = 0.2/km
Distance to White House: 0.36 km
Now use the measured brightness of the distant shaded vertical white wall to obtain the brightness of a hypothetical nearby white shaded surface by "removing" the atmospheric brightening (Eq. 4 of Table I): 0.039 + (0.018 - 0.039)e^(0.2x0.36) = 0.0164 (+ /-)0.001.
Now assume 0.0164 to be the intrinsic "brightness" of the bottom of the UO and calculate its range:
r = (1/(0.2/km.) x Ln[(0.0164 - 0.039)/(0.022 - 0.039)] = 1.42 (+/-) 0.6 kilometer.

Accurate calculations of object brightnesses require corrections for veiling glare, as pointed out by Sheaffer. Since, in the first approximation, the phenomenon (scattering) which produces veiling glare simply adds light (from the brighter areas) to the darker areas, it is only necessary to subtract the amount of glare from an image to find the object brightness (Eq. 3). The problem is to find the amount of glare on an image. After some considerable thought and experimentation I found a way to estimate the glare on the Trent photos using laboratory simulations.

In order to estimate amounts of glare on the images of interest in these photos, I have conducted laboratory experiments with several camera lenses, one of which was comparable (but not identical) to the lens on the camera that took the photos. I simulated the brightness distribution of the sky with a large screen which was illuminated from behind. Below the simulated "horizon" (the bottom of the bright area) there were no sources of light. I then measured brightness distributions in the bright and dark areas when there were varying amounts of grease on the lens. (Measurements were made with a linear photodetector and a small aperture that could be moved about in the focal plane of the lens.) The light that "turned up" in·the dark areas was the glare light, G, which would have appeared on any images that might have been present in the dark areas (although no such images were present in the laborstory simulation). Values of G were proportional to the "sky" brightness, Bs, so that at each point on the image plane a glare index, gi, could be defined as gi = Gi/Bs. For the present work it was important to have values of gi for images 2 degrees below the horizon (the angle of the image of the distant house) and for images at (or just below) the horizon, when the glare index for an image of the angular size and shape of the elliptical bottom of the UO was a particular value.
I carried out the experiments as follows. First I placed an ellipse of dark paper with the angular size of the UO in photo 1 on the bright screen. I then put some dirt or grease on the lens in order to increase the glare and measured the amount of glare light at the center of the image of the dark ellipse. This was defined as the "glare index" for a particular amount of grease/dirt. I also measured brightness variations in sumulations of other images in the photos with the same grease/dirt. Of particular interest was the image of the large telephone pole in Photo 1. Measurements of the brightness variation of the image of the pole showed that below the horizon the image was of a nearly constant brightness, and that above the horizon the image increased in brightness as the angular altitude increased. I attributed this increase in brightness to an increase in the glare light added to the pole image (thus implicitly assuming that the brightness of the pole was intrinsically constant from its bottom to its top; however, I have observed that, probably because of weathering, the brightness of many wooden telephone poles increases with height along the pole; the result, in these calculations, of my assumption of constant intrinsic brightness is an overestimate of the actual glare and therefore an underestimate of the calculated distance to the UO). I simulated the pole image in the laboratory setup by placing s strip of black paper of the same angular width and height as the pole on the bright screen above the simulated horizon. I measured the brightness of the image of the simulated pole on the focal plane of the simulated camera. Since the paper was black and the only illumination was from behind the paper the measurement would have given zero brightness if there had been no glare. However, by changing the amount of grease on the lens, I was able to adjust the brightness of the simulated pole image; the more grease the brighter then simulated image. Thus, a distribution of values of gp along the pole image (glare on the pole image vs height) was measured for each amount of grease. Then the laboratory determined values of gp vs. altitude alog the pole were multiplied by a value of Bs determined from the sky brightness of Photo 1 to obtain the amounts of glare, Gp, that would have been added to the actual pole image in Photo 1. By adjusting the amount of grease on the lens, I was able to obtain a set of values of gp, that is, a graph of gp vs height, which, when multiplied by the sky brightness of Photo 1, yielded a "theoretical" brightness increase that was close to the increase in brightness of the actual pole image, that is, the graph of pole image brightness vs height. (See Figure A16 in the Appendix.) In other words, I was able to approximately fit the laboratory data to the measured increase in pole brightness. I then measured the glare index (the glare in the simulated UO image as described above) for the same amount of grease on the lens. I also measured the glare below the horizon at the angular distance of the distant house below the horizon. (Briefly, I used the pole glare distribution in the photo to determine the amout of grease in a simulation and then measured the UO glare in the simulation and calculated from that the glare in the photo image of the UO.) The amount of grease which yielded the most correct set of values of gp for the pole image also yielded guo = 0.12 for the image of the UO, and the other values of gi given in Table I. These values have been used in the following analysis, even though other measurements have strongly suggested that guo = 0.12 is probably too high. (Typical values of veiling glare in an image the angular size of the UO in Photo 1 would be less than 0.09.) Moreover, measurements of the brightness variations in certain other images in the photos suggest that guo = 0.12 is be too high (0.07 might be better). More details of the result of the glare experments are presented in the Appendix to this paper.

The effect of the inclusion of veiling glare is readily apparent when it is applied to the image illuminances, Ei, shown in Table II. For example, the horizon brightness is found to be Eh - Gh = Eh - ghBs (where, from Table I, gh= 0.05) = 0.039 - (0·05)(0·07) = 0·0355. Similar calculations yield the relative brightnesses given in Table III. Note that in this first order theory the small loss of brightness from the bright areas is ignored, so Esky = Bsky.

TABLE III

Relative Object Brightnesses with Esky = Bsky = 0.07:
Bhorizon = Eh - Gh = Eh - ghBs = 0.039 - (0.05)(0.07) = 0.0355;
Bdistant house shadow = 0.018 - (0.035)(0.07) = 0.0155.
After atmospheric distance correction,
Bnearby vertical shadow = 0.014;
Buo = 0.0136
CALCULATED DISTANCE = "ZERO"

From Table III one can observe that a major effect of the inclusion of veiling glare is to make the brightness of the bottom of the UO equal to (or slightly less than) the brightness of a vertical shaded white surface. Naive use of Eq. 5 with B(r=0) = 0.014 and B(r) = Buo = 0.0136 would yield a range of zero (negative numbers are not allowed), so Sheaffer's conjecture that the apparent distance of the UO could be explained by veiling glare has merit. (NOTE: If guo were 0.07 and the other values of gi were proportionately lower, the range would not be zero but about 400 meters.)

If there were no other correction factors this would be the end of the analysis. However, field measurements with a spot photometer have shown that it is incorrect to equate the brightness of a shaded vertical white wall with the brightness of a horizontal surface as seen from below.

A shaded vertical wall which is on the order of ten feet above the ground and which is not closely surrounded by trees is illuminated by direct sky light as well as by light reflected from the ground. On the other hand, the horizontal bottom surface of a body which is less than ten feet above the ground is illuminated only by light reflected from the ground. Since the ground reflectivity is not particularly high (15-30% for grassy ground), one would expect the illumination on the horizontal (or nearly horizontal) bottom of an object to be less than that on the vertical surface. Thus, from a priori reasoning one should not equate the relative intrinsic brightness of a white shaded vertical surface to the relative intrinsic brightness of a white shaded horizontal surface seen from below. To provide a quantitative estimate of the ratio of brightness of a vertical surface to a horizontal surface, Rg, (see Table I) I made field measurements with a calibrated panchromatic 3.5 degree field of view spot photometer. I measured the brightness of the white wall of a house when the wall was shaded by the eave and when the sun angle and sky conditions were similar to those at the time of the UO photos. Under the same environmental conditions, I measured the brightness of an opaque white paper surface held about seven feet above the ground. Many measurements of the surfaces were made with the result that the house wall was found to be 1.5 to 2 "stops" (photographic terminology) brighter than the bottom of the white surface, depending upon the exact nature of the ground (grassy, dirt, etc.) and upon the sky brightness distribution. Allowing a 1/4 stop possible error in the readings, the brightnass ratio lay within the range 2^1.25 = 2.4 to 2^2.5 = 4.7 (see Table I). To be "conservative" I have used Rb = 2.4 in these calculations. (NOTE: This ratio was measured with panchromatic meter. If a filter had been used to simulate the orthochromatic Verichrome spectral response, the measured ratio might have been as much as 30% greater.) The measured brightness of the bottom of the horizontal surface did not change noticeably when the surface was tilted by as much as 20 degrees.

From Table III the relative brightness of a nearby vertical white shaded surface was 0.014. From the field measurements this value should be divided by a number at least as great as 2.4 to obtain the relative brightness of a nearby horizontal white shaded surface, which is assumed to be the brightness of the bottom of the nearby UO. With Bh = 0.0355, Buo = B(r=0) = 0.0136 (see Table III), with B(nearby horizontal surface viewed from below) =·0.014/2·4 = 0.0058, and with b = 0.2 (Table I) the range calculation yields about 1.5 km.
Variations in the calculated range with variations in the parameters of the range equation are as follows: (a) the calculated range increases as the glare decreases; for example, if there were no glare the range would be calculated from Euo = Buo = B(r) = 0.022, Bh = 0.039, (from Table II) B(r=0) = 0.0164 /2.4 = 0.0068 and Eq. 5 would yield about 3.2 km.; (b) the calculated range increases with increases in the ratio Rb; for example, if Rb = 3, using the brightnesses in Table III and B(r=0) = 0.014/3 = 0.00467, Eq. 5 yields arange of about 1.7 km.; (c) the calculated range increases with gamma as indicated in Table IV.

TABLE IV

gamma	Eo	k	Buo/B(r=0)	Range	Diameter*	Thickness**
1.0	0.00436	0.0025	2.75	2.4 km	68m	9.6m
0.7	0.0063	0.0017	2.60	1.5	44	6.2
0.6	0.0068	0.00055	2.34	1.52	43	6.1
0.5#	0.0076	0.0002	2.18	1.06	30	4.2
0.3#	0.0093	0.00009	<1	0.0	0	0

IF NEARBY UNDER THE OVERHEAD WIRES: 5m 14 cm 2 cm

*angular diameter in photo 1 is 0.0283 radians (in photo 2, 0.0248 radians) based on the assumed focal length of 103 mm which is the approximate value for the cameras of the type used (assumed to be a Kodak Monitor or Vigilant)
**angular thickness excluding "UO pole" in photo 2 is 0.004 rad. based on the 103 mm focal length
#curves for these values of gamma were synthesized by extrapolation from published curves·which show gamma in the range 0.6 to 1.0. These results are included for completeness. However there is no evidence at all that the gamma would have been lower than 0.6. In fact, it is more likely that gamma was greater than 0.6. See note 11.

Table IV also contains a list of ratios of the brightnesses of the bottom of the UO to the expected brightnesses if the object were close and had a white bottom (the brightnesses of a nearby horizontal shaded white surface). Since the expected relative brightnesses were calculated using a white surface (the distant house wall or the nearby house wall - see Appendix) as a reference, the ratios imply that the bottom of the UO was "brighter than white" whenever reasonable values of gamma, i.e., gamma > 0.6, were used in the calculation. White surfaces reflect most of the incident light (both white paint and white paper have reflectivities in the range(6) of 60-80%). If we assume, for example, that the white paint on the distant (or nearby) house reflected only 60% of the incident light, then a brightness ratio greater than 1/0.6 = 1.67 would imply that, if the UO were a small nearby model. then its bottom was a source of light (it could not reflect more light than 100% of what was incident on it; 1.67 X 60% = 100%). As shown in Table IV, for reasonable values of gamma the calculated ratio Buo/B(r=0) exceeds 1.67 by a considerable margin. Actually 1.67 is an upper bound on the ratio if the distant house reflected 60% of the light because any white surface which the witnesses would have available to place on the bottom of their hypothetical nearby UO would have a reflectivity lower than 100%. If the bottom were white paper, the reflectivity would be, at maximum, about 80%, in which case the maximum expected ratio of the brightness of the bottom to the expected brightness would be 0.8/0.6 = 1.33. (NOTE: If the white painted surface were known or assumed to be dirty, the reflectivity would be decreased and the brightness ratio increased. For example, to obtain the brightness ratio 2.34 which is obtained when gamma = 0.6 (see Table IV) with 80% reflective paper on the bottom of the object, the distant wall reflectivity would have to be as low as 0.8/2.34 = 0.34. On the other hand, measurements of the image density of the shaded wall of the nearby Trent house, after correction for veiling glare, yielded an upper bound on the relative brightness of a shaded white vertical surface of 0.0171, which is only 0.0031 units higher than the value 0.014 in Table III. This house was reportedly painted in the year previous to the sighting date, so the paint must have approached its maximum reflectivity. Use of this value, after dividing by 2.4, with the other brightnesses in Table III yields a distance of about 1.3 km, and a brightness ratio of 1.9, which is still larger than 1.67 and 1.33.)

The implication of the brightness ratios for reasonable values of gamma is that the bottom of the UO was itself a source of light if it were nearby (e.g., within 20 feet under the wires). To be a source of light it would have to have (a) contained a source of light, or (b) been made of translucent materials so that light could filter from the sky above through the bottom surface. Requirement (a) is considered beyond the capabilities of the photographer because a very small illumination apparatus would have been required and because the illumination mechanism, a small light bulb, would have produced a very uneven distribution of light over the bottom surface in contradiction to the fact that there are no "hot spots" of brightness in the image of the bottom (see TrntDensUO1.gif and TrntDensUO2.gif). Requirement (b) above is considered a possibility if the upper body of the UO were a translucent material.(7) Any holes through the upper body would allow direct sunlight through, and these would cause brightness "hot spots" on the bottom surface. On the other hand, a translucent or transparent material such as glass would probably not "look" the same in a side view as the object appears in photo 2 (apparently shiny like the nearby tank, but not a mirror - like specular surface). Any hypothetical translucent UO must appear, in a side view, as bright and "shiny" as does the object in photo 2 (also, it must be shown that an appropriately translucent or transparent material in the proper shape was available to the photographers).