NGC 157: There is a reasonable agreement between our results and the literature.
NGC 224: All methods agree beautifully. From the literature values we mention for brevity only that of Brinks & Burton (1984), but there are several more with exactly the same value. We assign to them globally a very high weight.
NGC 300: This is a well studied galaxy. The PA and IA given by photometric methods (Carignan 1985) are in good agreement with the values given by the study of the HI velocity fields (Shobbrook & Robinson 1967 and Rogstad et al. 1979) and from the spiral structure analysis (CA88). The PA given by optical kinematics studies (Marcelin et al. 1985) does not agree so well. In this case both our methods do not give good results and thus get zero weight. This is probably due to the fact that the HII region distribution does not delineate sufficiently the axisymmetric component, since the distribution deprojected by the values given by our second method looks rounder than when deprojected with the literature values.
NGC 470: There is general agreement between the results obtained by our two methods and photometry (G85). Since for this galaxy the number of HII regions is small and their distribution is not very regular, we put a rather low weight to our first method.
NGC 598: The kinematic and photometric determinations are of high quality and agree well between them. They are thus assigned a high weight. Our first method fails as the HII regions do not delineate the disc but rather the spiral arms. The second method is in rough agreement with the photometry and kinematics. It should be mentioned that Danver (D42) found quite different values (49°, 40°), while the spiral structure analysis does not give sufficient variations of the signal-to-noise ratio to be of much weight, while still disfavouring the photometric and kinematic value (Considére & Athanassoula 1982). On the other hand Sandage & Humphreys (1980) find that for the spirals to be strictly logarithmic the galaxy's plane has to warp, even within the optical image.
NGC 628: Since the galaxy is quite face-on, neither our methods nor photometry can give accurate values for the PA. The double weights (i.e. different for the PA and IA) given are a result of this.
NGC 772: The shape of the HII region distribution is very irregular, while the optical image shows a strong arm which could bias the photometrically determined values (G85). Thus none of the values are very reliable.
NGC 925: There is a very good agreement between the values obtained by the HI studies (Gottesman 1980; Wevers et al. 1986) and the photometric results (G85). Unfortunately, the strong concentration of the HII regions in the arm makes this galaxy ill-suited for our methods, which thus get zero weight.
NGC 1073: This is a ringed barred galaxy. Our two methods and the HI kinematics (England et al. 1990) agree well, as far as the PA goes, while Grosbol's photometry might be influenced by the bar. The values of the inclination angle vary between 20° and 40°. For lack of any clear criterion we give to all inclination values the same weight. We repeated our first method omitting the five HII regions in the bar, but the result stayed the same.
NGC 1084: Our methods are in general agreement, but we think that the HII region distribution is too poor to give reliable results. The two photometric results agree very well between them (Bernacca & Bertola 1969 and Blackman 1979).
NGC 1232: There is a general agreement between the results of our two methods and photometry (G85). We repeated the first method after omitting roughly the innermost quarter of the HII regions, and the values of the deprojection parameters found were the same.
NGC 1313: This galaxy is asymmetric and one cannot unambiguously assign its center (Marcelin & Athanassoula 1982). The deprojection parameters depend on whether one considers the southern appendage or not and where one places the center. We thus give no values in Table 3.
NGC 1566: This galaxy has an oval dominating the inner parts. Both our methods tend to circularize this and thus give wrong results. If we omit the HII regions in the oval there are too few left for our first method to work. On the other hand, our second method does not seem to be hindered by the low number of regions and gives values in good agreement with the kinematics and photometry.
NGC 1832: The HII region distribution does not delineate the axisymmetric component, but is rather concentrated in the ring and surrounding spiral. The galaxy is barred and the ring could be oval. Both our two methods might be affected by this fact, so we give a higher weight to the G85 values.
NGC 2276: ARP 25 shows an important m = 1 asymmetry which could bias the photometric and/or our results.
NGC 2403: This is a well studied galaxy. If all the regions are used, then our first method gives (125°, 38°). The deprojected distribution shows that the low value of inclination is due to the outermost 53 regions. Omitting these we find (115°, 50°), i.e. a much better agreement with Begeman's (1987) values. Our second method is not influenced by these outermost regions and gives with them or without them (120°, 50°), in good agreement with the kinematics.
NGC 2805: NGC 2805 is member of a small group of galaxies and thus its outer parts are heavily perturbed and its light and HII region distribution asymmetric, similarly to M101. The inner velocity field does not look perturbed and we therefore give highest weight to the PA obtained by Bosma et al. (1980). The HII region distribution obtained after deprojection with the values given by our first method is the least satisfactory and thus has been given zero weight. We repeated the evaluation after omitting the HII regions in the arc but the result remained the same.
NGC 2835: This is a strongly barred ringed galaxy with a strong outer spiral for which no HI studies have been published. Since the HII regions do not delineate any axisymmetric component, our first method cannot be expected to work. We get results in good agreement with the literature values using our second method.
NGC 2841: This is a well studied galaxy. Both our methods are in agreement with the HI results by Begeman (1987) and Bosma (1981) and the photometric ones by Boroson (1981) and Van der Kruit (1979).
NGC 2903: This is also a well studied galaxy. The HII regions concentrate in the two strong arms, clearly visible in the optical photographs, a fact which should handicap both our methods. Nevertheless they give good agreement with the kinematics from Begeman (1987), Marcelin et al. (1983) and Wevers et al. (1986).
NGC 2976: This galaxy has an HII region distribution which is well suited for both our methods. They give results in agreement between them and the, unfortunately, very poor values in the literature we can compare with.
NGC 2997: Our two method give results in good agreement between them and with the kinematical studies by Peterson (1978), the spiral analysis by Milliard & Marcelin (1981) and the photometric values from G85. The same values were found for the first method after evicting the central region.
NGC 3031: Due to the strong arms our two methods are not expected to do well. On the other hand omitting the HII regions in the arms we find a good agreement between the values they give and the literature values.
NGC 3184: It is a very regular galaxy as showed in the optical images, and seems to be nearly face on. Due to the concentrations of HII regions our first method does not work well, even after evicting the center. With the second method we obtain a value in reasonable agreement with G85. NGC 3310: This is a peculiar galaxy (Arp 217) with a very strong emission at the center. There is reasonable agreement between our two methods, the kinematical study of the central part by Van der Kruit (1976a) and photometry (085) about the PA However the spread in inclinations is large (33° - 51°). The values given for the second method change by only 5° for the PA if we omit nine regions in a sort of straight outer feature (see Fig. 3) while the values of IA remain unchanged.
NGC 3344: Our results for the PA are in agreement between them and with the ones from G85, but not with the ones from the spiral structure analysis (CA88).This is probably due to the low inclination of the galaxy. The spread in inclination value is again large (15° - 36°).
NGC 3351: This galaxy is strongly barred and has
an inner ring. Our methods are in
excellent agreement with each other and with the PA obtained from
photometry (G85) and
the H
kinematics from
Buta (1988),
and in good agreement with the IAs of those two methods.
NGC 3486: This is a galaxy with a rich spiral structure. Thus, our first method does not work due to the concentration of HII regions in the arms. Our second method, however, gives good agreement with G85 and other values found in the literature.
NGC 3521: Our methods are in good agreement between them, while their inclination values are 10° higher than that found by Kent (1985).
NGC 3627: There is a great dispersion of the values of PA found by different methods, which seem to depend on radius, as can be seen in the photometric study by Burkhead & Hutter (1981). On the other hand there is a general agreement on the inclination values, as found in the literature and with our second method. Our first method does not work in this case due to the small number of HII regions, which are, furthermore, to a very large extent placed in the arms.
NGC 3631: This is a galaxy with a well defined spiral structure, and nearly face on, so large uncertainties can be expected in the values of PA Indeed a wide spectrum is found. Our first method is hampered by the fact that the HII regions are concentrated in the arms.
NGC 3938: This galaxy also is nearly face-on, so a comment similar to that for the previous galaxy can be made about the values of PA. Our first method does not work at all, affected by the concentration of the HII regions in the spiral. The second method is in agreement with the kinematical values from Van der Kruit & Shostak (1982) and Foster & Nelson (1985). Note however the very different value of the PA given by G85, who might be biased by a spiral feature in the outer parts.
NGC 3992: There is a good agreement between our two methods, the kinematically obtained values from Gottesman et al. (1984) and the photometric values from G85.
NGC 4254: With the second method we get results in agreement with the kinematics from Guhathakurta et al. (1988). The strong external arm may bias both our first method and photometry (G85).
NGC 4298: Our first method gives a deprojected distribution which is not pleasing to the eye and a too high value of IA. With the second method we obtain results in agreement with the values from Boroson et al. (1983) and G85.
NGC 4303: The small inclination angle of this galaxy makes its position angle badly defined for all methods except kinematics. Our first method finds a broad minimum so that any PA between 95° and 140° is acceptable.
NGC 4321: The value found by our first method is near that found by G85, but these results differ a lot from the kinematical ones by Guhathakurta et al. (1988, hereafter GGKB88). The value given by our second method is the principal minimum. However a valley of relatively low values is obtained near the kinematical values. Our second method thus gets a low weight.
NGC 4535: Our methods are in good agreement with the photometry from G85 and the kinematical values from GGKB88.
NGC 4559: No reliable photometric or kinematic values for PA and IA were found in the literature, but both our methods are in reasonable agreement between them.
NGC 4568: This galaxy is in interaction with NGC 4567. Our two methods agree between them and with the inclination given by Fraser (1977), (the deprojected distribution is more pleasing to the eye with the values obtained with the second method). GGKB88 find a considerably smaller inclination.
NGC 4654: There is very good agreement between the PAs of our two methods and those found by G85 and between the IAs of our second method and that of G85. The inclination angle of our first method deviates considerably, perhaps due to the irregularity of the HII region distribution at large radii.
NGC 4689: There is good agreement between the results from photometry (G85) and kinematics (GGKB88). The first method did not converge, and the second gave more than one minimum, perhaps due to the irregularity of the HII region distribution in the northern part.
NGC 4736: Our first method agrees well with the kinematical values derived by Van der Kruit (1976b) and Bosma et al. (1977). The photometric values (Boroson 1981, G85) give a different PA.
NGC 4939: Our methods are in agreement between them but no reliable values were found in the literature.
NGC 5055: Our two methods agree with the values derived for the optical part of the galaxy as obtained by HI mapping (Bosma 1981), with the photometry from Grosbol (G85), and the spiral structure analysis by CA88.
NGC 5128: All methods agree well.
NGC 5194: The values obtained for this galaxy by the different methods are very discordant. Preliminary values from the high resolution HI study by Rots et al. (1990) for the PA agree with those of Tully (1974), Shane (1975) and Goad et al. (1979). Thus the kinematical studies agree between them (170°) and with the 160° adopted by Elmegreen & Elmegreen (1984). On the other hand photometry by Boroson (1981) and by G85 and spiral structure analyses (Considére & Athanassoula 1982 and CA88) give correspondingly 37°, 27° and 30°. Thus there seems to be two disagreeing groups, each with good internal agreement. For the inclination Tully (1974) gives 20° while all the others between 30° and 40°. In particular Shane (1975) gives 30°, Boroson (1981) 33°, Goad et al. (1979) 35°, G85 and CA88 37° and Considére & Athanassoula (1982) 40°. On the other hand the simulations of Toomre & Toomre (1972) favour values around 15° and place an upper limit to 25° for the fits to be acceptable. However if a sizeable halo is included even high inclination angles may give a bound orbit for the companion.
It is very difficult to come to any conclusion about this complicated case. Athanassoula (1990) showed with the help of numerical simulations that during a strong interaction the outermost isophotes could become oval. It could of course be argued that the kinematics would have equally suffered. However there is no obvious change of PA with radius in NGC 5194, except perhaps in the innermost part where there could be an oval as discussed by Pierce (1986). We will thus favour the kinematical values, to which we give the highest weight, and put no weight to the other values.
NGC 5236: Kinematical values (Rogstad et al. 1974 and Comte 1981) agree very well with the second method. Our first method is hampered by the concentration of the HII regions in the arms and oval. G85 values do not agree with the rest.
NGC 5248: The various methods are only in rough agreement.
NGC 5457: The first method does not converge, presumably due to the fact that the HII regions delineate more the arms than the axisymmetric component. After omitting the outer asymmetric part it still does not converge to a plausible maximum. The second method gives too high a value for the IA and a good agreement with the PA obtained by the kinematics from Comte et al. (1979) and Bosma et al. (1981).
NGC 5678: Good agreement of all methods.
NGC 5921: Our two methods are in reasonable agreement between them and in rough agreement with the photometry (G85). The values found by Grosbol (1980) are quite different, presumably biased by the bar and ring region.
NGC 5962: Very good agreement found between our second method, photometry (G85) and the inclination angle found by the first method. The inclination angle found by Kent (1985) and the PA of the first method are more discordant The distribution deprojected with the values of the first method is less convincing than that with the second method.
NGC 6015: No kinematically derived values exist. In order for our second method to work we had to omit the outermost four regions.
NGC 6384: Our first method does not converge to a plausible value, even after omitting the outermost HII regions (the value in Table 3 corresponds to the latter case). Our second method is only in rough agreement with the photometric results (G85).
NGC 6503: The values obtained by our two methods are in very good agreement with the kinematical values of Shostak et al. (1981). Cutting out the outermost 11 HII regions gives exactly the same values for our first method and a very small difference for our second one. The optical kinematics from de Vaucouleurs & Caulet (1982) give a somewhat smaller inclination.
NGC 6643: There is only a rough agreement between the different methods. No values from a complete velocity field have been published so far for this galaxy.
NGC 6946: The galaxy has an oval and strong spiral arms, which could bias all methods. There is an agreement between the inclination values of all methods, while the PA range between roughly 60° (kinematical methods) to 80° (photometry), while our two methods and the spiral structure analysis (CA88) give intermediate values.
NGC 7331: Excellent agreement between our two methods and the values from photometry, (Boroson 1981), kinematics (Begeman 1987) and spiral structure analysis (CA88). We note that this is often the case for very inclined galaxies where the outer oval shape is well outlined.
NGC 7479: This is a barred galaxy and the HII regions are essentially in the bar and the arms. Thus our first method should not be reliable. Photometry of this galaxy was carried out by G85, Baumgart & Peterson (1986) and Okamura (1978).
NGC 7741: As in the previous case, the HII regions are essentially in the bar and the arms. Thus our first method does not work, while our second one gives more than one minimum between which it is difficult to choose. Table 2 gives the one nearest to the literature values.
NGC 7793: There is a very good agreement between all methods for the inclination angle of this galaxy. The PA values range between roughly 90° (our first method) and 108° (kinematics by Davoust & de Vaucouleurs 1980), with intermediate angles by the photometry (de Vaucouleurs & Davoust 1980 and Carignan 1985) and our second method.
IC 342: The kinematically obtained values of the PA (Newton 1980b) is the only reliable one because of the galaxy's low inclination angle. There is a rough agreement for the value of the IA. Our second method is hampered by a clump of HII regions at the NE part of the galaxy and the minimum found is secondary.
IC 5325: No literature values were found, and only our second method gave reliable results.