Hipparchus' Celestial Globe

TABLE 5. Positions of stars off the circles.

On the Farnese Atlas Star Position in 125 B.C.

# Position Star α(°) δ(°) λ(°) β(°) α(°) δ(°) λ(°) β(°) ∆λ(°) ∆β(°)

48 Argo’s s. rudder tip α Car 77.4 –49.4 62.7 –71.9 84.4 –52.7 75.7 –76.1 –13.0 4.2

49 CMa’s mouth α CMa 76.3 –17.6 72.8 –40.5 77.7 –16.8 74.6 –39.9 –1.8 –0.6

50 Corvus’s beak α Crv 152.3 –16.6 161.0 –26.2 155.7 –13.2 162.8 –21.7 –1.8 –4.5

51 Middle of Orion’s belt ε Ori 60.6 –2.3 57.9 –22.7 57.5 –5.1 53.9 –24.8 4.0 2.0

52 Hydra’s eye δ Hya 108.8 5.5 109.6 –16.9 100.7 10.7 100.8 –12.6 8.8 –4.3

53 Scorpius’s sting λ Sco 229.5 –30.0 235.0 –11.2 228.8 –32.3 235.0 –13.5 –0.1 2.4

54 Middle of Sco’s body α Sco 211.6 –23.6 217.6 –10.0 216.3 –19.1 220.2 –4.3 –2.6 –5.7

55 Tip of Sgr’s arrow γ Sgr 234.5 –29.0 239.1 –9.1 238.0 –27.3 241.7 –6.7 –2.6 –2.4

56 Taurus’s s. eye α Tau 46.7 12.2 47.6 –5.3 39.6 9.6 40.2 –5.7 7.4 0.4

57 Pisces, head of ﬁ sh γ Psc 315.9 –6.6 316.4 10.0 322.0 –7.4 321.9 7.3 –5.5 2.7

58 N. tip Cap. rear horn α Cap 276.8 –12.0 276.7 11.5 274.4 –16.4 274.2 7.2 2.5 4.3

59 Medusa’s head β Per 29.3 28.6 37.4 15.4 15.5 30.9 26.7 22.2 10.7 –6.8

60 Aries’s muzzle α Ari –5.6 18.4 2.6 19.0 3.5 12.2 8.2 9.8 –5.5 9.2

61 Andromeda’s head α And 339.7 17.2 348.3 23.9 335.9 17.5 344.9 25.6 3.5 –1.7

62 Pegasus’s muzzle ε Peg 302.5 10.2 307.5 29.7 299.8 1.8 302.4 22.2 5.1 7.5

63 Delphinus’s head α Del 287.4 15.3 291.4 37.7 285.2 10.5 288.0 33.2 3.5 4.5

64 Ophiucus’s head α Oph 240.0 21.6 231.7 41.3 239.5 16.3 232.9 36.1 –1.1 5.2

65 Hercules’s head α Her 233.0 25.2 222.0 42.9 234.8 19.1 226.6 37.5 –4.5 5.3

66 Cassiopeia’s breast α Cas 333.9 40.2 356.0 46.5 343.8 44.8 8.5 46.5 –12.5 0.1

67 South edge of CrB α CrB 224.5 33.5 207.8 47.7 211.3 35.4 192.6 44.5 15.2 3.2

68 Cygnus’s beak β Cyg 273.0 25.3 274.2 48.9 271.4 25.5 271.9 49.2 2.3 –0.3

69 Cygnus’s tail α Cyg 299.5 42.7 319.1 61.4 292.4 39.1 306.2 60.0 12.9 1.4

70 Centre of Lyra’s shell α Lyr 261.5 38.3 255.9 61.6 261.6 38.7 255.9 62.0 0.0 –0.4

On each of my pictures of the Farnese Atlas on which a given constellation ﬁ gure is visible, I have measured its position and calculated its corresponding right ascension and declination. I have a total of 67 such positions for all 23 points. I have averaged together all the positions for each point, and the resulting right ascensions and declinations are presented in Table 5. I have also calculated the corresponding ecliptic coordinates,21 and these too are presented in Table 5.

The ﬁrst column of Table 5 lists a running number, which is a continuation of the numbering from Table 3. The items are ordered by increasing ecliptic latitude. The second column gives a verbal description of the constellation position selected, while the third column gives the modern name of the star at that position. The next two columns give the derived α and δ value in the reference frame of the Farnese Atlas, these being the observed positions. These equatorial positions are converted to ecliptic positions (longitude λ and latitude β) in columns 6 and 7. Columns 8–11 give α, δ, λ and β of the modern stars as precessed back to the epoch of 125 B.C. Columns 12 and 13 are the differences between the observed and the model star positions in ecliptic coordinates.

The RMS scatter in the differences gives us a reasonable measure of the total uncertainties in the placements. The RMS scatter in the errors in ecliptic latitude is 4.1°. The deviations in ecliptic longitude will vary with ecliptic latitude by a factor of 1/cos (β) due to the convergence of the lines towards the pole. With this, I ﬁ nd that the RMS scatter of the errors in ecliptic longitude is 5°/cos (β). These errors have a good Gaussian distribution: 15/46 = 32% deviate by more than one-sigma, 1/46 = 2% deviate by more than two-sigma, while 12/23 = 52% and 11/23 = 48% deviate less than the average.