Fahrenheit's Thermometer 50°. English Barometer 30 Inches. 48.08 2.22552 404 10 49.65 2.22956 407 20 51.25 2.23363410 20 52.87 2.23773413 30 40 54.53 2.24186 417 40 50 56.21 2.24603419 50 57.92 2.25022 423 82 0 203 30 10 20 55.81 2.06376 312 20 10 201 8 81 0 5 53.79 2.54874 7590.010 0.05 10 6 0.04 2.55635 772 0.042 0.06 6.50 2.56407 785 0.044 0.06 13.18 2.57192 7970.0460.07 20.09 2.57989 8110.049 0.07 27.26 2.58800 824 0.051 0.08 6 34.68 2.59624 8380.053 0.08 42.37 2.60462 851 0.057 0.09 50.33 2.61313 866 0.060|0.09 58.59 2.62179 883 0.063 0.10 7.19 2.63062 899 0.067 0.10 16.13 2.63961 9140.0710.11 25.40 2.64875 9310.0740 11 35.05 2.65806 9490.0790.12 45.10 2.66755 967 0.084 0.12 55.58 2.67722 986 0.089 0.13 6.50 2.687081006 0.095 0.14 17.90 2.69714 1026 0.101 0.15 29.80 2.70740 1047 0.107 0.16 23.18 2.307894700.006 42.24 2.71787 1069 0.1140.17 25.39 2.31259 475 0.006 55.25 2.72856 1092 0.122 0.18 27.66 2.31734 479 0.007 30 9 8.88 2.73948 11150.130 0.20 29.95 2.32213 483 0.008 40 23.16 2.75063 1139 0.1390.21 32.30 2.32696 488 0.008 50 38.12 2.76202 11650.149 0.23 34.70 2.33184493 0.00985 0 9 53.84 2.77367 11910.159 0.25 37.16 2.33677 497 0.009| 10 10 10.35 2.78558 12190.171 0.26 39.65 2.34174 502 0.010 27.73 2.79777 1248 0.1840.28 42.21 2.34676 507 0.010 30 46.03 2.81025|1277|0.198 0.31 44.822.35183 512 0.011 4011 5.30 2.8230213090.213 0.33 47.48 2.35695 517 0.011 50 25.66 2.836111340 0.229 0.36 50.21 2.36212 523 0.01286 011 47.152.84951|13740.248 0 39 53.00 2.36735 528 0.012 10 12 9.88 2.86325 1410 0.269 0.43 55.85 2.37263 533 0.013 20 33.97 2.87735|1447|0.292 0.47 58.76 2.37796 538 0.013 30 59.51 2.89182 1484 0.3170.51 1.74 2.38334 545 0.014 40 13 26.61 2.90666 1523|0.345|0.56| 4.79 2.38879 551 0.014 50 55.40 2.92189|1565|0.376|0.62 7.91 2.39430 557 0.01587 0 14 26.04 2.93754|1608|0.410 0.68 11.11 2.39987 563 0.015 10 58.71 2.95362|1654 0.448 0.75 14.39 2.40550 569 0.016 33.60 2.970161701 0.490 0.83 17.74 2.41119 576 0.016 10.89 2.98717|17490.5380.91 50.8 3.00466 1801 0.593 1.01 50 17 33.6 3.02267 1855 0.6541.13 018 19.6 10 19 9.0 20 10 20 30 40 20 40 10 40 50 50 66 02 10.48 2.1155533776 03 10 11.50 2.11892 339 10 12.52 2.12231 340 301 13.57 2.12571 342 30 14.62 2.12913 345 404 50 15.70 2.13258 345 50 67 02 16.78 2.1360334877 04 17.88 2.13951 349 10 8.49 2.10886 334 9.48 2.11220335 20 39 49 59 69 0.03582 18 0.03484 27 4 0.03386 36 6789 GDC 20 0.03288 4.5 0.03191 54 7 0.03094 63 78 8 0.02997 72 29.99820 5 6 9.99550 9.99460 79.99371 9.99282 Log. 10° 0.00173 50° 0.00000 11 0.00169 51 9.99996 12 0.00164 52 9.99991 13 0.00160 53 9.99987 14 0.00156 54 9.99983 15 0.00151 55 9.99978 16 0.00147 56 9.99974 17 0.00143 57 9.99970 0.00138 58 9.99965 49.99640 P. P. Bar. Log. 88 5 9.96943 71 1 X P The true refraction is computed by the following formula, viz. r = 1+6(r 50) 30 dde dde × do + (r— 50°) - (30-p); in which r denotes the true refraction, p=.002084 dr dp the expansion of a given volume of air at the surface of the earth for one degree of Fahrenheit's thermometer, p the height of the English barometer, the temperature in the open air dde by Fahrenheit's thermometer, de the mean refraction for 30 inches and 50°; and dr are expressions for determining the effects of changes in the temperature and barometric pressure respectively. and dde dde Table XVII. contains de, the mean refractions, and the expressions for and dr dp 0 90 0.00 0.00 0.00 0.00 0.00 000 189 0.24 0.25 0.27 0.29 0.31 0.33 288 0.48 0.50 0.54 0.58 0.62 0.65 387 0.71 0.75 0.80 0.86 0.92 0.97 486 0.95 1.00 1.07 1.15 1.23 1.30 585 1.18 1.25 1.34 1.43 1.53 1.62 684 1.41 1.50 1.60 1.71 1.83 1.94 783 1.65 1.75 1.87 2.00 2.13 2.26 882 1.88 2.00 2.14 2.28 2.43 2.58 981 2.11 2.25 2.40 2.56 2.73 2.90 1080 2.35 2.50 2.67 2.85 3.03 3.22 1179 2.58 2.75 2.94 3.13 3.33 3.54 12 78 2.81 3.00 3.20 3.41 3 63 3.86 1377 3.04 3.25 3.47 3.69 3.93 4.18 1476 3.27 3.50 3.73 3.97 4.23 4.49 1575 3.50 3.74 3.99 4.25 4.52 4.80 1674 3.73 3.98 4.25 4.53 4.81 5.11 1773 3.95 4.22 4.51 4.80 5.10 5.42 1872 4.17 4.46 4.76 5.07 5.39 5.73 1971 4.40 4.70 5.02 5.35 5.68 6.04 20 70 4.62 4.94 5.27 5.62 5.97 6.35 2169 4.84 5.18 5.52 5.89 6.26 6.65 2268 5.06 5.42 5.77 6.16 6.55 6.95 2367 5 28 5.65 6.02 6.42 6.83 7.25 2466 5.49 5.88 6.27 6.68 7.11 7.54 2565 5.71 6.11 6.52 6.94 7.39 7.84 26 64 5.92 6.34 6.76 7.20 7.66 8.13 2763 6.13 6.56 7.00 7.46 7.93 8.42 2862 6.34 6.79 7.24 7.72 8.20 8.71 |29|61| 6.55 7.01 7.48 7.97 8.47 9.00 3060 6.75 7.23 7.71 8.22 8.74 9.28 3258 7.15 7.67 8.17 8.72 9.26 9.84 3456 7.55 8.09 8.63 9.20 9.78 10.39 3654 7.93 8.50 9.07 9.67 10.28 10.92 38 52 8.31 8.90 9.51 10.13 10.78 11.42 40 50 8.67 9.30 9.93 10.58 11.26 11.92 4248 9.03 9.68 10.34 11.02 11.72 12.44 44 46 9.38 10.05 10.74 11.44 12.17 12.92 4644 9.72 10.41 11.1211.85 12.61 13.38 48 42 10.05 10.76 11.49 12.25 13.03 13.83 50 40 10.37 11.10 11.85|12.63|13.43 14.25 52 38 10.67 11.42 12.19 12.99 13.82 14.66 54 36 10.95 11.72 12.5213.34 14.19 15.06 56 34 11.22 12.01 12.83 13.67 14.55 15.44 58 32 11.48 12.2913.12 13.99 14.88 15.79 6030 11.72 12.55 13.40 14.29 15.20 16.13 62 28 11.95 12.79 13.66 14.57 15.50 16.45 64 26 12.17 13.02 13.91 14.83 15.78 16.75 66 24 12.37 13.24 14.14 15.08 16.04 17.03 68 22 12.55 13.44 14.36 15.30 16.28 17.28 7020 12.72 13.62 14.55 15.51 16.50 17.51 72 18 12.88 13.79 14.73 15.70 16.70 17.73 74 16 13.02 13.94 14.89 15.87 16.88 17.92 76 14 13.14 14.07 15.03 16.02 17.04|18.09 7812 13.24 14.18 15.15 16.15 17.18 18.24 80 10 13.33 14.28 15.25 16.26 17.30 18.36 82 813.40 14.36 15.34 16.35 17.39 18.47 84 613.46 14.42 15.41 16.42 17.47|18.55 86 413.50 14.46 15.45 16.47 17.52 18.60 88 213.53 14.49 15.48 16.50 17.55 18.63 90 013.54 14.50 15.49 16.51 17.57 18.65 1 3 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 70 72 74 76 78 80 82 84 86 88 90 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.4 1.4 1.3 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.7 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.7 1.7 1.8 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 2.0 20 2.0 2.1 2.1 2.0 2.0 2.1 2.1 2.1 2.2 2.3 2.3 2.1 2.2 2.2 2.3 2.3 2.3 2.4 2.4 2.3 2.3 2.4 2.4 2.5 2.5 2.5 2.6 2.4 2.5 2.5 2.6 2 6 2.7 2.7 2.8 2.6 2.6 2.7 2.7 2.8 2.8 2.9 3.0| 2.9 3.0 3.0 3.1 3.1 3.2 3.2 3.3 3.3 3.3 3.4 3.4 3.5 3.6 3.6 3.7 3.6 3.7 3.7 3.8 3.9 3.9 4.0 4.1 3.9 4.0 4.1 4.2 4.2 4.3 4.4 4.6 4.3 4.4 4.5 4.6 4.6 4.7 4.8 4.9 4.7 4.8 4.8 4.9 5.0 5.1 5.2 5.3 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.1 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.5 6.6 6.7 6.9 7.0 7.1 7.2 7.3 6.9 7.0 7.1 7.2 7.4 7.5 7.6 7.7 7.2 7.3 7.5 7.6 7.7 7.9 8.0 8.1 7.5 7.7 7.8 7.9 8.1 8.2 8.4 8.5 7.9 8.0 8.2 8.3 8.1 8.6 8.7 8.9 8.2 8.3 8.5 8.6 8.8 8.9 9.1 9.2 8.5 8.6 8.8 8.9 9.1 9.3 9.4 9.6 8.8 8.9 9.1 9.2 9.4 9.6 9.7 9.9 9.0 9.2 9.4 9.5 9.7 9.9 10.0 10.2 9.3 9.4 9.6 9.8 10.0 10.1 10.3 10.5 9.5 9.7 9.9 10.0 10.2 10.410.6 10.7 9.7 9.9 10.1 10.210.4 10.6 10.8 11.0 9.9 10.1 10.3 10.4 10.6 10.8 11.0 11.2 10.0 10.2 10.410.6 10.811.011.2 11.4 10.210.4 10.6 10.7 10.9 11.111.3 11.5 10.310.5 10.7 10.9 11.111.311.4 11.6 10.4 10.6 10.8 11.0 11.2 11.4 11.5 11.7 10.5 10.6 10.8 11.0 11.2 11.4 11.6 11.8 10.5 10.7 10.9 11.1 11.3 11.5 11.7 11.9 10.5 10.7 10.9 11.111.3 11.5|11.7 11.9 TABLE XXIII Logarithms of the Earth's Radii, in each Angles of the Vertical with the Ra Parallel of Latitude; the Equatorial Radius being Unity, and Compression dius; or Reduction of the Latitude, in each Parallel, the Compression being o Lat. Reduc. Lat. Reduc. Lat. Reduc. M N " h.m. 65.45 0.63 5 081.42 0.41 For determining the Latitude, at any time, by the Pole Star. MIN h.m. " h.m. 0 0 0.00 0.00 1 10 0.17 0.00 10 20 0.66 0.01 30 1.49 0.03 40 2.63 0.05 4 | M N " h.m. h.m. "I h.m. 5.85 0.11 2 0 21.82 0.373 043.63 0.60 4 7.89 0.14 10 25.19 0.41 10 47.44 0.62 20 10.20 0.19 20 28.71 0.46 20 51.21 0.64 30 12.78 0.23 30 32.34 0.50 30 54.93 0.65 40 15.59 0.27 40 36.06 0.53 40 58.56 0.65 50 4.09 0.08 50 18.61 0.32 50 39.83 0.57 50 62.07 0.64 105.850.112 021.82 0.373 043.63 0.604 065 45 0.635 " " 10 68.66 0.61 3 1083.18 0.35 20 84.64 0.28 3085.78 0.22 40 86.60 0.15 50 87.10 0.07 087.26 0.00 - the Zenith 12h t in the first Quadrant ; t in the second; =t— 12h in the third; and 24h t in the fourth; M and N being the Tabular Quantities. The quantity M is = p2 sin.2 t, and is always positive; but the quantity N = p3 sin. 2t cos. t, becomes negative in the second and third Quadrants of t. When p (the Polar Distance) augments or diminishes 1', the Tabular Quantity must also be augmented or diminished by 0.02M; and for any other quantity of variation in the same proportion. |