Treatise on the principal mathematical instruments employed in surveying, levelling, and astronomy : explaining their construction, adjustments, and use. With an appendix, and tables / By Frederick Walter Simms.

Frederick Walter Simms

Date:: 1844

Credit: Treatise on the principal mathematical instruments employed in surveying, levelling, and astronomy : explaining their construction, adjustments, and use. With an appendix, and tables / By Frederick Walter Simms. Source: Wellcome Collection.

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$TABLE VIII. Showing the Length of a Second of Longitude and Latitude in English Feet, on the Earth’s Surface. Compression = 347 Computed by Mr. Baity’s Formula XLIIL. Second | Second *} of Long. | of Lat. Ft Ft. 83.17 |101.75 82.15 81.10 80.02 78. 92 77.80 |101. 84 76. 65 75. 48 | 74, 29 44 | 73.07 89 101, 71.83 |101.93 70.57 ; 69. 29 ; 67.99 14 | 98. 66. 66 65. 32 |102. 02 102.19 ———_—_——_ J ——————]———_ | |__|, ———_—_ | —______ 102. 26 ‘¢ If the equatorial diameter of the earth be assumed equal to 7924 miles, a degree of longitude at the equator will be equal to 69.15 miles = 365110 feet; and consequently one second in time at the equator will be equal to 1521.3 feet.” TABLE IX. Reduction in Links and Decimals upon each Chain’s Length, for the fol- lowing Angles of Elevation and Depression. Re- ey Re- Angle. |duct™|} Angle, |duct®|/ Angle. |duct® 3°, 0'0.14]} 9° O}1.24]/} 15°. 0/3. 40 30/1.38 30/3. 64 4°, 0/0. 25|| 10°. 041. 52// 16°. 0/3. 88 30} 1. 68 30/4, 12 5°, 0/0.38]] 11° 041. 84)|/17°. 0/4. 37 30/2. 01 30} 4. A3 6°, 0/0.551] 12%. 0/2. 191) 18°. 0/4. 90 30/0. 65 302. 37 30/5. 17 7°. 0/0.75 || 13° 0}2.56|/ 19°. 0/5. 44 30 | 0. 86 3012.77 3015.74 8°. 0/0.98)| 14°. 0)2. 97 || 20°. 0/6. 03 30/1.10 3013.18 30/6. 33 The reduction for one chain (from the above Table) multiplied by the number of chains, will give the quan- tity to be subtracted from the mea- sured length of an inclination, to re- duce it to horizontal measure. TABLE X. Shewing the Rate of Inclination of Inclined Planes, for the following Angles of Elevation. Angle.|One in| | Angle.|One in|| Angle. |One in 0°15/| 228 ||3°30| 17 || 7°0/| 8 0.30] 114 |{3.45| 16 |] 7.30] 72 0.45] 761|/4. 0/15 || 8 0} 7 1. 0| 56 |/4.15] 14 |] 9. 0] 63 1.15] 46 |/4.30] 13 |}l0. 0} 6 1.30] 38 |/4.45| 12 |I1l. Oo] 53 1.45} 32/5. 0| 11% |/12. 0} 54 2. 0} 28 |/5.15/ 11 {/13. 0] 5 2.15| 26 |/5.30| 10% |{14. 0] 44 2.30] 23 ||5.45| 10 ||15. 0} 4 2.45| 21 1/6. 0| 9% ||16. 0) 33 3. 0} 19 116.30} 9 ||k7. 0] 3% 3.15 6.45| 8k |[18. 0} 3% ne A$