Reducing then the Numbers 66 and 72, to the lowest Denomination, thus 6)⁶⁶⁄₇₂ = ¹¹⁄₁₂ the Proportion which the _Length_ of the _Shadow_ bears to the _Height_ of the _Object_ is thereby obtained: that is [26] If the _Length_ of the Shadow be divided into 12 Parts, the Height of the Object would be 11 of those Parts. See Moore’s Practical Navigator. See Page 98 [34]. PROBLEM. An +easy+ Way to find the Proportion which the _Length_ of the Shadow bears to the _Height_ of an Object is, +AT ANY TIME WHEN THE SUN SHINES+, to fix a Plummet Line and +frame+ _upright_ in the Ground; measure the _Length_ of its _Shadow_, and compare _it_ with the _Height_ of the +frame+. [27] Equal to 3 Quarters of a Mile and 121 Yards. [28] i.e. When the Barometer _below_ is at 30 Inches, and Thermometer _below_ at 60° viz. about 1000 Yards high in _fine_ Weather, and 500 in _changeable_. [29] Being 1083 Yards, i.e. half a Mile, and 203 Yards. [30] It was High Water at Chester and Frodsham-Bridge, at 38 Minutes past I. [31] Articles parted with, to check the _first_ Descent at Bellair, near Frodsham: and to ascend the _second_ Time. To check the _first_ Descent. Pounds. Ounces. Ballast, at twice: 24 0 To clear Trees and Hedges, and _re-ascend_: Barometer and Frame, 0 12½ Basket with Tunning Dish and Bottles (except the Flask with Brandy and Water) 4 10 Half Mile of Twine on the Reel 1 0 Speaking Trumpet 0 8½ Woollen Gloves 0 1 ——————— 31 0 24 0 ——————— Remains for Re-ascent 7 0 [32] The Sun’s Azimuth from the North Point _Westward_, being 118.26′: its Supplement to 180° is 61°.34′ South westerly: i.e. South West by West, half West _nearly_. [33] The _Length_ of the Shadows being more than _double_ the Height of the +Objects+: see [34]. [34] To find the Length of the Shadow at half past III. (See Section 84, Note _a_.) {Lat. of Chester, 53° 12′} Given {Sun’s Dec. 5 29 } To find Sun’s Alt. {Hour III, 30M. 52 30 } This is the Case of an oblique spheric Triangle, wherein are two Sides and one Angle between them given, to find the Sun’s Azimuth, and the Sun’s Co-Alt. Side 84. 31 } Sum of Sides 121. 19 Side 36. 48 } Diff. of Sides 47. 43 (3½ Hour) Angle contained 52. 30 Half ditto 26. 15 } 63. 45 Half Sum of Sides 60. 39 } Co. 29. 22 Half Difference ditto 23. 51 } 66. 9 THE FIRST PREPARATIVE PROPORTION.