As Sine of ½ Sum of Sides 60. 39 0.05966 Co-Ar. To Sine of ½ Difference of Sides 23. 51 9.60675 So Co-Tangent ½ contained Angle 63. 45 10.30703 —————— ———————— To T. of ½ Diff. of the other two Angles 43. 15 9.97344 SECOND PREPARATIVE PROPORTION. As Co-Sine ½ Sum of Sides 29. 21 0.30968 Co-Ar. To Co-Sine ½ Diff. 66. 9 9.96123 So Co-Tangent ½ contained Angle 63. 45 10.30703 ———————— To T. ½ Sum of other Angles 75. 11 10.57794 Half Diff. before found 43. 15 —————— Sum, is greater Angle 118. 26 = Sun’s Azim. Diff. is lesser Angle 31. 56 = S’s right Asc. Then by first Axiom in Trigonometry, to know the Sun’s Altitude say, As Sine Sun’s right Asc. 31. 56 0.27659 To Sine Co-Lat. 36. 48 9.77744 So Sine of the contained Angle 52. 30 9.89947 ——————— To Co-Sine of the Sun’s Alt. 63. 57 9.95350 from 90. —————— Sun’s Alt. 26. 3 Having Sun’s Alt. to find the Shadow, As Sine Sun’s Alt. 26. 3 0.35738 Co-Ar. To Person’s Height, 66 _Inches_, 1.81954 So Co-Sine of the Sun’s Alt. 63. 57 9.95350 ———— To Length of Shadow, 135 _Inches_, 2.13042 Then 6(⁶⁶⁄₁₃₅ = ¹¹⁄₂₂ - | - ³⁄₆ or ½, i.e. as 22 to 45: supposing the Length of the Shadow divided into 45 Parts; the _Height_ of the Object woud be 22 of those Parts; or not quite _half_ the _Length_ of the Shadow, at half past III. See Section 84, Note [26]. [35] See “Priestley on Electricity.” [36] Εὔροια. [37] [Sidenote: An Account of the _Breath_ being visible at Sea, when the Thermometer was at 61.] The Breath is said to become _visible_ at Sea or Land at any Temperature of the Thermometer not _exceeding_ 60°: tho’, in Latitude 41°, and Westward of the Azores Islands, being in Sight of the Peak of +st. george+, (which probably equals, if not exceeds, the Height of Teneriffe) the Observer has seen his _own Breath_, and _that_ of the Sailors on Deck, when the Thermometer in the _Shade_ was at 61: the Air (in January) being _then remarkably_ damp. [38] This Assertion may seem to contradict what was said in Section 44: When—“every Thing, that coud be seen at all, was seen +distinct+:” but it only proves that the Balloon had attained a greater Altitude during the Re-ascent, and that the +shadows+ were _much lengthened_, as the Evening advanced. [39] Angelica Kauffman.