is 5, and altitude 6 inches; it is required to determine how much water will run over?

Ans. 26-272 cubic inches, or near 35 parts of a pint. QUEST. 50. The dimensions of a sphere and cone being the same as in the last question, and the cone only full of water; required what part of the axis of the sphere is immersed in the water? Ans. 546 parts of an inch. QUEST. 51. The cone being still the same, and full of water; required the diameter of a sphere which shall be just all covered by the water? Ans. 2-445996 inches.

QUEST. 52. If a person, with an air balloon, ascend vertically from London, to such height that he can just see Oxford appear in the horizon; it is required to determine his height above the earth, supposing its circumference to be 25000 miles, and the distance between London and Oxford 49.5933 miles?

Ans. of a mile, or 547 yards 1 foot.

QUEST. 53. In a garrison there are three remarkable objects, A, B, C, the distances of which from one to another are known to be, AB 213, AC 424, and Bc 262 yards; 【 am desirous of knowing my position and distance at a place or stations, from whence I observed the angle asb 13° 30′, and the angle CSB 29° 50', both by geometry and trigonometry.

QUEST. 54. Required the same as in the last question, when the point в is on the other side of ac, supposing ab 9, AC 12, and BC 6 furlongs; also the angle ASB 33° 45', and the angle BSC 22° 30′.

QUEST. 55. It is required to determine the magnitude of a cube of gold, of the standard fineness, which shall be equal to a sum of 960 millions pounds sterling; supposing a guinea to weigh 5 dwts 9 grains. Ans. 23.549 feet. QUEST. 56. The ditch of a fortification is 1000 feet long,

MENSURATION.

9 feet deep, 29 feet broad at bottom, and 22 at top; how much water will fill the ditch?

Ans. 1158127 gallons nearly. QUEST. 57. If the diameter of the earth be 7930 miles, and that of the moon 2160 miles: required the ratio of their surfaces, and also of their solidities: supposing them both to be globular, as they are very nearly?

Ans. the surfaces are as 13 to 1 nearly; and the solidities as 49 to 1 nearly.

QUEST. 58. Let ABC be the profile, or perpendicular section of a breast-work, and EP that of a ditch.

Now, sup. pose the area of the section ABC is 88 feet, the depth of the 3 feet; what is the breadth of ditch RD 6 feet, ER SO= the ditch at top when the sections of the ditch and the breast-work are equal; that is, when the earth thrown out of the ditch is sufficient to make the breast-work?

Log. N. 1 0.000000 26 1.414973 2 0.301030 271.431364 3 0.4771211 28 1.447158 4 0.602060 29 1.462398 5 0.698970 30 1.477121 6 0-778151

51 1.707570|
52 1.716003
53 1.724276
541-732394
55 1.740363)

311-491362 561-748188

7 0.845098 32 1.505150 57 1.755875 8 0903090 33 1.518514 58 1.763428 9 0 954243 34 1.531479 59 1.770852 10 1000000 35 1.544068 60 1.778151 11 1041393 36 1.556303 61 1.785330 12 1079181 37 1.568202 621-792392 13 1113943 38 1.579784] 63 1.799341 14 1146128 39 1.591065 64 1.806180 15 1.176091 401.602060 65 1.812913) 16 1.204120|| 41 1.612784 66 1.819544 17 1.230449. 42 1.623249 67 1.826075 18 1.255273 43 1.633468 68 1.832509 191-278754 441.643453 69 1-838849 201301030 45 1.653213 70 1.845098 21 1.322219 46 1.662758 71 1.851258 22 1 342423 47. 1.672098 72 1.857333 23 1.361728 48 1.681241 73 1.863323 241.380211 49 1.690196 74 1.869232 25 1.397940 50 1.698970 75 1.875961

76 1.880814

77 1.886491 78 1.892095 791-897627 801.903090

81 1.908485 82 1.913814 83 1.919078 84 1.924279 85 1.929419 86 1.934498 87 1.939519 88 1.944483 89 1.949390 90 1.954243 911-959041 921.963788 93 1.968483 94 1.973128 951-977724 96 1.982271 97 1.986772 981-991226 99 1-995635 100 2.000000

N. B. In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are now introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the corresponding natural number in the first column stands in the next lower line, and its annexed first two figures of the Logarithm in the second column.

N. 0

2 3 4 5 6

7

89 1000000000434 0868 13011734 2166 2598 3029 3461 3891 101 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 102 8600 9026 9451 9876 .300 .724 147 1570 1993 2415 103012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 104 7033 7451 7868 8284 8700 91169532 9947 .36 .775 105 021189 160S 2016 2428 2841 3252 3664 4075 4486 4896 106 5306 5715612565336942 7350 7757 8164 8571 8978 107 9384 9789.195 .600 1004 1408 1812 2216 26193021 108 033424 3826 4227 4628 5029 5430 58306230 6629 7028 109 7426 7825 8223 862090179414 9811.207 .602 .998 110041393 1787 2182 2576 2969 3362 3755 4148 4540 4932 111 112

16

117

127 128

5323 57146105 6495 6885 7275 7664 8053 8442 8830 9218 9606 9993 .380 .766 1153 1538 1924 2309 2694 113053078 3463 3846 4230 4613 4996 5378 5760 6142 6524 114 6905 72867666 80468426 8805 9185 9563 9942 .320 115060698 1075 1452 1829 2206 2582 2958 3333 3709 4083 4458 4832 52065580 5953 6326 6699 7071 7443 7815 8186 8557 892892989668 ..38 .407 .776 1145 1514 118071882 2250261729853352 37 18 4085 4451 4816 5182 119 5547 5912 6276 6640 7004 7368 7731 8094 8457 8819 120 9181 9543 9904 .266.626 .987 1347 1707 2067 2426 121 082785 3144 35033861 4219 45764934 5291 5647 6004 122 6360 6716 7071 7426 7781 8136 8490 8845 9198 9552 123 9905 .258 .611.963 13151667 2018 2370 2721 3071 124 093422 3772 4122 4471 4820 5 169 5518 5866 6215 6562 125 6910 7257 7604 7951 8298 8644 8996 9335 9681 .026 126100371 0715 1059 1403 1747 2091 2434 2777 3119 3462 3804 4146 4487 4828 5169 55 10 5851 6191 6531 6871 7210 7549 7888 8227 8565 8903 9241 95799916 .253 129 110590 0926 1263 1599 1934 2270 2605 2940 3275 3609 130 3943 4277 4611 4944 5278 5611 5943 6276 6608 6940) 131 7271 7603 7934 8265 8595 892692569586 9915 .245 132 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 3852 4178 4504 4830 5156 5481 5806 6131 6456 6781 7105 7429 7753 8076 8399 8722 9045 9368 9690..12 135130334 0655 09771298 1619 1939 2260 2580 2900 3219 136 3539 3858 4177 4496 48145133 5451 5769 6086 6403 137 6721 7037 7354 7671 7987 8303 8618 8934 9249 9564 138 9879.194.508 822 1136 1450 1763 2076 2389 2702 139 143015 3327 3639 3951 4263 4574 4885 5196 5507 5818 140 6128 6438 6748 7058 7367 7676 7985 8294 8603 8911 141 9219 9527 9835.142.449 .756 1063 1370 1676 1982 142 152288 2594 2900 3205 3510 38154120 4424 4728 5032 143 5336 5640 5943 6246 6549 6852 7154 7457 7759 8061 144 8362 8664 8965 9266 9567 9868 .168 .469 .769 1068 145 161368 1667 1967 22662564 2863 3161 3460 3758 4055 146 4353 4650 4947 5244 5541 5838 6134 6430 6726 7022 147 7317 761379088203 8497 8792 9086 938096749968 148 170262 0555 0848 1141 1434 1726 2019 2311 2603 2895 1491 3186 3478 3769 4060 4351 4641 4932 5222 55125802

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