ing only according to the square of the velocity, the least resistance that such a ball would meet with, when moving with a velocity of 1600 feet, would be equal to the pressure of 4171b, and that independent of the pressure of the atmosphere itself on the fore part of the ball, which would be 487lb more, as there would be no pressure from the atmosphere on the hinder part, in the case of so great a velocity as 1600 feet per second. So that the whole resistance would be more than 900lb to such a velocity.

9. Having said, in the last article, that the pressure of the atmosphere is taken entirely off the hinder part of the ball moving with a velocity of 1600 feet per second; which must happen when the ball moves faster than the particles of air can follow by rushing into the place quitted and left void by the ball, or when the ball moves faster than the air rushes into a vacuum from the pressure of the incumbent air let us therefore inquire what this velocity is. Now the velocity` with which any fluid issues, depends on its altitude above the orifice, and is indeed equal to the velocity acquired by a heavy body in falling freely through that altitude. But, supposing the height of the barometer to be 30 inches, or 21 feet, the height of a uniform atmosphere, all of the same density as at the earth's surface, would be 2 x 13.6 × 833 or 28333 feet; therefore 16:28333 :: 32: 8√28333 = 1346 feet, which is the velocity sought. And therefore, with a velocity of 1600 feet per second, or any velocity above 1346 feet, the ball must continually leave a vacuum behind it, and so must sustain the whole pressure of the at-mosphere on its fore part, as well as the resistance arising from the vis inertia of the particles of air struck by the ball.

10. On the whole, we find that the resistance of the air, as determined by the experiments, differs very widely, both in respect to its quantity on all figures, and in respect to the proportions of it on oblique surfaces, from the same as determined by the preceding theory; which is the same as that of Sir Isaac Newton, and most modern philosophers. Neither should we succeed better if we have recourse to the theory given by Professor Gravesande, or others, as similar differences and inconsistencies still occur.

We conclude therefore, that all the theories of the resistance of the air hitherto given, are very erroneous. And the preceding one is only laid down, till further experiments, on this important subject, shall enable us to deduce from them another, that shall be more consonant to the true phænomena of nature. LOGARITHMS

77 1.886491 78 1.892095 791-897627 80 1.903090 811'908485 82 1-913814 83 1.919078 84 1.924279 85 1.929419 86 1-934498 87 1-939519

1 9000000 || 26 1-414973 51 1707570 76 1.880814 230103027 1431364 52 1716003 3 0477121 28 144715853 1-724276 4000.000 29 1-462398 54 1-732394 50.698970 301-47712155 1-740363 6 0778151 31 1.491362 56 1.748188 7 0.845098 32 1.505150 57 1755875 8 0903090 33 1518514 58 1.763428 9 0954243 34 1.531479 59 1.770852 10 1000000 35 1.544068 | 60 1778151 11 1041393 36 1.556303 61 1.785330 121079181 37 1.568202 62 1.792392 13 1113943 38 1.579784 || 63 1.799341 14 1.146128 39 1.591065 || 64 1.806180 891949390 15 1.176091 40 1.602060|| 65 1.812913 90 1.954243| 16 1.204120 41 1.612784 66 1.819544|| 91 1.959041 171230449 42 1.623249 || 67 1.826075|| 921063788 18 1.255273 43 1.633468 68 1.832509 93 1.968483 191278754 44 1.643453 69 1-838849 94 1.973128 201301030|| 45 |¡·653213 || 70 1.845098|| 95 1.977724

21

88 1.944483

132221946 100275871 1851258 96 1982271 22 1312423 47672098|| 72 1-857333 97 1.986772 23 1301728 43 1.68124173 1.863323 98 1-991226 24 1.3 021. 10 1.690196 74 1-869232 99 1.995635 251397940 20 9897075 1875061100 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 0's, points or dots are now introduced instead of the 0 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 twe figures of the Logarithm in the second column.

N.

1

2

3

111 112

114

4 5 6 7 8 9 100 000000 0434 0868 1301 1734 2166 2598 3029 3461 3891 101 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 102 8600 9026 9451 9876.300.724114715701993 2415 103 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 104 7033 7451 7868 8284 8700 9116 9532 9947.361.775 105 021189 1603 2016 2428 2841 3252 3604 4075 4486 4896 106 5306 5715 6125 6533 6942 7350 7757 8164 8571 8978 107 9384 9789 195.600 1004 1408 1812 2216 2619 3021 108 033424 3826 4227 4628 5029 5430 5830 62306629 7028 109 7426 7825 8223 8620 9017 9414 9811.207.602.998 110 011393 1787 2182 2576 2969 3362 3755 4148 4540 4932 5323 5714 6105 6495 6885 7275 7064 8053 8442 8830 9218 9606 9993.380.766 1153 1538 1924 2309 2694 113 053078 3463 3846 4230 4613 4996 5378 5760 6142 6524 6905 7256 7065 8046 8426 8805 9185 9563 9942.320 115 060698 1075 1452 1829 2206 2582 2958 3333 3709 4083 116 4458 4832 5206 5580 5953 6326 6699 7071 7443 7815 117 8186 8557 8928 9298 9668..38 407.776 1145 1514 118 071882 2250 2017 2985 3352 3718 4085 4451 4816 5182 119 5547 5912 6276 0640 7004 7368 7731 8094 8457 8819 120 9181 9543 9904.266.626.987 1347 1707 2067 2426 121 082785 3144 3503 3861 4219 4576 4934 5291 | 5647 6004 122 6360 6716 7071 7426 7781 8136 8490 8845 9198 9552 123 9905 258.611.963 1315 1667 2018 2370 2721 3071 124 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562 125 6910 7257 7604 7951 8298 8644 8990 9335 9681.0261 126 100371 0715 1059 1403 1747 2091 2434 2777 3119 3462 127 3804 4146 4487 4828 5169 5510 5851 6191 6531 6871 128 7210 7549 7888 8227 8565 8903 9241 9579 9916. 253 129 110590 0926 1263 1599 1934 2270 2605 2940 3275 3609 3943 4277 4611 4944 5278 5611 5943 6276 6608 6940 131 7271 7603 7934 8265 8595 8926 9256 9586 9915.245 132 120574 Og03 1231 1560 1888 2216 2544 2871 3198 3525 133 3852 4178 4504 4830 5156|5481|5806 6131|6456|6781 134 7105 7429 7753 8076 8399 8722 9045 9368 9690.. 12| 135 130334 0655 0977 1298 1619 1939 2260 2580 2900 3219 136 3539 3858 4177 4496 4814 5133 5451 5769 6086 | 6403 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 6128 6438 6748 7058 7367 7676 7985 8294 8603 8911 449.756 1063 1370 1676 | 1982

130

137

140

141

9219 9527 9835. 142

142 152288 2594 2900 3205 3510 3815 4120 4424 4728 5032 143 5336 5640 5643 6246 6549 6852 7154 7457 7759 8061 144 8362 8664 8965 9266 9567 9868.168.469.769|1068 145|161368|1667|1967 2266| 2564 2863|3161|3460|3758 4055 146 4353 4650 4947 5244 5541 5838 6134 6430 6726 7022 147 7317 7613 7908 8203 8497 8792 (086 9380 9674 9968 148 170262 0555 6848 1141 1434 1726 2019 2311 2603 2895 149 3186 3478 3769|4060|4351|4641 4932 5222 5512 5802

154

156

157 158

150 176091 6381 6670 6959 7248 7536 7825 8113 8401 8689 151 8977 9264 95529839.126.413 699.980 1272 1558 152 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407 153 4691 4975 5259 5542 5825 6108 6391 6674 6956 7239 7521 7803 8084 8366 8647 8928 9209 9490 9771..51 155190332 0612 0892 1171 14511730 2010 2289|2567 2846 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 5899 6170 6453 6729 7005 7281|7556| 7832 8107 8382 8657 8932 9206 9481 9755 .29. 303.577.850 1124 159 201397 1670 1943 2216 2488 2761 3033 3305 3577 3848 160 4120 4391 4663 4934 5204 5475 5746 6016 6286 6556 161 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 162 9515 9783..51.319.586.853 1121 1388 1654 1921 163 212188 2454 2720 2986 3252 3518 3783 4049 43 14 4579 164 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 165 7484 7747 8010 8273 8536 8798 9060 9323 9585 9846 166 220108 0370 0631 0892 1153 1414 1675 1936 2:96| 2456 167 2716 2976 3236 3496 3755 4015 4274 4533 4792 5051 168 5309 5568 5826 6084 6342 6600 6858 7115 7372 7630 169 7887 8144 8400 8657 8913 9170 9426 9682 9938. 193 170 230449 0704 0960 1215 1470 1724 1979 2234 2488 2742 171 2996 3250 3504 3757 4011 4264 4517 4770 5023 5276 172 5528 5781 6033 6285 6537 6789 7041 7292 7544 7795 173 8046 8297 8548 8799 9049 9299 9550 9800..50.300 174 240549 0799 1048 1297 1546 1795| 2044 2293|2541 2790 175 3038 3286 3534 3782 4030 4277 4525 4772 50195266 176 5513 5759 6006 6252 6499 6745 6991 7237 7482 7728 177 7973 8219 8464 8709 8954 9198 9443 9687 9932. 176 178 250420 0664 0908 1151 1395 1638 1881 2125 2368 2610 2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 180 5273 5514 5755 5996 6237 6477 6718 6958 7198 7439 181 7679 7918 8158 8398 8637 8877 9116 9355 9594 9833 182 260071 0310 0548 0787 1025 1263 1501 1739 1976 2214 2451 2688 2925 3162 3399 3636 3873 4109 4346 4582 4818 5054 5290 5525 5761 5996 6232 6467 6702 6937 185 7172 7406 7641 7875 8110 8344 8580 8812 9046 9279 186 9513 9746 9980.213.446.679.912 1144 1377 1609 187 271842 2074 2306 2538 2770 3001 3233 3464 3696 3927 4158 4389 4620 4850 5031 5311 5542 5772 6002 6232 6462 6692 6921 7151 7380 7609 7838 8067 8296 8525 8754 8982 9211 9439 9667 9895. 123.351.578.806 191 281033 1261 1488 1715 1942 2169 2396 2622 2849 3075 192 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 193 5557 5782 6007|6232|6456|6681| 6905 7130 7354 7578 194 7802 8026 8249 8473 8696 8920 9143 9366 9589 9812 195 200035 0257 0480 0702 092511471369 1591 1813 2034 190 2256 2478 2699 2920 3141 3363 3584 3804 4025 +246 197 4466 4687 4907 5127 5347 5567 5787 6007 | 6226|6446 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 199 8853 9071 9289|0507|0725 0943 161 378 595813

179

183

184

188

189

190

198

N.

0

1

2

201

202

203 204

206

207 208

7 8 9

2547 2764 2980 4706, 4921 5136 6854 7068 7282

3 4 | 5 6 200 301030 1247 1464 1681 1898 2114 2331 3196 3412 3628 3844 4059 4275 449 5351 5566 57815996 6211 6425 6639 7496 7710 7924 8137 8351 8554 8778 8991 9204 9417 96309843.56.268 481 693.906 1118 1330 1542 205 311754 1960 2177 2389 2600 2812 3023 3234 3445 3656 3807 4078 4289 4499 4710 49205130 5340 5551 5760 5970 06180 6390 6599 6809 7018 7227 7456 7646|7854 8003 8272 8481 8C89 8898 9106 9314 9522 9730 9938 |209 320146 0354 0502|0769 0977|1184|1391|1598|805|2012 2219 2426 2633 2839 3046 3252 3458 3665 3871 4077 4282 4488 4694 4899 5105 5310 5516 5721 526 6131 6336 6541 6745 6950 7155 7359 7563 7767 7972 8176 8380 8583 8787 8991 9194 9398 9601 9805 ...8.211 214 330414 0617 0819 1022 1225 1427 1630 1832 234 2236 215 2438 2640 2842 3044 3246 3447 3649 3850 40514253 216 4454 4655 4856 5057 5257 5458 5658 58596059 6260 217 6460 6660 6860 7050 7260 7459 7659 7858 8058 8257 8456 8656 8855 9054 9253 9451 9650 9849

210

211

212 213

218

220

222 223

225

226

227

228

231

232

233 234

.47.246

698.883

219 340444 0642 0841|10391237|1435 1632 1830 2028 2225 2423 2620 2817 3014 3212 3409 3006 3802 3999|4196 221 4392 4589 4785 4981 5178 5374 5570 5766 5962 6157 6353 6549 6744 6939 7135 7330 7525 7720 7915 8110 8305 8500 8694 8889 9083 9278 9472|9666 9860..54 224 350248 0442 0636 0829 1023 1216 1410 1603 1796 1989 2183 2375 2568 2761 2954 3147 3339 3532 3724 3916 4108 4301 4493 4685 4876 5008 5260 5452 5643 5834 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 7935 8125 8316 8506 8096 8886 9076 9260 9456 9646 229 9835.25.215.404 593.783.972 1161 1350 1539 230 361728 1917 2105 2294 2482 2071 2859 3048 3236 3424 3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 5488 5675 5862 6049 6236 6423 0610 6796 6983 7169 7356 7542 7729 7915 8101 8287 847 3 8659 8845 9030 9216 9401 9587 9772 9958. 143.328.513 235 371068 1253 1437 1622 1806| 1991 |2175 2360 2544 2728 2912 3096 3280 3464 3647 3831 4015 4198 4748 4932 5115 5298 5481 5664 5846 6029 6212 6394 238 6577 6759 6942 7124 7306 7488 7670 7852 8084 8216 239 8398 8580 8761 8943 9124 9306 9487 9668 9849..30 240 380211 0392 0573 0754 0934 1115| 1290 14761656 1837 2017 2197 2377 2557 2737 2917 3007 3277 3456 3636 3815 3995 4174 4353 4533 4712 4891 5070 5249 5428 5606 5785 5964 6142 6321 6499 6677 6856 7034 7212 244 7390 7568 7746 7923 8101 8279 8456 8634 8811 8989 9166 9343 9520 9698 9875..51.228.405.582.759 246 390935 1112 1288 1464 1641 1817 1993 2169 2345 2521 247 2697 2873 3048 3224 3400 3575 3751 3926 4101 4277 243 4452 4627 4802 4977 51525326 5501 5676 5850 6025 249 6199 6374 6548 6722 6896 7071 7245 7419|7592|7766||

236

237

241

242

243

245

3824565