1. That the resistance is nearly as the surface; the resistance increasing but a very little above that proportion in the greater surfaces. Thus, by comparing together the numbers in the 6th and last columns, for the bases of the two hemispheres, the areas of which are in the proportion of 174 to 32, or as 5 to 9 very nearly; it appears that the numbers in those two columns, expressing the resistances, are nearly as 1 to 2, or as 5 to 10, as far as to the velocity of 12 feet; after which the resistances on the greater surface increase gradually more and more above that proportion. And the mean resistances are as 140 to 288, or as 5 to 10%. This circumstance therefore agrees nearly with the theory. 2. The resistance to the same surface, is nearly as the square of the velocity; but gradually increasing more and more above that proportion, as the velocity increases. This is manifest from all the columns. And therefore this circumstance also differs but little from the theory, in small velocities. 3. When the hinder parts of bodies are of different forms, the resistances are different, though the fore parts be alike; owing to the different pressures of the air on the hinder parts. Thus, the resistance to the fore part of the cylinder, is less than that on the flat base of the hemisphere, or of the cone; because the hinder part of the cylinder is more pressed or pushed, by the following air, than those of the other two figures. 4. The resistance on the base of the hemisphere, is to that on the convex side, nearly as 23 to 1, instead of 2 to 1, as the theory assigns the proportion. And the experimented resistance, in each of these, is nearly 4 part more than that which is assigned by the theory. 5. The resistance on the base of the cone is to that on the vertex, nearly as 2 to 1. And in the same ratio is radius to the sine of the angle of the inclination of the side of the cone, to its path or axis. So that, in this instance, the resistance is directly as the sine of the angle of incidence, the transverse section being the same, instead of the square of the sine. 6. Hence we can find the altitude of a column of air, whose pressure shall be equal to the resistance of a body, moving through it with any velocity. Thus, Let Let a the area of the section of the body, similar to any of those in the table, perpendicular to the direction of motion; r = the resistance to the velocity, in the table; and the altitude sought, of a column of air, whose base is a, and its pressure r. Then at the content of the column in feet, and fax or fax its weight in ounces; therefore arr, and x = x is the altitude sought in feet, namely, of the quotient of the résistance of any body divided by its transverse section; which is a constant quantity for all similar bodies, however different in magnitude, since the resistance ris as the section a, as was found in art. 1. When a of a foot," as in all the figures in the forego = r a ing table, except the small hemisphere: then, r = { x becomes rr, where r is the resistance in the table, to the similar body. If, for example, we take the convex side of the large hemisphere, whose resistance is 634 oz. to a velocity of 16 feet per second, then r634, and x = $r 2·3775 feet, is the altitude of the column of air whose pressure is equal to the resistance on a spherical surface, with a velocity of 16 feet. And to compare the above altitude with that which is due to the given velocity, it will be 322: 162 :: 16:4, the altitude due to the velocity 16; which is near double the altitude that is equal to the pressure. And as the altitude is proportional to the square of the velocity, therefore, in small velocities, the resistance to any spherical surface, is equal to the pressure of a column of air on its great circle, whose altitude is 12 or 594 of the altitude due to its velocity. = But if the cylinder be taken, whose resistance 1·526: then rr = 5.72; which exceeds the height, 4, due to the velocity in the ratio of 23 to 16 nearly. And the difference would be still greater, if the body were larger ; and also if the velocity were more. 7. Also, if it be required to find with what velocity any flat surface must be moved, so as to suffer a resistance just equal to the whole pressure of the atmosphere: The The resistance on the whole circle whose área is of a 43443 foot, is '051 oz. with the velocity of 3 feet per second; it is of 051, or 0056 oz. only, with a velocity of 1 foot. But 2 × 13600 × 3 = 7555 oz. is the whole pressure of the atmosphere. Therefore, as 0056: √7556 :: 1: 1162 nearly, which is the velocity sought. Being almost equal to the velocity with which air rushes into a vacuum. 8. Hence may be inferred the great resistance suffered by military projectiles. For, in the table, it appears, that a globe of 63 inches diameter, which is equal to the size of an iron ball weighing 36lb, moving with a velocity of only 16 feet per second, meets with a resistance equal to the pressure of of an ounce weight; and therefore, computing 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 417lb, 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 24 feet, the height of a uniform atmosphere, all of the same density as at the earth's surface, would be 21 x 13.6 x 8334 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 atmosphere 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. 1 0.000000 26 | 1·414973 || 51 | 1.707570 76 1.880814 77 1.886491 79 1.897627 80 1.903090 81 1.908485 82 1-913814 83 1.919078 84 1.924279 85 1.929419 86 1.934498 87 1.939519 88 1944483 89 1-949390 90 1.954243 91 1.959041 92 1.963788 93 1.968483 94 1.973128 20 301030 27 1-431364|| 52 | 1-716003 30-477121 28 1-447158 53 1-724276 78 1.892095 4 0.602060 29 1462398 54 1732394 5 0.698970 30 1-477121551.740363 6 0.778151 31 1491362 || 56 1.748188 70-845098 || 32 1.505150 57 1.755875 80-903090 331-518514 || 581.763428 9 0.954243 34 1531479|| 591770852 10 1.000000 35 1-544068 60 1.778151 11 1.041393 || 36 1.556303 61 1.785330 12 1.07918137 1.568202 62 1.792392 13 1113943|38| 1·579784 || 63 |1·799341 14 1146128 39 1.591065 64 1.806180 15 1.176091 || 40 | 1·602060 | 65 1.812913 16 1204120 |41|1.612784 661-819544 17 1230449 42 1623249 671-826075 18 1255273 43 1.633468 68 1-832509 19 1.278754 44 1643453 69 1-838849 20 1.301030 45 1.653213 70 1.845098|| 95 1.977724 21 1322219 46 1.662758 71 1.851258 22 1.34242347 1.672098 72 1.857333 23 1-361728 48 1-68124173 1.863323 98 1.991226 24 1-38021149 1.690196 74 1.869232 99 1.995635 1397940501·698970 || 75 | 1·875061 || 100 | 2.000000 25 96 1.982271 97 1.986772 |