The opinions which prevailed at this time respecting the extreme rarity and tenuity of the air, prevented phi losophers and military engineers from availing themselves of this important pa'rt of Galileo's work. They anticipated no great variation from the theory, and accordingly we find it to have been, for a long time, the received opinion, that all projectiles moved in a parabolic curve.
This erroneous opinion was stoutly maintained by our countryman Anderson, in his treatise Of the Genuine use and effects of the Gun, published in 1674. This work is founded on the Galilean theory ; and its author boldly un dertakes to overturn all objections that can be urged against the parabolic motion of projectiles.
A similar notion is maintained by M. Blondel, in his 12.4rt de jetter les bombes, which appeared at Paris in 1683. He applies the doctrines of Galileo to the flight of shells and bullets of every kind ; and after a long discus sion relative to the air's resistance, he concludes that it is too minute to affect the accuracy of his deductions.
The celebrated Dr Halley held the same false opinion. He was, however, not merely misled by a belief in the extreme tenuity of the air ; but lie was confirmed in his errors by some very imperfect experiments. After treat ing of the motion of projectiles, (See Phil. Trans. 1685, No. 179. p. 3.) he that these rules would be •igidly true, were it not for the resistance of the medium, by which not only the direct impressed motion is continu ally retarded, but likewise the increase of the velocity of the fall, so that the spaces described thence are not ex actly as the squares of the times; but what this resistance of the air is, against several velocities, bulks, and weights, is not so easy to determine. It is certain that the weight of air to that of water is nearly as 1 to 800 ; whence its weight to that of any project is given. It is very likely, that to the same velocity and magnitude, but of different matter, the resistance will be reciprocally as the weights of the shot ; as also, that to shot of the same velocity and matter, but of different sizes, it should. be as the diame ters reciprocally ; whence, generally, the resistance to shot with the same velocity, but of different diameters and materials, should be as their specific gravities into their diameters reciprocally ; but whether the opposition to dif ferent velocities of the same shot be as the squares of those velocities, or as the velocities themselves, or other wise, is yet a more difficult question. However it be, it is certain, that in large shot of metal, whose weight many thousand times surpasses that of the air, and whose force is very great in proportion to time surface, this resistance is scarcely discernible; for by several experiments made with all care and circumspection, with a mortar-piece, extraordinarily well fixed to the earth on purpose, which carried a solid brass shot of 41 inches diameter, and of about 14 lb. weight, the ranges above and below 45 de
grees were found nearly equal ; if there were any dif ference, the under ranges went rather the farthest ; but those differences were usually less than the errors com mitted in ordinary practice, by the unequal goodness and dryness of the same sort of powder, by the unfitness of the shot to the bore, and by the looseness of the carriage.
In a smaller brass shot, of about 11 inch diameter, cast by a cross-bow, which ranged it at most about 400 feet, the force being much more equal than in the mortar-piece, this difference was found more curiously, and constantly, and most evidently the under ranges exceeded the upper. From which trials I conclude, that although, in small and light shot, the opposition of the air ought and must be accounted for, yet, in shooting of great and weighty bombs, there need be very little or no allowance made ; so that these rules may be put in practice, to all intents and purposes, as if this impediment were absolutely re moved." Although the opinion which we have been considering was entertained chiefly by speculative writers, yet those who made extensive experiments on the motion of pro jected bodies, began to suspect some lurking error. An derson, whom we have alrea• mentioned, as a keen abettor of the parabolic theory, had occasion to make a number of new experiments on the ranges of shells dis charged with small velocities, which he published in 1690, in his treatise entitled, To hit a mark. He found that the track of shells and bullets was much less incurvated in the first part of their path than they ought to be, on the Galilean theory ; but instead of supposing the theory practically incorrect, or conjecturing that the deviations were produced by the resistance of the air, he imagined that the shell or bullet was discharged from the gun to a certain distance in a right line, and that gravity only began to deflect it into a parabolic curve at the end of this line, which he calls the line of the impulse of the fire, and which he supposes to be the same at all elevations. By giving a proper magnitude to this imaginary line, he was always able to reconcile the ranges of any two shells projected at different elevations ; though, as :11r Robins remarks, he would have found it impossible to reconcile the irregularities of three or more ranges.