imself, therefore, attempted to compare his propositions with experiment. Some were made by experiments dropping balls from the dome of St Paul's cathedral; and all these showed as great a coincidence with his theory as they did with each other; but the irregularities... ties were too great to allow him to say with precision what was the resistance. It appeared to follow the proportion of the squares of the velocities with sufficient exactness; and though he could not say that the resistance was equal to the weight of the column of air having the height necessary for communicating the velocity, it was always equal to a determinate part of it; and might be stated \( n \cdot a \), \( n \) being a number to be fixed by numerous experiments.

One great source of uncertainty in his experiments seems to have escaped his observation: the air in that dome is almost always in a state of motion. In the former season there is a very sensible current of air downwards, and frequently in winter it is upwards: and this current bears a very great proportion to the velocity of the descents. Sir Isaac takes no notice of this.

He made another set of experiments with pendulums; and has pointed out some very curious and unexpected circumstances of their motions in a resisting medium. There is hardly any part of his noble work in which his address, his patience, and his astonishing penetration, appear in greater lustre. It requires the utmost intrepidity of thought to follow him in these disquisitions; and we cannot enter on the subject at present: some notice will be taken of these experiments in the article RESISTANCE of Fluids. Their results were much more uniform, and confirmed his general theory; and, as we have said above, it has been acquiesced in by the first mathematicians of Europe.

But the deductions from this theory were so inconsistent with the observed motions of military projectiles, when the velocities are prodigious, that no application could be made which could be of any service for determining the path and motion of cannon shot and bombs; and although Mr John Bernoulli gave, in 1718, a most elegant determination of the trajectory and motion of a body projected in a fluid which resists in the duplicate ratio of the velocities (a problem which even Newton did not attempt), it has remained a dead letter. Mr Benjamin Robins, equally eminent for physical science and mathematical genius, was the first who suspected the true cause of the imperfection of the usually received theories; and in 1737 he published a small treatise, in which he showed clearly, that even the Newtonian theory of resistance must cause a cannon ball, discharged with a full allotment of powder, to deviate farther from the parabola, in which it would move in vacuo, than the parabola deviates from a straight line. But he further asserted, on the authority of good reasoning, that in such great velocities the resistance must be much greater than this theory affirms; because, besides the resistance arising from the inertia of the air which is put in motion by the ball, there must be a resistance arising from a condensation of the air on the anterior surface of the ball, and a rarefaction behind it: and there must be a third resistance, arising from the statical pressure of the air on its anterior part, when the motion is so swift that there is a vacuum behind. Even these causes of disagreement with the theory had been foreseen and mentioned by Newton (see the Scholium to prop. 37, book ii. Princip.), but the subject seems to have been little attended to. The eminent mathematicians had few opportunities of making experiments; and the professional men, who were in the service of princes, and had their countenance and aid in this matter, were generally too deficient in mathematical knowledge to make a proper use of their opportunities. The numerous and splendid volumes which these gentlemen have been enabled to publish by the patronage of sovereigns are little more than prolix extensions of the simple theory of Galileo. Some of them, however, such as St Remy, Antonini, and Le Blond, have given most valuable collections of experiments, ready for the use of the profound mathematician.

Two or three years after this first publication, Mr Robins hit upon that ingenious method of measuring the great velocities of military projectiles, which has handed down his name to posterity with great honour, and respect. And having ascertained these velocities, he discovered, also, the prodigious resistance of the air, by observing the diminution of velocity which it occasioned. This made him anxious to examine what was the real resistance to any velocity whatever, in order to ascertain what was the law of its variation; and he was equally fortunate in this attempt. His method of measuring the resistance has been fully described in the article GUNNERY, No. 9, &c.

It appears (Robins's Math. Works, vol. i. page 205.) that a sphere of 4½ inches in diameter, moving at the rate of 25½ feet in a second, sustained a resistance of 0.04914 pounds, or \( \frac{4914}{10000} \) of a pound. This is a greater resistance than that of the Newtonian theory, which gave \( \frac{765555}{1000000} \) in the proportion of 1000 to 1211, or very nearly in the proportion of five to six in small numbers. And we may adopt as a rule in all moderate velocities, that the resistance to a sphere is equal to \( \frac{5}{6} \) of the weight of a column of air having the great circle of the sphere for its base, and for its altitude the height through which a heavy body must fall in vacuo to acquire the velocity of projection.

This experiment is peculiarly valuable, because the ball is precisely the size of a 12 pound shot of cast iron; and its accuracy may be depended on. There is but one source of error. The whirling motion must have occasioned some whirl in the air, which would continue till the ball again passed through the same point of its revolution. The resistance observed is therefore probably somewhat less than the true resistance to the velocity of 25½ feet, because it was exerted in a relative velocity which was less than this, and is, in fact, the resistance competent to this relative and smaller velocity.

Accordingly, Mr Smeaton, a most sagacious naturalist, places great confidence in the observations of Mr Roufe of Leicestershire, who measured the resistance by the effect of the wind on a plane properly exposed to it. He does not tell us in what way the velocity of the wind was ascertained; but our deference for his great penetration and experience dispenses us to believe that this point was well determined. The resistance observed by Mr Roufe exceeds that resulting from Mr Robins's experiments nearly in the proportion of 7 to 10. They differ widely in Chevalier de Borda made experiments similar to those of Mr Robins, and his results exceed those of Roufe's, in the proportion of 5 to 6. These differences are so considerable, that we are at a loss what measure to abide by. It is much to be regretted, that in a subject so interesting both to the philosopher and the man of the world, experiments have not been multiplied. Nothing would tend so much to perfect the science.