I shall not need to speak of the Facility of these Solutions, I shall only observe that they are both General, without Exception or Caution, and derived from the Knowledge that these two Elevations are equidistant above and below the Line, bisecting the Angle between the Object and the _Zenith_. _A Discourse concerning the Measure of the Airs Resistance to Bodies moved in it. By the Learned _John Wallis_, S. T. D. and R. S. S._ 1. That the Air (and the like of any other _Medium_) doth considerably give Resistance to Bodies moved in it; and doth thereby abate their Celerity and Force; is generally admitted. And Experience doth attest it: For otherwise, a Cannon Bullet projected Horizontally, should (supposing the Celerity and Force undiminished) strike as hard against a Perpendicular Wall, erected at a great distance, as near at hand; which we find it doth not. 2. But at what Rate, or in what Proportion, such Resistance is; and (consequently, at what Rate the Celerity and Force is continually diminished) seems not to have been so well examined. Whence it is, that the Motion of a Project (secluding this Consideration) is commonly reputed to describe a Parabolick Line; as arising from an Uniform or equal Celerity in the Line of Projection, and a Celerity uniformly accelerated in the Line of Descent; which two so compounded, do create a Parabola. 3. In order to the Computation hereof, I first premise this _Lemma_, (as the most rational that doth occur for my first footing,) That (supposing other things equal) the Resistance is proportional to the Celerity. For in a double Celerity, there is to be removed (in the same time) twice as much Air, (which is a double Impediment) in a treble, thrice as much; and so in other Proportions. 4. Suppose we then the Force impressed (and consequently the Celerity, if there were no Resistance) as 1; the Resistance as _r_. (which must be less than the Force, or else the Force would not prevail over the Impediment, to create a Motion.) And therefore the effective Force at a first Moment, is to be reputed as 1 - _r_: That is, so much as the Force impressed, is more than the Impediment or Resistance. 5. Be it as 1 - _r_ to 1; so one to _m_. (which _m_ is therefore greater than 1.) 6. And therefore the effective Force (and consequently the Celerity) as to a first Moment, is to be 1/_m_ of what it would be, had there been no Resistance. 7. This 1/_m_ is also the remaining Force after such first Moment; and this remaining Force is (for the same Reason) to be proportionally abated as to a second Moment; that is, we are to take 1/_m_ thereof, that is 1/_mm_ of the impressed Force. And for a third Moment (at equal distance of time) 1/_mmm_; for a fourth 1/_m_⁴; and so onward infinitely.