C !3 8 ] 
than ever neceffary, and as Gentlemen employ'd in 
the Pradice of that Art are (I am fenfible) too 
often deterr'd from applying themfeives to the The- 
ory, by the Difficulties they imagine they fhall meet 
with in the Conic Sections, you will, I hope, par- 
don the Liberty I have taken, in troubling you with 
my Thoughts on a Subjed, inf which little or no- 
thing new is to be expeded beftdes the Method. 
When I hid drew up this Paper (which was about 
two Years ago) I did intend, had Health permitted 
me to make the proper Experiments, to have alio 
attempted fomething with refped to the Refinance 
of the Atmofphere, whereof the Effeds are indeed 
too eonfiderable to be intirely difregarded : But if 
the Amplitude of the Projedion, anfwering to one 
given Elevation, be firft determined by Experiment 
(which our Method fuppofes) the Amplitudes in all 
other Cafes, where the Elevations and Velocities do 
not very much differ from the firft, may be deter- 
mined, by the Proportions here laid down, to a fuf- 
ficient Degree of Exadnefs- Bccaufe, in all fuch 
Cafes, the Etfeds of the Refiftance will be nearly 
as the Amplitudes themfeives ; and were they accu~ 
rately fo, the Proportions of the Amplitudes, at 
different Elevations, would be exadly the fame as 
in vacuo ; which Proportions I now proceed to 
determine* 
Problem I. 
Let two Balls be pro jetted with the fame Celerity, 
at different, but given Elevations , ' tis propofed 
to determine the Ratio of the Times of their 
Flight, 
