^72 1>HIL080PHICAL TRANSACTIONS. [aNNO 1 685-6. 



genuine use and effects of the gun, printed in l674; but his solution required 

 so much calculation, that it put me on finding out whether it might not be 

 done more easily; and accordingly, in 1678, I discovered the rule I now pub- 

 lish, and from it the geometrical construction. 



Now these rules would be rigidly true, were it not for the resistance of the 

 medium, by which not only the direct impressed motion is continually retarded, 

 but likewise the increase of the velocity of the fall, so that the spaces described 

 thence are not exactly 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 deter- 

 mine. 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 diameters recipro- 

 cally ; whence generally, the resistance to shot with the same velocity, but 

 of differing diameters and materials, should be as their specific gravities into 

 their diameters reciprocally ; but whether the opposition to differing velocities 

 of the same shot be as the squares of those velocities, or as the velocities them- 

 selves, or otherwise, is yet a more difficult question. However it be, it is cer- 

 tain 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 the surface; this 

 resistance is scarcely discernible, for by several experiments, made with all care 

 and circumspection, with a mortarpiece extraordinary well fixed to the earth on 

 purpose, which carried a solid brass shot of 44- inches diameter, and of about 

 14 lb. weight, the ranges above and below 45 degrees were found nearly equal; 

 if there were any difference, the under ranges went rather the farthest; but those 

 differences were usually less than the errors committed 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 l-J- inch diameter, cast by a cross bow, 

 which ranged it at most about 400 feet, the force being much more equal than 

 in the mortarpiece, 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 prac- 

 tice to all intents and purposes, as if this impediment were absolutely removed.* 



* The experiment mentioned in the preceding lines, as well as in those that follow, appear to have 

 been made with too little force, or charge of powder, to determine the point in qaestion. For with 



