VOL. LXVIII.J PHILOSOPHICAL TRANSACTIONS. '1Q7 



neousl}-, seeing that almost the whole of the charge fires, though the time be 

 much diminished. 2. The velocities communicated to balls or shot of the same 

 weight, with different quantities of powder, are nearly in the sub-duplicate ratio 

 of those quantities. A very small variation, in defect, taking place when the 

 quantities of powder become great. 3. And when shot of different weights are 

 fired with the same quantity of powder, the velocities communicated to them are 

 nearly in the reciprocal sub-duplicate ratio of their weights. 4. So that, 

 universally, shot which are ol' different weights, and impelled by the firing of 

 ditTerent quantities of powder, acquire velocities which are directly as the square 

 roots of the quantities of powder, and inversely as tlie square routs of the 

 weights of the shot, nearly. 5. It would therefore be a great improvement in 

 artillery, to make use of shot of a long form, or of heavier matter ; for thus the 

 momentum of a shot, when fired with the same weight of powder, would be 

 increased in the ratio of the square root of the weight of the shot. 6. It would 

 also be an improvement to diminish the windage ; for by so doing, one-third or 

 more of the quantity of powder might be saved. 7- When the improvements 

 mentioned in the last 2 articles are considered as both taking place, it is evident 

 that about half the quantity of powder might be saved, which is a very consider- 

 able object. But important as this saving may be, it seems to be still exceeded 

 by that of the article of the guns ; for thus a small gun may be made to have the 

 effect and execution of a gun of 2 or 3 times its size in the present mode, by 

 discharging a shot of 2 or 3 times the weight of its natural ball or round shot. 

 And thus a small ship might discharge shot as heavy as those of the greatest now 

 made use of. 



Finally, as the above experiments exhibit the regulations with regard to the 

 weights of powder and balls, when fired from the same piece of ordnance, &c. ; 

 so by making similar experiments with a gun, varied in its length, by cutting off 

 from it a certain part before each course of experiments, the effects and general 

 rules for the different lengths of guns may be certainly determined by them. In 

 short, the principles on which these experiments were made, are so fruitful in 

 consequences, that, in conjunction with the effects resulting from the resistance 

 of the medium, they seem to be sufficient for answering all the inquiries of the 

 speculative philosopher, as well as those of the practical artillerist. 



IF. A New Case in Squinting. By Erasmus Darwin, M. D., F. R. S. p. 86. 



Dated Lichfield, March \777- 



The following case in squinting, as a similar one has not been recorded or 

 explained by others, may perhaps merit attention from its novelty. 



In 1771, Dr. D. was desired to see a child of the Rev. Dr. Sandford, in 

 Shropshire, to determine if any method could be devised to cure him of squint- 



voL.xiv. Qa 



