THE ROYAL ARTILLERY INSTITUTION. 
183 
Starting from the vertex, we know “ % ” 
now are:— 
and the steps 
Estimate for 7f; mean velocity = 1010, X = 77'5.* 
Calculate y. 
Calculate 0 # 3 , 0 y 3 , 0 t%. 
/ioooy = /ioooy + £.f P 
\ % / \ / CJ w * 
«3= 982-7. 
Estimate again for A; mean velocity = 970, .*. A = 69'6.* 
/loooy _ /loooy __K& p 
\ «J " \ M / 7 w 2 ‘ 
This gives the new value of u 0 , and the next section is similarly 
determined. 
Thus there are five distinct steps for each section, involving only 
arithmetic and logarithmic computation. 
The most laborious step is the calculation of x, y , and t, especially 
when very great accuracy is required, and interpolation, instead of 
proportional parts, is used for intermediate values of y or 0 not given 
in the tables. The next section will give a brief account of one of 
twelve trajectories, in calculating which the writer of this paper ex¬ 
pended a great deal of unnecessary labour by aiming at too great 
accuracy, and always interpolating when the differences were not 
regular ; whereas the advantage obtained in the way of accuracy was 
entirely neutralised by the slight inaccuracies due to the values taken 
for K being necessarily, to a certain extent, incorrect. 
( 1 ) 
( 2 ) 
(3) 
(4) 
(5) 
( 6 ) 
14. Problem on Trajectories. 
The following problem was put to the writer:— 
At what distances from the muzzle of the gun will a 9-pr. and 16-pr. 
projectile be at heights above the muzzle of 2 ft. 3 ins, and 5 ft. 3 ins. 
(both in the ascending and descending branch), it being considered 
that at these heights respectively a man on foot and on horseback 
would be just cleared; elevation to be taken at 1°, 2°, 4°, 6° in sue-* 
cession? [Vide diagram.) 
The solutions obtained for the whole problem agreed well with what 
was to be expected in each case, and these notes are the result of the 
experience gained in working them out. 
Take the case of the 16-pr. at 4° elevation. 
w = 16 lbs., 7=3-54", V = 1855. 
* The corrected values would be 80-1 instead of 77*5, and 7T1 instead of 69*6. 
