THE ROYAL ARTILLERY INSTITUTION. 
181 
or, putting P for (Sp + p*), the values of which are tabulated, we have Tables 
the form best adapted for use— IIL & V * 
^ioooy = ^ioooy 
_ k ' <P p 
a w 
W 
“ K” can be obtained for any given velocity in Table I., but it is 
evident that for any section of the trajectory some mean velocity should 
be chosen to give the value of K. 
For this purpose the velocity at the end of the section must be esti¬ 
mated, and K may be taken corresponding to the velocity intervening 
about one-third from the higher to the lower velocity. This is a very 
rough approximation, but it has been already remarked that slight § 9. 
errors in K are of very trivial consequence in the results. 
If greater accuracy is required, the velocity at the end of the section 
may be roughly calculated with the approximate value of K } and then 
the mean of all values of K for the intermediate velocities can be taken 
as the basis for the more accurate calculation. 
Thus (Art. 71), 
^ 5 = 1329*9, Ua 
= 1238*5. Take the mean of the 
ten values of K for the velocities intermediate to 1240 and 1330 (both 
K 
inclusive), which is 108. Or, in like manner, the mean of log — might 
be found to be *52618—which would, however, be but very slightly 
more accurate than *5253, which is the value used. 
It will be seen that the trajectory is divided into sections, sometimes 
of 1°, sometimes of 2° {i.e., 1° or 2° change of inclination). The 
length that ought to be adopted depends upon the degree of rapidity 
with which K alters. If K is nearly constant, a large section may be 
chosen. With an initial* velocity of 1300 f.s., 3° would not be too large 
an interval, since the velocity at the end would probably be about 
1100 and K would be nearly constant throughout; but the next section Table I. 
ought not to exceed 1°, because the velocity would be less and rate of 
variation of K greater. Thus, to ensure accuracy, smaller intervals 
should be adopted for the- descending than for the ascending branch. 
If larger intervals are used, more care must be taken in choosing the 
mean value for A; however, the latter portion of the trajectory need 
not be calculated with quite as much care as the first portion—any 
error in which affects the whole of the succeeding portions. It is for 
this reason that larger intervals are used for the descending branch in 
Art. 71. 
13, Calculation of Trajectories. 
Formulas for ascending branch 
/loooy _ zioooy 
\ u o ) \ u 1 
^ioooy _ floppy 
, Kd* p , 
+ I, to find 
gw 
K 
— — P, to find u at end of section, 
9 w 
_ Mu* _ k &/ u 0 y 
~~ 9 “ 9 ' w \ 1000 / 
Eq‘> (»). 
Eq n O). 
Eq n (m). 
* i.e., horizontal component of initial velocity. 
