ii. External causes, such as wind, and varying density

of the air.

Errors due to the gun will arise if the twist of rifling is unsuited to the length of the projectile.

Errors due to the projectiles will arise if their density has not been distributed in the best manner, or if they are inaccurately centred or vary in weight.

Errors due to the charge can be reduced to a minimum by using explosive of the same lot throughout the experiment, and by giving each charge the same air space to secure uniformity of loading density.

Errors will also arise if the mounting, or the gun on its mounting, is unsteady when the gun is fired, as this would cause a variable “_jump_” and consequently a variable angle of departure.

3. The following is an example of one series:--

------+---------+-----------+---------+----------- No. | Range. |Difference |Deviation|Difference of | | from | right. | from round.| | mean. | | mean. ------+---------+-----------+---------+----------- | yds. | yds. | yds. | yds. 1 | 4,968 | 22·8 | 24·4 | 3·0 2 | 4,954 | 8·8 | 21·6 | 0·2 3 | 4,962 | 16·8 | 22·8 | 1·4 4 | 4,908 | 37·2 | 20·0 | 1·4 5 | 4,934 | 11·2 | 18·4 | 3·0 ------+---------+-----------+---------+----------- | 24,726 | 96·8 | 107·2 | 9·0 +---------+-----------+---------+----------- Mean | 4,945·2 | 19·4 | 21·4 | 1·8 ------+---------+-----------+---------+-----------

The second column in the above table gives the actual ranges. The mean range is obtained by adding all together and dividing by 5, since 5 rounds were fired.

The third column contains the difference of each round, _irrespective of sign_, from the mean range just found. The mean of these differences is then obtained, and called the mean error in range or mean longitudinal error. Evidently, if all the projectiles fall nearly at the same range, this mean error must be small.

The fourth column gives the lateral deviation from the direction in which the axis of the gun points; the mean deviation is at the bottom of this column. If any shot had fallen to the left, then the deviation would be reckoned from a line passing through either the extreme right or the extreme left shot.

The fifth column gives the difference from the mean deviation, with a mean at the bottom called the mean error in deviation or mean lateral error.

Collecting the results from the table we have:--

Mean range 4945·2 yards. Mean longitudinal error 19·4 ” Mean deviation right 21·4 ” Mean lateral error 1·8 ”

It can be shown by the theory of probabilities that if each mean error is multiplied by the factor 1·69, the breadths of zones (of infinite length), which will contain 50 per cent. of the hits, are obtained.

4. As a result of these and other tests the following information is embodied in the various columns of the range table.

i. _Elevation and Range._--The angle of elevation in degrees and minutes is shown for every hundred yards up to the limit of effective range of the gun.

ii. _Fuze Scale._--The fuze scale column shows the graduation at which the fuze must be set due to the time of flight for the range shown on the table. In the range table for the 18-pr. Q.F. we find for a range of 4,000 yards the fuze graduation is 12·8. As the fuze scales are compiled for a barometric pressure of 30 inches, this means that a shell with a fuze set at 12·8 will burst at 4,000 yards from the gun when fired at the sea level under normal conditions. For various reasons mentioned in Sec. 112, the fuze scale can only be taken as a guide.

iii. _Angle of Descent._--The angle of descent is shown either in degrees and minutes or as a slope.

As a field gun has only one charge, the only way to increase the angle of descent is to increase the range. With field howitzers varying charges are used, so that any required angle of descent can be obtained by a judicious selection of the position of the gun and the charge to be used.

iv. _Remaining Velocity._--This column shows the actual velocity of the projectile at any given range.

v. _Five Minutes Alteration of Elevation or Deflection._--These columns show what alteration in the range or point of impact is caused by an alteration of 5 minutes in elevation or deflection. The former is useful in ranging a howitzer battery, and the latter is useful in calculating the deflection to be given to concentrate the fire of the guns of a battery on to one point, and also in calculating the correction required to get parallel lines of fire when using an aiming point (_See_ Sec. =122=.) Thus, suppose the range to an aiming point is estimated at 2,800 yards, and the virtual displacement of the gun 16 yards, the displacement difference will be 20 minutes, as the range table shows that 5 minutes deflection alters the point of impact 4 yards at that range.

vi. _Time of Flight._--Time of flight is shown in seconds.

vii. _Deflection for Drift._--The sights of some howitzers not being arranged to counteract the drift of the projectile, it is necessary to give deflection. The amount required at the various angles of elevation is shown in the table. It is always given to the left.

viii. _Accuracy Tables._--These columns give the length or breadth or height within which 50 per cent. of rounds should fall and are based upon actual practice.

_Example._--As an example take the 18-pr. Q.F. gun. At 3,000 yards the 50 per cent. length is given as 20 yards, and the breadth as 1·44 yards. A series of rounds might fall, as in Fig. 16, round about a target T. Of these 50 per cent. would be contained between the two lines AB, CD, 20 yards apart, 10 yards on each side of the centre of the group. All the rounds should fall within two lines four times that distance apart, that is 40 yards on each side of the centre of the group.

Again, of the rounds that fell right and left of the centre of the group 50 per cent. would be enclosed by the two lines FE, HG, Fig. 17, 1·44 yards apart, and all should be contained by two lines four times that distance apart.

If now one pair of parallel lines are placed over the other as in Fig. 18, evidently the rectangle enclosed by them will contain 50 per cent. of 50 per cent., that is 25 per cent. of the total.

The width of other zones (containing a different percentage of hits) can be obtained by multiplying the width of the 50 per cent. zone by a varying factor (_see_ Text Book of Gunnery).

If the target is a vertical one, the figures in the column “_height_” should be taken, instead of those under “_length_.”

5. It is important to realize the effect of these laws in cases of ordinary practice, where errors in range are of chief moment. We have seen that at 3,000 yards, with the 18-pr. Q.F. gun, a series of rounds would fall within two lines 40 yards on each side of the centre of the series; therefore a shell falling 39 yards short is within normal limits of error, but it should be counterbalanced by other shots falling over.

6. Accuracy of fire is a comparative term; it is said to be good when a group of projectiles, fired under as nearly as possible the same conditions, falls close together.

The probable percentage of hits obtainable from an 18-pr. Q.F. on a shield 4 feet 6 inches high and 5 feet wide, fired under experimental conditions,

is at 2,000 yards 60 per cent. 2,500 ” 33 ” 3,000 ” 16 ” 3,500 ” 8½ ” 4,000 ” 5 ”

Under service conditions these percentages would be considerably reduced.