THE trajectory of a bullet is the curved path of its flight. Every missile travels in a constantly increasing curve. The height of that curve, for a given range, depends upon the speed at which the projectile flies. No trajectory can be flat, because no curve is flat; it will be low with a swift bullet and high with a slow one. The advantage of a low trajectory is that it extends the range throughout which one can hit game without making a close guess at the distance and precise allowance for the drop of bullet.

Imagine yourself hunting with an accurate but low-speed rifle—say a .38-55 or a .45-70 of the type favored a few years ago. In your hunting ground the cover is so thick that the guides say: "Don't bother about trajectory; nine-tenths of big game is shot within a hundred yards, and any rifle will carry ' level' enough to do the trick at that distance".

But the days slip by, your vacation is near spent, and you have no trophy. Then the extraordinary happens. A fine bull moose steps out to the lake's margin. There he stands, clearly outlined against sky and water, as fair a mark as any bull'seye on your target range at home. It is your last chance to retrieve from failure a trip you have planned these three years past, and one that has cost you a pretty penny, withal.

The beast is a good way off; just how far is not easy for city-trained eyes to gauge. You say to yourself " three hundred yards," and raise the rear sight accordingly. Beside you is a big, old mossy log—as good a muzzle rest as man could wish. It is a fair advantage to take for so long a shot. The moose does not wind you. There is no hurry. You aim as you never aimed before, draw trigger with never a blink or shrink, and—miss!

" Chr-r-ristopher Columbus! " or words to that effect.

The moose has vanished forever. And what's to blame? Trajectory is to blame. Your guide was right about the nine times in ten; but about this supreme and never-to-be-forgotten one chance in ten he was dead, dead wrong.

You overestimated the distance by fifty yards— not a very bad guess, under the circumstances. At two hundred and fifty yards where the moose really stood, your slow-moving bullet, aimed for three hundred, flew nearly or quite two feet too high. Had you been armed with an accurate high-speed rifle, say a .30 U. S., 9 06, the bullet would have landed on the moose, from two to seven inches above the point you aimed at, with strong probability of bringing meat to camp and a fine head for the wall of your den at home.

These figures are not the kind reprinted by catalogue experts in the gun-talk pages of magazines. They are the kind that bring results. No gun ever shoots swift for one man and slow for another. Its trajectory is pre-determined when the cartridge is loaded, and one can no more alter it by anecdotes of fluke shots than he can by pulling harder on the trigger.

Trajectory, then, is something that every up-to-date sportsman should understand. To do so, one must give attention to a few figures. Those commonly printed in catalogue tables do not tell • the facts that a hunter most needs to know. The midway rise of a bullet over certain ranges may j have some value in comparing weapons, but little r in hunting; for nobody will make a mistake of ■ fifty per cent in judging distance. The zone of -probable error is the twenty-five to seventy-five yards nearest the mark shot at, both on the hither side and beyond the object.

Trajectory tables, to be of practical use to sportsmen, should show the height of bullet curve every twenty-five or fifty yards from muzzle to range sighted for; also the drop below line of aim, at similar intervals, for some distance beyond that range. It is not expedient to publish many such tables in this place, nor is it needful to do so. Rifle ammunition may be classified in a few well-defined groups, and a typical cartridge of each group will serve for comparison. The meaning of the tables published herewith can be taken in at a glance.

I have selected four typical cartridges, and give their trajectories, at sporting ranges, in detail. They may be compared with others by noting, first, the relative length of bullet in calibers, and, second, the midway height of curve over a given range, as shown in catalogues. The cartridges chosen for illustration are as follows—

(A). The .22 long rifle. Typical of miniature rim-fires used on very small game and vermin; also by beginners, as primers of marksmanship, and by older sportsmen to " keep their hands in".

(B). The .32 Winchester auto-loading cartridge. Type of cheap, short-range ammunition suitable for shooting in settled regions at small game generally and at predatory creatures, yet powerful enough for an occasional deer or black bear.

(C). The well known .30-30. Differing but little from others in a series of cartridges of about two thousand feet a second muzzle velocity which are much used on game from deer to elk, having fairly low trajectory, fair accuracy, and enough power for all but the largest American game.

(D). The .30 U. S., model of 1906, with Spitzer bullet. Typical of the latest {military and big game cartridges of highest velocity associated with fine accuracy and great shocking power.

The calculations are my own, checked against results of careful tests, and are close enough averages for all practical purposes. Be it remembered, however, that trajectories for the same arm vary a little, even at moderate ranges, according to atmospheric conditions and elevation above sea-level; more still, according to the vertical deviation of shots fired and the flip or stiffness of gun barrel. Some of these points will be considered later.