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"high old time” and do a little patriotic betting. The more solid alumnus wants them for the sake of meeting old friends. Alumni living too far from the scene of hostilities to witness them show their interest in the system, and their patriotism to their alma mater, by making up purses to send back poor but athleticallydeserving high-school lads as “material” for teams.

To this sort of thing it may reasonably be objected that the main function of a university is to provide for the welfare of the students actually under its charge, and not to furnish amusement for the alumni and the general public, and further, that the alumni, having had their innings as students, should not stand in the way of changes designed to meet the changed conditions of a later academic generation. But abstract arguments of this sort do not go with many of the more enthusiastic alumni; what they want is big game, the bigger the better, to show the other colleges and the world at large that “old Bohunkus is on the map," and for various and perhaps obvious reasons alumni influence bulks large with university authorities in determining athletic policy.

But alumni influence is not the only, nor indeed the chief, influencing factor in making for a misshapen development of college sports. A more potent and more demoralizing factor is commercialization, and, be it said straightway, commercialization is not widely remote from professionalization. An issue of the New York Evening Post a few months back is

a authority for the statement that one Glenn Warner was paid some $8000 for ten weeks of service in coaching the University of Pittsburg football team-not the Pirates of baseball fame, but a 'varsity team. What is the difference? Well, the writer lives too far distant to discriminate fairly the nuances in the situation. Perhaps the gentlemen backing the 'varsity team got more of a run for their money in football than in baseball. But if Pittsburg sins, it sins in good company; respectable old Harvard with its enormous football budget is hardly in a position to point the finger of scorn at Pittsburg. In fact, all over the country, in a large majority of the colleges, the expenses of football, and to a less degree, of the other sports, are excessive, inordinate and demoralizing. The parasitic growths-coaches, rubbers, trainers, training-tables, lavish equipment-demand “big gate money," and consequently big games. Big games in their turn, as played

here, call for the parasitic growths. And so the vicious circle is closed and goes eddying around a sort of financial maelstrom.

But a system of this kind does not whirl along the high water of finance without impulsion from certain outside forces-forces which are various in origin but united in their push towards the business side of things. First of these comes the not very ancient and not entirely honorable guild of mercenary coaches. The love of sport for sport's sake developed in these gentlemen, is hardly sufficient to bring them to look with complacency on changes in the athletic régime which might cut their emoluments down to figures within the reach of assistant or associate professors. In fact, they might be dropped into a state of "innocuous desuetude” altogether, if ever the principle of development of leadership through athletic sports should get a foothold in the colleges.

They have worked persistently, though not too conspicuously, in behalf of big games and big gate receipts, and inasmuch as a successful coach, in undergraduate opinion, considerably outranks in importance the president of a college, it cannot be said that the coach's influence is a negligble quantity in equating the ticket office with the field of play. As auxiliaries to the small but heavy-armed phalanx of coaches we find the writers of sporting news for the daily press and the agents of sporting goods houses who also fail to "see reasons” for changing a system which brings shekels into their purses.

Now at this point emerges a well-known argument which few colleges in the United States feel they are in a position to meet with satisfaction to themselves or to the reformers. It runs as follows: “If you do not make money from games how are you going to finance them? If you do not draw big crowds in football and charge all the traffic will bear how are you going to carry on sports at large?" For most colleges the question is a serious problem; their athletic fields are commonly limited to a “diamond” together with a football field surrounded by a track, an admirable arrangement for converting sports into shows and hippodromes. For other colleges the situation presents no problem at all; they deliberately plan to let the sports pay for themselves and regard the arrangement as a clever piece of academic economy. What such a plan leads to we have seen above. Manifestly it is the duty of a college to provide sufficient grounds for general participation in sports and to maintain them in fitting condition

together with what may be termed their proper permanent improvements-hot and cold showers, dressing-rooms and lockers. The day for regarding college sports merely as idle play has long gone by; no sane man who has watched college “ athletics ” has failed to see their potency in character building and their powerful influence for good or bad on academic life.

If proper provision were made for the “educational values" of sport, to use pedagogical parlance, it is evident that a good deal of wind would be taken out of the sails of the commercial argument, and even where no such provision has been made, a vigorous lopping off of the parasitic expenses of intercollegiate games would take from the “sport for revenue" argument considerable of its headway.

But granting a sufficiency of fields and a reasonable bill of expense in our sports, would general participation in them follow? Not necessarily, and perhaps not probably. Many generations of college students have grown up whose view of sports is bounded by the "team," the big game, and the bleachers, and college traditions of this kind have a tenacity of grip which usually requires a surgical operation by the faculty to unloose. Moreover, in the case of fall sports there would still remain the very greatest obstacle to general participation and that is the game of American football.

From the coaches' premonitory "now fellers” to the final blast of the whistle, American football is an intercollegiate event sang pur. In no sense is it a sport in the sense in which Rugby football, soccer, la crosse, and polo are sports, nor is it played in a like spirit. It is played by undergraduates for many reasons, but the pleasure of the play and sport for sport's sake are not conspicuous among them. It is a game for coaches, of coaches and by coaches, and a team is as frequently known by the name of its coach as by its college. In short, as one of our players remarked. “It's a bully game for the coaches.” Attempts to make it a "general sport" have rarely succeeded and where successful it has only been through assiduous dry-nursing with quick and long relapses. If left to the step-motherly treatment meted out to soccer in our colleges, it would collapse altogether.

Now, the main reason for this is not far to seek; it is a signal 'game. It presupposes a team of 1 men drilled by arduous and monotonous practice in a series of signals to make concerted

plays. It also presupposes another team of 1 men similarly drilled but with a different set of signals. Neither team may know the other team's signals. It usually calls in addition for a drill master in the shape of the coach who commonly works up the signals and the plays. As our colleges are constituted such an arrangement militates in the strongest way against any broad participation in football, even if the grind of practice and the list of injuries did not work in the same direction. The writer is not entering here into a discussion of the numerous objections that have been made to American football as a game: the ignorance of football technique of a majority of a team, the exhausting and mechanical character of the plays, the premium placed on weight as against dexterity, the expense of the outfit, the dependence on the coach, and the suppression of leadership. The point at issue is that the constitution of the game is such that it blocks the way for general participation.

When therefore a mere college faculty starts out to expiate the crime of the college against sane athletics by measures of reform, it finds itself up against a serried army of opposing powers, the influence of alumni and sometimes of trustees, a firmly entrenched commercialism, and student tradition.

And the hottest focus for all these influences may be found in the American game of football.

(COPYRIGHTED]
U. S. NAVAL INSTITUTE, ANNAPOLIS, MD.

TRAJECTORIES AND THEIR CORRECTIONS
By Lieut. COMMANDER A. G. Kirk, U. S. Navy

In the Naval Institute issue for January, 1919, whole No. 191, is published an article by Captain E. F. Eggert, Construction Corps, U. S. Navy, descriptive of a method of computing trajectories by mechanical integration. The method is essentially similar to that already in use by the Ordnance Department of the army, and now being adopted at the naval proving grounds for long-range work. The present system was developed by Professor F. R. Moulton, Professor of Astronomy at Chicago University, while serving as major in the ordnance reserve corps of the army during the war. And it is gratifying to find that from within the regular navy should come a scheme whose general principles are identical. Major Moulton's method, however, has several refinements of detail so that it will be of interest to reproduce it. Likewise Professor G. A. Bliss, at the Aberdeen Proving Ground, has developed a system of differential corrections to the undisturbed trajectory from which so-called weighting factor curves are drawn. From these differential corrections and weighting factor curves the calculated trajectories can be corrected accurately for all variations from standard conditions-muzzle velocity, angle of departure, wind, density of the air, and particularly wind and density which vary at different altitudes.

The reasons why the old methods of Alger and Ingalls must be discarded for long-range work have been clearly shown. The quantities B and fa are not known, and any assumptions of their values are bound to be in error. The only way of finding them is by calculating backwards from observed ranges, and even this cannot be done accurately unless the observed ranges are corrected for all variations from standard conditions. By mechanical

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