**A Few Notes On Alternating Current**

(SEE PAGE 1171, WHOLE No. 197)

LIEUTENANT ELLERY W. STONE, U. S. N. R. F.—While Lieut. Commander Anderson's purpose in presenting an elementary paper on alternating current is an excellent one, several statements are made in his article which may bear criticism. They will be taken up successively below.

In Note 5, Mr. Anderson regrets the lack of text books which avoid the use of calculus in the presentation of the elements of alternating current. His attention is invited to the treatise on alternating current in Book Four of the Hawkins Electrical Series and to Part Two of Sheldon-Hausmann's "Dynamo Electric Machinery" in both of which lie will find the matter presented in simple and lucid style.

On page 1173 of his article, he defines high frequency as being frequencies in excess of 100,000 cycles. From this, are we justified in assuming that a current of 50,000 cycles is of low frequency? As a matter of fact, the terms "high" and "low" can only be used relatively, and certainly may not be employed to draw a sharp and definite line' of demarcation between currents of different frequencies. When quenched gap sets using 500 cycles were first introduced into this country they were often termed, and quite properly so, "high frequency" transmitters in contradistinction to the 600-cycle sets previously in use. Yet Mr. Anderson's definition would place all frequencies less than 100,000 cycles in the realm of low frequencies.

On page 1194, he correctly states that when a tone is of more than 20,000 vibrations per second it is inaudible, yet on page 1174 in his definitions of radio and audio frequencies he makes 20,000 *cycles* the upper limit of audibility. Since each cycle of alternating current produces two clicks of a telephone receiver, *i. e.,* one for each alternation, it will be seen that his second value is twice the first, for a current of 20,000 cycles will sound a pitch of 40,000 in a receiver. In radio engineering, it is customary to make 10,000 cycles—20,000 alternations—the dividing line between radio and audio frequencies.

On page 1175, the statement is made that there are two conceptions of the electro-magnetic induction of potentials but the distinction between the two is erroneously drawn. The two illustrations given are identical. There is but one requirement for the generation of electric potentials by electro-magnetic means and that is that there be relative motion between a conductor and the lines of magnetic force about it. The turns of the secondary of a transformer are cut by the expanding and collapsing lines of force due to the alternating current in its primary quite as effectively as are the armature coils of a generator by the flux of its fields. If there are two conceptions, we should expect to find two fundamental formulæ for the generation of potentials but there is, of course, but one—applicable alike to generators and transformers.

The "sine" curves shown in Figs. 2 and 9 are not sine curves but series of straight lines joined at their extremities by curves. A table of natural sines will show that a straight line variation of the sines of angles of widely different sizes does not obtain.

In the first paragraph on page 1190, the statement is made that reactance depends upon the frequency of the current, for it increases with the rate of change of current. This should be qualified to show that it is inductive reactance to which the author alludes, for condensive reactance decreases in value for increase in frequency. Further on in the same paragraph, Mr. Anderson states that "as the rotor gets up to speed and the frequency becomes less, more currents are sent through the low resistance winding.” This would seem to indicate that two resistance windings are supplied, one of low and one of high resistance, whereas, as stated in the beginning of the paragraph, but one resistance winding is supplied. "Impedance" should be substituted for "resistance" in this sentence. To be correct, this paragraph should be written as follows:

"The double squirrel cage has two windings that parallel each other but are not connected. One is high resistance, the other is high inductance. The reactance, and hence impedance, of an inductance depends upon the frequency of the current, for it increases with the rate of change of current. Therefore at starting, the frequency being the greatest; there will be a maximum impedance of the inductive winding with the result that most of the currrent will flow through the resistance coil due to its lower impedance. As the rotor gets up to speed and the frequency becomes less, the decreasing reactance of the inductance will cause its impedance to become very much less than that of the resistance winding, so that practically all of the current will flow through the inductance. In this type of rotor, then, the insertion of starting resistance is automatic."

In Fig. 11, the customary resistance in series with the arc and generator has been omitted. If connected as shown, the generator would be practically short circuited by the arc, as the resistance of the blow-out magnets, which are wound with heavy copper wire, is not great enough to sufficiently limit the arc current. This resistance is often called the "ballast," which term Mr. Anderson appears to have applied to the ground.

In the first paragraph on page 1195, the statement is made that each wave train as it comes in gives one impulse. If this be true, it is not clear why the current must be *rectified *in order to make one click of the telephone diaphragm from one impulse of incoming signal current. Actually, the frequency of the incoming current is inaudible and is determined by its wave length. This holds true whether the waves be damped or undamped. The wave train is rectified in order to charge a condenser with recurring direct current impulses at radio frequency, just as alternating current must be rectified in order to charge a storage battery. The summation of these unidirectional charges is discharged once per wave train into the telephone receivers, but it should be noted that the change from radio to audio frequency occurs after rectification—not before. The number of discharges of the condenser per wave train is unity, the number of charges per wave train is equal to the number of waves in the train which depends on the damping or logarithmic decrement, while the *rate* of charge of the condenser depends on the frequency.

If the same method of reception were applied to undamped as to damped waves, we should have one click of the telephone receiver for each depression of the transmitter key since one wave train is radiated for each dot and dash sent. Accordingly, as stated by Mr. Anderson, beat reception is necessary for receiving undamped waves.

**Trajectories and Their Corrections**

(SEE PAGE 1375, WHOLE No. 198)

COMMANDER E. F. EGGERT.-In this article the author refers so frequently to my article on a similar subject, making comparisons between the method described therein and one by Professor Moulton, that he imputes to my article a purpose quite foreign to it. It seems therefore fair that I should endeavor to place my article in its proper relation to ballistics.

It happened that the Board of Control followed my article by a special statement, generally to the effect that during the war it had been obliged to publish practically any material received, however worthless. I should regret it very much if my article could not rise above that mediocre plane, but perhaps that is where it belongs; nevertheless, when general condemnations are being passed around, one always hopes that perhaps after all the other fellow was meant.

Since the present article draws in my method as a proving-ground method, it is only just to me to show how the method came to originate, and what its purpose was. Had time and opportunity permitted, no doubt the method could have been developed for proving ground use also, but such was not its original purpose.

A few years ago, being interested in inclined armor protection, I obtained a copy of the Bureau of Ordnance range table for the 16”/45 gun intended for the *Maryland,* the first type to mount guns to give 30° elevation. To determine still greater ranges than this table contained, I plotted and endeavored to exterpolate the results, only to find that the curve was very flat at the end, an evidently impossible result. The range table was wrong, and the information therefore of no use to me for design purposes.

I had done no ballistic work since my Naval Academy days, and did not know whether the methods then taught were still in use. I obtained therefore a copy of Alger's latest work for the Academy, and found that the 16-inch range table was indeed made by the old Alger method.

What I wanted to know was whether the 16-inch gun was really much superior to the 14-inch gun at a given long range, what the approximate difference in range, for a given elevation was, and what were the final velocities and angles of fall; it was only such general questions I wanted answered, and not questions of difference in range due to a variation from standard conditions.

Being fairly familiar with mechanical integration, from study in other directions, I began to apply it to this subject, since the difficulty in integration was the chief trouble with the Alger method. It took considerable time to get far enough to use it, since the subject was nothing more than a means of amusement in my idle hours, and, moreover, one stationed here is fairly out of the world, and thrown entirely on his own resources: The new method gradually came to a working basis, however. Then many months elapsed before I had computed, and often recomputed, enough trajectories to answer my immediate purpose. I was then so struck by the great amount of the correction necessary in the Alger method, that I determined to publish the results, more to indicate the possibilities of mechanical integration, and to call attention to the great errors in the old method, than to claim finality of precision.

My own method having now been put in its proper place, it might be permissible to say a few things in criticism of the other method, even though it was developed by a professional astronomer, of long experience, and with a large staff, unlimited time, and great experimental facilities available.

To begin with, the Moulton method is distinct from the Bliss sequel, and the former accomplishes only the same thing that my own does. It is in fact identical with it in most details. The chief difference is in the use of second differences, which I neglect. The effect of these is, however, easily determined by a short subsequent correction, if needed, but for most purposes the difference can be neglected.

That I used Mayevski's equations in my article has no bearing on the method. It was the latest information the navy had at the time my article was prepared. Whether the present accepted resistance results are more precise has yet to be proved, but at any rate the difference is not very much.

To revert to the example shown by Lieut. Commander Kirk, which is the same trajectory as given in my article, I have recomputed this, using the new resistance tables, with the following results:

Method Range

Siacci 20,000

Eggert, original 19,931

Moulton 19,910

Eggert, new tables 19,949

These are all uncorrected for *?R,* and it appears that the difference in the range, due to the difference in the tables, is 18 yards.

Lieut. Commander Kirk has neglected to correct his range for variation in the amount of *g*. The actual mean value of *g* in this trajectory is 32.151, but he has used a uniform value of 32.185. The difference accounts for a variation of range of 18 yards, to be added to his value, making it 19,928 yards.

Correction for second differences shows that in this case the range is increased by less than a yard. The remaining difference between the ranges, as given by the two methods, is then 21 yards, and it is due to accidental errors of calculation, probably caused by small differences in the tables.

The author, on page 1384, states that with so large a ballistic coefficient, and at so short a range, there would not be much variation between the two methods. We have usually to deal with such large coefficients, but, when we calculate trajectories for small-arms projectiles, then, as I had already stated, a shorter interval than one second may be necessary. As regards the short range, it need only be said that, for one-second interval, the second difference correction is but eight yards at 37,000 yards' range.

Comparing the two methods, it can easily be maintained that the Moulton method is by far the more cumbersome. It would be conservative to say that it takes twice as long as the other. The apparent precision is hardly worth while, since we all know that, after making all possible corrections, we still have a mean dispersion in range, on actual firing, of from 40 to 80 yards, and we know also that actual measurements of ranges, when made by different methods, vary by 10 to 20 yards. The small integration error is swallowed up in this much larger error in firing, and of course the actual error of any one round may be much larger.

Now as regards the Bliss sequel to the Moulton method. This is a calculation to obtain differential equations, to correct the trajectory, and for proving-ground purposes something of the kind is desirable. As stated by the author, however, the calculation is as long as that of the original trajectory, and as it is of an entirely different character, and requires a new form, it is an awkward complication.

Most of the variables can be corrected, as I have indicated in my article, by a simple equation of the form, *s=½at ^{2}*, where

*s*is the correction in

*X*or

*Y*, due to a change a in the given variable, for the time of flight

*t*. This correction can be determined in a minute, with a slide rule. In this way there would be handled changes in diameter or weight of projectile, in coefficient of form, in density of air, in gravity, or in resistance of air, the mean change in these cases being used.

Changes in range, due to variation in angle of elevation, are readily handled, as in the oldest method, on the principle of the rigidity of the trajectory.

Except for wind effect, this leaves only change in initial velocity to consider. There is no way of correcting for this, by my method, except by recalculation of the trajectory, with a new velocity. To do this, however, requires only one recalculation, and the two calculations will take not more than as much time as is required by the Moulton method for the original trajectory, besides being a check on each other, and a new form, with its distinct method, is avoided.

Coming to wind effect, although the Bliss method includes a correction for wind, the correctness of the principles involved is in my opinion much in doubt, and the results are open to question. We are still far from knowing the effect of the wind, and we still have much to learn by experiment. Much of what has been assumed the effect of wind is undoubtedly drift, and until we can make projectiles that are and remain dynamically balanced on their axes, and that rotate in exactly the same way, we cannot hope to solve satisfactorily the question of either wind or drift, which are closely related.

To return to the question of time required in my method, it should be noted that in the last paragraph of the body of my article I referred to the use of an interval of two seconds for ordinary large-caliber trajectories. This is really the best interval, and, for the 20,000-yard trajectory illustrated, takes up but half the space shown, and half the time. It can be corrected, just as for a one-second interval, for integration error, so as to give the same precision, and thus is both easy and accurate.

The correction referred to, for second differences, is carried out as indicated below. Taking as example the first integration, that of *r _{h}*, it appears that we have neglected to subtract in each case one-twelfth the second difference. The last value of

*V*should therefore have

_{h}*added*to it one-twelfth the summation of all the second differences in the

*r*column, multiplied by the interval, in this case unity. This summation is nothing but the arithmetical difference between the first and last first differences in this column. In the example in my article, the first of these first differences in 4.1, and the last is .2. The difference 3.9, divided by 12, or .3, should be added to the last value of

_{h}*V*. The effect of this error in

_{h}*V*on

_{h}*X,*is found by multiplying by half the time of flight, since half the error can be taken as the mean error in the velocity, and the resulting correction in

*X*is +4.8 feet.

The correction of the integration in the *V _{h} *column is effected in the same way. The first of the first differences is 63.4, and the last is 23.0. One-twelfth the difference is 3.3, which is the effect on

*X*, and must be subtracted. The total of these two corrections is +1.5 feet.

In the same way the effect on *Y* is determined. We find the mean error in *V _{v},* from their

*r*column, and the integration error of the

_{v}*V*column. The first is +.05, causing an error of 1.6 feet in

_{v}*Y*. and the second is —1.8, or a net reduction of the last value of

*Y*or .2 foot. This is multiplied by cotan.

*w*to get the corresponding error in

*X*, which is —.6 foot.

We find therefore that the error in *X* is composed of an error of +1.5 feet due to the *X *integration, and of an error of —.6 foot due to the* Y* integration, or a final correcion in *X* of +.9 foot. It should be noted that the variations in velocity are not great enough to cause secondary corrections in *r*.

When the interval is two seconds, the method is similar, proper use being made of the interval.

In discussing precision of calculation, the precision of measurement must be a guide, and there is no use in carrying precision farther in calculation than in measurement. Since the error of measurement is greater than these errors of integration, for a one-second interval, with ordinary large projectiles, there is not much gained by applying the correction. There is besides some uncertainty in the basic tables, and it is well known that the coefficient of form is not a constant.

Since receiving the new tables of air resistance and air density, I have changed that part of my method which requires curves of these values, and have computed convenient tables of these values. All this material is arranged on the two adjoining pages of a notebook, for values of *r* from zero to the resistance at 6000 foot-seconds, and for values of the density to a height much beyond my present requirements. These tables accelerate the work considerably. Their place, in the Moulton method, is taken by tables covering 12 pages, to give a precision that is entirely useless. This will indicate how cumbersome the method is.

**Opposition to Sane Sport in American Colleges**

(SEE PAGE 1369, WHOLE No. 198)

LIEUT. COMMANDER K. C. MCINTOSH (S. C.), U. S. Navy.—Mr. Frank Angell opens his argument with the following: "My point is that this grinding drill takes out of a sport its essential element, which is the enjoyment of the player. . . . .”

There is no sport of any kind which has come under my notice in which anything approaching success may be attained without "grinding drill" of a more or less monotonous character. There is certainly no sport which has a greater individual element therein than golf, and no sport which gives the player greater freedom to stop when he is tired or disgusted or out of temper. Golf is not learned by playing matches, and of all the unenjoyable performances in the world, standing at a tee and driving one ball after another for a caddie to chase and bring back, swinging hour after hour in the hope of eliminating that exasperating slice, is about the most disheartening. Any modern game from beginning to end is *work.* Its value to the individual is not in the enjoyment or fun he gets out of every minute spent on it, but in the discipline, mental and physical and psychological.

My football experience began while the "flying wedge" was still the accepted method of putting the ball in play, and continued with few breaks until the first .year of the forward pass. The bulk of it was done in the "guards back" and "tackles back" days. During this period my weight gradually increased from 110 pounds to a triumphant 135. Many and many a night during football season have I wept into my pillow from sheer discouragement and the pain of my bruises; many and many a day my knees have knocked together as I trotted out of the gym, thinking of the many times I was about to run in to take the place of my drawn-back tackle and in some desperate manner hold two men in their places till the half-back was clear, each man weighing from 50 to 80 pounds more than I. The pleasure I derived from it then was non-existent. But aside from the fact, brought out by Commander Taylor, that the rigid training of those eight years has left me under the necessity of careful exercise to avoid gout and muscle-binding, there is nothing in my entire school and college course which has been of so much use to me. I do not mean that the plaudits of the multitude ever paid me for my trouble, for if anybody ever called for a "long yell with three Mc's on it" I was too busy or too stunned to hear it. But in that grinding drill and hard punishment, I got a pretty fair grounding in the first necessity of success in any line—perseverance and subordination.

I agree heartily with Mr. Angell's stand against commercialism, but I do not agree with him in his belief that varsity teams and big games are undesirable. They are the best that a college has to offer in the way of general training for making one's way in the world, and Commander Taylor's objection to overtraining is being slowly recognized and met by a system of college physicians whose business is to see that no boy is driven to the danger point.

"Big games" are good for the college and good for the boys. .They must remain unless we want to go backward. The answer apparent to my mind is to have athletics endowed in the same manner as Greek or Biology, and an intercollegiate agreement on a maximum salary for coaches.

Mr. Angell repeats the fallacy of the "premium on weight as against dexterity." Weight has been and continues at a premium because of the absence of dexterity. There are many big men in the aristocracy of football, but they all got there by dexterity. But where is the big man whose game outshines that of Frank Hinkey (133 pounds), McBride of Yale (145), Johnny Hart (130), Arthur Poe (148), or Daly in his Harvard days? The University of Minnesota once put out a mammoth team, the "little man" of which—who is now Commander Hancock, S. C., by the way—weighed 185 pounds. Herschberger of Chicago and Pat O'dea of Michigan had no great difficulty in piloting lighter teams through them. Eckersall, Ristine, "Biscuit" Howard, Bullock, "Cracky" Dague—does anyone know any big men who could outshine them at any stage of the game?

It is to be regretted that more colleges have not followed the lead of Amherst and provided large fields for scrub games of all sorts, with room for five or six games going on at once. It is still more regrettable that more colleges do not follow the Naval Academy system of making each student pick at least one sport and go in for it to a prescribed minimum. But do not damn the big game. Without it, there would be no minor games with any educational value and very little to be gained physically which could not just as well be gained with the exciting dumbbells or the thrilling Indian clubs. The training in keeping one's temper, in merging one's entire strength into the team, in the suppression of self-seeking and loyality to the college—which is the beginning of loyalty to the firm or the navy or to America—the psychology of playing till you drop because the Idea needs you no matter how battered you are—all these depend on the big game. Not necessarily on making the varsity and playing in it, but in driving oneself to unsuspected limits in trying to make good enough to get there, and in heartily cheering your head off for the fellow who got your place away from you by superior playing. Baseball players call it "heart"; bluejackets call it "guts," generals and admirals call it "morale," but we've got to have it; and very few boys ever wore padded moleskin without finding it. Nobody ever made a varsity team who did not have it. A game that does not call for considerable sacrifice of comfort or pleasure may build up a few muscles, but will do nothing towards making men.