As I told you, I have no objection to your making a few pounds by doing minor calculations for the Army, but this is foolishness. You have gone to a great deal of trouble for nothing; as you gain more experience, you will realize the folly of such things.
As to your theory of "fluxions," I admit myself to be completely at a loss. You seem to be a.s.suming that a curve is made up of an infinite number of infinitely small lines. Where is your authority for such a statement? You append no bibliography and no references, and I cannot find it in the literature.
Apparently, you are attempting to handle zero and infinity as though they were arithmetical ent.i.ties.
Where did you learn such nonsense?
My boy, please keep it in mind that four years of undergraduate work does not qualify one as a mathematician. It is merely the first stepping stone on the way. You have a great deal of studying yet to do, a great many books yet to read and absorbbooks, I may say, written by men older, wiser, and more learned than yourself.
Please don"t waste your time with such frivolous nonsense as toying with symbols derived from wine barrels. No good can come out of a wine barrel, my boy.
I hope you will soon find yourself in a position to aid"me in some of the calculations on conic sections as I outlined them to you in my letter of the 28th December last.* I feel that this is important work and will do a great deal to further your career.
With all best wishes, Sincerely, Isaac Barrow
*This letter was either lost or returned to Dr. Barrow.-S.H.
5 January 1667 London
Dear Mr. Newton: Thank you for your tabulations on the seven-pounder. I must say you were very prompt in yourwork; there was no need to work over the holidays.
Your questions show that you are unacquainted with the difficulties of manufacturing military arms; I am not at all surprised at this, because it takes years of training and practical experience in order to learn how to handle the various problems that come up. It is something that no university or college can teach, nor can it be learned from books; only experience in the field can teach it, and you have had none of that.
I can, however, explain our method of approach thus: Each cannon to be tested is fired with several b.a.l.l.s-some of iron, some of lead, some of bra.s.s, and some which have been hollowed out to make room for a charge of gunpowder in order that they may explode upon reaching the target. With each type of ball, we find the amount of powder required to drive the ball five yards from the muzzle of the piece; this is considered the minimum range. (Naturally, with the testing of hollow, explosive missiles, we do not fill them with gunpowder, but with common earth of equal weight. To do otherwise would endanger the cannoneer.) After the minimum range is found, more b.a.l.l.s are fired, using greater amounts of powder, added in carefully measured increments, and the distance achieved is measured off.
This process is kept up until the safety limit of the weapon is reached; this point is considered the maximum range.
Naturally, the weights of different b.a.l.l.s will vary, even if they are made of the same metal, and the bores of cannon .will vary, too, but that can"t be helped. What would you have us do? Make all cannon identical to the nearest quarter-inch? It would not be at all practical.
I am happy to see that you are enthusiastic over the work we are doing, but please, I beg you, wait until you have learned a great deal more about the problem than you have done before you attempt to make suggestions of such a nature.
As to the paper which you enclosed with your tabulations, I am afraid that it was of little interest to me. I am a military man, not a mathematician.
Thanking you again for your excellent work, I remain.
Yours sincerely, Edward Ballister-ffoulkes, Bart.
9 January 1667 Cambridge
My dear Isaac, I have known you for more than five years, and I have, I might say, a more than parental interest in you and your career. Therefore, I feel it my duty to point out to you once again that your erratic temper will one day do you great harm unless you learn to curb it.
You take me to task for saying to you what is most certainly true, viz.: that you are not yet a mathematician in the full sense of the word. You are young yet. When you have put in as many years at study as I have, you will understand how little you now know. Youth is inclined to be impetuous, to rush in, as the saying goes, where angels fear to tread. But better men than yourself have come to realise that the brashness of youth is no subst.i.tute for the wisdom of maturity.
As to your other remarks, you know perfectly well what I meant when I said that no good can come out of a wine barrel. To accuse me of sacrilege and blasphemy is ridiculous. You are twisting my words.
Please let us have no more of this name-calling, and get down to more important work.
Sincerely, Isaac Barrow
12 January 1667 London
Dear Mr. Newton: Thank you again for your rapid work in tabulating our results. It is most gratifying to find a young man with such zeal for his work.
As I have said before, I am no mathematician, but I must confess that your explanation makes very little more sense to me than your original mathematical formulae.
As I understand it, you are proposing a set of equations which will show the range of any weapon by computing the weight of the ball against the weight of the powder. (Perhaps I err here, but that is my understanding.) It seems to me that you are building a castle-in-Spain on rather insubstantial ground.
Where is your data? What research have you done on cannon-fire? Without a considerable body of facts to work with, such broad generalisations as you propose are quite out of order.
Even if such a thing could be done-which, pardon me, I take the liberty to doubt-1 fear it would be impractical. I realise that you know nothing of military problems, so I must point out to you that our cannoneers are enlisted men-untutored, rough soldiers, not educated gentlemen. Many of them cannot read, much less compute abtruse geometrical formulae. It will be difficult enough to teach them to use the range tables when we complete them.
Indeed, I may say that this last point is one of the many stumbling-blocks in the path of our project.
More than one of the staff at the War Office has considered it to be insurmountable, and many times I have fought for the continuance of research in the face of great opposition.
I greatly fear that using any but methods known to be practicable would result in our appropriation being cut off in Parliament.
Again, however, I thank you for your interest.
Most sincerely, Ballister-ffoulkes
24 January 1667 Cambridge
My dear Isaac, I am truly sorry I didn"t get around to looking over your second ma.n.u.script until now, but, to be perfectly truthful, I have been outlining our course of work on conic sections, and had little time for it.
As it turns out, it was all for the best that I did so; it would have been sinful to take valuable time away from my work for such trivialities.
You are still harping on your wine-barrel fluxions and your Army cannon b.a.l.l.s. Am I to presume that the whole thing is a joke? Or are you seriously proposing that the path of a cannon ball is related to the moon? That is rank superst.i.tion! Sheer magic! One would think that even a lad as young as yourself would have grasped the basic concept of the Scientific Method by this time.
How have you tested this absurd thing experimentally? Where are your measurements, your data?
Your references?
Do not think, my boy, that fame and fortune in the sciences can be achieved by pulling wild hypotheses out of your imagination. There is no short-cut to mastery of a difficult subject like mathematics; it requires years of hard work and study.
As an example of what can happen when one has not learned enough of the subject, look at your own work. You appear to be handling Time as though it were a spatial dimension. You even end up, in several equations, with square seconds! Now, a yardstick will show that a foot up-and-down is the same as a foot East-and-West or a foot North-and-South. But where can you find a foot of time?
Please, dear boy, use your time to study the things you have yet to learn; don"t waste it exploring anonsensical cul-de-sac.
I will send you the outline on conic sections within the week.
Sincerely, Isaac Barrow
1 February 1667 London
Dear Mr. Newton: In reference to your letter of 14 January 1667, on the simplified algebraic formulae for the prediction of the paths of cannon b.a.l.l.s, our staff has considered the matter and found that not only is your mathematics incomprehensibly confusing, but the results are highly inaccurate. Where, may I ask, did you get such data as that? .On what experimental evidence do you base your deductions? The actual data we have on hand are not at all in agreement with your computations.
Men with more experience than yours, sir, have been working on this problem for several years, and nothing in our results suggests anything like what you put forth. Finding data is a matter of hard work and observation, not of sitting back in one"s armchair and letting one"s mind wander.
It would, indeed, be gratifying if our cannon would shoot as far as your equations say they should-but they do not. I am afraid we shall have to depend on our test results rather than on your theories. It is fact-not fancy-which is required in dealing with military operations.
Sincerely, Edward Ballister-ffoulkes, Bart.
General, Army Artillery
3 February 1667 Cambridge
My dear Isaac: I feel it would clear the air all round if we came to an understanding on this thing. Your continued insistence that I pay attention to theories which have no corroboration in the literature and are based on, to say the least, insufficient confirmatory data, is becoming tedious. Permit me, as a friend, to show you where, in your youthful impetuosity, you err.
In the first place, your contention that there is a similarity between the path of a cannon ball and the moon is patently ridiculous. I cannot imagine where you obtained such erroneous information. A cannon ball, when fired, strikes the earth within seconds; the moon, as anyone knows, has been in the sky since-according to Bishop Ussher-4004 B.C. Your contention that it remains held up by a force which pulls it down is verbal nonsense. Such a statement is semantically nothing but pure noise.
You state that the path followed by a cannon ball is parabolic in nature. How do you know? Can you honestly say that you have measured the path of a cannon ball? Have you traced its path, measured it, and a.n.a.lysed it mathematically? Can you prove a.n.a.lytically that it is not an hyperbola or part of an ellipse? Have you any data whatsoever to back up your statements, or any authority to which you can refer?
You make broad generalisations on the a.s.sumption that "every body is attracted equally to every other body;" that the earth attracts the moon in the same way that it attracts an apple or a cannon ball.
Where is your data? You have not, I dare say, measured the attraction between every body in the universe. Have you checked the variations in apples according to sugar content or the variations in cannon b.a.l.l.s with reference to their diameters? If not, have you checked with any reliable authority to see if such work has already been done? And where did you learn that anyone can just sit down and make up one"s own mathematical systems? I am certain that I taught you no such thing. Mathematics, my boy, is based on logical interpretation of known facts. One cannot just go off halfc.o.c.ked and make up one"s own system. What would happen to mathematics as a science if anyone should just arbitrarily decide that two added to two yields five or that two multiplied by two equals one hundred?
You said that the whole thing came to you loin a flash" last summer when you were sitting under an apple tree and one of the fruit fell and struck you on the head. I suggest that you see a good physician; blows on the head often have queer effects.
If you have the data to prove your contentions, and can show how your postulates were logically deduced; then I will be very happy to discuss the problem with you.
As soon as you feel better, and are in a more reasonable frame of mind, I hope you will return to Cambridge and continue with the studies which you so badly need.
Sincerely, Dr. Isaac Barrow
P.S.: It occurs to me that you may have meant your whole scheme as some sort of straight-faced pseudo-scientific joke, similar to that of another gentleman who bears our common Christian name.* If so, I fail to comprehend it, but if you would be so kind as to explain it to me, I will be only too happy to apologise for anything I have said.
Is. Barrow
*I have no idea who this might be. The reference is as obscure as the joke.-S.H.
8 February 1667 London
Dear Mr. Newton: I have tried to be patient with you, but your last letter was sulphurous beyond all reason. I may not, as you intimate, be qualified to judge the mathematical worth of your theories, but I can and do feel qualified to judge their practical worth.
For instance, you claim that the reason your computations did not tally with the data obtained from actual tests was that the cannon ball was flying through the air instead of a vacuum. By whose authority do you claim it would act thus-and-so in a vacuum? Do you have any data to substantiate your claim?
Have you ever fired a cannon in a vacuum? For that matter have you ever fired a cannon?
What would you have our cannoneers do-use a giant-sized Von Guericke Air Pump to evacuate the s.p.a.ce between the cannon and the target? I fear this would be, to say the very least, somewhat impractical and even dangerous under battle conditions. I presume a tube of some kind would have to be built between the enemy target and the gun emplacement, and I dare say that by that time the enemy would become suspicious and move the target.
You speak of "ideal conditions." My dear Newton, kindly keep it in mind that battles are never fought under ideal conditions; if they were, we should always win them.