Part 2 (1/2)

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