[別館]球面倶楽部零八式markIISR

東大入試数学中心。解説なので解答としては不十分。出題年度で並ぶようにしている。大人の解法やうまい解法は極めて主観的に決めている。

1924年(大正13年)東京帝國大學理學部(物理科、化學科)英文和譯

[1] The whole habit of making excuses is the relic of a time of moral slavery, when the first object of any man who had done wrong was to try to prove to somebody else that he had not done wrong. If a man is his own master, the thing for him to do is to find out exactly what he has done, in order to avoid making the same mistake again. In the curiously candid account of his own military achievements which Frederick the Great has left us he says, in substance, summing up one of his earlier campaigns: ``The king during these weeks committed almost every fault to which a general is liable. The conduct of his adversary shines out by contrast, and deserves the careful attention of all students of military art. The king himself has many times told me'' — so runs the quaintly impersonal language of the narrative — "that if ever during his later campaigns it has fallen to his lot to achieve any considerable success, it was largely due to the seriousness with which he pondered the lessons derived from a comparison of his own conduct and that of his adversary in this campaign."

[2] Huxley's comparison of mathematics to a mill, which only gives out in another form what was put into it, is often quoted. At the same time we must not forget that this new form is much more useful than the original one. As Arrhenius points out the expression of experimental results in a formula shows their relation to known laws in a way which is otherwise very difficult or impossible to attain. One is enabled to see whether all the factors have been taken into account and even an empirical formula may assist in deciding whether irregularities are due merely to experimental error or to some unsuspected real phenomenon in the process.


2019.04.12

[1] Jelliffe, Robert Archibald, A handbook of exposition, p.41
(Arthur Twining Hadley, Moral Lessons of Collage Life)
A handbook of exposition : Jelliffe, Robert Archibald, 1883- : Free Download, Borrow, and Streaming : Internet Archive

参考書の解答。

[1] 言ひ譯をするのは道徳の奴隷時代の名殘である、其の時代には誰か一人悪いことをする第一目的は、他の一人に自分は悪いことはしなかつたと證明することであつた。若し一人の人が主人だつたなら、二度と同じ誤をしない樣に、自分のやつたことを正確に見付けることであつた。フリートリツヒ大王が私どもに殘した軍事上の功績の彼としては不思議に公明なる説明中に言つて居る。「自分の初期の戰爭の一つは要するに實際は殆ど一将軍が犯し易い失敗を皆やつたのだ。彼の反對の行爲はくつきりと輝き出して、戦術に從事する皆の學生の周密なる注意を要求して居る。王地震屡々私に継げられたと---不思議にも非人稱の物語で書いて---若しも後年の戰爭に一つでも大きい成功を擔ひ得る運命が落ちて來たとするならば、そは大體に於いて此の初期の戰爭に於ける自分の行動と敵の行動とを比較して得た教訓を、よく考慮して見た眞面目に歸せなければならない。

[2] ハツクスレーが數學を水車に比べ、入れられたものが外の形になつて出て來るんだとは度々引用される。それと共に忘れてならんのは、此の新しい形となつたものは、元のものよりも遙かに役に立つことである。アルケニウスは指摘して居るやうに、實驗的結果の公式説明は、此の證明でなければ大變に困難であり、或は達し得ない道にある既知の法則との相互關係を示して居る。私どもは總べての因子が説明されたか、而して一經驗的公式さへも、弦則に合わない事柄が、單に實驗的の過失か或は實驗過程中の疑ふことの出來ぬ現象であるかを、決定する助けとなるかも知れないことを見ることが出來る。