deposed Euclid from his pinnacle of correctness. It was thought until recent times, that, as Sir Henry Savile remarked in 1621, there were only two blemishes in Euclid, the theory of parallels and the theory of proportion. It is now known that these are almost the only points in which Euclid is free from blemish. Countless errors are involved in his first eight propositions. That is to say, not only is it doubtful whether his axioms are true, which is a comparatively trivial matter, but it is certain that his propositions do not follow from the axioms which he enunciates. A vastly greater number of axioms, which Euclid unconsciously employs, are required for the proof of his propositions. Even in the first proposition of all, where he constructs an equilateral triangle on a given base, he uses two circles which are assumed to intersect. But no explicit axiom assures us that they do so, and in some kinds of spaces they do not always intersect. It is quite doubtful whether our space belongs to one of these kinds or not. Thus Euclid fails entirely to prove his point in the very first proposition. As he is certainly not an easy author, and is terribly long-winded, he has no longer any but an historical interest. Under these circumstances, it is nothing less than a scandal that he should still be taught to boys in England. A book should either have intelligibility or correctness; to combine the two is possible, but to lack both is to be unworthy of such a place as Euclid has occupied in education.'

"A note was added in 1917:

"Since the above was written, he has ceased to be used as a text-book. But I fear many of the books now used are so bad that the change is no great improvement.'

"I am more than glad that I never attempted to learn these first eight propositions of Euclid. It was not considered a suitable study for young ladies by early Victorian educationists, though I never heard of the correctness of his propositions being questioned by even the most advanced don at either of the Universities." *

Apart from actual learning and accomplishments my moral and ethical training was founded chiefly on Miss Edgeworth. It was a very fascinating coincidence that she had written a book

* "Recollections of Lady Georgiana Peel."

called "Frank," and I naturally read it with avidity, and had my attention called to the many and detailed prohibitions and instructions for the young to be found in that volume and in Edge

worth's "Early Moral Lessons." As to the sanctions I suppose

both my father and mother were unbelievers at this time. Certainly I never recollect hearing of God or being bothered with the theory of divine rewards and punishments. If living in conformity with the supposed laws of an imaginary deity and doing or not doing things because they were pleasing him was no part of my training or of the sanctions put before me, neither were the lesser, more changeable, and less ultimately defensible sanctions of doing things because they were pleasing to father or mother used as a motive. I do not mean to say that my parents were so unnatural as never to make use of the ordinary expressions of approval or disapproval, but I do mean that never, absolutely never, was "do this to please mother " or " father orders it " offered as a sufficient motive for any action on my part. I can scarcely think that I was ever taught anything like a full ethical code of moralities or duty to the community as an incentive because I think if I had been I should still remember something of it, but I do not doubt that the exhortations addressed to me were based upon a general rather than a personal view. Nor was this general view merely the code that such things were not done or that such and such actions were not becoming to a gentleman, but it was always reasoned. I didn't tell lies as far as I can recollect because my people succeeded somehow in implanting in me a distaste for telling lies and a dislike for the sort of people who told lies, but I know they gave me no theological reasons for this. Nor do I remember any definite ethical ones, probably because they were of so simple a character as to be adapted to my young understanding, and I am quite sure that it was not put on the basis of ultimate personal profit. The great Maria was a very suitable coadjutor for my parents, because she also makes no reference to divine sanctions, but relies solely on moral considerations. I shall never forget the intense shock I received at my private school when having got hold of a novel called "Helen," by Miss Edgeworth, it was confiscated by the headmaster on the ground that it was an improper book for me to read. Maria, the friend of my youth-Maria, the severe preceptor-capable of writing an improper book! the thought was annihilating. No doubt in later years my regard for Maria Edgeworth would have been increased by this circumstance, but at

that time and in the priggishness of youth, it gravely diminished her glory.

I probably had some more advanced training in self-control and self-discipline, for at a later stage I remember reading Rousseau's "Emile" aloud with my father and mother, probably when I was a little over eight, but I think it must have been in an English translation. How much I understood of that remarkable book I should hesitate now to say. Among my earlier lessons on punishments and self-control perhaps the greatest impression was made upon me by the story of Rosamund and the Purple Jar which has remained clearly before my mind ever since. I cannot have been the unendurable prig that I sound like, for I distinctly remember that I used to steal apples from the orchards of the farmers round about, and was duly beaten when discovered. I don't know that my truthfulness extended to making a voluntary confession although it did to not telling lies about it. I expect I stole jam on occasion, but all I recollect of this sort is helping myself to my father's medicine of which he took about six drops at a time. As it contained arsenic it is perhaps fortunate that I am still alive to tell the tale. My Aunt Maude also has told me since that I was a very naughty boy, while my grandmother Stanley whom I dearly loved, told me that I was an unwashed, ill-bred, impertinent little child dressed in rags. It would appear therefore that the education which so entirely satisfied my parents and myself and is so agreeable in the retrospect, was not equally pleasing to the conventional when they were brought into contact with its results.

As an illustration of my parents' methods I will relate the episode of the treacle. As a matter of education and experience I was told on my seventh birthday that I might do exactly as I liked all day. What I did like was to throw myself upon my pony, ride to the village of Trelleck a mile away, and purchase from the grocer with my own money a quantity of treacle. I carried this home and continued to consume it with a spoon until the stage of repletion was passed, and by the afternoon after some discomfort, the final stage of regurgitation per os was reached. Thus early was firmly impressed upon my youthful mind that there were natural laws quite apart from the commands of parents which no one could disobey with impunity, however great his measure of freedom. appeared to be. Incidentally I have never been able to endure treacle from that day to this.

I have been told that I had a very naughty and passionate

temper when I was a small boy, but I don't remember this. I had some kind of brain illness as a result of which the doctor gave orders that I was not to be overworked, and not to be contradicted, according to what my Aunt Maude told me later, and this possibly helped to develop obstinacy and naughtiness. I remember one occasion when my father beat me on my bare flesh with the prickly side of a hair brush, which looks as if I must have been very naughty.

A

CHAPTER IV

TRAGEDY

T some date which I am not able to fix, but it must have been when I was about seven and a half, there entered into our life a man called Robert Spalding. I do not know who he was, but I think a student of some Scotch university of scientific attainments, and I believe it was Sanderson who brought him to the notice of my parents. His nominal position was that of tutor to me, but he also became the friend and confidant of the household, and exercised a sinister influence over it. My first very definite recollection of him is at the age of about eight when we spent some weeks or months alone together at a farm house on the river Dee. I suppose that we did lessons, but the only recollections that survive definitely are of his scientific experiments. One was to cut the heart out of a freshly killed salmon and stand it by itself on a dish, when it continued to beat for an incredible time-my impression is more than twenty-four hours. The other was to take eggs which were just hatched, and see how soon the chicks began to pick up crumbs and feed; the answer was at once, as soon as they were released from the egg, with no more delay than kittens show in seeking sustenance from their mother. Another experiment was neatly to decapitate a wasp, when it continued with its legs to clean the place where its head ought to be.

At Ravenscroft Spalding occupied two rooms which had been the day and night nurseries. I was at this time in the new room which had been built for me, with a separate staircase to the garden, and Rachel was, I think, in the passage room adjoining. He was a consumptive in a rather advanced stage, with hollow sunken cheeks, a sallow complexion and rather long black hair, and I was much intrigued by a little wooden tube which he always kept in his mouth to breathe through-why, I do not know. I did lessons with him, but on the whole I do not think I liked him. He was not the type to attract children, and I dare say he found me a spoilt and tiresome boy. He used to beat me-I dare say