taught us—­our own utter worthlessness and His infinite worth; and that He has brought us back to our one Father, and made us His brethren, and so brethren to one another—­we shall have all we need to guide us through the shadows.

Most assuredly I accept to the full the doctrines you refer to—­that Christ died to save us, that we have no other way of salvation open to us but through His death, and that it is by faith in Him, and through no merit of ours, that we are reconciled to God; and most assuredly I can cordially say, “I owe all to Him who loved me, and died on the Cross of Calvary.”

He spent the Long Vacation at Eastbourne as usual, frequently walking over to Hastings, which is about twenty miles off.  A good many of his mornings were spent in giving lectures and telling stories at schools.

A letter to the widow of an old college friend reveals the extraordinary sensitiveness of his nature:—­

    2, Bedford Well Road, Eastbourne,

    August 2, 1897.

My Dear Mrs. Woodhouse,—­Your letter, with its mournful news, followed me down here, and I only got it on Saturday night; so I was not able to be with you in thought when the mortal remains of my dear old friend were being committed to the ground; to await the time when our Heavenly Father shall have accomplished the number of His elect, and when you and I shall once more meet the loved ones from whom we are, for a little while only—­what a little while even a long human life lasts!—­parted in sorrow, yet not sorrowing as those without hope.

You will be sure without words of mine, that you have my true and deep sympathy.  Of all the friends I made at Ch.  Ch., your husband was the very first who spoke to me—­across the dinner-table in Hall.  That is forty-six years ago, but I remember, as if it were only yesterday, the kindly smile with which he spoke....

September 27th and 28th are marked in his Diary “with a white stone":—­

Sept. 27th.—­Dies notandus. Discovered rule for dividing a number by 9, by mere addition and subtraction.  I felt sure there must be an analogous one for 11, and found it, and proved first rule by algebra, after working about nine hours!

Sept. 28th.—­Dies creta notandus. I have actually superseded the rules discovered yesterday!  My new rules require to ascertain the 9-remainder, and the 11-remainder, which the others did not require; but the new ones are much the quickest.  I shall send them to The Educational Times, with date of discovery.

On November 4th he wrote:—­

Completed a rule for dividing a given number by any divisor that is within 10 of a power of 10, either way.  The principle of it is not my discovery, but was sent me by Bertram Collingwood—­a rule for dividing by a divisor which is within 10 of a power of 10, below it.

My readers will not be surprised to learn that only eight days after this he had superseded his rule:—­