# Collection of manuscripts once belonging to William Wallace

A previously unknown and substantial collection of manuscripts formerly owned by William Wallace has been preserved by members of his family as part of their family archives. Thanks to the generosity of Mr Michael C G Cox, acting on behalf of the family, these have been made available for copying and posting on the St Andrews History of Mathematics Archive. There, they are publicly accessible for the first time. The copying was done by John O'Connor and the accompanying transcriptions are by Michael Cox and Alex Craik.

William Wallace's biography is available at THIS LINK

Click on one of the links below to see a picture of the original (in a new window).

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Note by David Gregory, dated 3 May 1698, about a heavy snowfall in Oxford that day and subsequent frost. Signed annotations by D[uncan] F[arquharson] Gregory that it is the handwriting of David Gregory, Savilian Professor of Astronomy; and by William Wallace, that he received it from Duncan F. Gregory on August 28th, 1835. Notes on reverse, probably by D. Gregory: "To buy for my self Day Shirts Night Shirts Handkerchiefs Sleeves of Holland"/ "Mr Wetsteins[?] Architectura Navalis"/ "Justus Byrgius qu[ ]/ Vossius De Natur[ ]/ Kepleri adversaria" [Two of these may be Nicolaus Witsen's Architectura navalis, Amsterdam, 1690; Isaac Vossius' De lucis natura et proprietate, Amsterdam, 1662.]

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"Autograph of Sir Isaac Newton Restored by me Anne Charlotte Wallace A.D. 1871 February 27 No 7 Newbattle Terrace Morningside Edinburgh"
Notice of election of Council and Officers of the Royal Society on 30 November 1715, signed "Is. Newton P.R.S."
Reverse gives addressee as "the Revd. Dr. Bentley" and ten lines of Greek, annotated in pencil (correctly) as being verses 5, 6, 8 of Chapter 5 of the First Letter of St John in the New Testament.

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Letter from William Herschel to W.W. dated 9 Dec 1803, addressed: "Mr. Wallace, To the Care of Mr. Mill No 5 Southampton Buildings, Holborn, London"
"My Dear Sir
I received the favour of your letter and shall be in London next Thursday. I shall be glad to introduce you to Sir Josph Banks. Mrs . Herschel is now in London at No 24 Southampton Street Covent Garden. and if that should be in your way she will be glad to see you. Perhaps you would like to go to the meeting of the Royal Society with me on Thursday and if you can be in Southampton Str between four and five I will introduce you to dine with Sr J. Banks at the/ Crown and Anchor, and afterwards carry you to the Meeting. I remain

Dear Sir
Wm Herschel

Slough
Near Windsor
Friday Decr 9.
1803."

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Letter from William Herschel to W.W. dated 7 April 1805, addressed: "Mr. Wallace at the Royal Military College. Great Marlow Bucks"
"My Dear Sir,
We have not had the pleasure of seeing you at Slough this good while. I have kept a little problem for you which a friend of mine has sent me who says he cannot find a solution of it. I mentioned to him that I had a friend who would probably help him to one.

The problem is this. Given $AB$the diar of a circle.
$CD$ a chord cutting it at right angles in $K$
$EF$, and $HG$ two other chords drawn any how through the
point $K$; and $HF$, $EG$ chords joining the extremes of $EF$, $HG$.
Required to prove that $MK$ is equal to $LK$.

As we have now hopes of fine weather, we may probably soon take a ride over to Marlow/
By way of an airing to see our good friends Mrs . Herschel joins with me in best respects to Mrs . Wallace and Mrs . Leybourn and their two good husbands. I beg also to be remembered to the other two mathematical Gentlemen, and remain

My dear Sir,
Faithful Servt
Wm . Herschel

Slough
Near Windsor
April 7. 1805

P.S If by chance you should hear of a good footman I shall be glad if you will send him to me"
A proof of this theorem was found attached to a letter from Wallace to Herschel in the archive of the Royal Astronomical Society. You can see a reproduction of this proof at THIS LINK and a transcription of the proof at THIS LINK.

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Letter from William Herschel to W.W. dated 20 July 1813, addressed: "Mr. Wallace at the Royal Military College. Blackwater near Bagshot"
"Slough
Near Windsor
July 20. 1813.
Dear Sir
We have not seen anything of you this great while, and as your long Vacation is now coming on you will probably have time to pay us a visit at Slough where we shall be glad to see you. We also wish much to se the noble College and the Houses you now occupy, and mean to come a spend a night at Blackwater or at an Inn nearer to you if there is one where we can sleept [sic] at; and where we shall be glad to see you, Mr Ivory and Mr Leybourn to dine with us. Will you be so good as to let us know how long you remain at the College. For if you leave it soon we will defer our visit till after your return. With Mrs Herschel's Miss Baldwin's & my Son's complits to you and all friends I remain

Dear Sir yours very sincerely
Wm . Herschel

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Letter from Henry Brougham to W.W. dated 6 Nov. 1798, addressed to "Mr Wallace, Academy, Perth" [not shown].
"Edinr : Novr . 6, 1798

Dear Sir
I received your letter and have to return you my very best thanks for your kindness in attending so much to the trifling communication which I last summer [?, year del.] made to the R. Society - and for giving me your remarks upon the porism concerning the Circle. Your observation is certainly just and I find in my original copy of the proposition a note to the following purpose -
"In giving the more general enunciation [with? del.] the limitation is not to be mentioned as possibly it may not be necessary -- In the particular one it is so very evidently" ----
Accordingly you will find that this intention has been fulfilled in the Printed paper, only it is not obvious from my not having repeated the whole enunciation./
At the same time I scarce think it necessary to trouble the Society with a note on this subject as from reading the Proposition the matter is by no means decided either way- The truth is, that prop. [was mine? del.] occurred to me 3 or 4 years ago (as did most of the paper) and I minuted it down according to my custom; since that time I have not thought of attending to the limitations more minutely having been wholly occupied with other less agreeable (& less difficult [insert]) tho more worldly Stud[ies of] Law & Politics -
It will always give me great pleasure to hear from you & the communication of any Scientific remarks will for a short time draw me into my old line of study- I hope you have not forgot the Academy - It is waiting in expectation for your Communications. The Members desire their compts to you & I remain

Ever, Dear Sir
Yours Sincerely
Henry Brougham Jnr

P.S. If there is any commission which I can execute for you here it will give me great pleasure to do it -- "

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Letter from Henry Brougham to W.W. dated 13 Feb. 1798, addressed to "Mr Wallace, Academy, Perth".
"No 7. George Street Edinr

Sir,
We have long looked for your promised communication either of the formula for finding small circular arcs, or of new geometrical propositions; and I now trust that you will soon comply with our expectations
The following problems have been for some time under the Academy's consideration; and as no solutions have as yet been offered, I take the liberty of requesting that you will turn your attention to them. -----

I. The lines drawn bisecting the angles at the base of a right angled triangle to the opposite sides, being given in magnitude, to find the triangle. -----

II. From a given point to draw a line to a given circle, making a given angle with the tangent at the point where it cutts [sic] the circle. -----

III. From two given points, to inflect to a given circle two lines, whereof the one bisects the angle that the other/
Other make with the tangent. --------

There is another subject well worthy the attention of so able and experienced a geometrician as you -- the invention of topics; that is general methods or rules of analytical investigation in mathematical science -- We know that the Ancients possessed above thirty treatises on this subject and prized them above all their other geometrical Writings. -- much of the reasoning upon it must of course be particular, and will, indeed, chiefly consist of instances as illustrations. -- But convinced as I am, that by attending to the process of your own mind in the investigation of difficult problems and comparing the way in which different solutions occur, you may without much labour deduce some general principles or at least draw some rules [that del.] which may be of the greatest use in other cases, I earnestly recommend it to you as highly deserving consideration. ------------

The Academy is about to engage in some geological inquiries concerning several curious strata in the confines of Angus and Perthshire- and as, from what I could perceive last summer in visiting/
visiting these counties, a general character appears to run thro' most of the sandstone and other rocks, between Perth and Blairgowrie, you would confer a favor on the Academy by either giving yourself, or procuring from some of your friends who have more leisure, a short sketch of the mineralogy in the neighbourhood of Perth; especially on the Hill of Kinnoul, and on that quarter whence the stone used in building the bridge was brought. -----

I am, Sir
Your mo. Obt . Hble Servant-
Henry Brougham. Junr.
Corresponding Secretary. ---

Feby: 13th. 1798
PS.
Dear Sir -- Having addressed you as secy; I hope you will after answering me in that capacity, favor me wt a note as to what objects at present engage your attention. --- I have sent to the R:S: a paper, "General theorems (chiefly porisms) on ye properties of curve lines["], but it will not soon be published -- Mr Reddie & the other members desire their compliments to you -- Pray do not wait for the solution of the problems, if your paper is ready; Send it addressed to me, per carrier-

I remain, Dr Sir- Yours &c. H: B: -----"
[The "Academy" referred to is the Academy of Physics at Edinburgh, largely founded by Brougham, which existed for just three and a half years.]

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Letter from Henry Brougham to W.W. dated 1809, addressed to " [... ?? 1809] Mr W. Wallace, Royal Military College, Great Marlow Bucks"
"Monday

My Dear Sir
I have [insert] received your parcel & letter - I return you many thanks for your kind & valuable present from [insert] which I promise myself great pleasure as soon as the holidays shall give me time to peruse it - I send [sent?] Mr Windhams, as soon as I received it [insert] with a note informing him [I had got it del.] that it came for you - This I thought necessary lest you should have omitted to write to him -

I beg my best cmpts to Mr Ivory - Mr Playfair is expected here early in May - Yrs truly
H Brougham"

Picture 22
A page of 'The Residual Analysis' in John Landen's hand, annotated by Wallace:
'the above is Mr Landens own handwriting received from his grandson Mr Ibbetson April 1826 W.W."
"Handwriting of John Landen Author of the Residual Analysis Mathematical Lucubrations &c. This was got from his Grandson Mr Ibbotson when a Cadet at the Royal Military College and at the same time a large paper Copy of his Residual Analysis also a brass protracter that had belonged to him with the Makers name Heath on it.

W. Wallace Edinburgh July 1832"

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"Attempt towards obtaining an Invariable [del. Standard] Measure By Whitehurst
Dent[?] Paternoster Row"

"Mr . Whitehurst's experiment, as calculated by Dr . Rotherham, and examined and approved by Dr . Hutton; gaves [sic] the length of the seconds Pendulum 39,1196, when vibrating in a total arc of 6° 40', and in air at a temperature of 60°.
... .

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Plans by W.W. of Edinburgh Observatory showing location of pillar for a mural circle.
"Edinburgh 15th May1829

Gentlemen,
I here send you a plan of the pillar and a sketch of the interior of the Observatory If any further information is wanted be so good as let me know & oblige your most Obt. Serv.

William Wallace"

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Letter to W.W. dated April 17th 1823 from Edward Troughton giving costs for a choice of five microscopes and "a Case of Micrometers for measuring objects", manufactured by "Mr Bancks Optician in the Strand." Also some frivolous remarks about Scottish politics.

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Two letters to W.W. from Alex Christison, dated 13th and 14th July 1820, concerning Euclid's 5th definition of the 5th Book.
This definition concerns the equality of proportions. Christison claims that "the following deduction enabled my twins, with the utmost facility, to understand" it.

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[Copy of?] letter "To the Secretary to the Senatus Academicus" dated November 13th 1838 and signed by George H.E.[?] Bell, Macvey Napier, D. Cheape, George Skene.
"We, the Members of the Law Faculty in the University, hereby suggest the propriety of conferring upon Mr Wallace, late Professor of Mathematics, the honorary title of Doctor of Laws and recommend him to the Senatus Academicus as eminently entitled to that honour."

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Letter to W.W. dated 25 July 1827, addressed:
"With a Dog Professor Wallace University Edinburgh", from W.E. Cormack of St Johns Newfoundland.
Cormack has sent a Newfoundland dog to Greenock for Wallace in "thanks for your kind and disinterested services to me in 1823."

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Letter to W.W. dated 10th May 1825, from James Veitch of Inchbonny reporting "a very remarkable phenomenon which I observed here, on Monday 8th March 1825."
He writes "the Moon was surrounded by five bright and well defined concentric circles" coloured yellowish green, bright orange, bluish green, red, and dark green. He encloses a coloured sketch.

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[Copy of?] letter from W.W. to Sir Patrick Murray, Baron of Exchequer, proposing that a standard length of land measurer's chain be set up on the parapet wall in front of the College and requesting funds to do this.

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Letter to W.W. dated 16th April 1812 from Mrs Greig [later Mary Somerville].
She thanks Wallace "for the very handsome manner in which he interested himself in the solution of the problem which she sent last year. She now encloses solutions of three of those problems in No. 11 of the Mathematical Repository, and would be much flattered should any of them be found worthy of his approbation."

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Autographs of twenty-nine Edinburgh professors on parchment[?].
(As P. Kelland is one, these date from after Wallace's retirement.)

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Printed Annuity Department leaflet from National Security Savings Bank of Edinburgh (inst. 1836).

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Printed pamphlet by W.W. regarding the burial place of John Napier, dated Nov. 1838.

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Small booklet listing "Books which formed LIBRARY in 1792 W. Wallace"; "The Books which formed my Library in the beginning or rather early years of my Mathematical Studies that is about 1792 or 3 before leaving Edinburgh W. Wallace"
[a surprisingly large collection].

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Letters of Appointment of W.W. to the Edinburgh chair, 1819, 1820.

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Letter to W.W. from Sir Walter Scott, dated 13th May [no year], introducing his son Walter
"just returned from the continent. We have for him the offer of a vacancy at Sandhurst, and he is anxious to avail himself of the opportunity of prosecuting his military studies. Will you be so good as to point out to him any proper person to read over his mathematics with him to prepare him for the previous[?] examination as he suspects he may be a little rusted.

I have pleasant accots .[?] of my nephew the other Walter from Addiscombe ..."

Picture 69
Note regarding the above "Written by Sir Walter Scott to Professor Wallace when he was Mathematical Professor at Addiscombe."
[This statement is rightly queried in pencil annotation. It is unclear whether Wallace was still at Sandhurst or by then in Edinburgh.]

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Letter to W.W. from Sir Walter Scott, dated 21 October [no year].
"My Dear Sir
The Bearer is my nephew whom I have undertaken to take care of as a son of my own. He is a very fine boy and shows I am told some turn for mathematics which induces me to think his destination may be for the engineer service in India. May I beg you to ask him a few questions and favour me with your opinion which of your classes he may attend with most advantage this season. I will esteem it a great favour if you will mention to him at the same time [del.] at what time the class sits down and what other studies you would advise him to pursue with the view which / I have mentioned He has sense rather beyond his years and I am sincerely anxious for his progress in such branches of learning as may be most useful to him May I trouble you for a few lines on the subject addressed to me here

I am with sincere regard
Dear Sir
Walter Scott

Abbotsford/Melrose
21. October"
[The classes referred to seem likely to be those at Edinburgh University as those at Sandhurst would have been restricted to cadets. Also, this letter was probably written before the letter above, as Scott's nephew is there described as already at Addiscombe, the India College.]

Russian translation of Wallace's work on Conic Sections

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Title page and Contents

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Translation into English of Ostragodsky's Preface to the translation

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Translation into English of the translater's Preface (by Michael Lenin)

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Letter from Vice Admiral Krusenstern to William Wallace

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Address label of the above letter

Further items in the collection not copied:
1. The Life of Sir Isaac Newton with an Account of his Writings, printed and sold by J. Roberts, 1728. 30 page booklet. This is one of the English translations of Baron Fontanelle's Éloge of Newton.
2. Handwritten family tree of Isaac Newton.
3. Pencil outline sketch: a S.E. View of Sir Isaac Newton's house at Woolthorpe 1796, made "in great haste on a cold frosty day" by John Robison, Professor of Natural Philosophy in Edinburgh.
4. Notice of meeting of the Royal Society in Fleet Street on 13th May 1762, signed by Francis Hauksbee, Chairman, and addressed to James Short.
5. Printed booklet of testimonials for William Wallace as candidate for the mathematics chair in Edinburgh University, Sept. 1819. [There is a copy of this booklet in Edinburgh Univ. Library and elsewhere.]
6. Memoir of Professor Wallace, published in 1844 in Report of the Royal Astronomical Society.