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Wishes to receive honorary degree of Doctor of Science with Stokes and Cayley, therefore wishes to withdraw as University's representative at the University of Bologna's eighth centenary celebrations.

Acknowledgement of paper on Hansen's theory. AC's treatment of Lunar theory by method of variation of elements is new; outlines the possible difficulties. JCA is applying this method to the secular inequalities of the moon's mean motion, further to paper in PTRS, 1853.

Acknowledgement of copy of paper on Disturbing functions. Origin of error of Hansen's. Agrees to look at remainder of development of [omega].

Explanation of peculiar numbers.

Probably the reply to 6/7/7 of 10 Apr. [no year]. Reply to question about Plana.

In French. Acknowledges honour done him by Camb. Phil. Soc. A. Cayley and corresponding membership of L'Academie des Sciences. See also slip attached to C.D. to J.C.A. 22 Dec.1862.

Reply to J.C.A. of the 4th. Presidency of the R.A.S. Sends copy of letter he has written to Cayley.

G.B.A. has read paper on Lunar Acceleration before the R.A.S. Regrets that neither J.C.A. nor A. Cayley was there to hear it.

Contents:

'Abel's Works Vol. I pages 69 and 70.' f.1.

'Bacon's Works Vol. I.' f.2-3.

'Bacon's Works IV.' f.4.

'Bacon repetitions.' f.5.

'Bertrand Calc. Diff.' f.6-14.

'Bertrand Integral Calculus.' f.15-22.

'Memoir by M. Ossian Bonnet. Lionville Vol. 17.' f.23.

'Professor Boole's manuscripts.' f.24-27.

'Supplementary Vol. of Boole.' f.28-35.

'Boole's Differential Equations.' f.36-38.

Autograph letter signed from Arthur Cayley to Todhunter, dated 31 March [1865]. Paper ascribed by Todhunter to Boole is in fact by G.G. Boldt. 2p. f.37*.

'Supplementary volume.' f.39-40.

'Frost & Wolstenholme.' f.42-61.

'Hamilton's Quaternions.' f.62-74.

'Heine page 207.' f.76-77.

'Elemente der analytischen geometrie Joachimsthal.' f.78.

'Kastner.' f.79.

'Kirckhoff Vorlesungen uber Mathematische Physik.' f.80-83.

'Merrett's Land and Engineering Surveying.' f.84.

'Routh's Rigid Dynamics.' f.85-86.

'Analytic geometry of three dimensions.' f.87-91.

'Schlomilch Handbuch der algebraischen Analysis.' f.92.

'Scientific Journals.' f.93.

'Serret Vol. I.' f.94-100.

'Serret Third Edition.' Notes dated 4 Dec. 1866. f.101.

'Serret Vol. II.' f.102.

'Algebra.' f.103-104.

Autograph letter signed from Archibald Sandeman, Manchester, to Todhunter, dated 1 May 1858. Thanks T for copy of his Algebra. Regrets that it contains 'same old confusions and errors' and gives examples. 4p. f.105-106.

Mathematical proof sent to Todhunter by Mr Jenkins 27 June 1873. f.107-108.

'From Mr Levett March 1877.' Laying out theories and corollaries. f.109-111.

Autograph letter to Todhunter from a teacher in Yorkshire (the signature cut out), undated. Regarding T's Algebra. 3p. f.112.

Mathematical notes headed 'R. Rickard Birmingham Feby 1869'. f.113.

Autograph letter signed from Charles Dodgson, Christ Church Oxford, to Todhunter, 20 Mar. 1876. Regarding probability as treated in T's Algebra. 4p. f.114.

Mathematical notes sent to Todhunter by the Rev. H.L. Guillebaud 3 Nov. 1865. f.115.

Autograph letter signed from Artemas Martin, Erie Pennsylvania, to Todhunter, 12 June 1875. Points out an error on p.462 of T's History of the Theory of Probability. Sends T various mathematical publications asking for solutions to various problems. 4p. f.116.

Autograph letter signed from Artemas Martin, Erie Pennsylvania, to Todhunter, 2 Sep. 1875. Giving various problems and solutions arising from the 4th ed. of Todhunter's Algebra. 3p. f.117-118.

'Methods of solving equations. By Mr Tucker.' f.119-120.

'Algebra.' f.121-123.

'Algebra. Notes. Articles of the Fifth Edition.' f.124.

'Key to Algebra for the use of Colleges and Schools.' f.125.

Autograph letter signed from R. Levett, King Edward's School Birmingham, to Todhunter, 16 Nov. 1878. Notes problem in Art. 604 of T's Algebra (1866). Offers to send proofs. 3p. f.126.

'Note on Algebra, Art. 604.' In the hand of R. Levett. f.127-129.

Notes on trigonometry 'From A.D. Mathews BA of St John's Coll. Sept. 1862'. f.130.

Various notes dated 1859-65. f.131.

'Plane Trigonometry. Fifth Edition. Examples.' f.132.

'Key to Plane Trigonometry.' f.133.

Autograph letter signed from Archibald Sandeman, Manchester, to Todhunter, 9 Mar. 1859. Thanks T for copy of Plane Trigonometry. Criticises lack of distinction between magnitude and quantity and T's algebraic use of the minus sign. 2p. f.134.

Mathematical notes sent to T by J. Brook Smith 15 Feb. 1873. f.135-136.

'Trigonometry for Beginners. Fourth Edition.' f.137.

'Mechanics for Beginners.' f.139-155.

'Differential Calculus. 5th edition.' f.156-159.

'Serret. Calcul Différentiel.' f.160-164.

'Proposition in the Differential Calculus.' f.166.

'Integral Calculus. 5th Edition.' f.168-175.

'Laplace's Functions.' f.176-177.

'Treatise on Laplace's and allied Functions.' f.178-187.

'Approximate area of a segment of a circle.' f.189-192.

Note on Trigonometry Art. 331. f.193.

'To shew the truth of Professor Cayley's remarks on my investigations on the method of Least Squares.' f.194.

'Potential of an Ellipsoid at an external point.' f.195-206.

'Problems of max and min in Slegmann.' f.207-208.

Notes on calculus of variations. f.209-210.

'Symmetrical solutions.' f.211.

'Resistance on a Solid of Revolution.' f.212.

'Solid of Minimum Relative Resistance.' f.213-220.

'Terms of the second order.' f.221-224.

'Curve of Minimum Resistance.' f.225-230.

'De Problematis quibusdam Isoperimetricis.' f.231-232.

'Jany 16 61.' Problem with solution. f.233.

'Christ's College Problems 1863 Second Year.' f.234.

'Jany 4 1866.' Problem with solution. f.235.

'Jany 15 1866.' Problems with solutions. f.236-237.

'Jany 16 1866.' Problem with solution. f.238.

'First BA Honours 1866.' Solutions. f.239-241.

'First BA & BSc Honours July 29 1868.' Solutions. f.242-243.

'Second BA 1866.' Solutions. f.244-245.

'2nd BA and BSc Honours 1868.' Solutions. f.246-248.

'MA 1866.' Solutions. f.249-252.

'MA 1867.' Solutions. f.253-254.

'MA 1868.' Solutions. f.255-257.

'MA 1869.' Solutions. f.258.

Will let AC know if successful in competition for Lowndean Professorship. Outline of position of Professorship in Mathematics in St. Andrews, duties and work load, in case AC interested in applying.