206 Proceedings of the Royal Society of Edinburgh. [Sess. 
made several contributions. A list of these and other papers is given 
below : — 
“ Note on the Probability that a Marriage entered into by a Man above the 
Age of 40 will be fruitful,” Proc. Roy. Soc. Edin., vol. x, 1880, p. 202. 
“ On the Nature of the Curves whose Intersections give the Imaginary 
Roots of an Algebraic Equation,” Trans. Roy. Soc. Edin., vol. xxx, 
1883, p. 467. 
“ On a New Algebra by means of which Permutations can be transformed 
in a Variety of Ways and their Properties investigated,” Trans. Roy 
Soc. Edin., vol. xxxvii, 1893, p. 399. 
“ On the Adjustment of Numerical Results derived from Observation,” Brit. 
Assoc. Report, 1883, p. 446. 
“Note on the Evaluation of Functions of the Form 0°,” Proc. Edin. Math. 
Soc., 1884-85. 
“ On the Different Possible Non-linear Arrangements of Eight Men on a 
Chess Board,” Proc.. Edin. Math. Soc., 1889-90. 
“ On the Transformation and Classification of Permutations,” Proc. Edin. 
Math. Soc., 1890-91. 
“ On the Geometrical Interpretation of i ” Proc. Edin. Math. Soc., 1893-94. 
“ On the Eight Queens’ Problem,” Proc. Edin. Math. Soc., 1898-99. 
“ On the Singular Points of Plane Curves,” Proc. Edin. Math. Soc., 1902-03. 
The following were communicated to the Edinburgh Field Naturalists 
and Microscopical Society : — 
“ Bones and Shells taken from a Kitchen Midden on Inchkeith during 1881.” 
“ The ‘ Green Balls ’ of Loch Kildonan.” 
“ On the Growth of Leaves.” 
“ Fibre Balls.” 
“ Ripple Marks on Sand,” 
“ On the Occurrence of the Fresh- Water Mussel.” 
“Notes on the Bournemouth Cliffs.” 
“ Notes on the Entomostraca (Water Fleas) of Midlothian.” 
Dr Sprague was twice married : first, in 1859, to Miss Margaret Vaughan 
Steains, younger daughter of Mr James Steains of Liverpool, by whom he 
had eleven children, eight of whom survive ; and second, in 1908, to Miss 
Jean Elizabeth Stuart of Edinburgh, who also survives him. 
He was elected to the Fellowship of the Royal Society of Edinburgh 
in 1874, and served on the Council from 1885-1887. He died at West 
Holme, Woldingham, Surrey, on 29th November 1920. 
