xxviii Proceedings of Royal Society of Edinburgh. 
devotion to science, and his rewards in a worldly sense were far 
from commensurate with his great and valuable labours. In writ- 
ing this paper a free use has been made of the Transactions of the 
Royal Scottish Society of Arts, a short autobiography, and informa- 
tion kindly supplied by the Misses Sang. It may fitly be closed 
by a quotation from one of Miss Sang’s letters. Speaking of her 
father, she says : — “ To investigate, to endeavour if possible to reach 
the fundamental principle, and so be able to build a firm super- 
structure on a sure foundation, was a passion with him in which he 
found a happiness few could realise, and he was always ready to 
communicate to others from his own stores.” Let us hope that the 
promise of his favourite motto is being amply fulfilled in another 
sphere, where he now finds how true it is, with reference to a 
Supreme Ruler, that “ He rewardeth the searcher and the keeper of 
His laws.” 
LIST OF WRITINGS. 
1. “Solution of Algebraic Equations of all orders, whether involving 
one or more Unknown Quantities.” Edinburgh, 1829. 
2. “ On a Remarkable Analogy between the Primitives and Derivatives of 
the Product of two Monome Functions.” Annals of Philosophy, August 
1829. 
3. “ Observations on the Theory of Capillary Action given in the supple- 
ment to the ‘Encyclopedia Britannica.’ ” Edinbtirgh Philosophical Journal , 
February 1830. 
4. “ On the Adaptation of the Fly-wheel and Pully of the Turning-Lathe 
to a given length of Band.” April 1831. 
5. “ Experiments made to Determine the Thermal Expansion of Marble.’’ 
June 1831. 
6. “A New Solution of that case in Spherical Trigonometry in which Two 
Sides and the Contained Angle are given.” 1832. 
7. “Analysis of the Vibration of Straight Wires.” Edinburgh Philo- 
sophical Journal, April 1832. 
8. “A few Remarks on the Relation which subsists between a Machine and 
its Model.” November 1832. 
9. “ Remarks on some Prevailing Misconceptions concerning the Actions 
of Machines.” January 1833. 
10. “ On the Advantages of a Short Arc of Vibration for the Clock Pendu- 
lum, with a Table of Corrections of the Daily Rate.” July 1833. 
