Hi Magnus
By the reuse of the names it would appear that Katherine b. 1733, Androw b. 1734, Euphame b. 1736, Thomas b. 1737 and Eupham b 1741 all died young and their names given to later siblings.
So you are really looking for descendants of the remaining 13 children.
Marriage in Edinburgh:
"Chalmers, Andrew, writer, in N.E.p ; Eupham Rankin, d. of William R., wright, in N.W.p 15 Aug 1725, m. 2 Sept 1725"
Marriage of Eupham's parents in Edinburgh:
"Rankin, William, wright, Burgess ; Elizabeth Cairns, d. of late Robert C., wright, burgess, in N.W.p 27 Feb. 1704
Her 7 siblings are on the IGI if you don't already have them.
From the Roll of Edinburgh Burgesses and Guild Bretheren (
http://www.scotsfind.org/)
"Ranken (Rankine), Wm., wright, B., as p. to dec. Robert Cairnes, wright, B. (26 Mar 1690) 17 Sept 1701"
Possible entry for your Andrew:
"Chambers (Chalmers), Andrew, B. and G. be r. of fr. Wm. C. writer, B. and G., gratis, by act of C.for good services 10 Nov. 1736"
(B. and G. = Burgess and Guild brother)
(by act of C. = by act of town council, not in burgess register)
(be r. of = by right of)
(fr = father)
(p. = 'prentice)
Kirsty