644 
Proceedings of Royal Society of Edinburgh. [suss. 
It follows that Du Boys’ rule should give for the uninodal 
period of a concave lake a value which is too large. This we 
have found to he the case in Loch Earn and Loch Treig, the two 
concave lakes whose periods we have as yet examined. 
It is perhaps worthy of note that, if we denote the ratio T 2 /T x 
by r, then it follows from (24) and (41) that 
§ 14. For the periods of a purely convex quartic lake the formula 
of Du Boys gives 
C&v 
2 
f p dx 
J q (ft + £ 
v J(gh)J q a 2 + x 
va J(gh) 
k 
ya J (gh) 
tan 
a 
tan 
a 
(43) 
Hence 
and, in particular, 
k 2 \ 
4^vy ; 
(44) 
*1 -A 1 -*)- ■ - ■ <"» 
Hence Du Boys’ formula gives too small a period for the 
uninodal seiche in a purely convex lake. 
If XJ% 1 = r , we get, as in the last paragraph, 
’d3* 
■ T. 
: - y(i^) 
(46) 
§ 1 5. The results of the last two paragraphs explain a matter 
that at first puzzled me considerably. The fact that, in order to 
get good results with Du Boys’ rule (Tj = 2 jdl/ J{gli) ) , we 
must integrate along the line of greatest depth, and pay no 
attention to the area or breadth of the section, makes it very 
difficult to believe that the formula can have any definite physical 
meaning. Indeed, from his point of view, the formula ought 
rather to be T x = 2 
j dljifijag) , 
where b is the surface breadth 
and a the area of a cross-section. This last formula, however, 
gives less satisfactory results where we have tried it than 
Du Boys’ own. 
