20D 
of Edinburgh, Session 1873-74. 
fixed pressure, for a given time, through each, and its quantity 
measured. The following are the experimental results : — 
Weight 
Efflux per 
min. 
Axes of sections 
Ratio of 
Cal. weight 
Section. 
of 1 inch 
Hg. 
T. 
P. 
in hundredths 
of an inch. 
axes. 
of 1 inch. 
Hg. 
Elliptic. 
Cub. in. 
C. 
In. 
I. 
•249 
3-30 
9-4 
23*65 
8-5 ) 1 
8-25 \ \ 
>1-5 
1 1-8 
5-073 
•238 
II. 
•357 
7-87 
9-5 
23-65 
U !! 
| 2-3 
1 2-3 
3-956 
•359 
III. 
•441 
12- 
10- 
23-57 
9-4 / j 
10-1 \ \ 
, 2-6 
1 2-7 
3-679 
•445 
IV. 
•685 
21-77 
10- 
23-57 
ir 76 | | 
i 3-1 
3-2 
4-087 
•683 
Circular. 
Diameters of 
ends. 
I. 
•223 
6-16 
I0‘ 
23-1 
* 3-6 3-6 
•223 
II. 
•301 
9-62 
io- 
23-1 
4-1 4-3 
•304 
III. 
•357 
11-81 
10- 
23-1 
4-4 4-5 
•341 
IV. 
•646 
22-6 
9-9 
23-1 
6-2 6-2 
•661 
V. 
1-213 
52-8 
11-5 
23-2 
8’3 8-6 
1-229 
VI. 
1-632 
67- 
11- 
23-2 
9*6 9-6 
1-587 
The two last were added with a view of finding the effect of still 
farther increasing the section. A comparison of the first and 
second groups of four shows the very considerable effect of the 
elliptic form in diminishing the rate of flow. 
2. Note on the Transformation of Double and Triple 
Integrals. By Professor Tait. 
1. If we have two equations of the form 
f( u , v> & v) = 0 , 
PO, a, £, v) = 0 , 
u and v are given as functions of £ and rj , or vice versa. Here 
either u and v, or £ and rj, may be the ordinary Cartesian x and y, 
or any given functions of them. 
Now, if we write with Hamilton, since we are dealing with two 
independent variables only, 
4 
. d 
3 dy 
v = v “" +v 4= v 4 +v 4 
du 
(i) 
we have 
