ON DR. WIENERS MODEL OF A CUBIC SURFACE. 
367 
The model is a solid figure bounded by portions of the faces of the cube, and 
by a portion of the cubic surface, being a surface with three apertures, the collocation 
of which is not easily explained. 
To determine the construction I measured, on the faces of the cube, the coordinates 
of the two extremities of each of the twelve lines; these were measured in tenths 
of an inch (taking account of the half division, or twentieth of an inch), and the 
resulting numbers divided by 16 to reduce them to the before-mentioned unit of 1*6 
inches. These reduced values are shewn in the table: knowing then the coordinates 
of two points on each line, the equations of the several lines became calculable; the 
true theoretical form of these results—(viz. the form which, but for errors of the 
model, or of the measurement, they would have assumed)—is 
z=l, 
*1, 
x = B Y z + D, 
y = B'z + D', 
b 2 , 
x — 0, 
be, 
x — B 3 {z + ßß, 
y = Bs (z + ß 3 ), 
b 4 , 
x = B 4 (z + &), 
y = B 4 (z + ß 4 ), 
bs , 
y = 0, 
be, 
X = B 6 (z + ße), 
y = Be (Z + ß 6 ). 
<h, 
x = 0, 
y = 0, 
a 2 , 
x = A»z + C 2 , 
y = A/(z- 1), 
Cl/ 3) 
x = A 3 (z + 1), 
II 
1 
^i—j 
«4, 
x = A 4 (z + 1), 
y = A 4 (z - 1), 
«5> 
x = A 5 (z+ 1), 
y = A 5 ' z + G', 
®6> 
x = A 6 (z + 1), 
y = Ae (z- 1); 
z = -l, 
but in consequence of such errors, the results are not accurately of the form in question. 
The faces of the cube being as in the diagram : 
the Table is 
1!