[107 
is in any case precisely 
therefore be two non 
class of skew surfaces 
hrough two fixed lines 
d appear that surfaces 
he class in question.) 
d by the consecutive 
ermined by this point 
es through the point; 
nt lines through the 
loped by the tangent 
ane is of the n th class, 
le surface in n points, 
through the line and 
ne : that is, n tangent 
g through the vertex, 
t is the same thing, 
ould imply the inter- 
since the number of 
therefore the number 
no such plane passes 
in general a certain 
have therefore a cone 
of stationary tangent 
er of its double lines, 
-1). 
ble curve is sub modo 
iation of the general 
of the double curve, 
cone is equal to the 
anything to determine 
considered as forming 
them. 
intersects the surface 
108] 
35 
108. 
ON CERTAIN MULTIPLE INTEGRALS CONNECTED WITH THE 
THEORY OF ATTRACTIONS. 
[From the Cambridge and Dublin Mathematical Journal, vol. vn. (1852), pp. 174—178.] 
It is easy to deduce from Mr Boole’s formula, given in my paper “ On a Multiple 
Integral connected with the theory of Attractions,” Journal, t. n. [1847], pp. 219—223, 
[44], the equation 
d% dr] 
fg ■■■'* 
h n 
[(£ - of + (v - ß) 2 + • • • J] in - q OCT (±n-q)T(q + l) 
/: 
«9- 1 (0 1 S - <r)9 ds 
where n is the number of variables of the multiple integral, and the condition of the 
integration is 
(£-«i) 2 , (v ~ ft) 2 =| . 
-t- ... < i , 
P 
+ 
also where 
and e is the positive root of 
(a-Oj) 2 , (ß~ft) 2 , v- 
+ —7~‘" * 
s+ % 
a 2 _ (« - «0* , (6 - ft) 2 , v- 
‘ “ T F" 
+ ft 3 + 0j 2 . 
Suppose f = g ... = 0i, and write (a. — ai) 2 + ... = k*, we obtain 
d%... _ 7ri n [ co s9- 1 (0 1 2 - <r)«ds 
s 
[(£ - a) 2 + • • • v-^-i T (in - q) T (q + 1) 
/; 
(1 + s) in 
5—2