82 
ANALYTICAL RESEARCHES CONNECTED WITH 
[114 
and it is easily seen also that the coordinates of the point of contact are 
s v<a 
x = 0, y = v, z = p, w = ~- 
also 
a/ 41 V J, 
J h 
1 - 
V<£\ JJ 
Hence substituting and introducing throughout the quantities f, g, h, J, also forming 
the analogous equations, the equations of the tactors are 
f2 (“ f 2 + g 2 + h 2 ) + (g + h) J if 2 - (g - h) 2 - —ß 
2f 2 gh\) 1 
r= X 
J\ 
- _ (g _ h y _ ggh(g- h )]. 
J 
V<ZD 
J 
+ 2V/f Y gh (1 ~ j) (1 “ jd (f 2 ~(g-h) 2 ) V -pw = 0, 
- jg 2 - (h - f) 5 + J (i _ f 
+ |g 2 (f 2 - g 2 + h 2 ) + (h + f)J (g 2 - (h - f) 2 - *£)} -g y 
+ 2 1 
J. 
J, 
2 — (h — f) 2 ) a/ — pw = 0, 
j j 
j. 
3$=lV;4(.-5 
2fgh'- 
+ jh 2 ( f2 + g 2 - h 2 ) + (f + g) J [h 2 - (f- g) 2 - 
+ 2Vg yfg (i - i) (i -1) (h*-(f-g) ! ) ^ -1»=o-