28 Professor Hamitton’s Third Supplement 
no aaaaee ago (38s vem) t a (asm + ae) ! 
+a + Vasa) nk 
® 30.= oer + eee +5 (Bet 8a) Sg (a +738) 
‘hy Ber ve aay, 
yoaanaey 498 ST (3, vam) se ee ~+V3e 
“Eee. Vass 
nmansden + Va 8s +e OS + Se tan Ca +t £2, 
“bau, vee | 
if we put for abridgment 
ay ae da” + aay oy + ae ~ 82 + = dy, ] 
oF Fl , OF OB a SV See | 
ay ~ aan © + ay Y 2 ayer + aye, 
ye Hore ar + a ay + Sas be + = dy 
Ny aa ou’ + wy oy + ae oz) + wi 8x; (Z) 
y men oa + aa oy + a dz’ + = by; 
i) ae oa" Oe. by/ ton 2 +E by, 
FB oy)” aydy 
using 8 as in the notation (D*); and if we observe that the partial differential equa- 
tion of the fifth number, 
=o (¥ VV WV =): 
dc’ dy? ds’ (vo) 
gives 
