597 
Vina Tai Ie Qla,z! — MVa,y' oe: Um,y We + Maz’ — PVar' + 
dva,z' 
+ ee me 
and subtract from this the equation that results from the second of 
(7) by differentiation, it becomes in the first place apparent that 
we can replace the third of (7) by 
Var! I myx ar Vay! Jmy == Var! Jm == 
which can also be seen directly. 
For the locus of is the euspidal curve of the developable 
surface described by the polar axis (axis of curvature) of the path 
of P, which is always perpendicular to the plane of osculation in 
P, in which lie the velocity and the acceleration of P. 
We find therefore again 
Var! Oma + Vay’ Umy + Var! Un,z = 0 | 
Vax! Ime Bik Vay’ Jm,‚y zi var Jm,z a= 
If we now write the latter equation 
ide IA: 
Jinx § = fear a | ae tap + Jy UI + re 7 pe a We at 
| | t dz 
+ Jm,z 5 + py =~ Oe Je Fr =S 
and subtract from this the equation that is found from (85) through 
differentiation, we find 
Ne (2) eG) dé dy dh 
m Y dm m,z — 3 ra va St | 
ID UD + Jl (aat 
ze (s! ye Ja a z ) (8e) 
dr ÒH(S, 7,5) 
med +1 4 +2 —— 
dt" dt dt dt dt og 
(see for the meaning of H § 2). 
Through the three equations 
U Um, x aE Ymy ze Z Ome = §# + Ny + Sz 
' ! ! Sy (*) 
Imex + y'Jmy + #Jmz = 2S Ee |. (8) 
» (2 1 2 7 (2 ds „(i) 
ot J, =e y jen = al id 2s, — és v 
a cubical correspondence is defined between the points P (a, y, 2) 
P’ (a', y', 2’). Hence: 
there exists a cubical correspondence when a point P of the system 
