220 REPORT—1862. 
@, the inclination, 7, the angular distance of X from node, and the formule 
xe N 7 
of transformation then are 
coe TEE Ih in et 
x uy’ Z 
x | cos7 cos@—sinr sin@ cos@ |—sinz cosO—cosr sin@ cosg| sin @ sing 
y | cosr sin@+sin r cos@ cos |—sinr sin@-+cosr cos cos ¢ | —cos 0 sin 
z sin 7 sing cos T sin @ cos @ 
The foregoing very convenient algorithm, viz., the employment of 
| Be | o-Y | Z 
| esai\ discal 
y | @ p' y’ 
aime AL 9? at 
to denote the system of equations 
vw=aX +BY +yZ, 
y=aX +BY +72, 
z= "X+pB"Y+ y'Z, 
is due to M. Lamé. | 
131. But previously to the foregoing investigations, viz.,in the memoir “ Du 
Mouvement de Rotation &e.,’’? Mém. de Berlin for 1758 (pr. 1765), Euler had 
obtained incidentally a very elegant solution of the problem of the transforma- 
tion of coordinates; this is in fact identical with the next mentioned one, the 
letters 1, m, 2; X, p, v being used in the place of Z, 2’, 6"; n, n,n". 
132. In the memoir “Formule generales pro translatione &c.” (1775), Euler 
gives the following formule for the transformation of coordinates, viz., if the 
position of the set of axes XYZ in reference to the set wyz is determined by 
