The observatory, which is connected with the university, stands on the summit of the Hill of the Nymphs; like the Academy, it was erected at the expense of a wealthy Greek, Baron **Sina** of Vienna.

Comparing this equation with ux 2 +vy 2 +w2 2 +22G'y2+2v'zx+2W'xy=0, we obtain as the condition for the general equation of the second degree to represent a circle :- (v+w-2u')Ia 2 = (w +u -2v')/b2 = (u+v-2w')lc2 In tangential q, r) co-ordinates the inscribed circle has for its equation(s - a)qr+ (s - b)rp+ (s - c) pq = o, s being equal to 1(a +b +c); an alternative form is qr cot zA+rp cot ZB +pq cot2C =o; Tangential the centre is ap+bq+cr = o, or **sinA** +q sin B+rsinC =o.

Rate at which the plane HOJ revolves about OH, we have **sina** Ccosa ii~~A cosI3iU~, (8)

X **sina** ce.

From this point the line crosses the Cordillera Real through the valley of the San Juan del Oro to Suches Lake, follows the Cololo and Apolobamba ranges to the headwaters of the **Sina** river, and thence down that stream to the Inambari.