CESSER—CLAIRAUT. 
82 
Cesser: points of, iv, 130. 
Challis, J.: integration of differential equations, vn, 36. 
Chance (see Probability). 
Characteristic Function: of Hamilton, hi, 217; for systems of rays, xn, 571. 
Characteristics: logic of, ill, 51—2; of Chasles, v, 552; theory, vi, 594, xm, 468—72; of triple theta 
functions, x, 441—5. 
Chartography: surface representation on plane, vm, 538—9; colouring of maps, xi, 7—8; map projec 
tions, xi, 448. 
Chasles, M.: intersections of curves, i, 25—7 ; Pascal’s theorem, i, 45; theorem on correspondence, i, 212; 
a theorem of, demonstrated, i, 355 ; analogue of Pascal’s theorem, i, 427; transformation of curves, 
i, 478—80 ; homography, n, 538; cubic curves, iv, 122, 495 ; inertia, iv, 561, 586 ; kinematics of 
solid body, iv, 580, 586; curves on a quadric, v, 11; on a cubic, v, 19; conics touching curves, 
v, 31—2, 552; scrolls, v, 169, 201, vi, 328 ; quartic scrolls, v, 201 ; cubic curves and cones, v, 401; 
equilibrium of four forces, v, 540—1 ; correspondence of points in plane curve, v, 542 ; contact of 
conics, v, 552 ; characteristics, v, 552 ; on united points, vi, 9; curves which satisfy given con 
ditions, vi, 191, 192, 200—26; principle of correspondence, vi, 264, xi, 4S2, 485—8; foci of conics, 
vn, 1; six coordinates of a line, vn, 93; attraction of ellipsoids, vn, 380—3; locus in piano, 
vn, 605; cones satisfying six conditions, vm, 99 ; penultimate forms of curves, vm, 258; theory 
of duality, xi, 467. 
Chemistry: Cayley’s interest in, vm, x; application of trees to, ix, 202—4, 427—60, 544—5. 
Chessboard : topology of, x, 609—10. 
Chord: angle between normal and bisector, x, 576; of two circles, xi, 552—6. 
Christie, J. T.: Cayley’s law work, vm, xiii—iv. 
Christoffel, E. B.: orthomorphosis, xm, 180. 
Chrystal, G.: uniform convergence, xm, 343—4. 
Chuck: for quartic curves, vm, 151—5; for curve-tracing, vm, 179—80; bicyclic, vm, 209—11. 
Circle: Salmon’s equation for orthotomic, hi, 48—50; and points, v, 560; and ellipse, v, 561; line 
and parabola, v, 607 ; envelope of, v, 610; equation of, vi, 501, xi, 558—61; potential of, ix, 
290—301; quadrilateral inscribable in, x, 578; orthomorphosis, xn, 328—36, xm, 20, 182, 202—5; 
Wallis’s 7r investigation, xm, 22—5; transformation into bicircular quartic, xm, 185; and circum 
ference, the terms, xm, 194; the nine point, xm, 517—9, 520—1, 548—51; of curvature of an 
ellipse, xm, 537. 
Circles: powers of, i, 581 ; systems of, hi, 111—4, x, 566 ; in-and-circumscribed polygon, iv, 303—8; 
a pair touching three given, vi, 65—71; involution of four, vi, 505—8; relation between two, 
vm, 12—3 ; equal, vm, 31; minimum enclosing three points, x, 576; system of 15 connected with 
icosahedron, xi, 208—12; radical axis, xi, 465; radical centre of three, xi, 552; Mascheroni’s 
geometry of the compass, xn, 314—7; system of three which cut each other at given angles, xn, 
559—61, 564—70; the two relations connecting the distances of four points on a circle, xn, 576—7; 
roots of algebraic equation, xm, 37; problem of tactions, xm, 150—69; tetrads of, xm, 425—9; 
(see also Casey, Orthomorphosis). 
Circuit: the word, xi, 480. 
Circular: the word, xi, 481. 
Circular Cubic: and polyzomal curves, vi, 522—8. 
Circular Points: at infinity, vm, 32. 
Circular Relation of Mobius: m, 118—9, ix, 612—7. 
Circumference: and circle, the terms, xm, 194. 
Cissoid: the term, xi, 461. 
Clairaut, A. C.: lunar theory, iv, 518, 586; demonstration of his theorem, x, 17—8; curves of double 
curvature, xi, 489.