198 Mr. WuHEWELL on the Angle made by 
parallel to yz meet this line in /, k, l. Then AL is x. And if 
a, a’, a", be the cosines of the angles which «,, y,, and z,, make with 
Al, we shall have 
Al=Ah+hk +hl=aa,+a'y, + a"2,. 
And, if the cosine of the angle L4/, which w makes with a per- 
pendicular to yz, be d, we shall have, 
d 
Similarly, if a perpendicular to the plane xz make with y an 
angle whose cosine is e, and with a,, y,, z,, angles whose cosines 
AL = el" or2= 5 (anit ay, SMES eae a1). 
are 6, 6’, b”; and, if a perpendicular to the plane vy make with = 
an angle whose cosine isf, and with «,, y,, 2, angles whose cosines 
are c, c’, c”, we shall have 
Sh : (bx, + b’y, + b's,)...-.(1). 
2 (cx, + c’'y,+ c’2,)..+.-(1). 
z;= 
Also, we have 
Gf 2S Pee PR, (SEINE ES EP ASRS = Mona (2a 
And the equation, to the rectangular co-ordinates, 
of the plane yz is aa,+a’'y, + az, = 0, 
of xz....ba, + by, +'b”z, = 0, 
of ry... ca, + 'c'y, + c's, = 0. 
The formula for the angle made by two planes referred to rect- 
angular co-ordinates is known, and since «a is the angle of the 
two latter planes, we have, by applying the formula, 
be + Uc + b'c" 
O08; OF Dab) (Cb em pc) 
Sunilarly, maa (2 
—cos.B =ac +a'c' + a"c" 
— cos. y= ¢b'+a'l' + ab” 
=be + b'c' + b'c”. 
