on Change of Temperature. 425 
The direction-cosines of A'", B'", C" are defined by the 
following numbers (§ § I. & XV.) : — 
logcosA'"X=9-9543897-7, cosA"T=0, logcosA'"Z=9-6387478-0 ; 
logcosB"'X=8-7111119-6,logcosB'"Y=9-9987746-4 ) logcosB'"Z=8-7373442-7; 
cosC"'X=0, cosC"'Y=0, cosO'"Z=l; 
for from these we find 
Beckenkamp. 
B'"C" ... 93 7 51-6 93 7 51-6 
C'"A'" . . . 115 48 6-4 115 48 6-4 
A'"B'" ... 91 17 25-1 91 17 25-1 
(a) To find A, the position of A'" at 20° 0. 
Let A be xy z, and A"' be f rj £*, where y=r) = 0. In this 
case the formula of § XIII. becomes 
£ = (1 _ r+p) |_ & 
We have seen (§ XV.) that for the temperatures 20°— 200° G., 
p= + -0017017, d=+ -0001257, 
q = --0000238, e= + -0010007, 
r= + -0000327, /= --0004525; 
whence 
- = 1-001669|- -0010007; 
x £ 
and substituting; the values of % or 7-777^. given above, we 
find * cosA"'X 8 
log cosAX, 9-9540818-3: cosAY=0; log cosAZ, 9' 6400605-8. 
(6) To find B, the position of B'" at 20° C. 
Since y is not small, we may here conveniently use the 
formulae (§ XIII.) 
which on substitution become 
-=•9982745? + -0004525, ) 
-= -9999435-^--0010007?--0001257; I 
y V V 
