APPENDIX B. 223
It is important to notice that all sections parallel to the same
co-ordinate plane have the same probable error.
4. The ellipses (2) when referred to their principal axes become,
after some arithmetical simplification,
x2 y2
20 68+ 592 = constant,
the major axis being inclined to the axis of x at an angle whose tangent is 0.5014. [In the approximate case the ellipses are
72 + 22 = const., and the major axis is inclined to the axis of x at
an angle tan-1$.]
5. The question may be solved in general terms by putting YON = 0, XOM = 0, and replacing the probable errors 1.22 and 1.50 by a and b respectively; then the ellipses (2) are,
. . (6)
equation (3) becomes
|
,aye + (x -- ,y 0)2 = C.
titan |
7
() |
| |
|
a2 + tan Bx=?rbtan 8 = 0
2 . |
(8) |
|
tan tan 0
X = = 62--' + a2 tan28 |
|
|
1 1 tan20 |
|
|
_
e2 a2 + b2 . . |
(9) |
|
tan 0_e2
_ |
(10) |
|
. .
tan 6 b2 |
If c be the probable. error of the projection of p's whole motion on the plane of xz, then
0 = a2 tan2 0 + b2,
which is independent of the distance of p's line of motion from the
axis of x.
Hence also
tan 0 = a2
tan 0 b2 .
. (11)
Problem 2.-An index q moves under some restraint up and down a bar AQB, its mean position for any given position of the bar
