Miscellaneous Notices . 
33 
1830.] 
3 . — On Deducing a Mean Result from Observations of a broken Number of the Wires 
in a Transit Telescope: by Mr. V. Rees, of the Surveyor General's Office. 
Many years practice, in finding the mean result from the observed transits of a 
heavenly body, over the several wires of a transit telescope, have led me to investi- 
gate formulae calculated to give to every observation an equal share in the result, 
when from accident, inattention, or other cause, one or more of the wires may not 
have been observed. 
Some observers, in this case, reject the observation of the wire which corresponds 
to the deficient one, and thus, instead of one, lose two observations : — the one re- 
jected beitfg, very possibly , the best. Again, if the 1.2.5. or 1.4.5. wires be observed, 
a similar inconvenience follows ; while in the case of the 1. 2. 3. or 3. 4. 5. wires 
being observed, the whole is rejected, or else the middle one only taken. Others 
supply the deficiency of one, or even more lost wires, by adding to the preceding 
or subtracting from the following \vp - e the mean difference ; but a little consideration 
will show, that should the wires to o> from, with this mean difference, be added or 
substracted, be taken too great or too small, (and this supposition amounts almost 
to a certainty,) so this supplied wire will hear exactly the same error ; which error of 
one wire will be taken in the sum twice or three times, as one or two wires have 
been supplied. 
To obviate these objections, I have drawn up the following formulae, which I have 
been in the habit of using in calculating the observations made ia the Surveyor 
General's Office. They may be of use to the practical Astronomer, and as such are 
offered. 
e — e — b 
1st Wire wauting, mean result= jr- 
a-f-c-f-tf-f-e e — a 
5th 
2d 
4 th 
1st and 2d 
4th and 5th 
1st and 4th 
2d and 5 th 
1st and 3d 
3d and 5th 
2d and 3d 
3d and 4th 
4 16 
a-f-fi+c-j-e — a 
' 4 ^~nr 
a-\~bAr c A~d d — a 
4 h 6 
c-M-f e e — c 
3 P 
a-\-b-\-c , c—a 
3 + 2 
5-f-c-fc £ — b 
3 P 
a+cArd , d — a 
3 
b^dAr e 2 (e &) 
3 " 9 
a -f” b -f- d . 2 (d a) 
3 9 
a'\'d-lre e — a 
3 TP 
a +M- e e — a 
—3—+ 12 
4. Supply of Wholesome Water, 
Amon" the first cares which ought to occupy the attention of the founders or in- 
habitants of a great city, one would suppose that a supply of good and wholesome water 
would occupy the principal place. Strange to say, however, such is not always the 
case, and amongst others, London has still to reckonthisamongst her desiderata. But 
from the attention lately given to the subject, it appeal’s, that though a late yet an 
effectual remedy will be applied to remove the evils under which her inhabitants at 
present labour on this score. A Mr. Wright appears to have engaged in the question, 
with a commendable zeal and intelligence; and from some notices on the subject 
we have lately seen, the inhabitants appear desirous of acknowledging his services 
by some appropriate means. Questions have also been brought forward for discus- 
sion and enquiry before the Society of Civil Engineers, having for their object to 
throw light on the subject of boring to a great depth for overflowing springs. 
