GALBRAITH'S ASTRONOMICAL OBSERVATIONS. 
585 
306. M scandens. On the Ghauts. 
307. ,, Sirissa. 
308. ,, glaucit. 
309. „ dulcis. 
{To be continued.) 
ON SOME METHODS OF ASTRONO- 
MICAL OBSERVATION. 
By William Galbraith, A. M., 
Teacher of Mathematics, Edinbursrh, 
(Continued from pat'C 452.) 
ON THE METHOD OF FINDING THE VALUE OF 
THE DIVISIONS ON THE SCALES OF LEVELS 
applied to altitude and azimuth cir- 
cles, REGISTERING OBSERVATIONS, &C. 
All the more usual astronomical instru- 
menis have a level applied to them so as to 
insure the verticality of their axis, or to make 
the necessary allowance for their deviaiion 
from it. The scale of the level is so graduated 
as to show single seconds, or some multiple 
of the second, and reads most conveniently 
from a central zero. In those instruments 
that revolve in azimuth, which all the smaller, 
and more especially the portable, circles do, 
(andeventhe largeeight feetcirde at Dublin, 
though provided with a plumb line ratlier in- 
conveniently situated, and the most accurate, 
perhaps in principle, of any hitherto con- 
sti ucted,) the observations are repeated several 
times in pairs near the meridian, reading the 
divisions at both extremities of the air bubble 
on the scale of the level each time along with 
the verniers or microscopes. When there are 
three vernieis and aliout six observations 
made, it is advantageous to have a simple and 
convenient method of registering the obser- 
vations, tak’ing the means, and allowing for 
the effects of the level. 
The value of the divisions of the level is 
generally got from the maker, or it may be 
readily found by an instrument called the 
level trier, consti ucted expressly for this 
purpose. 
If the observer has not had these communi- 
cated to him, or if he wishes to satisfy him- 
self with regard to the accuracy of the values 
given to him along with the instrument, he 
may either ascertain these by tiie circle itself, 
when the verniers or reading microscopes are 
competent to the purpose, or he may have 
recourse to the following methods, which, in 
the course of my experience, I have found 
very convenient. 
1. Put up the usual levelling rod of the 
best constiuction truly vertical, at such a 
distance from the circle as may be most con- 
venient, tliough somewhat considerable. 
2. Set the level exactly in the direction of 
two of the feet screws, or one perpendicular 
to the line joining the other two, when there 
are three; clamp the verniers, and direct the 
intersections of the cross wires of the telescope 
to the mark on the sliding vane, which must 
be moved up or down till an exact coincidence 
takes place. 
3. By turning one of the feet screws cause 
the bubble to move through a given number 
of the divisions of the scale, comprehending 
those usually employed in recording observa- 
tions, while at the same lime the sliding vane 
must be moved till its mark again coincides 
with the intersection of the cross wires in the 
telescope, still clamped to the circle, and the 
number of divisions on the rod which it has 
passed over to thoasandths, or, at least, hun- 
dredths of a foot, by this motion must then 
be recorded. 
4. Measure the horizontal distance with 
great care between the eentre of the circle 
and the levelling rod. These afford data for 
computing trigonometrically the value of the 
divisions of the scale of the level. 
5 To investigate foimulse for this purpose 
let R be the length of an arc equal to the 
radius in seconds, D the horizontal distance, 
d the distance passed up or down by the vane 
A" the arc in seconds subtended by d, at the 
distance D then by the principles of trigono- 
metry, 
R" X d 
— 
If L be the length of a given number of se- 
conds. a ’ on the scale of the level, and r the 
length of the whole run in the same measure as 
D and d, 
D X «■' X r 
L- .. (2) 
R X d 
Indeed, if any four of the five quantities, D, 
d,r, a", and L he known, the value of the 
fifth may be found by transforming the pre- 
ceding equation, tlius; 
R" X L d 
«■ = — T (3) 
D X >• 
If n be the number of divisions in the run 
of the level , 
R" X d 
= (4) 
D X w 
If p be the radius of curvature of the level, 
R" X L R' X r 
p=—— .. .. (5) 
a" A" 
Examples for the use of these formulae. 
1. Tlie cross wires of the telescope of an 
astronomical instrument, at tlie distance of 
250 feet from a levelling rod, moved over two 
inches in a run of tlie bubble through an inch 
and a half, by turning the feet screws in the 
flirection of the level and rod, what was the 
value of the whole arc A ' passed over by the 
bubble, and the length L, of a division of a" 
(10 ) on the scale of the level ? 
R" X d 
By formula (1) A” 
D 
206264"-8 
X 2 
=137' 
’.5l 
3000 
By formula (2) L ^ 
30OO X 10 X 1.5 
D X a" X r 
R X d 
2062G4’8 X 2 
:Oa09 in. 
