154 
Analyses of Boohs. 
using the time for the calculation of the azimuth. The alteration of the azimuth, 
however, from a variation in the refraction, should be taken into account ; and there- 
fore the altitude of the star must be obtained. It would not be “ necessary to ob- 
serve the star when very near the horizon, as the error in the azimuth arising from 
the level decreasesas the tangent of the altitude ; and at an elevation of 1 2°, is scarce- 
ly more than two tenths of the error in the horizontally of the axis of the telescope." 
In determining the differences of level of the several stations, the refraction was 
found to vary from T ' T to i* s of the contained arc the mean value being 
The result of the whole is, that Calais is east of Greenwich 1°. 51'. 18", 7. and 
adding 0°. 28° 59" the difference of Calais and Paris, we obtain 2°. 30'. 17".7. or 
9m. 21,18s. as the difference of longitude of Paris and Greenwich ; “ differing 28s. 
in defect, from the admirable results obtained by the operations with fire signals 
(Phil. Trans. 1826) bv Mr. Herschel.” 
It is proposed, at some future period, to repeat the measurement of the base. At 
present, the truth of the above result depends on the accuracy with which General 
Roy’s operations were conducted. 
In an appendix. Captain Kater throws together such remarks, as could not very 
well be introduced in the body of the work. 
On the subject of applying five microscopes instead of the former pair, he enters 
into considerable detail ; and shows this method to be preferable to taking the angle 
on various parts of the limb. With one reversal, readings are obtained on 10 differ- 
ent parts of the limb ; which would be equivalent to changing the zero (using 2 mi- 
croscopes) five times. He states Mr. Pond to be the original proposer of this very 
important suggestion. As the second original microscope was not removed, it afford- 
ed an opportunity of comparing the results by the two methods. We shall note 
some of these differences. The greatest difference of the mean of 10 microscopes, 
direct and reversed observation, is 4",1 that is, when confined to the same divisions; 
but if the divisions he changed, the difference goes to 7",0. These differences are, 
it may be well supposed, generally much less ; but it is the knowledge of the extreme 
differences that is useful, as enabling the observer to say what he can calculate on. 
The first difference 4",1 must be due either to the imperfection of the observation, 
or to some uncertainty of the microscopes, or reading of them, or lastly, and this 
appears to be Captain Rater’s view, to lateral refraction. The difference of 7 ,0 
and 4", 1 2”, 9 must be, we suppose, the effect of. errors of division, and must 
therefore represent the amount of the sum of 40 errors -J- and — . The greatest dif- 
ference in the results of 5 and 2 microscopes (two observations each) is 7", 8. In 
general it is scarcely 2" and when the observations are taken on different points of 
the limb, the mean result deduced from 5 microscopes and from 2 scarcely differ 1 ' 
on an average, certainly not more. We may draw one conclusion from these details, 
if observations on different parts of the limb of this instrument, which is 3 teet dia- 
meter, on a mean of 10 microscopes, differ 7' ,0; then on a circle 1 feet in diameter, 
with only 3 verniers, they may well differ 7",0 X 1 — 21" which as such a circle 
is divided to 720° = 42".* 
In the course of this work Captain Kater remarked a curious fact, which was 
new to him. “ In hazy weather when the staff was so faint as to be only just visi- 
ble, it disappeared upon bringing it to the intersection of the cross wires, so that the 
angle, could not be observed. A remedy for this inconvenience was suggested and 
put in practice by Mr. Gardner. The horizontal spider's Web of the micrometer 
being moved about the ceutre, Mr. Gardner succeeded in lodging upon it a particle 
of dust. When the inrage of the staff was brought to this, it appeared as if planted 
upon a mole hill, and we were thus enabled to observe with great accuracy. I con- 
sider this as a very important improvement in the theodolite ; and we availed our- 
selves of it upon all occasions, excepting in the observations of the pole star.” 
Some trials were made by the two methods of intersection, and it was found that- 
with the dot the facility was nearly twice as great, as measured by the time taken to 
make ten observations. The precision too was greater, as with the dot the. extreme 
difference from the mean was 4", while with the cross wires it was 7." Captain 
Kater considers these quantities as the maximum values of the errors due to the 
telescope and microscopes. 
Much stress has been laid on an objection, often made, as to the unequal expan- 
sion of the limb of a circle. It was satisfactorily determined, that though the read- 
ings of the different microscopes, one being assumed as a standard, were different on 
disturbing the equilibrium of temperature, yet the mean appeared to be always the 
same : this is an additional reason for using a number of microscopes, 
* Tile difference has been found by actual examination to be about 40." 
