Description of a new Transit Instrument. 5 
Now, suppose the transit instrument, whose axis is accurately 
levelled, and of course in the meridian at Z, to pomt at the ho- 
nzon to K (it is obvious from its construction that the tele- 
scopic axis will be at right angles to the meridian line) instead 
of I, the true meridian; then at 3 (the altitude of the pole star 
under the pole) it will point at B, and the arch 3 B will be to 
IK as the cosine of the altitude 3 I to radius ; but 3 B, measured 
on the diurnal circle of the pole-star, will be the sine of its di- 
stance from the meridian to the radius P3 or PB: and as, in 
small arches, the arch of a great circle, or of a small circle, or 
their sines, are nearly coincident, we shall have very nearly, As 
Z3 (the zenith distance) to P3 (the polar distance), so is the 
value of 3 B, in degrees of the pole-star circle, to its value in 
degrees of a circle whose radius is Z3. And as the radius Z3 
is to P 3 very nearly as 23 to 1 , the error of the transit telescope, 
at the altitude 3 I, will be measured by a scale (if it may be so 
called) 23 times as great as itself, 
Now, let there be another star A, whose northern meridian 
altitude is as small as it conveniently can be; for example, 5°, 
whose polar distance is, therefore, 46° 30’, and whose right 
ascension is the same as that of the polar star; then, if the 
transit telescope be in the meridian, both these stars will pass 
through it at the same time ; but if it be out ef the meridian by 
the quantity IK, the star A will pass through it when it comes 
to C, but the polar star not till it comes to B, when the star A 
is got to D, in its diurnal circle. 
The value of AC being therefore found, by multiplying IK by 
the cosine of its altitude Al, that value being reduced to the 
angular value to the radius PA, will give the time of the star A 
passing through the transit telescope, after the time of its 
passing the meridian; and the same operation being performed 
for the pole-star as before directed, the difference of these times 
will be the error in time of the transits, answering to the given 
deviation IK of the transit telescope, And tables having been 
previously constructed for such stars as shall be thought con- 
venient, the transit telescope may, in a very short space of 
time, be set to the meridian, with a degree of precision unattain- 
able by any other method. 
If the star A precedes the pole-star in its passage under the 
pole, rio tables are requisite, nor any thing necessary tu be known 
but the exact difference of the right ascension between the two 
stars; for, having observed the transit of the star A (the in- 
strument being previously brought near the meridian, suppose 
half a degree), then elevate the telescope to the pole-star, by 
moving the horizontal adjustment of the axis : keep the pole- 
star on the middle wire till the due interval of time between 
As their 
