132 Mr. William Galhraith, on some 



second. Such is also the case with the errors of pointing, 

 or those arising from directing the intersection of the cross 

 wires of the telescopes to the objects observed, which, though 

 small of themselves, are destroyed like those of the level by 

 their fortuitous compensation in many thousands of obser- 

 vations. These errors exist also (though I may add in a 

 less degree) in the observations made with large instru- 

 ments, as the mural circles. For the error of pointing is 

 still found, though diminished by the greater power of the 

 telescope, and that of the level is represented by the error 

 of the plumb-line. But in this case the small number of 

 observations does not admit of a compensation as exact as 

 in the repeating circle. If we suppose that the accuracy 

 of mean results is in the ratio compounded of the number 

 of observations, and of the length of the radius of the in- 

 strument, one hundred observations made with a repeating 

 circle of two decimetres, or about eight English inches 

 radius, would be equivalent to one observation made with a 

 mural circle of twenty metres radius, or about sixty-six 

 English feet. " Could we obtain such instruments," says 

 M. Biot, *' and, above all, could we employ them in obser- 

 vations which require us to transport them from place to 

 place ?" Now, though the repeating circle is in the hands 

 of an able observer an instrument capable of great pre- 

 cision, yet we cannot assent to the extravagant eulogium 

 thus betowed upon it by M. Biot in his Astronomic Phy- 

 sique, because it rests on assumptions too gratuitous to be 

 grarxted without qualification ; and, as we have already re- 

 marked, he has not alluded at all to the errors inseparable 

 from its construction, and the method of using it when exe- 

 cuted by the best artists. 



However perfect the damping screws may be, yet still, 

 by repeating the observations, repeated small relative mo- 

 tions by pressure must take place between the verniers and 

 limbs, which remain as a constant error that no continua- 

 tion of the process of repetition can remove, because it 

 arises from that very principle. If, however, an equal 

 number of observations at nearly equal zenith distances on 

 opposite sides of the zenith be taken, then on the principles 

 of probabilities, it may be expected that the errors from 

 this cause will likewise have a tendency to destroy each 



