130 Mr, William Galhraith, on some 



proper time near the meridian ; on the principles of the 

 theory of probabilities, the errors arising from all the dif- 

 ferent causes affecting the accuracy of the results must, in a 

 great degree, destroy each other. 



Though this conclusion is the most probable in reference 

 to a steady well constructed instrument, yet it must be re- 

 ceived under certain qualifications, since too much praise 

 has doubtless been lavished on the omnipotence of Borda's 

 repeating circle, especially by foreigners. M. Biot, after 

 explaining the principles of the repeating circle, says, ** Let 

 us examine, novr, in vt^hat respect the repeated multiplica- 

 tion of the angle proves advantageous. It would have none, 

 if the divisions cut upon the circle were mathematically 

 exact, and if the observer could direct the intersections of 

 the cross wires in his telescope perfectly correct, for, in that 

 case, one observation would give the zenith distance exact. 

 But as these conditions cannot be accomplished in practice, 

 the repetition of the angles supplies the defect by compen- 

 sations. With regard to the error of the divisions, it is 

 clear, that the arcs measured, follow without interruption 

 upon the limb, in such a manner that the print of the 

 limb, which is the termination of the previous observa- 

 tion, becomes the origin of the succeeding. From this it 

 follows," says M. Biot, " that the sum of the observa- 

 tions, or the whole arc passed over by the verniers, com- 

 prehends no intermediate error, but the errors of the two ex- 

 treme readings at the commencement and termination of 

 the observations." That this conclusion of M. Biot may be 

 true, it is necessary that there be no, or at least an insen- 

 sible, resistance in the centre work to the action of the tan- 

 gent screws, and that there is no imperfection in the tangent 

 screws in producing motion, nor in the clamping screws in 

 securing permanent positions. Now, it is clear that if 

 there is the least defect in all or any of these, M. Biot's 

 conclusion will be erroneous, and such must of necessity be 

 the case to a certain degree, since it depends upon the ma- 

 terials of which the instrument is constructed, and cannot 

 be removed by the abilities of the artist, or the perfection 

 of the workmanship, however excellent it may be. Hence, 

 it necessarily follows that a slight relative motion must take 

 place between the verniers and the circle for each repetition, 



