282 Royal Astronomical Society. 



When the causes of error in measuring an angle, terrestrial or ce- 

 lestial, are separately considered, the sum of the errors of division 

 and of reading off will in some cases be much larger than the error 

 of bisecting the object or of reading off the level. Whenever this is 

 so, then, supposing no fresh error to be introduced, the repeating 

 principle may be advantageously applied, since the errors of division 

 and reading off are divided by the whole number of observations, 

 and not by the square root of the number, as is the case in non-re- 

 peaters. 



The defect most to be feared in repeating instruments is the slip- 

 ping of a part which should be fixed while another part is moved. 

 This may probably be avoided in the repeating stand for a theodolite, 

 by making the lower motion exceedingly heavy while the upper mo- 

 tion is exquisitely light, and by affixing the clamp of the stand at as 

 large a distance as may be from the centre of motion. By measu- 

 ring the angle twice over, first moving the theodolite and stand the 

 same way, and again moving them the contrary way, any error from 

 slipping will be detected. The coincidence of results by the two 

 methods will be a satisfactory test of their truth. 



When the repetition is in altitude, the level, if attached to the 

 circle, is a sufficient protection against slipping. It is, perhaps, 

 owing to the mistake of fixing the level to the vertical axis, and po- 

 lishing the limb so highly that the clamp could not bite hard, that 

 the repeating circle lost much of its reputation. 



In Borda's circle, the clamp for moving the vertical circle is in- 

 conveniently placed ; two observers are required (unless the support 

 of the instrument is immoveable), and the telescope, in the original 

 construction, 1 ^ very loosely held. The last fault is easily amended, 

 and by sacrificing the motion round the upper axis (which is utterly 

 useless in an astronomical instrument), a convenient situation may 

 be given to the circle clamp. Mr. Sheepshanks exhibited a form of 

 the instrument which can be used single-handed. The line of sight 

 of the telescope is turned by a prism down the tube which forms the 

 axis of the vertical circle ; thus the observer, without changing his 

 position, can read off the level immediately after the bisection of the 

 star ; but the instrument has not as yet been tested experimentally. u 



To measure the effect of flexure in the telescope, which seems to 

 be the only fixed source of error in this class of instruments, Mr. 

 Sheepshanks proposes either to measure the angle of 180° between 

 two collimating telescopes, after Bessel's method, or to observe the 

 circum-meridian altitudes of the same star in three fashions : first 

 in the ordinary manner, in which the flexure tells one way ; secondly, 

 observing the star in mercury, where the nadir distances will be 

 affected by flexure to the same amount but the contrary way from 

 the zenith distances ; and thirdly, by stepping from the star seen 

 directly to the star seen by reflexion, which is not affected by flex- 

 ure at all. A careful set of observations would probably give the 

 constant of flexure with great nicety. 



