24 



has two microscopes ; so also those made of a portable size by Messrs. 

 Gary and Troughton ; the circles of Dr. Brinkley and Professor 

 Gauss have 3, 90° asunder ; Mr. Troughton makes his reflecting cir- 

 cles with 3 equidistant verniers, Mr. Reichenbach's instruments have, 

 I believe, four, and the Greenwich circles have six microscopes. 

 Among these influential names, that of Mr. Troughton will weigh 

 the most with all who feel the high perfection to which he has carried 

 the art of which he is the pride and ornament. He evidently consi- 

 ders multiples of 3 preferable to those of two. Mr. Pond also speaks 

 highly of 3, though from circumstances probably connected with the 

 difficulty of illumination, he uses but two when the utmost precision 

 is not required. 



Since the publication of Mr. Troughton's method of graduation, 

 original errors of division are scarcely to be feared, and those 

 which we have to consider arise from excentricity, from expansion of 

 the materials of the instrument, and from the flexure by its own 

 weight. 



1. Excentricity is of two kinds which may be called variable and 

 fixed ; the latter existing when the line connecting the centres of 

 the pivots on which the axle turns does not pass through the centre 

 of its graduation, the former caused by a defect of the figure of the 

 pivot. As the deviation from a circular figure is always minute, we 

 may suppose the section of the pivot to be an ellipse of small excen- 

 tricity : supposing this to roll in a rectangular Y, as is usual in as- 

 tronomical instruments, it is easily shewn that its centre describes 

 round the angle of the Y a circular arc whose radius is r x \/2 — e^, 

 and its sine ^ e^ x sin. 2 0, r being the greatest semidiameter of the 

 pivot, 6 the angle made by it with the vertical. Hence we see that 

 the horizontality of an axis supported by such a pivot is not changed 

 during its revolution, but that its extremity moves in azimuth through 



