176 Mr. Nixon on the Curvature of Spirit-Lcvcls. 



quisite degree of accuracy, it will, however, be necessary, as an 

 error of one minute might be committed in the graduation of 

 the arc, or in the reading off, to continue the operation of 

 first depi'esslng the telescope by the same screws of the parallel 

 plates, and of subsequently elevating it by the tangent-screw 

 of the vertical arch, noting in the proper column after every 

 depression or elevation of the telescope the distance of the 

 ends of the bubble from the zero of the scale, until a sufficient 

 multiple of the mean angle shall be obtained. Lastly, find 

 the sum of each column, and divide the angle read off the 

 vertical arch by half thuir difference, which will give the value 

 in seconds of one division of the scale. The original scale 

 may now be taken off, and the one substituted, divided into 

 e(jual parts of one second each. A black-lead pencil being 

 used in marking and numbering the divisions, the whole may 

 be varnished over to prevent obliteration, &c. 



The reversing point of a similar level will be equal to one- 

 fourth of the sum of the divisions from zero of the extremities 

 of the bubble noted before and after reversing the telescope 

 within its Ys. Temporary reversing marks may be conve- 

 niently made on the tube with a camel-hair pencil dipped in 

 white water-colour ; each mark being equidistant from the 

 division, answering to the reversing point by half the length 

 of the bubble. In addition to the facility and accuracy with 

 which minute vertical angles may be measured on a similar 

 scale, it would be found particularly serviceable in a novel 

 method of levelling, of which I shall beg leave at some future 

 opportunity to transmit a notice. 



The two levels of the horizon-sector are mounted in brass 

 cases, in which, as the telescope requires to be inverted at 

 every other observation, they are necessarily fitted as closely 

 as practicable. Each division of the scale of forty to the inch, 

 was found from repeated trials with the sector, to be l"-906 

 in the right-hand level, and 2"- 124 in the other ; or double the 

 estimated value. As the (glass) tubes are slightly fiexible, 

 I suspected that their curvature might have been augmented in 

 the mounting, and made the following experiments with the 

 shortest of the two spare levels, with a view to gain informa- 

 tion on the subject. 



Experiment I. — Two Ys, cut out of a mahogany board 0-1 

 inch thick, were glued to the upper surface of an inflexible bar 

 of oak laid securely on the cylinder of the sector. The short 

 level furnished with a scale was then placed quite loose within 

 the Ys, each end overhanging its Y by one-diird of die length 

 of the tube. The space traversed by the bubble of the short 

 level being compared with that passed over by the bubble of 



one 



