1':^ Royal Astronomical Society. 



four spindles, Nos. 1, 2, 3 and 4, No. 1 revolving in a mean solar 

 day of 24 hours, and if No. 1 carries a wheel of 96 teeth working in 

 a wheel of 79 teeth on No. 2, and if No. 2 also carries a wheel of 157 

 teeth working in a wheel of 133 teeth on No. 3, and if No. 3 also 

 carries a wheel of 72 teeth working in a wheel of 103 teeth on No. 4, 

 f len No. 4 will revolve in 23^ 56"" 4»-09235. The length of the side- 

 real day adopted in the Nautical Almanac is 23'> 56"^ 4»-0906. The 

 approximations to it obtained above are very remarkable. By reversing 

 the same train of wheels, accurate motion corresponding to sidereal 

 time will be made to generate motion corresponding with the same 

 degree of approximation to mean solar time. 



A Method of Correcting the Errors due to the Forms of the Pivots 

 of a Transit Instrument. By Professor Challis. 



The method proposed by the author requires the solution of the 

 following problem : — Having drawn from a selected point of the 

 middle wire of the telescope, situated near where the transits are 

 usually taken, a straight line to the optical centre of the object- 

 glass, it is required to find, independently of the forms of the pivots, 

 the small angle made by this line with the plane of the meridian for 

 any position of the telescope. The solution of this problem may be 

 effected by employing Bohnenberger's collimating eye-piece in con- 

 junction with the method of measuring by micrometer-microscopes 

 the positions of two dots at the extremities of the pivots, first sug- 

 gested by the Astronomer Royal and applied by him in testing the 

 forms of the pivots of the new altitude and azimuth instrument at the 

 Greenwich Observatory. The collimating eye-piece gives the angle 

 (a) which the line of collimation makes with the meridian plane 

 when the telescope is directed to the nadir. If y, y^ ^e the vertical 

 microscope readings for bisections of the dots in this position of the 

 telescope, y\ y\ be the vertical microscope readings, and x\ x\^ the 

 horizontal microscope readings for bisections of the dots, when the 

 telescope is pointed to an angular distance, z, from the zenith south- 

 ward, and ^ be the small angle required, then 



^=a+ ^^ — — + p. — ^-icos z+ — i — —5 sm z, 



D being the distance between the dots, and h and k certain con- 

 stants, by means of which the readings of the two microscopes are 

 referred to the same vertical and horizontal planes. The constant k 

 is found by measuring the difference of altitude of the dots in re- 

 versed positions of the instrument, the telescope being directed to 

 the nadir, and at the same time noting by the collimating eye-piece 

 the change of inclination of the line of collimation to the vertical 

 caused by the reversion. The correction to be applied to an ob- 

 served time of transit across the middle wire to reduce it to the time 



t 

 of meridian transit is-5-x cosec N.P.D. Hence A may be found 



15 ^ 



by two consecutive transits of Polaris. These constants being 

 known, the angle ^ may be calculated for zenith distances separated 

 by intervals of 5°, and extending from — 90° to + 90°. The differences 

 "between these values of ^ and the values of the same angle which 



