Mechanical Science. 605 



an horizontal cylindrical axis, exactly similar to the axis on which the 

 telescope of the transit revolves. The instrument is first so placed that 

 the telescope descrihes a vertical line not much differing from the 

 meridian. Transits of stars north and south of the zenith are then 

 ohserved in the two contrary positions of the axis. The time of the 

 place of observation, and the azimuth of the axis of revolution, will 

 thus be obtained. The compass is next substituted for the telescope, 

 and the difference between the magnetic and astronomical azimuths 

 immediately determined, the compass being furnished with the neces- 

 sary means for ensuring the parallelism of the diameter of the com- 

 pass passing through the zero of the divisions, and the line passing 

 through the middle of the cylindrical axis of the compass resting on 

 the Ys of the transit. M. Erman estimates the error which may 

 arise from the determination of the time at 5", and that from the 

 mean of all the readings of the compass needle at 30", so that 

 the whole uncertainty of the determination would not exceed 30" or 

 40". There were considerable differences between the observed va- 

 riations, according to the time of the day in which the observations 

 were made. M. Erman took, therefore, sets of hourly observations, 

 embracing altogether nearly two full days. The observations could 

 not be brought to perfect regularity ; but he found in general that 

 the maximum of variation is at about 2h. P. M., and exceeds the 

 mean variation by 10', whereas the minimum, which takes place be- 

 tween six and eight o'clock A. M., falls short of it by about 8'. It 

 is remarkable that the time of the maximum thus found at St. Pe- 

 tersburgh agrees with that observed in the more western parts of 

 Europe, but that the minimum which, in western Europe, is found 

 to take place at 2 h . A.M., should be found by M. Erman's observa- 

 tions to be six hours later at St. Petersburgh. The mean variation 

 at St. Petersburgh, in the beginning of June, 1828, may be taken 

 at 6 47' 20", which is not likely to deviate more than a minute 

 from the truth. 



ii. Dip of the Needle. The dipping compass which has been 

 employed was made by M. Gambey for Professor Hansteen's ex- 

 pedition. The vertical circle is ten inches in diameter, and is 

 divided to ten minutes. The instrument is furnished with two per- 

 fectly similar needles, with cylindrical axes that terminate in steel 

 points of about two- tenths of a line in diameter. With these thin 

 ends, the needles rest on convex pieces of agate of a high polish. 

 The artist has endeavoured to construct the needles in such a manner 

 that there should be but a slight difference between the centres of 

 gravity and of figure. This construction allows to dispense with the 

 employment of counterpoises, as invented by Meier, which, in 

 needles of less exact equilibrium, serve to magnify the errors arising 

 from the position of the centre of gravity, in order to be eliminated 

 by calculation. It is easily proved that, if the centre of gravity 

 differs little from the centre of the figure, the formula of Meier is 

 reduced to the taking of the arithmetical mean between the readings 

 before and after the inversion of the poles of the needle in two con- 



