Translation from the Astronomical Jour, of Hamburgh. 229 



sides made upon twelve different parts of the division. This 

 two feet theodolite is very properly considered as the main 

 instrument for the survey. For the other observations, re- 

 peating circles of eighteen inches, repeating theodohtes of 

 twelve inches, and repeating reflecting circles of ten inches 

 diameter, smaller theodohtes, needles, planetables, &c. are 

 provided. To the most of these instruments Mr. H. has giv- 

 given a peculiar construction, but it would be too long, and 

 perhaps without figures not sufficiently intelligible, to give a 

 description of them here. 



As signals Mr. H. employed truncated cones of block tin, 

 about nineteen inches high, seventeen inches diameter at bot- 

 tom and fourteen at top ; these were erected upon poles eight 

 feet high, and rendered the best services. At a distance of 

 about forty (English) miles they appeared as a luminous 

 point, when the sun stood so that the rays of it were reflec- 

 ted towards the observer, which lasted during a sufficient 

 length of time. At shorter distances the light was so strong, 

 that a dark glass was often required for the observation. 

 Here the same principle is made use of which in Mr. Gauss's 

 heliotrope, produces such a decided effect, but the advan- 

 tages of the different arrangements are very unequal, because 

 the cones of Mr. H. do not constantly reflect an image of 

 the sun to the observer, while the heliotrope is constantly 

 kept in the proper position to produce this effect. If the an- 

 gle of the cone is represented by 2 m, then the cosine of half 

 the azimuthal angle, when light shall be reflected to the ob- 

 server, must be equal to the sine of half the sun's altitude 

 divided by the sine of m. This would take place only du- 

 ring a moment if the sun had no diameter, and generally 

 speaking, one signal would be invisible, when the other is 

 visible, but as, m, is only a small angle, in the cones used by 

 Mr. H. it is only 4° 38' ; and as from the altitude of the sun, on 

 account of the magnitude of its disk, two limits may be accep- 

 ted, which are at 32' distance from each other, the azimu- 

 thal distance corresponding to the altitudes of the sun, which 

 admit of a reflection to the observer in a direction nearly ho- 

 rizontal, has a considerable magnitude within these Hmits ; 

 it therefore can have rarely happened, that both the signals 

 needed for the measurement of an angle, could have shewn 

 at the same time, an equally well reflected image of the sun ; 

 it seems therefore, that the use of these signals might rather 

 be recommended in particular cases than generally. Hovv< 



