accurate Survey of the United States of America. 405 



free from eccentricity, from any error arising from the incli- 

 nation of the circle towards the axis, or from any inequality 

 in the supports of the axis, the readings being besides made 

 upon twelve different parts of the division. This two-feet theo- 

 dolite is very properly considered as the main instrument for 

 the survey. For the other observations, repeating circles of 

 eighteen inches, rei)eating theodolites of twelve inches, and re- 

 peating reflecting circles of ten inches diameter, smaller theo- 

 dolites, needles, plane-tables, &c. are provided. To the most 

 of these instruments Mr. Hassler has given a peculiar con- 

 struction, but it would be too long, and perhaps without figures 

 not sufficiently intelligible, to give a description of them here. 



As signals Mr. Hassler employed truncated cones of block- 

 tin, about nineteen inches high, seventeen inches diameter at 

 bottom 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 reflected 

 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 advantages of the 

 different arrangements are very unequal, because the cones of 

 Mr. Hassler 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 angle of the cone 

 is represented by 2 in, then the cosine of half the azimuthal 

 angle, when light shall be reflected to the observer, must be 

 equal to the sine of half the sun's altitude divided by the sine 

 of m. This would take place only during a moment if the 

 sun had no diameter, and generally speaking, one signal would 

 be invisible, when the other is visible ; but as ?k is only a small 

 angle, in the cones used by Mr. Hassler 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 assumed which are at 32' distance 

 from each other, tiie azimuthal distance corresponding to the 

 altitudes of the sun, which admit of a reflection to the ob- 

 server in a direction nearly horizontal, has a considerable 

 magnitude within these limits. Yet it can have rarely hap- 

 pened, that both the signals needed for the measurement of an 

 angle, could have shown at the same time an c(|ually well re- 

 flected image of llie sun ; it seems therefore that the use of 

 these signals might rather be reconuncndcd in particular cases 

 than geucnilly. However, Mr. Hassler says, tliat even with- 

 out 



