258 PROCEEDINGS OF THE AMERICAN ACADEMY 



such a value as to make the angle at D nearly twice the diameter of 

 the field. To determine the degree of accuracy attainable with such 

 an instrument, suppose the diameter of the field of view 1'^, and that 

 an error of .1' or 6" is committed in the measurement, — a large error, 

 considering how accurately seconds are determined with the spider-line 

 micrometer in astronomical work. Su2)pose, again, that the object D 

 is ten thousand metres distant, or 6.21 miles, and that AB \?, taken 

 equal to two hundred metres : the error in question would then equal 

 only fourteen metres, or forty-six feet, — a quantity quite insensible on 

 the scale proposed above. Again : if the object is fifty or a hundred 

 kilometres distant, it is only necessary to increase AB in the same 

 proportion, and we shall still be able to measui'e the distance of D 

 with the same proportionate accuracy, without yet using a base of 

 inconvenient length. In this way, if the country is dangerous, the 

 observer may measui'e the distance of all visible objects without going 

 far from camp. Comparing this instrument with the stadia, we see 

 that it has the advantage that it is not necessai-y to send a man to the 

 point to be measured, and that the accuracy is the same as if he could 

 carry a pole one or two hundred metres in length. 



Three methods have been employed for the determination of 

 heights. First, by the barometer. But this involves a visit to every 

 point to be measured, and, at the best, is very inaccurate. Observa- 

 tions in Switzerland and California have shown, that with the best 

 barometers, after applying all the known corrections, and even if each 

 observation is the mean of thirty, taken once a day for a month at the 

 same hour, at both the upper and lower stations, there still remains 

 an uncertain error, amounting sometimes to two per cent of the 

 whole height. How much greater, then, must be the error of a single 

 reading, often made without simultaneous observations below, and 

 with the defects of an aneroid added to the other errors! The most 

 accurate method of determining a height is by levelling ; but the labor 

 and expense of this are too great to allow its frequent use in moun- 

 tainous countries. The third method is that of zenith distances, 

 which is largely used in the Coast Survey for determining heights. 

 The altitude is here observed by a large vertical circle, which must be 

 read with the utmost precision, since the angle, if the object is distant, 

 rarely exceeds two or three degrees. It is claimed that at least an 

 equal degree of accuracy may be attained by the instrument described 

 below, while the expense of a graduated circle and delicate mounting 

 is wholly avoided. The principle employed is that of the zenith 

 telescope, so largely emjjloyed in determining the latitude. It consists 



