OF ARTS AND SCIENCES. 287 



The use of the micrometer level is limited to altitudes of three or 

 four degrees ; but within these limits the refraction and its uncertain 

 variations are so large that angular measurements of great accuracy- 

 are not required. The only instruments needed are the micrometer 

 level, a chronometer with some means of determining its error and 

 rate, a barometer, and a thermometer. 



The observations described below consisted in a series of determina- 

 tions of the corresponding altitudes and times at which the sun or a 

 star gradually approached the horizon. A complete observation con- 

 sisted in observing the temperature and pressure of the air, and de- 

 termining the error of the chronometer by comparing it with a standard 

 clock whose error was known. The micrometer level was then placed 

 in position on the west balcony of the dome of the Harvard College 

 Observatory, and its collimation and level constants determined as 

 described on page 2G9, The telescope was next turned nearly in the 

 direction in which the sun or star would set, and several readings of 

 the level taken in various azimuths. A series of measures was then 

 made of the apparent altitude of the object as it approached the hori- 

 zon, and the corresponding times. Finally, the preliminary measures, 

 or such a portion of them as seemed to be essential, were repeated. 

 When the sun was observed, the settings were first made on its lower 

 limb until it disappeared below the horizon, and then the upper limb 

 was measured until it also disappeared. For night observations, a fine 

 needle was inserted in the field, and this formed a dark bar, which 

 was visible against the sky without the necessity of a special field 

 illumination. 



A summary of the measures is contained in Table VIII., which 

 gives, in successive columns, a number for reference, the date, the 

 approximate Greenwich mean time, and the object observed. These 

 are followed by the number of settings made, the corrected atmos- 

 pheric pressure in inches, and the temperature in Fahrenheit degrees. 



Series 2 to 8 inclusive were made by Mr. D. B. Pratt, the others by 

 myself Of the settings, 329 were made on a Bootis, 294 on the upper 

 limb of the sun, and 122 on the lower limb, or 745 in all. 



The value of the instrumental constants employed are given in Table 

 IX. The successive columns give a number for reference, the date, 

 and the Greenwich mean time. The next four columns give the ap- 

 parent elevation of the object observed with the instrument placed m 

 its four diflerent positions, 0^, 0^„ E^, and E,,. The mean of these 

 four readings gives the apparent height of the object. The excess of 

 either of the four readings over the mean gives the correction to 



