370 Astronomical and Nautical Collections, 



D. Of the Density of the Atmosphere. 

 The corrections for the height of the barometer and thermo- 

 meter may be taken from the new table in the Nautical 

 Almanac for 1822, and applied immediately to the correction 

 of the moon's altitude, (R. T, VIII.) as well as to that of the sun 

 (R. T, Appendix); and they will obviously affect the magnitude 

 , of the true altitudes employed in the correct computation. The 

 logarithmic differences of Dunthorne (R. T. IX.) may be rea- 

 dily corrected for temperature and pressure, by adding "8, or 

 .000008, for every inch that the barometer is above 30, and "05, 

 or .0000005, for every degree that Fahrenheit's thermometer is 

 below 50° ; or subtracting a similar quantity when the baro- 

 meter falls, or the thermometer rises. 



E. Example of all the Corrections. 

 Let the latitude be 35°, the observed distance of a star from 

 the moon's nearest limb 30° 57' 12'', the altitude of the lower 

 limb 8° 10', and that of the star 35° 40', the height of the 

 barometer 28.70, and that of Fahrenheit's thermometer 78° ; 

 the moon's semidiameter at the time being 16' 22", and the 

 horizontal parallax 60' 0". 



A. The augmentation of the moon's semidiameter (R. T.) 

 being 2", and the diminution for refraction (A) 11", the correct 

 vertical semidiameter is 16' 13". 



B. The ellipticity requires a deduction of 4" from the paral- 

 lax, making it 59' 56" instead of 60'. 



C. To find the oblique semidiameter, we have k — 37°, k — s , 

 — 1°, and d zz 31°, whence the argument is found 90 -j- 924 

 -f 29 3: 1043, or 43, rejecting the 1000 ; whence the diminu- 

 tion is 10", and the oblique semidiameter, instead of 16' 24", 

 becomes 16' 14". 



D. For the density of the atmosphere, the moon's refraction 

 at 8° 26' requires a diminution of 27" x 1.3 =: 35" for the ba- 

 rometer, and of 2" x 28 — 56" for the thermometer, making to- 

 gether r 31"; and the star's, at 36°, a diminution of 2",68 

 X 1.3 = 3",5, and ",161 x 28 = 4",5, making 8": and the 

 correction of the logarithmic difference for the same variations 

 will be — 1'04 — 1-40 = — 2-44. 



