ASTRONOMY AND GEODESY. 



l^^O 



Numbers 1, 3, 5, and 6 are by myself. Numbers 2 and 4 are by Lieutenant Whipple. 



The tracing of the line on the ground was partly by mj^self and Lieutenant Whipple, but 

 chiefly by Captain E. L. F. Hardcastle, corps topographical engineers. 



The computation of the azimuth of the line was made in the field. In this computation the 



earth was supposed to be a spheroid of revolution of the following dimensions, wliich are those 



determined by Bessel from all the measurements up to that time, (1849,) and the elements 



given by him were converted into English measure by adopting the following value of the 

 metre, viz : 



39.6850 inches; logarithm 1.5951741293. 



Equatorial radius = G974129.339 yards. 



Polar radius - = 6950815.059 '' 



I am indebted to Professor Airy for the observations at Greenwich for 1819 ; and for the 

 recomputation of the longitude and the application of the correction due to the corresponding 

 observations on moon and moon culminating stars^ I am indebted to the assistance of Professor 



Hubbard 



I. LONGITUDE 01 CAMP RILEY, NEAR TUE INITIAL POINT. 



The observations with the transit instrument have been reduced in the following manner: 



The equatorial intervals of the transit wires having been determined as accurately as possible, 

 the imperfect transits were corrected, by applying to the mean of the observed wires the mean 

 of their equatorial intervals, multiplied by the secant of the stars* declination. 



For circum-polar stars, each wire was reduced separately, and the mean of the results taken. 

 In the case of the moon, allowance was made for its motion hy the method and tables of Bessel. 

 (TabuliB Regiomontann3, pp. LII and 537.) 



Denoting by a the constant of correction for azimuth of the instrument, by I the constant for 

 level, and by c that for collimation, and by d the star's right ascension, S its declination and z 

 its zenith distance, and by t the chronometer time of its transit, and by A t the correction of the 

 chronometer at the time ty we have the known formula — 



a=: t -{- ^ t -{- a sin. z. sec. ^ -f~ ^" cos. z. sec. 8 -j- 



If ^ denote the latitude of the observer, and if 



m =: b. COS. f -{- a. sin. ^, 

 n =z b. sin. ^ — a. cos. f^, 



the expression above becomes 



a 



^_j_ Af-j-OT + 7i. tan. d -{- c. sec. S^ 



or a = f + A ^ -|- w -f (n -j- c.) tan. o + c. (sec. o — tan, d) 



which last form has been employed in the reductions. 



In the observations at Camp Eiley, c = o for nearly the whole series, and is small enough at 

 all times to have no effect in the last term of the formula ; in the other series, one or two cases 

 occur where it has been necessarv to take this last term into account. 



Where, as in the present case, only the right ascension of the body is wanted, the quantities 

 A t and m being constant for the evening, may be combined together, and then the last term of 



Vol. 1—^19 



