MHO 



ASTRONOMY. 



LONGITUDE 



ulmmtiimi. and the results will consequently be affected 

 with the tabular error* of the moon'* right asconsion in 

 the tfautieal Almanac, an approximation to which, how- 

 erer, may be made by observations on other days at any 

 standard observatory. The methods of M. Uii inker and 

 Professor Strove are intended for corresponding obser- 

 vations ; the former having bean Applied in the determi- 

 nation of thu l.m-itii.K- -:->phens, New South 

 I, and Uu> lttr in tho longitudes of several places 

 in Turkey, during the years 1828 to 1833 inclusive. 



Tho first method of determining longitudes is by the 

 absolute right ascensions of the moon's limb, and is only 

 to be used when there are no corresponding observations 

 of moon-culminating stars. It consists in making two 

 assumptions of loiuitudf, differing by any known qu.in- 

 tity, and interpolating, for these times, the right ascensions 

 of the moon's limb from the numbers given in the section 

 of " Moon-Culminating Stars," in tho -Vauftrol Almanac. 



These tabular right ascensions are given fur tlu> time of 

 transit of the upper and lower mrridi.ui at Greenwich. 

 By comparing the interpolated data with the result of 

 the meridian oluorvation :it the place, the exact <li;)' r- 

 enoe of longitude may be found by a simple proportion. 

 Tho true difference of ! "ing supposed to Ho 



between two assumptions 1' different, the following will 

 be the proportion : 



As the difference of tho two interpolated R A.'s : 

 CO mo. : : the difference between the 11. A of observa- 

 tion, and the computed R A : the correction of tho 

 first assumption. 

 The data from tho Nautical Almanac are aa follows : 



Moon's 11. A. on preceding day. 



K. A. at lower passage, preceding day. 



R. A. of corresponding day. 



Moon's R. A. at next lower passage. 



Moon's R. A. at following day. 

 The following method of interpolation may be used, the fourth differences being considered constant : 

 Suppose a h - a + bk + ch* -f dh* + eh*. In this, for h write 2, 1, 0, + 1, + 2, aud take the dif- 

 ferences. This givi 



a , a o + c d + e 



o - o 



i -a +& + e <*+ 



g *"* **0 ' 



1st difference*. 



+b+c+d+* 



Sad difference!. 



2c-6d+14 



2c + Gd-fl4e] 



3rd difference*. 4th difference*. 



! - 12 e \ 

 ' + 12 e I 



6 d - 12 e 

 Gd 



24 e 



Now take the differences of the terms a 2 , a i, o , a lt a 3 , thus 



Comparing this with the foregoing 

 difference, we shall have 



2c + 2e = 



c + d e= 



, .'.6- A/ + 



.'.a - 



Tin* interval between any two consecutive terms of tho 

 given quantities, as a-^ t , a lt is supposed to be unity, 

 nn.l therefore h must be a fractional part of this unit. 

 Thus, if thin interval be 12h., and tho time for interpo- 

 lation 3h. 20m., then h - 



If the interval be- 

 tween the consecutive quantities be 24h., then we should 



3h. 20m. 

 -g^g j and so on for other intervals. 



Tho following example will illustrate tho whole pro- 

 eessi : 



Longitude of Port Essington, north-east coast of Aus- 

 tralia, deduced from lunar transits observed there in 



-- -J Captain Owen Stanley, R.N. 



The following meridian right ascensions of the moon's 

 1 " ** "oft Kwington are found by tho usual means 

 g carefully the error and rate of the chrono- 



1839, June 20, J 1 L. 



June 22, J 1 L. 



June 24, J 1 L. 



June 25, J 1 L. 



ic. 



24 " 



R.A. 



h. in. s. 

 12 50 14-38 

 14 20 67-01 



2 

 69 



16 

 16 



69-99 

 11-11 



By assuming two longitudes, 8h. 49m. east, and 

 8h. 48m. east, and interpolating, with fourth differences, 

 the right ascension of the moon's limb, from the data for 

 upper and lower transit over tho Greenwich meridian, 

 we find for longitude 8h. 49m. east, right ascension of 

 the moon's 1 L., 12h. 60m. 14s. '64; and for longitu.lo 

 8h. 48m. east, ri^ht ascension of the moon's 1 L., 12h. 

 60m. 16s. '46. The correction to the tabular right ascen- 

 sion of the moon's 1 L. is 03.-27, from an observation 

 inade at tho Royal Observatory, Edinburgh. 



The observed right .ascension of the moon's 1 L. is 



