for predicting Occidtations of Stars by the Moon. 411 



centre of the earth, for h and 12 h at Berlin. From these may 

 be found by an easy interpolation, as only entire numbers and 

 second differences enter into the calculation, time and place for 



h , ± l h , ± 2 h , 



referred to Berlin ; for any other place on the earth whose 

 longitude from Berlin, positive if eastern, is /, these places and 

 times would correspond to 



t = h + /, ± l h + /, ± 2 h + /, &c. 



The deduction of these three columns is strictly founded on 

 an interpolation with unequally increasing arguments. We 

 know and a for every mean noon and midnight, and from 

 these the times and oc and 8 are to be found which correspond 

 to — a = 0, and — a = 180°. If the values of — a. are cal- 

 culated for every noon and midnight, and are assumed as ar- 

 guments of tables whose functions are respectively the mean 

 half days, and a and 8 from 12 to 12 mean hours, the formu- 

 las explained in the paper " On Interpolation *" may be em- 

 ployed for finding the values of the above functions for 0— a 

 = 0, and 0-a = 180°. 



The greatest strictness, however, would not be required in 

 these calculations. Even in the latest tables of the moon's 

 motions there occur errors in longitude of 10", and the posi- 

 tion of the smaller stars may possibly likewise be wrong by 

 5" ; and consequently the strictest calculation may still be liable 

 to an error of half a minute in time. It is therefore not ne- 

 cessary in calculating the predicted occultations, to have the 

 moon's place nearer than to 0*1 minute of a degree, and the 

 time nearer than to 0*1 minute of time. Under these circum- 

 stances it will be sufficient, in deducing the time of the culmi- 

 nation from the values of 0— a formed as above described, to 

 use an indirect method by winch, agreeably to the paper " On 

 Interpolation," the mean days being considered as arguments, 

 and the 0— a as functions, the first differences of 0— a are so 

 corrected by an approximate estimation of the factor of cor- 

 rection, that they may be simply regarded as divisors, and the 

 times of the culminations are then found by the quotients 



.^ is* and ("-=£!£ +iW 



A(*— ft) \ A(0-u) / 



In this manner the times of the culminations have been found 

 accurately to 0*1 minute of time; an accuracy which has caused 

 no greater trouble than the common results would have re- 

 quired, as it is always necessary to use logarithms. 



By means of these times the corresponding places of the 



* This paper will appear in our next Number.— Edit. 



3 G 2 moon 



