and the Methods of calcidating their Results. 275 



the times T- 2 h , T— l h , T, T + l h , T + 2 h ...*, and from 

 these the values of P and Q for the same moments. Let us 

 suppose these values respectively with their successive differ- 

 ences to be arranged in this form : 



£ ~ ? a " b" 



T a ', c i, e 



T + 1 a' % c< d 

 T + 2 a" ° 



If we now put 2 6 = b\ + b', 2d = d t + d 1 ; then P and Q, 

 or the parts of which they are composed, viz. p,p',q,q' be- 

 come dependent on T and a, b, c ... ; the formulas by which 

 they are expressed, shall be given when their application will 

 be required. In this manner p' and q' are found in parts of 

 an hour ; the formulas (5) and (6) suppose, therefore, the same 

 unity of time. It is, however, more convenient to express d 

 in seconds of time. This is obtained by multiplying formula 

 (6) by such a number of seconds of that kind of time in which 

 the observation is given, as is equivalent to the hour here 

 assumed; this number I will generally denote by s. Then 

 t — T will be expressed in seconds of the same time, or T 

 denotes now that time (uniformly expressed with t), for 

 which a, b, c have been calculated. It is therefore not ne- 

 cessary to convert the times given by the observers into that 

 sort of time in which T has been fixed, but the process is 

 quite the contrary. Besides saving some trouble, we shall then, 

 not even for converting one time into another, require any 

 approximate value of the unknown difference of the meridians. 

 For the sake of completeness I observe in this place that as 

 the sidereal time, on which the u involved in the expression 

 for u and v depends, corresponding to an observation given 

 in solar time of an unknown meridian, cannot be calculated 

 before the difference of meridians is known, it becomes neces- 

 sary to apply to u and v small corrections of the forms id T' 

 and tf T. By this means the method directly leads like- 

 wise in this case to a result; but it will be unnecessary to dwell 

 further on this subject, which can hardly have any practical 

 interest. 



[To be continued.] 



* It would be convenient for various purposes, if a logarithmic table 

 of interpolation similar to the one which I have given in the Astr. Nachr. 

 No. 145. (Phil. Mag. Nov. 1829. p. 340.), but for intervals of 10 minutes, 

 were inserted in the collections of astronomical tables. 



2N2 XLV. No- 



