256 DETERMINATION OF THE LONGITUDE OF SEVERAL, 



the diameter, in the Nautical Almauac, to the same dimensions as 

 that which has been observed. It is obvious that the error arising 

 from this source must vanish, when each limb of the moon has 

 been observed the same number of times, and with equal weights. 

 Though this can hardly be expected, still, the error would vanish on 

 using the mean of a great number of results for each limb, and giving 

 equal weights to the results by each limb. The mode of deducing the 

 correction of this error is given below, for the several instruments, and 

 is derived from the observed interval between the transits of the two 

 limbs of the moon, when nearly full; this duration being corrected for 

 the defective illumination of one of the limbs. It appears from ex- 

 perience that there still remains an error of irradiation, which no mul- 

 tiplication of observations by the same observers, with fixed telescopes, 

 can completely remove. Thus the Dorpat and Paris transit instru- 

 ments appear to be liable to a constant error of this kind ; and the dif- 

 ference of longitude between those observatories, derived from moon- 

 culminations, cannot, without correcting for it, be made to agree 

 with the results of occultations and of geodetic measurements. Ar- 

 gelander found that his transit instrument at the Abo observatory, 

 while it gave correct longitudes, when compared with several instru- 

 ments of nearly equal capacity at the German observatories, required 

 a constant correction to reconcile with these the results by the Green- 

 wich ten feet transit instrument. Again, Dr Robinson finds that 

 without the application of such a correction, it is im.possible to deduce 

 a correct difference of longitude by the Greenwich and Armagh 

 transit instruments. In some of the instances referred to, the outstand- 

 ing error, even when the mean of the results by both limbs is used, 

 amounts to three seconds of longitude in time. Dr Robinson has 

 proposed to deduce this correction by means of comparison of the ob- 

 served diameter of the sun, as deduced from the transits by the same 

 instruments. Though successful, in his own case, I do not know that 

 his method has been generally adopted. I will here make a remark 

 which I have not noticed in any papers on this subject, that it seems to 

 me highly probable that there is a personal equation, arising from the 

 difficulty of noticing the precise instant when the moon's limb is tan- 

 gent to the centre of the wire of a transit instrument. If such be the 



