142 Proceedings of Philosophical Societies, [Aug. 



temperature. In the Greenwich system of observations, assist- 

 ance from the spirit-level or plumb-line, or indeed from any 

 previous verification, is rejected altogether. Two circles are 

 employed simultaneously, each of which is furnished with six 

 microscopes, which it is desirable should be placed at nearly 

 equal distances on the limb ; and previous to observation each 

 circle is placed nearly in the plane of the meridian, and nearly 

 perpendicular to the horizon. Each circle is provided with an 

 artificial horizon of mercury, so as to command the greatest 

 possible portion of the reflected meridian. 



The first part of the process consists in observing a number 

 of stars simultaneously with each instrument, either by direct, 

 or by reflected, vision : the object of this is to determine the 

 exact quantity that one instrument marks more or less than the 

 other, when both arc directed to the same object. This is 

 determined, not by a single observation, but by a great variety; 

 thus obtaining the quantity denominated the mean dijferejice 

 for every 24 hours. 



In the second part of the process, a series of stars is observed 

 reciprocally y that is, the direct image of a star by one instru- 

 ment, at the same time that its reflected image is observed by 

 the other. This, combined with the results of the previous pro- 

 cess, in which the mean difference serves the same purpose as the 

 index error in Hadley's sextant, enables the observer to ascer- 

 tain the altitude ; with which is likewise obtained the know- 

 ledge of the position of the horizontal diameter of each instru- 

 ment. The observer, however, does not rest contented with a 

 single determination of one diameter ; but must in a similar 

 manner, from altitudes, observed on various points of the arc, 

 and by taking sometimes the direct, and sometimes the re- 

 flected, observation with the same instrument, endeavour by 

 every possible variety to obtain the maximum of precision of 

 which the method is capable. 



The position of the horizontal diameter of each instrument 

 being thus deduced from a mean of all the preceding experi- 

 ments, sufficient data are obtained for computing the places of 

 those stars that have been observed in tne first part of the 

 process, and employed in computing the mean difference ; 

 because, without the knowledge of the position of their hori- 

 zontal diameters, the instruments, with respect to the stars in 

 question, give nothing but differences of declination, but such 

 position being known, their altitudes can be accurately deter- 

 mined. 



The Astronomer Royal terminates his paper by pointing out 

 the principal advantages of the method described. 



There were next read Extracts of three letters addressed 

 by M. Gambart, Director of the Observatory of Marseilles, to 

 James South, Esq. respecting the discovery and elements of 



