TOL. LXXV.] PHILOSOFHICAL TRANSACTIONS.' 7- 



XVI II. A Description of a New System of Wires in the Focus of a Telescope, 

 for Observing the comparative Right Ascensions and Declinations of Celestial 

 Objects, &c. By the Rev. Francis fVollaston, LL. B., F. R. S. p. 346. 



The rhombus (for a rhombus, and not a rhomboid, it ought most properly to 

 be called) is very good in theory ; but very difficult to get executed with pre- 

 cision, and liable to some inaccuracy in the observation. The truth of it de- 

 pends on the longer diagonal being exactly twice the length of the shorter one ; 

 which requires an awkward angle (53° 7' 48 ) at the vertex, not easily to be hit 

 by the workmen, and therefore seldom sufficiently true. Beside this, as the 

 sides of the rhombus, on which depends the calculation for differences of decli- 

 nation, are but 26° 33' 54'' declining from the perpendicular or horary wire, a 

 very small error in observing the passage of a star makes a very material differ- 

 ence in the result. 



This determined Mr. W. to make trial of a square placed angularly, an addi- 

 tion to M. Cassini's wires at 45°, which seems to answer better. The whole 

 extent of the field is employed as it is in the rhombus (the want of which was 

 said to be Dr. Bradley's objection to M. Cassini's wires) ; but being formed of 

 right angles or half-right angles, to which workmen are most accustomed, they 

 will alvv;4ys be apt to execute their part better ; and the obliques, from the differ- 

 ences being just double to what they are in the rhombus, give the comparative de- 

 clinations with twice the certainty. To this the number of corresponding observa- 

 tions in the passage of every star add considerably ; since we may calculate its dis- 

 tance from the centre, or from the angles, or from one of the intermediate angles, as 

 occasion may require, with double the precision of the rhombus. In each of 

 them, the parallel wires will tell whether the placing of the instrument be true 

 or faulty ; because, if truly made and truly set, th6 same star must take the 

 same time in passing from one wire to its corresponding parallel ; which will 

 differ considerably, and in every star the same way, if the position be faulty. 



It may be proper to add, what indeed is nothing new, that if the position of 

 the instrument be found erroneous, the formula given by M. De Lalande in his 

 Astronomy will serve to rectify the observation. Calling the larger interval 

 between the passage of any oblique and the horary wire m, and the smaller one 



n, then — ^ — ~!^ will give the difference of declination (in time to be converted 



into degrees, and multiplied by the cosine of declination) from the angle where 



that oblique meets the horary ; and — -— the difference in rierht ascension from 



the same angle. It is almost needless to mention, that where the position is 

 true, half the interval of time between a star's passing any two corresponding 

 obliques, converted into degrees, and multiplied by the cosine of declination. 



