164 
PRESTON. 
sists in applying Bessel’s numbers by differences, enables 
the computer to obtain the places for succeeding dates in 
about one-fourth the time required by the usual way. There 
are many cases, however, that do not fall strictly within the 
two foregoing categories, and to meet these the present 
graphic method has been devised. Its advantages are rapid¬ 
ity and ease of application. No numerical work being neces¬ 
sary, the fatigue attending such operations is entirely avoided. 
The accuracy of the method can be increased to any desir¬ 
able extent by enlarging the scale. That adopted in the 
following description will, however, meet all the require¬ 
ments of our present instruments and methods of observation. 
This method was originally devised to shorten the work in 
the latitude computations, and has therefore been used for 
declinations only, but following the same principles its ap¬ 
plication to right ascensions is easily made. 
Description arid Explanation .—Three general diagrams are 
given. The first (plate 7) shows the lines necessary for all 
the stars and is a reduced copy of the regular working sheet. 
The second and third (plates 8 and 9) are intended to show 
the construction for star No. 1381.* In plate 7 we have a 
graphic representation of the day numbers, A , B, C, D. The 
dimensions given refer only to the scale used in actual work 
and not to the illustrations, which have necessarily been 
reduced for convenience of publication. 
On a quadrant drawn with a radius of 20 inches (plate 7) 
spaces are laid off equal to half degrees, corresponding to 
two minutes of right ascension. By this scale declinations 
to the nearest tenth of a degree and right ascensions to the 
nearest half minute may be indicated with the greatest 
facility. With the exercise of a little care, on a slightly 
increased scale the error in plotting the former need not be 
more than a minute or two of arc, and the latter may be 
plotted with a corresponding accuracy in time. Roughly 
speaking, the uncertainty of plotting the two functions may 
* Catalogue of Stars for Observations of Latitude, Appendix No. 7, C. 
and G. S. Report for 1876. 
