128 Mr, William Galbiaith^ on seme 



is made, extend to 30 minutes of time ; though, no doubt, 

 this error is diminished when combined with observations 

 made near the meridian. Again, when the latitude is 40°, 

 the declination 20°, and the zenith distance also 20°, the 

 same formula to three turns gives results incorrect to about 

 half a second in excess, while the first two turns, or those 

 commonly used, give an error of about 4 " in defect. Lastly, 

 when the latitude is so high as fifty degrees, the declination 

 still 20°, and the zenith distance 30°, Delambre's formula 

 to these turns gives, at 30 minutes distance from the 

 meridian, correct results ; while two turns give a small 

 error of about half a second in defect. Assuming different 

 numbers somewhat analogous but with similar relations, 

 the same conclusion would follow. It may, therefore, be 

 concluded that when the zenith distance in mean latitudes 

 amounts to about 30°, two terms of Delambre's formula, or 

 their results in tables, are sufiSciently correct for practical 

 purposes at a horary distance from the meridian of about 

 30 minutes, and then the calculation for the mean of a con- 

 siderable number of repetitions is comparatively simple. 



Instead of Delambi'e's formula, or tables derived frOm it, 

 some practical astronomers recommend a table given by 

 the late Dr. Thomas Young, consisting of natural versed 

 sines, which are nothing more than the first part of 

 Delambre's table in a less convenient form, and requiring 

 the additional trouble of employing a constant log within 

 to convert them into Delambre's numbers in every opera- 

 tion, without any equivalent advantage in any respect over 

 the other method ;* in the words of Dr. Pearson, " Dr. 

 Young having simplified (complicated he should have said) 

 the preceding formula by omitting the second term," &;c. 

 Now it has already been shown that the second term cannot 

 be admitted unless the zenith distance be considerable, not 

 less than 20° or 30°, at 30 minutes from the meridian, or 

 the object to be observed be a circumpolar star not very 

 distant from the pole, in mean latitudes, and of this any 

 observer may easily satisfy himself. 



If, for example, at London circummeridian observations 

 be made extending to 24 minutes from the meridian, (the 

 extent to which Dr. Young's table has been carried, in a 



• The author of these remarks has endeavoured elsewhere to remedy this. 



