Astronomical and Nautical Collections. 287 



the N. Almanac [?]. Neither is it obvious how this method is to be 

 used when the difference between the given apparent altitudes of 

 the two objects is greater than the apparent distance in Table 

 XVIir, next less than the given apparent distance ; as for instance, 

 when the starts apparent altitude is 54°, the moon's 15°, and the 

 apparent distance 39® 30'. Lastly, it is a serious defect in this 

 method that no means are pointed out of applying a correction for 

 any extraordinary change in the state of the atmosphere, nor any 

 satisfactory rule given for estimating the effect of the unequal 

 refraction at the upper and lower limbs of the sun and moon, when 

 observed near the horizon. These, however, are considerations of 

 too much importance to be altogether neglected in the present 

 state of Nautical Astronomy. By taking them into the account 

 in the example at page 282 of Mr. Lax's book, the longitude is 

 made to differ more than 23 miles from the longitude deduced in 

 the same example at page 273, where they are neglected. 



[It is, however, but fair to remark, that the finding the differ- 

 ences of the corrections for fractional parts in this, as in almost all 

 other cases, will be much more expeditiously done by the arith- 

 metical rule of Practice than by the Rule of Three. Thus in the 

 proportion 4° : 3' 37":: + 24', it is easy to perceive that 24'= t?^, 

 and to take at once 2r'.7 as the result. When the parallax is 

 very great or very small, the correction by Captain Thomson's 

 method must confessedly be defective.] 



ii. Tables of Third and Fourth Differences, /or interpolating the 

 Moon's place. By Thomas Henderson, Esq. 



In calculating the moon's place by interpolation from the Nautical 

 Almanac, especially in right ascension and declination, when great 

 precision is required, the equation of mean second difference alone 

 will not be sufficient, but the third, fourth, and fifth differences 

 must be taken into account, as the corrections arising from them 

 may sometimes amount to 3 or 4 seconds. The two small Tables 

 annexed are designed to give these corrections, and are to be used 

 thus: 



Take out of the Ephemeris the three right ascensions and pre- 



