26ft Astronomical and Nautical Collections. 



taking- out the logarithms and the natural number ; and accordingly 

 only three openings are put down on these accounts in the above 

 statement. There will always be the same number of openings of 

 the book, and of pages in the tables used, in these two methods, 

 and very nearly the same number of figures to be written down. 

 In Captain Thomson*s method likewise there will always be the 

 same number of openings of the book, and of pages in the tables 

 used ; but in general there will be fewer operations, and of course 

 fewer figures to be written down, than in the above example ; be- 

 cause whenever the difference between the two successive correc- 

 tions in Table XVIII. is very small, the proportional part may be 

 taken out by inspection. But if two of them could be thus satis- 

 factorily taken out, and only one proportion were required to be 

 written down, still the operation would not be shorter than in other 

 methods. It may be remarked, too, that although an opening of 

 the book is saved in clearing the distance by including the refrac- 

 tion of the two objects in the quantity taken from Table XVIII, 

 this correction must afterwards be made in deducing the time from 

 the observed altitude of one of them ; so that, in fact, the openings 

 ought to be considered as eight instead of seven, as stated above. 

 The moon's altitude indeed is evidently not intended to be used 

 fbr this purpose, which is certainly a great defect, as the altitude 

 of the moon will frequently be preferable to that of the other 

 object, and will very often be the only one that can be employed. 

 No table, however, is given of its corrections ; and of course, if 

 its altitude were to be used in finding the time, the correction 

 must either be taken from another book, or computed by a trouble- 

 some process. It may be observed, likewise, that the combining 

 together of positive and negative quantities in the third correction 

 must be embarrassing in practice, and may sometimes be the occa- 

 sion of error. It is, moreover, unpleasant to have to subtract the 

 correction for one distance from that of another when they lie on 

 different sides of a leaf, as is always the case in Table XVIII. A 

 further objection is, that the method does not apply to cases in 

 which the apparent distance is less than 20°, though not unfre- 

 quently the distance between the moon and star is much less in 



