451' Reviews, and Notices respecting Nc'<i) Booh. 



of the Ecliptic to the Equator," is only a modification of Table V., 

 the difference between the sun's longitude and right ascension being 

 given in space. Table X., entitled "Reduction to either Solstice," 

 furnishes the means of obtaining the sun's declination at the solstice, 

 {i. e. the apparent obliquity of the ecliptic,) from observations of his 

 right ascension and declination when near the solstice. We refer our 

 readers to this, and Table XX., with our author's explanation of both, 

 and also to his explanation of the discrepancy existing between the 

 winter and the summer reductions to the solstice, according to the 

 Greenwich observations. TablesXI.and XII. contain minute equation.-? 

 of the ef|uinox and obliquity depending on the small oscillations of the 

 earth from the mean plane of her orbit, produced by the combined dis- 

 turbances of the Moon, Venus, and Jupiter. The Tables XIII. to XIX. 

 are all useful, and for their application we refer tothe explanation given 

 in the work. — When the time ofapparent noon is determined bymeansof 

 equal altitudesof the sun, asmaliequationis found requisite on account 

 ofthechangein the sun's declination in the interval of the observations. 

 The Tables XXI., XXII. by Delambre, and XXIll., XXIV. by Zach, 

 contain the corrections to be applied to obtain the true time of the 

 passage of the sun's centre over the meridian. These Tables are 

 essential when a sextant or any equal altitude instrument is made 

 use of, but are superseded by the use of the transit instrument. 

 Table XXV. being the last of the Solar Tables, contains the sun's 

 parallax in altitude: and the method of taking this from the Table, 

 when the horizontal parallax is given, is obvious. 



The Tables next in order are the Lunar Tables. There are fifteen 

 of these contained in pases 181 to '203 inclusive. Table I. contains 

 the epochs of the mean longitude of the moon's ascending node, for 

 120 years, beginning with the year 1800; and Table II. contains the 

 proportional parts of the annual regression to be applied to the mean 

 longitude of any epoch, to obtain the mean longitude for any day of 

 the corresponding year. Table III. gives the moon's semidiameter 

 for every second of her equatorial horizontal parallax. Table IV. 

 contains the differences of the moon's horizontal parallax in the 

 sphere and s^jheroid computed for two difl'crent compressions. For 

 the use of Table V., and also that of Table VI., containing the angles 

 between the normal and the radius, in different parallels, we refer 

 to our author. Table VIII. gives the moon's parallax in altitude, 

 and is very conveniently arranged. Table IX. gives the time of the 

 moon's semidiameter passing the meridian, and is of use in deter- 

 mining the moment of the passage of the moon's centre over the 

 meridian : the example given by our author fully exj)lains its use. 

 Table X. is also for the same purpose. 



The changes which take place in the moon's right ascension, de- 

 clination, &c. being far from uniform, we cannot interpolate by means 

 of parts taken proportional to the time elapsed, since she was in any 

 given position : we must, therefore, in order to obtain a tolerable 

 approximation, make use of the second differences. Table XI. is 

 constructed for this purpose. Tables .\1I. and XIII. are both of 

 considerable use for the ])ractical purposes lor which they are con- 



