370 Notices respecting New Books. 



1 : 74, and the change in the value of 4>'— ty will, therefore, 

 principally determine the value of e\ Now the logarithmic 

 tables will show, that a change of 1" in m' and X will produce 

 a change in the logarithmic tangent \J/ (to seven decimals) of 

 6 and 51 . 6 and an equal variation of m and a/ will change the 

 logarithmic tang \J/ 5*2 and 51*2, and a change of 60*2 in the 

 logarithms of tang vj/ and tang \[/ will change these angles 1". 

 The difference of iff and \J/ is 2"*00 . . and therefore a change 

 of 1" in the value of \(/— \J/ will reduce the ellipticity to one 

 half or increase it by one half of its value ; that is to say, will 



change it from——- to— ^ or to — . This circumstance is no 



doubt one of the principal causes of the failure of the method 

 in its application to small geodetical lines ; and however cor- 

 rect in theory, such an application of it must clearly always 

 lead to erroneous results. 



If we change the conditions of the problem, and assume the 

 ellipticity of our spheroid or the length of any one of the axes, 

 the length of the geodetical line together with a and m of one 

 place will give those of the other place their difference of longi- 

 tude, and the linear dimensions of the spheroid very nearly 

 correct, as has been satisfactorily proved by Mr. Ivory. 



There can be little doubt at present that the difference of 

 longitude between Beachy Head and Dunnose, does not much 

 differ from 1° 27' 5" ; and this proves, as Professor Airy has cor- 

 rectly observed, that there is an error of about 13" in the sum 

 of the azimuths. A new determination of the azimuths at these 

 places would certainly be desirable, and might lead to a deci- 

 sion of the question, whether local attraction has had any ef- 

 fect in producing these erroneous measurements. 



Oct. 13, 1828. : J. L. Tiarks. 



LXIV. Notices respecting New Books. 



Elements of Algebra: being a short and practical Introduction to that 

 useful Science; on a new Plan; including a Simplification of the 

 Rule for the Solution of Equations of all Dimensions. By Robert 

 Wallace, A.M. late Andersonian Professor of Mathematics, Glas- 

 gow. London, 1828 ; 8vo : pp.60. 



T^7"E extract from this work the table of contents, and the simpli- 



Tt fied rule for solving equations of all dimensions; the latter 



involves some interesting particulars respecting part of the modern 



ist ry of Algebra. 



Contents : Definitions— Characters or symbols of operation — Less 



common symbols of operation — Terms — Equations — General Rule 



to obtain an equation —Axioms — Addition — Equations to be resolved 



by 



