(29) 



132 Reviews, and Notices respecting New Books. 



by interpolating for the interval of time ; and denoting the ap- 

 proximate value of p thus found by (p), the above values of M 

 are to be respectively multiplied by one of these quantities, 



L'./Znl ^ ) R'/l _ l_x! 

 Y * T T sin(a'- a ) '{p)\r* R-y / 



/*i»w fit* 5!(^_1_J_U 



[ * tanS'cos(a-0')-tan8cos(a'--©') , (p)\r 3 R 3 / J 



accordingly as the first or second formula has been used. The 

 error of this new value of M will generally be of the second 

 order of the intervals of time; and with this value the calcula- 

 tion may in most cases be completed, as, besides, in such a 

 distribution of the observations the accuracy of the determina- 

 tion of the orbit is somewhat more restricted than in the cases 

 in which the more direct process can be adopted. 



As an example of approximation I will apply the formula 

 to the above observations. The two first expressions of M 

 will be here 



log M = 9-70341 and 9*73397, 



the latter of which, on account of the great change in latitude, 

 would be preferable. Taking now for r' and (p) their correct 

 values, viz. log r' = 0*12401 



log (p) = 9*80364, 



(because although the values calculated by the erroneous hy- 

 pothesis for M would indeed deviate, yet not so much as to 

 sensibly alter the result), the logarithms of the correcting fac- 

 tors will be 



0*05522 and 0*02427, 

 or the corrected values of M, 



log M =. 9*75863 and 9*75824, 

 while the correct expression, as found above, is 

 log M = 9*75799. 



The difference is inconsiderable enough to be neglected al- 

 together in the case of observations so unfavourably situated. 

 [To be continued.] 



XVI. Reviews, and Notices respecting New Booh. 



Illustrations of the Botany and other branches of the Natural History 

 of the Himalayan Mountains, and of the Flora of Cashmere. By 

 J. Forbes Royle, Esq., F.L.S. F.G.S. &c. 



AT a time when title-pages often promise so much more than 

 the reader is unfortunately capable of discovering in the works 

 to which they are prefixed, it is refreshing to take up a volume 



