84< Notices respecting New Booh. 



" If the form of the present planetary tables be abandoned which 

 give the longitude, and tables be formed which give the value of z, 

 most of the numerical calculations contained in the third volume of 

 the Mec. C41. will be thrown away. It would be better to subject 

 those figures, and particularly the quantities b, to a careful exami- 

 nation. 



" Public institutions, established with the view of contributing to 

 the progress of astronomy, would confer more essential services to 

 science if their strength were devoted to purposes of this kind 

 rather than to the inconsiderate multiplication of unreduced or not 

 wanted observations. The determination of the perturbations of 

 the small planets is a matter of urgency. Moreover, the perturba- 

 tions of the comet which bears the name of Encke, are of too great 

 cosmological importance to be properly entrusted to any single 

 hand, however skilful and conscientious, or indeed even to a single 

 method. But such troublesome computations, to be conducted with 

 a fair chance of success, must be undertaken with the requisite ap- 

 pliances, and seem therefore properly to fall under the superintend- 

 ence of those astronomers who are placed in public situations. 

 Mutual cooperation upon a uniform system would prbduce more 

 important results than any incoherent computations founded upon 

 fantastical expressions." 



The applicability of the views suggested in the preceding para- 

 graph to the future proceedings of the British Association, the 

 Royal Astronomical Society, and other scientific bodies concerned 

 in the reduction of astronomical observations and the formation of 

 new astronomical tables, will immediately be perceived. 



The contents of the work itself (in this fourth part), are distri- 

 buted in the following order : — 



Calculation of the first term in the longitude, appertaining to the 

 arguments 0, 1,2, 3, 4, 5, 6 and 7, in illustration of M. Hansen's 

 equations. — Calculation of terms depending upon the second approxi- 

 mation, in further illustration of M. Hansen's equations. — Calcula- 

 tion of the first term in the reciprocal of the radius vector and of 

 the longitude of the moon, by means of the variation of the elliptic 

 constants. — On the variation of the arbitrary constants in mechanical 

 problems. — On the variation of the semi-axis major of the moon's 

 orbit. — On the divergence of the numerical coefficients of certain 

 inequalities of longitude in the lunar theory. 



In the calculation of the first term in the longitude, appertaining 

 to the arguments 0, 1, 2, 3, 4, 5, 6 and 7, in illustration of M. 

 Hansen's equations, Sir John Lubbock adopts an equation and ex- 

 pressions given by M. Encke, in his paper entitled " Uber die vom 

 Director Hansen eingefiihrte Form die Stbrungen in unserm Sonnen- system 

 vollstandig zu entwickeln." He then shows in what manner the same 

 terms may be calculated by his own methods. 



The terms depending upon the second approximation are next 

 calculated, in further illustration of M. Hansen's equations; and 

 then the first terms in the reciprocal of the radius vector and of the 

 longitude of the moon, by means of the variation of the elliptic con- 



