On a Method of Utilizing Compact Logarithmic Tables. 221 



by the same reasoning for incompressible as for compressible fluids, 

 we may assume that dr = dr'; and consequently the equation gives 



by integration V= 2—2 Hence when the motion is such that 



J o rr l 



r = r 1 , we have V= ^— , which is the same expression for the 



velocity as that which is obtained when the arbitrary disturbance 

 is supposed to be a function of the distance from a centre. On 

 account of this identity of the expression applicable to specific 

 disturbances producing central motion, with that which, being 

 derived from general antecedent considerations, gives the law of 

 the variation of the velocity in such motion, no difficulty occurs 

 like that met with in the application of analysis to problems 

 relating to compressible fluids. 



The foregoing arguments have been adduced on account of 

 their having a direct bearing upon the principles to be applied in 

 the solution of the problem which was stated at the beginning of 

 this communication to be its ultimate object, viz. to investigate 

 the motions of a spherical solid submitted to the action of the 

 vibrations of an elastic fluid for the purpose of ascertaining 

 whether a permanent motion of translation results from such 

 action. The second Part of these researches will be devoted to 

 the consideration of this problem. 



Cambridge, August 19, 1865. 



XXVII. On a Method of Utilizing Compact Logarithmic Tables. 

 By KobePvT Templeton, Esq.* 



Royal Hibernian Military School, 

 Phoenix Park, Dublin. 



THE fourth volume of the Annates de V Ohservatoire Imperial 

 de Paris came into my hands a few days ago; and in look- 

 ing through it I found in the appendix a paper by M. Lefort, 

 giving an account of the great Cadastral Tables, constructed 

 under the superintendence of Prony, and a copy of which is 

 preserved in manuscript in the library of the observatory. After 

 describing in minute detail the contents of the seventeen volumes, 

 he proceeds to remark that "Delambre, whose competence to 

 form an opinion is unquestionable, has written, ' The great 

 Cadastral Tables are not useful in common cases, but solely in 

 extraordinary cases ; like those of Briggs, they will be the source 

 whence will be derived whatever extension will be given to 

 the Tables in common use. They will likewise serve as a basis 

 of comparison for everything that has been done or will be done/ " 

 * Communicated by the Author. 



