Notices respecting New Books, 301 



The third vertical row in each of the columns in the group 

 C is formed by writing under its first letter, in order, the mul- 

 tipliers of that letter in the group B". The triplets, e. g. JimJu, 

 hlc\ phn'cyp'ul; xm'l, xcu\ fulfill the law spoken of. If now 

 under the group of triplets (B'B"C) we write two such groups 

 having the same initial letters, a final group C can be added 

 in the manner of C, completing the system of triplets made 

 with sixty-three symbols, by all which the law in question will 

 be satisfied. 



Croft Rectory, near Warrington, 

 September 3, 1850. 



XXXVII. Notices respecting New Books. 



Essay on the Theory of Attraction. By John Kinnersley Smythies, 

 Barrister '-at-Law of the Middle Temple. 



I^HIS paper consists of two distinct parts, geometrical and me- 

 chanical : in the former, the author deserves high praise for 

 his accuracy and ingenuity ; in the latter, he must bear to be told 

 that he is ingenious, but not accurate. 



The geometrical part of the paper consists in a determination of 

 the relation existing among the ten distances of five points in space. 

 This problem was first solved by Carnot, who published a tract on 

 the subject. Mr. Smythies appears not to be aware of this, by his 

 not alluding to Carnot. 



The mechanical part is the asserted deduction of a principle which 

 will startle every reader who is competent to be startled : it is, that 

 any five material* particles have a necessary mathematical relation 

 existing between their distances and central forces independently of 

 their velocities. The reasoning is of the following kind. The di- 

 stances between the five points being a, b, &c, the relation existing 

 between them leads to a relation of the form 



f(a, da, d*a, b, db, d*b,....)=Q. 



Where the particles are at rest, say that this becomes 



^(a, d'*a, b, d'*b ,....) = 0. 



We now quote from Mr. Smythies, altering the numbers of his 

 equations into the letters/ and \p. 



" The second differentials in (/) denote the whole forces, central and 

 centrifugal ; and as the central force is a function of the distances only 

 dependent on the positions not on the velocities of the points, the assump- 

 tion that the velocities vanish destroys the centrifugal forces but does not 

 alter the central. The result of that assumption, then, gives the ratios of 

 the central forces when the particles begin to move from a state of rest 

 when no centrifugal forces exist. But the ratios of the central forces in 



* Mr. Smythies ought to have expressed the supposition of equal par- 

 ticles, since he uses no ratio of masses different from unity. 



