70 EETIEWS — ANALYTICAL STATICS. 



to tell the pupil that we assume, the truth of such principles as the 

 inertia of matter and the transmissibility of force : build up the 

 whole system of Statics and Dynamics provisionally, and then 

 turn back and explain the foundations upon which such assertions 

 rest, viz. that the more nearly the conditions of these laws are ful- 

 filled the more nearly are their assertions verified ; and that their 

 truth may be considered established conclusively when we compare 

 with observation the results of our system of Physical Astronomy 

 which rests entirely upon the correctness of these principles. 



The consideration of these elementary points has detained us so 

 long that we shall have space only very briefly to notice some of 

 the remaining points in Mr. Todhunter's book which appear to de- 

 serve attention. The main body of the work is a re-print of Pratt's 

 Treatise, and the proofs are almost everywhere clear and satisfac- 

 tory. "Where Mr. Todhunter has made extensive additions of 

 his own, as in the chapter on the centre of Gravity, they are such 

 as to make us very greatly regret that he did not throw aside Pois- 

 son and Pratt, and publish a work of his own. The book as it 

 stands is well adapted to the wants of a student at Cambridge, or 

 at any University where the Cambridge system is followed. It 

 is not adapted, as Mr. Todhunter's other works so emphatically 

 are, to the use of persons reading by themselves, and, which is, 

 in some respects, to be regretted, it does not fit in very w ell as one 

 of a series of the same author's writings. In Mr. Todhunter's 

 Differential Calculus, he treats the subject entirely by the method 

 of Differential Co-efficients ; he has only a short chapter on Diffe- 

 rentials, and even there he studiously avoids the use of infinitesi- 

 mals. In his Co-ordinate Geometry he is at much pains to adhere 

 to this system, but in the Statics, as might be expected, he is almost 

 compelled to resort to infinitesimals ; and certainly a person whose 

 ideas on the Differential Calculus were entirely derived from Mr. 

 Todhunter's book on that subject would be rather amazed at the 

 boldness with which Differentials are treated in the latter treatise. 

 In some cases this boldness seems to us carried almost to excess. 

 Thus, for example, when he is investigating the conditions of equili- 

 brium of a string stretched over a cylinder, he has to consider the 

 equilibrium of an indefinitely small element of the string, PQ. 

 This element is kept at rest by the tensions at P and Q, and the 

 resistance of the cylinder, i.e., the resultant of the normal reactions 

 at the several points of the element, which, says Mr. Todhunter, is 

 ultimately in the direction of the normal at P. This is perfectly 



