.REVIEWS — ANALYTICAL STATICS. 71 



true, but it seems to us to want at least some explanation. The 

 student's objection is that if we are at liberty to consider the normal 

 action at the extreme point Q of the element as coincident with the 

 normal action at P, we might also consider the direction of the tan- 

 gential actions at the two points as ultimately coincident, which he 

 finds is not the case ; and it requires a clearer insight into the doc- 

 trine of infinitesimals than the student will generally possess to see 

 that the error in taking the directions of the normal actions as co- 

 incident will be of a higher order than that in treating the tangen- 

 tial actions in a similar manner, and that therefore in taking the 

 limits the former error will disappear. Perhaps the best mode of 

 remedying this defect would be the addition of a chapter on infini- 

 tesimals when a new edition of the Differential Calculus is called 

 for. We have not examined the book before us with sufficient care 

 to be able to say much as to the accuracy of the printing. One 

 strange blunder, arising we presume from the printer, we may point 

 out for the benefit of any of our readers taking up the book. It is 

 at the end of article (186) where he is finding the approximate ex- 

 pression for the tension at the lowest point of the catenary, where in 

 subtracting two expansions the first term of the difference is omitted. 

 (The left hand side of each of the two last equations should be 

 </Ji=h % — Jc). There is also, a few lines above, a singularly careless 

 mistake, the points of support being described as nearly in the same 

 straight line, instead of in the same horizontal line. 



Before we conclude, there is one point to which we should wish 

 to call the attention of our mathematical readers. In the chapter 

 on the Composition of Porces, Mr. Todhunter gives us first Duchay- 

 la's proof of the Parallelogram of Porces, (we wish he had substi- 

 tuted Duhamel's far more elegant demonstration) and then adds 

 Poisson's proof which does not assume the principle of the trans- 

 missibility of force. In passing we may remark that we never could 

 see that this wa3 any recommendation of this class of proofs. Writers 

 are accustomed to say that proofs such as Duchayla's will not apply 

 to the case of forces acting on a particle of fluid, or that the proof 

 is imperfect because the proposition would be true even if the trans- 

 missibility of force did not hold, by which if they mean anything 

 they must mean if no such thing as a rigid body ever existed. Such 

 objections seem to us about equivalent to saying that a brick house 

 cannot be built by means of a wooden scaffold. The rigid connec- 

 tions introduced into such proofs are purely imaginary, and when the 

 result is eatabb'shed it matters not the least of what body the particle 



