Notices respecting New Boohs. 139 



tial and Integral Calculus and the fundamental parts of Dynamics." 

 The endeavour has been " to solve the various problems which 

 present themselves with the aid of the Principles of Energy or 

 Momentum," fixed axes only being used in all but a few cases — 

 which might be passed over by those whom the employment of 

 moving axes would puzzle. Accordingly in Chap. I., on " Kine- 

 matic Theorems," in the few lines given to the Lagrangian Method 

 the fact that the axes are considered fixed is emphasized; but there 

 seems no reason why historical order should not be adhered to aud 

 the Eulerian given the priority to the Lagrangian method. What- 

 ever room allows to be done in directing the student's attention to 

 the history of the progress of his subject is valuable. So, later on, 

 under " Dynamical Theorems " — as in the Author's excellent larger 

 treatise — it is barely remarked that the principle involved in equa- 

 tion (30) is Bernoulli's Theorem ; but to which of the gifted family 

 it is due the student is left uninformed, as also of the work in 

 which it was originally given — Bernoulli's Hydrodynamica, or 

 John, his father's Hydraulica, 1738. In the case of living writers 

 the references are more fully given. Dr. Glaisher, in his Address 

 to Section A, British Association, Leeds Meeting of last year, 

 made a valuable recommendation that in all Mathematical Treatises 

 references should be given to the original memoirs &c. in which the 

 results noticed first appeared. The late Mr. Gregory, following 

 the precedent set by Dean Peacock, made such references (even 

 if at second hand) a feature in his well-known ' Examples,' 

 and Mr. Walton in his, on Dynamics and Hydrostatics, adhered 

 to the precedent, thereby giving a rough skeleton-history of the 

 subjects. It is, however, of more importance that condensation 

 to save space should not be carried to the point of merely writing 

 down a result without proof in cases where one of the classes of 

 students for whom the treatise is inteuded could not fairly be 

 considered competent — if willing to pause, in " getting up " the 

 book, and make the effort — to supply the details of proof. This is 

 the case when the equation [(7) Chap. I.] of continuity for liquids 

 in Polar Coordinates is merely set down ; while in the larger 

 treatise the details of the proof are given, though not with the 

 fulness which would be adequate to the wants of the reader of 

 the present "Elementary" one. Besides those alluded to, sub- 

 jects dealt with in this preliminary chapter are "Plow and Cir- 

 culation," "Sources," and "Doublets " and the "Velocity-Poten- 

 tials " due to them ; " Images ; " Eational Proofs of Torricelli's 

 Theorem and of the least section of the Vena Contracts being a 

 third harmonic to the areas of the (uniform) section of the vessel 

 aud that of the orifice, supposed horizontal, with no forces acting, 

 but a uniform pressure on the upper surface. Connected with 

 the last-mentioned subject there is an interesting and elementary 

 discussion of the theory of the "Vena Contracta" for a gravitating 

 liquid, the orifice being in the side of the vessel, by the late Mr. 

 li anion ; with a note thereon by Clerk-Maxwell in Loud. Math. 

 Soc. Proc. vol. hi. pp. 4, 5. 



