August 13, 1891] 



NATURE 



341 



would seem from the figure as if Dr. Mayr's Pinus pumila 

 might be referred to P. Ceinhra, whilst P. pentaphylla is 

 obviously a near ally of the East American P. strobtis. 



Dr. Mayr's "diagnose," however, is really a rather 

 diffuse description in German, not conveniently adapted 

 for the comparison of one form with another. In this 

 absence of concise comparisons in Latin, modern 

 botanists, especially German ones, compare unfavour- 

 ably with their predecessors. On the other hand. Dr. 

 Mayr establishes some sectional characters which may 

 prove useful, such as the three sections into which he 

 divides the genus Picea, viz. Morinda, Casieta, and 

 Omorica, the last, indeed, having been already proposed 

 by Willkomm. 



Hybrid forms between Pinus Thunbergii and P. densi- 

 flora are mentioned, as well as a whole series of garden 

 varieties which have either originated in Japanese gardens 

 or have occurred as " sports" on the wild trees, and which 

 have been propagated by grafting by the Japanese gar- 

 deners. These are likely to prove of scientific interest, 

 and will be specially interesting for garden purposes. 



Seven quarto coloured lithographic plates accompany 

 the volume, giving details of the foliage and cones. We 

 could have wished that representations of the trees them- 

 selves could have been supplied, and that an alphabetical 

 index of species and varieties had been added to the 

 classified table of contents. When we have so much 

 that is valuable and interesting presented to us, it may 

 seem ungracious to hint at deficiencies, but really in this 

 case to ask for more shows how greatly we appreciate 

 what we have, and is about the greatest compliment we 

 can pay to the author. Maxwell T. Masters. 



ELEMENTAR Y H YDROSTA TICS. 

 Solutions of Examples in Elementary Hydrostatics. 

 By W. H. Besant, Sc.D., F.R.S., Fellow of St. John's 

 College, Cambridge. (Cambridge : Deighton, Bell, and 

 Co., 1891.) 



THIS is a collection of solutions, or a crib, to the 

 author's well-known " Elementary Hydrostatics," 

 which has held the ground in elementary instruction 

 unchallenged since 1863. 



It was cruel, though, as Dr. Besant apologetically ex- 

 plains, unavoidable, to keep the world of instructors 

 waiting so long for these much-needed solutions and 

 explanations of the questions in his Hydrostatics. 



The Solutions are stated to be almost entirely drawn 

 up by Mr. A. W. Flux, who has found it necessary to 

 explain that the equation/ = gpz must be interpreted as 

 giving the pressure p in poundals per square foot (or in 

 C.G.S. bara'^s, might well have been added) ; but he has 

 not explained that the effect of this reverential interpre- 

 tation is to make p and w signify the same thing ; so that 

 two symbols are used to denote the same quantity, 

 although one, p, is called the density, and the other, w, 

 the intrinsic weight. 



But in 1863 the word poundal was' not known, nor 

 was any mode of measuring force and pressure in use, 

 except in terms of gravitation units. 



It would take too long to recount the despair of the in- 

 structor and the confusion of the stu lent at the different 

 NO. I 137, VOL. 44] 



modes of reconciliation of the equations p = gpz and 

 p = wz, variously used as measuring the pressure at a 

 depth of z feet. 



Because thirty and more years ago it was thought con 

 venient in dynamical equations to replace W/^by a single 

 letter M, merely for purposes of convenience in writing 

 and printing, it was and is still taught in our theoretical 

 treatises that the equation W = M.^ is the expression of 

 a subtle and fundamental law of Nature, to be introduced 

 even into a treatise on Elementary Hydrostatics, pre- 

 sumably taken up before a student has commenced 

 Dynamics, and before he can understand what accelera- 

 tion in general, and the particular acceleration g, can 

 mean. 



What must, for instance, be the feeling of Tommy 

 Atkins, when the Musketry Instructor begins on p. I 

 of the official "Treatise on Military Small Arms," 1888, 

 with this definition of Mass, taken in a garbled form from 

 chapter ii. of the Hydrostatics and elsewhere. 



" Mass : The quantity of tnatter in any body, the sum 

 of all the particles of the body ; it is proportional to the 

 weight, whatever be the figure, or whether the bulk or 

 magnitude be great or small ; for the weight is equal to 

 the mass multiplied by the force of gravity, or W = M^, 

 and the letters M and W are usually employed to denote 

 the mass and weight respectively." 



In short, this definition amounts to saying that mass is 

 something we denote by the letter M, while weight is 

 something we denote by the letter W ; but we must 

 always remember that W = M_^, where g is something 

 unexplained, even when we measure mass in pounds and 

 weight also in pounds ; so that if g appears in one place, 

 it will cancel again somewhere else, and not affect the 

 ultimate numerical result. 



But if, according to former instructions, we calculate the 

 pressure from the equation/ = gP^t we must notice that 

 p, the density as defined in chapter ii., " Elementary 

 Hydrostatics," is the weight in pounds of one-^ch part of 

 a cubic foot of the liquid, or gp is the weight in pounds 

 of one cubic foot of the liquid, so that gp and w now 

 measure the same quantity. 



The unfortunate instructor was formerly called upon to 

 reconcile these opposing statements, that w is sometimes 

 the same as p, and sometimes as gp ; now, however, he 

 can take refuge behind the definite statements of this 

 authorized collection of solutions. 



But what is most wanted is a mathematical Censorship, 

 to go through our hydrostatical treatises, expunging all 

 the ^'s. 



As to the mere mathematical geometrical part of the 

 solutions, this is doubtless carried out with true Cam- 

 bridge elegance, of which Dr. Besant is so well known an 

 exponent ; a trifle however, in comparison with the diffi- 

 culty of the interpretation of the units in some extra- 

 ordinary questions relating to the equations W = sV an J 

 W =_^'-pV, questions at one time considered a valuable 

 test of clear thinking on the part of the student. 



We counsel everyone who values his peace of mind 

 to procure a copy of these Solutions, if called upon 

 to interpret and expound the numerical results of the 

 original " Elementary Hydrostatics " 



A. G. Greenhill. 



