Ny4 TURE 



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THURSDAY, SEPTEMBER 14, 1893. 



THE MECHANICS OF FLUIDS. 

 Hydrostatics and Elemeittary Hydrokinetics. By George 

 M. Minchin, M.A., Professor of Applied Mathematics 

 in the Royal Indian Engineering College, Coopers 

 Hill. (Oxford: at the Clarendon Press, 1892.) 



\WORI< on this subject which should incorporate 

 the latest developments has long been wanted ; 

 and Prof. Minchin has performed a very useful service in 

 providing a treatise of a convenient size for purposes of 

 instruction. 



The first chapter starts with some general theorems on 

 the distribution of strain and stress in the interior of a 

 body, which to our way of thinking had better have been 

 relegated to Chapters iii. or iv., by which time the 

 student would be able to appreciate their importance. 

 Mr. Minchin, however, justifies his method in eloquent 

 language, but his simile of the danger of leaving uncap- 

 tured fortresses in the rear partakes of ante- Napoleonic 

 ideas ; as Napoleon proved it makes all the difference 

 whether the foe is stationary or mobile. 



We are pleased to see the author's practical protest 

 against the banishment of the notation (we cannot dis- 

 pense with the idea) of the Differential Calculus, tra- 

 ditional in our elementary treatises. A French schoolboy 

 acquires a working knowledge of the Differential Calculus 

 episodically, in the course of his studies of elementary 

 algebra and trigonometry. 



Mr. Minchin postulates at the outset a perfect fluid, that 

 is a fluid devoid of viscosity. This is necessary when 

 we come to the Motion of Fluids ; but the theorems of 

 Hydrostatics are true of all fluids, however viscous, such 

 as tar, or even pitch , a fluid from its general definition is 

 not capable of coming to rest till the normality of the 

 stress has been attained. 



The word intensity is prefixed by the author when it is 

 wished to indicate that a stress is estimated per unit area ; 

 thus, for instance, 150 pounds on the square inch he calls 

 the "intensity of the pressure." But this is contrary to 

 our ordinary language, where "intensity " is never em 

 ployed Mr. Minchin had better have adopted another 

 word, " thrust," to express total pressure or push against 

 a given area, leaving the words stress and pressure, as in 

 common usage, to imply that they are estimated per unit 

 area, square foot or inch, metre or centimetre. 



This would not be the work of a modern college pro- 

 fessor if the author did not explain at some length that 

 the -world has been calling things by their wrong names ; 

 thus it is maintained that the expression above •' a pres- 

 sure of 150 pounds on the square inch" is inaccurate, 

 and should always be replaced by " an intensity of pres- 

 sure of 150 pounds' weight on the square inch." 



This is a counsel of perfection which a careful search 

 would probably show is not always observed by the 

 author himself; and it is invariably ignored and rejected 

 by practical men, including his own engineering col- 

 leagues. 



Thus Prof Hearson, R.N., in a recent examination 

 paper at the Naval College, Greenwich, asks for the cal- 

 culation of the resistance of a train in '' pounds per ton 

 NO. [ 245, VOL. 48] 



weight"; but his M.A. colleague would edit this into 

 "pounds' weight per ton mass." 



The Coopers Hill student will have to be as careful to 

 recollect the expression appropriate for the class-room he 

 is attending, as the Chairman of the House of Repre- 

 sentatives in America, according to the story, in address- 

 ing the rival members of \\\\tioi and WXxnoise. 



The use of the word " weight " to designate only the 

 accidental quality of a body due to its position on the 

 surface of the Earth is much insisted upon by a certain 

 school of our writers ; but this temporary fad will soon 

 pass away, we hope, as it seems to be tainted with the 

 ancient heresy of the existence of bodies possessing 

 positive levitation, such as the fii e or inflammable air said 

 tohavebeen employed in Archytas's pigeon, or the rarefied 

 dew with which Bishop Wilkins proposed to fill a number 

 of egg shells, and thereby fly in the air. 



For instance, what is the weight of a ton (mass) of 

 hydrogen ; must we say that it is about — 13 tons ? 



Prof. Oliver Lodge would banish the word "hundred- 

 weight " from our language ; but what has he to offer the 

 architect in exchange } 



Pressures on foundations in architecture are most con- 

 veniently measured in cwt. per square foot, from the 

 simple fact that the average weight of a cubic foot of 

 brickwork is one hundredweight. 



If the architect of the Tower of Pisa had made a cal- 

 culation in accordance with the modern formula for the 

 resistance of foundations in earth, 



V I - sin (4 / 



in cwt. per sq. foot, at a depth of A feet in earth of density 

 iccwt. per cubic foot, denoting the angle of repose of 

 the earth, he would have found that his depth of 22 feet, 

 with tu = 08 and (p = 22°, would bear only 84 cwt. per 

 square foot ; while the pressure due to the weight of the 

 tower mounted up to 145 cwt. per square foot. 



Students owe a debt of gratitude to Prof. Minchin for 

 having almost entirely banished the old-fashioned mysti- 

 fications concerning 



W = iV .ind W = gpV ; 



and he very clearly points out that the pressure at a depth 

 s in liquid of density p is not given by pz gravitation 

 units, but by ifpz absolute units. 



But the introduction of the new term '' specific weight" 

 to designate what has hitherto been called the heaviness 

 (or density) of a substance is to be deprecated, especially 

 as the author is careful to explain that he does not mean 

 specific gravity by specific weight. 



But the German for specific gravity is spezifische 

 gewicht, so that confusion is sure to arise ; much the same 

 as with the word ntasseinheit, which means unit of 

 measure, and not unit of mass ^ as it has been incorrectly 

 translated. 



It is doubtful whether any advantage is gained by the 

 introduction of absolute units into a statical subject ; they 

 are never used in experimental and. practical work ; but 

 if the experimenter wishes to express his numerical results 

 in a cosmopolitan form, he can multiply his gravitation 

 results by the local value of ^, as the last operation of all. 



Unfortunately, in the C.G.S. system selected by scientific 

 men, the units are so minute that they are only suitable 



