March 15, 1888] 



NATURE 



465 



evening of the 1st inst. I observed a similar rainbow. I saw it 

 first at 7h. 25m. p.m., the registered time of sunset here for that 

 day. It lasted for nearly fifteen minutes. The western horizon 

 was cloudy, and the sunset a fine one. The bow Was exceed- 

 ingly brilliant, and as far as I could judge, a perfect semicircle, 

 the ends of the arc being about 4° above the horizon. There 

 was a secondary bow equally perfect, and of remarkable bright- 

 ness ; the brilliant glow below the primary, and the marked 

 dulness between it and the secondary, added to the beauty of the 

 sight. After reading Mr. Hill's letter, I published my observa- 

 tions in a letter to the Argus, that others might confirm or 

 correct them. I have received six replies, all in accord with my 

 observations. One of my correspondents informed me that he 

 had, some years ago, seen a lunar rainbow formed just before 

 the moon had risen. H. M. Andrew. 



The University, Melbourne, January 26. 



The Nest of the Flamingo, 



In an interesting article by Mr. Bowdler Sharpe, entitled 

 " Ornithology at South Kensington," published in the December 

 number of the English Illustrated Magazine, there is a descrip- 

 tion and figure of the flamingo's nest, and an opinion is ex- 

 pressed that the previously-held ideas about the nest being tall, 

 and the female sitting upon it in a straddling manner, might 

 now be considered as exploded. 



I have seen numbers of these tall nests in the shallow pans of 

 water — or "vleys," as they are locally called — in Bushmanland, 

 Cape Colony, particularly at Klaver Vley. These quaint nests 

 were built in the waterwhereitwasafew inches deep, and at a con- 

 siderable distance from the shore. They were conical in form, 

 about 18 inches high, and 6 inches in diameter at the top, with 

 a shallow basin-like cavity for the eggs ; built, so far as I can 

 recollect, of slimy mud. To perform the office of incubation, 

 the bird must have straddled over the nest. The species no 

 doubt differs from the one described in the article. There should 

 be no difficulty in securing specimens of these nests. Possibly 

 the object aimed at in building the nests in the water is to secure 

 them against soaae enemy, and the height of the nest, besides 

 conveniencing the long-legged owner, provides for the rising of 

 the water-level. E. J. Dunn, 



Pakington Street, Kew, near Melbourne. 



Dynamical Units and Nomenclature. 



In his review of Prof MacGregor's " Kinematics and Dy- 

 namics," on page 361, Prof. Greenhill tilts a lance against those 

 whom he terms mathematical precisionists. I do not know this 

 book, and I hold no brief in its defence ; but as I owe to these 

 precisionists whatever clear ideas I have on mechanics, I feel 

 bound to enter into the lists on their behalf, little as they need 

 my aid. 



Both the precisionists and practical men start with the same 

 two dynamical quantities, which they respectively call mass and 

 foixe, weiglit and. force ; of these they select arbitrary units, and 

 respectively name them pound and pound-weight, weight-of-a- 

 pound and force-of-a-poutni (or pound-weight and pound-force). 



To the single wonl pound the practical man does not, so far as 

 I know, attach any single definite idea, and he cannot, therefore, 

 use this word singly without introducing possible confusion ; for 

 it characterizes matter and force equally, and yet is neither. On 

 this view Prof. Greenhill's own expression "the attraction of the 

 earth on a pound," should for accuracy and consistency be "the 

 attraction of the earth on the weight of a pound {or on a pound- 

 weight)." 



To the precisionist a pound is a certain mass, just as a foot is 

 a certain length, so that the practical man's "weight of a pound " 

 is simply the "pound" of the precisionist, who would no more 

 dream of 'distinguishing' it as " the mass of a pound" than of 

 distinguishing a f(iot as " the length of a foot." 



The attraction of the earth on a certain amount of matter is 

 called "the force of 10 pounds" by practical men, and "the 

 weight of 10 pounds " by precisionists : these are purely defini- 

 tions, so that the phrases are absolutely equivalent. If, then, in 

 the specification of a force produced otherwise than by the 

 attraction of the earth a precisionist is required to speak of it as 

 "a force equal to the weight of 10 pounds," the practical man 

 must follow suit with "a force equal to the force of lo pcunds." 

 These expressions stand, or rather fall, together, and the con- 



sistent precisionist would specify the force as "10 pounds- 

 weight " merely. 



If, however, a body, such as a brickbat or the iron block sup- 

 plied with a balance and called a "pound weight," is to be 

 introduced into the specification, a precisionist would very 

 properly say " a force equal to the weight of 10 brickbats or of 

 10 pound-weights " ; and the complete idea hereby conveyed 

 cannot be expressed by the practical man otherwise than by 

 " the attraction of the earth on 10 brickbats or on 10 pound- 

 weights." 



In no way, then, is " a force equal to the weight of a mass of 

 10 pound- weights," the precisionist equivalent of the practical 

 " force of 10 pounds," nor is it even consonant with precisionist 

 nomenclature. 



Since, therefore, the precisionist uses mass, force, pound, 

 pound-weight, as the exact equivalents of the practical man's 

 weight, force, weight-of-a-pound, force of- a- pound, the advant- 

 age does not seem to lie on the side of the latter, more 

 especially when he is untrue to himself in loosely using the word 

 "weight " as often in the sense of " force" as according to his 

 definition. 



But so far both practical men and precisionists labour under 

 the immense disadvantage of dealing with a variable force-unit 

 which can be made precise only by a specification of place ; and 

 it is greatly to the credit of the latter that they have introduced 

 a simple invariable force-unit by which all forces, whether due 

 to gravitation or other physical action, may be expressed abso- 

 lutely in a form which allows of direct comparison between 

 them. With this unit ma is the correct measure of a force, and 

 when Prof. Greenhill speaks of "the mathematician straining 

 after the equation F = ma, when using the gravitation unit of 

 force," I utterly fail to understand what is meant, considering 

 that this expression of a force necessarily implies an absolute 

 force-unit ; and I further feel strongly tempted to deny that 

 either for this unintelligible operation or for any other the pre- 

 cisionist ever uses g pounds as a mass-unit, though, if he ever 

 does use a variable mass-unit in measuring the invariable mass 

 of a body, he is surely countenanced by the practical man who 

 does not hesitate to use a variable force-unit in measuring the 

 invariable force exerted by a given spring compressed to a given 

 extent. I might further add that the precisionist never measures 

 the weight of a body in "pounds," even if he denotes it by w, 

 and that, if he does sometimes denote this variable force by the 

 same number irrespective of place, it is only when using the 

 practical man's variable force unit. 



With regard to confusion arising from the use of the equation 

 w = mg any more than from the use of the equation w = m, 

 this would be to me inconceivable, did I not notice that Prof. 

 Greenhill uses the phrase " if the equation 7v = tngis supposed 

 to be used with absolute units." Does there indeed exist a 

 single man who thinks that this equation can be used with other 

 than absolute units ? If such there be, to him certainly will 

 confusion be not only possible, but probable too, and deservedly 

 so ; but to others there can surely be no more confusion in ex- 

 pressing a (precisionist) weight as m or ?ng indifferently than in 

 expressing an angle as or 180 fl/ir, it being of course premised 

 that the proper unit — [precisionist) pound weight or poundal, 

 radian or degree — is named. 



Further, how it can be a solecism to measure pressure in 

 poundals per square foot any more than in pounds-weight per 

 square inch — which latter is the precisionist equivalent of what 

 an engineer would loosely and most inaccurately call "pounds " — 

 I am at a loss to understand, since pressure is the measure of the 

 distribution of force over area, and a poundal is as much a force 

 as " the force of a pound," and very much more definite. And 

 how the expression of the (precisionist) weight of a body in 

 poundals rather than in pounds-weight is a solecism also demands 

 explanation. 



Lastly, I must seriously protest against the suggestion that a 

 precisionist should ever ask for, or want to buy, '" half a poundal 

 of tea " : what he wants is the tea itself, the substance of it and 

 not the earth's action upon it, and very rightly and properly he 

 asks for "half a pound," which the consistent practical man 

 would have to term "the weight of half a pound." 



In the above I am not concerned to defend the practice of 

 those mathematicians who select fantastic units of mass or force 

 as a foundation for some puzzling questions of no utility what- 

 ever : I have merely attempted to define the position of the 

 physicist or precisionist, and to rebut seriatim the charges 

 brought against him in Prof. Greenhill's criticism. 



February 27. RuBKUT E. BAVKE5. 



