August 7, 



1879] 



NATURE ^l 



337 



faced manner in which triangles and figures are moved 

 about and turned about and placed upon one another. 



The second chapter treats of the subject as handled in 

 the Elementary Treatises, taking chiefly for the basis of 

 remarks the fourth edition of the Geometry, by Messrs. 

 Rouchd and De Comberousse. 



Chapters III. and IV. are occupied with Trigonometry, 

 and Chapter V., closing the work, treats of Mechanics. 

 The volume is too technical to allow of an extended criti- 

 cism here, but we can commend it to geometrical 

 students. No statement is made as to how it comes to 

 pass that such a volume was issued under the auspices of 

 the Society named above. 



LETTERS TO THE EDITOR 



[ TTie Editor does not hold h imself responsible for opinitns expressed 

 by his correspondents. Neither can he undertake to return, or 

 to correspond with the writers of, rejected manuscripts. No 

 notice is taken tf anonymous communicmtions. 



[ The Editor urgently requests correspondents to keep their letters as 

 short as possible. 7 he pressure on his space is so great that it 

 is impossible othenvise to ensure the appearance even of com- 

 munications containing interesting and novel /cuts.] 



New Methods of Moving Ordnance 



In anticipation of an interesting paper and discussion at the 

 intended meeting of the British Association at Sheffield, a 

 complete set of working models has been prepared at the 

 Floating Dock, North Shields, to explain several new applica- 

 tions of a new method of moving ordnance with ease and 

 rapidity of motion in small space, with economy of time and 

 labour. 



The most recent of these improvements is an adaptation of the 

 principles of the tramway .-ind tram car, in making use of the 

 perfectly level surface, and the retaining groove, either on the 

 ship's deck or on the platform of a battery. But instead of 

 flanges on the wheels, that have a tendency to clog and 

 compress dirt into the grooves, and "gag" on the edge.':, 

 a hanging longitudinal guide-plate projects below the wheels 

 on the inside of the rails ; this allows greater freedom of 

 action to the wheel and gives greater security, and in order 

 to attain greater power of resistance to any shock or con- 

 cussion, the guide plates are strengthened by a cross connecting 

 the plate between them. The gun carriage slide has turn-table 

 pivots on four wheels, that can be placed anywhere ; as for the 

 real or imaginary centres of motion at the ends, or centrally or 

 to correspond with the present A B c D pivots of the Royal Ar- 

 tillery, which when in line or parallel or at any angle to each 

 other act as stationary or moving pivots or fulcra for a lever 

 movement of the slide, to turn or move in any direction on 

 perfectly straight lines, as the shortest route between any two 

 points, and also as best adapted for the application of a direct 

 action of any of the usual mechanical motive powers. 



North Shields, August i George Fawcus 



I 



"Law of Frequency" 



The term "law of frequency" seems to be used in two dis- 

 tinct senses by matlicmatical writers. In the ordinary theory 

 the ambiguity leads to little confusion except to beginners ; but 

 this is owing to a fortunate, though altogether special, pro- 

 perty of the hypothesis on which the theory is based. When 

 we come to investigate other possible theories, it becomes highly 

 important to keep the distinction in mind. Suppose, for clear- 

 ness' sake, that we have before us a large number of measure- 

 ments of a single unknown quantity. On examining them we 

 find that a considerable number agree pretty closely with each 

 other, several are more obviously discrepant, while one or two 

 are widely so. Conversely we are led to think of the frequency 

 with which a given measurement occurs as a function of the 

 magnitude of the measurement itself. Denoting this magnitude 

 by X, we may represent the relative frequency of its occurrence 

 by <p(x). This function is called the "law of frequency of the 

 mea-surement x," and it is in this sense that statisticians often 

 use the phrase. 



But if we consider all the possible measurements that may be 

 made of the quantity, we see that their number is practically 

 infinite Tlir relative frequency of any proposed measurement 



becomes therefore infinitssimal, and we must seek for some other 

 expression. This we find by inverting our ideas, as it were, and 

 asking, not "What is the frequency of a given measurement 

 -T?" but "What is the probability that a given measurement 

 shall lie between the two very near values x and x + Sx7" 

 Suppose that our particular theory gives us this latter probability 

 as i|/ (.r) S .V. Then mathematicians generally are wont to call 

 ^{x) " the law of frequency of the measurement x," 



A little consideration will show that on one hypothesis only 

 are <f (jr) and \(/ (x) necessarily of the same form. This hypo- 

 thesis is that the arithmetic mean of our fallible measure- 

 ments is the best value of the quantity measured which we can 

 obtain from them. From this the ordinary law, (p (x)a: e~^ -^i 

 easily follows. 



But if the nature of our measurements (or other discrepant 

 magnitudes) be such as to suggest that some other mean is likely 

 to be nearer the truth than the arithmetic mean, we shall find 

 that the forms of ip {x) and ^ (x) are not the same. It seems, 

 therefore, desirable that a real distinction in the things signified 

 should be marked by a corresponding distinction in the terms 

 applied to them. If it be not too bold a suggestion, might we 

 not " desynonymise " the terms "law of frequency" and "law 

 of facility," keeping the former for the function I have called 

 (p (x), and the latter for the commoner function I have repre- 

 sented by <fi (x) ? Donald McAlister 



St. John's College, Cambridge, July 28 



'^^ Carica Papaya 



Thanks to Mr. Whitmee for his timely correction of my 

 perhaps too dogmatic assertion as to the seeds of the Papau 

 being rejected by birds, at p. 241. Had I not written off-hand 

 I should have qualified the sentence " the birds however will not 

 touch them," i.e. the fruit, by adding "as far as I have 

 observed." 



We had flocks of small birds inhabiting the casuerinas and 

 banyans which shaded our sea-side quarters at Riviere Noire, 

 Mauritius ; they were mostly small birds such as "bengalis," 

 {Estrelda amandava), "senegalis," (Estrelda astrilda), " cal- 

 fats," {llfuma oryzivora) " tuit-tuits," (Oxynotus ferrugineus), 

 cardinals, crithagras, serins, &c., as numerous as finches and 

 sparrows in our B nglish gardens : but never did I see any of 

 these birds, which were as bold and tame as possible, peck 

 at the papaus either on the plants or on the ground ; had they 

 been in the habit of doing so I must have observed them. The 

 " martins" or minas of the interior did not trouble us with their 

 visits and noisy chatterings, so I cannot say whether they affect the 

 papau seeds much. It is possible that the " pigeons marrons" 

 and various ' ' tourterelles " may have fed on the papau fruit but 

 I never found any of the seeds in their crops. 



The flying foxes, "collets rouges," (Pteropus Edwarsit), used 

 to come down in numbers to eat the mangoes of our neighbour, 

 Mons. Geneve ; when we used to shoot them on moonlight 

 nights and find them remarkably good eating, but I never knew 

 or .heard of their eating the papau, which perhaps they do. 

 The conditions of the Mascarene and Navigator's islands are 

 probably different, as the Carica certainly does not spring up 

 as a weed wherever forests are cleared in Mauritius, or Bourbon, 

 The Carica papaya figures as a cultivated and not an intrusive 

 plant in Dr. Charles Pickering's table of observed localities of 

 plants introduced throughout Polynesia ; distinguishing for each 

 plant, whether it appears to be native, or spontaneously dissemi- 

 nated, and whether when introduced apparently by the hand of 

 man it has become naturalised or intrusive. Certainly Dr. 

 Pickering's work is out of date (184*), and I have not yet 

 seen his new work Chronological History of Plants (Triibner, 

 1879).. 



W hilst on this subject I may subjoin a paragraph I came across 

 in a number of the Gardener's Chronicle about the papau, with 

 which I conclude. 



" Utilisation of the Papaw. — The peculiar properties of the 

 Papaw (Carica papaya) in causing the separation of animal 

 tissues, and thus rendering newly-killed meat tender, is a 

 fact that has been frequently written about and commented 

 upon by travellers. Our contemporary, The Chemist and 

 Druggist, suggests, as a ' possible specialty,' the production of 

 some convenient preparation from the tree which should contain 

 the same properties as the leaves, or whether the leaves them- 

 selves might be dried and still retain their activity. ' There is 

 no doubt,' they say, 'that a preparation which really embodied 



