June 9, 1904] 



NATURE 



1 may further add that the formula for band spectrum, 



«' = tii' + i;'/«"- + ('//«'^ + ,'w'^ + r/"/«'''-r . . . 



which I have deduced as an extension of Deslandre's 

 formula, is one of the empirical formula; used by Kayser 

 and Runge for cyanogen bands (Ahhandl. d. Berlin. Akad. 

 d. Wissensch., iS8g, formula I„). From m'=o to m' = i5o, 

 the difference in wave-lengths between calculation and 

 observation seldom exceeds +0-03x10-'" m., which is quite 

 within errors of observation. H. Nacaoka. 



Physical Laboratory, Tokyo University, April 20. 



Electromotive Force between Two Phases of the 

 same Metal. 



1 WAS much interestc-d in the letter of Mr. George Beilby 

 in your issue of May 12. it may interest Mr. Beilby to 

 know that I contributed a paper to the Institution ot Civil 

 L-)ngineers on " The Effect of Stress on the Corrosion of 

 Metals " (Proc. Inst. C.E., vol. cxviii., session 1S93-4). On 

 perusing this paper it will be seen that the results were 

 somewhat analogous to the line of investigation Mr. Beilby 

 is undertaking. The experiments were on an extensive 

 scale, and were made on numerous samples of iron and 

 steel. In each case a polished bar of the steel or other 

 metal, of known chemical composition and physical proper- 

 ties, used was cut in two ; one half was stressed, and the 

 other remained in its normal state. Each pair of bars 

 was immersed in sea water, as an electrolyte, forming the 

 elements of a galvanic couple, with a delicate calibrated 

 galvanometer in circuit, when a decidedly measurable 

 E.M.F. was observed. It was invariably noticed that the 

 alteration in the physical properties of the metals produced 

 by the stress only in each stressed bar was sufficient to place 

 that bar in the position of copper in a zinc copper cell, the 

 normal unstressed bar answering to the zinc element in a 

 galvanic couple. 



.A current is also set up between two polished bars of the 

 same metal immersed in a suitable electrolyte, one being 

 in its normal state and the other having had its micro- 

 crystalline structure altered by annealing, in the manner 

 illustrated in a recent paper to the Institution of Civil 

 [•Engineers (" Effects of Annealing on Steel Rails," by 

 Thomas Andrews and Charles Reginald Andrews, Proc. 

 Inst. C.E., vol. clvi., session 1903-4, part ii.). When a 

 metal is stressed a similar effect is produced. I have for 

 some time past been working on a research on the E.M.F. 

 between normal and annealed metals, using in one part of 

 the investigation a complete series of specially prepared 

 pure iron and steel bars of varied and known chemical 

 composition, the object of the investigation being to show 

 the E.M.F. produced between annealed and unannealed 

 metals. I am much pleased to learn that Mr. Beilby is also 

 working on this very interesting subject. 



Mr. Beilby may also be interested in a research which I 

 made some years ago showing the E.M.F. produced 

 between polished bars of platinum or other metals, cut 

 from the same bar, the E.M.I*". being attributable to differ- 

 ence of molecular structure induced by heating one of the 

 bars. The electrolytes employed for these experiments were 

 fused salts at a high temperature (see " Electrochemical 

 Reactions between Metals in Fused Salts," bv Thomas 

 .\ndrews. Trans. Royal Society, Edinburgh, session 1885-6). 

 I venture to suggest that the following papers (" Observ- 

 ations on Variations of the Electromotive Force between 

 Metals at High Temperatures in Fused Salts," Trans. Royal 

 Society, London, 18S5 ; " Electrochemical Effects on Magnet- 

 ising Iron," parts i., ii., iii., iv.. Trans. Royal Society, 

 London, 1887, 1S88, 1889, 1892), which I published some time 

 ago, may perhaps be helpful to Mr. Beilby in the course of 

 his researches, the results of which I am looking forward to 

 with much interest and pleasure. Thos. .\ndrews. 



Wortley, near Sheffield, June 3. 



Graphic Methods in an Educational Course in 



Mechanics. 



In company, I think, with other correspondents, I have 



misunderstood Mr. Larden's use of the words "analytical 



methods." He alluded, it is true, to resolution and taking 



moments, but "analytical methods," especially when used 



NO. 1806, VOL 70] 



in contradistinction to "graphical," have a much wider 

 and more commonly received meaning. Dr. Murray's 

 dictionary defines modern mathematical analysis as " the 

 resolving of problems by reducing them to equations," and 

 cites Hutton, "Course Math.," 1827, "Analysis or 

 Analytical method is that which is commonly used in 

 Algebra." Prof. Croom Robertson, in " Analysis " in the 

 " Ency. Brit.," says : — " In modern times analysis has come 

 to mean the employment of the algebraical' and higher 

 calculus, and synthesis any direct treatment of the properties 

 of geometrical figures, in the manner of the ancients with- 

 out the use of algebraical notation or transformations." 

 " Analytical " is a hard-worked word, like potential and 

 polarisation, and no doubt it may be used in Mr. Larden's 

 sense. The word " analytical," in the sense of the employ- 

 ment of algebra and the higher calculus, is not self-explan- 

 atory, and " graphical " or " geometrical " are better for 

 this reason than "synthetical," unless the philosophical 

 aspect is under discussion. 



There can be no question that for almost all mathe- 

 matical calculation and research, algebraical methods are 

 far more powerful than geometrical {but I make reserv- 

 ations), and teachers are perhaps for this reason apt to 

 think that they are more useful and better suited for 

 educational explanations of phenomena or of natural laws. 

 If in mistaking Mr. Larden for an unusually pronounced 

 teacher of this type I have protested too strongly, I 

 apologise, but his parenthetical queries which I have pro- 

 voked I deny. 



That some persons have accurate musical "ears," and 

 others " no ear for music," that some can draw excellently 

 without having been taught, and others can never learn, 

 may perhaps be explained by physiological psvchology' 

 Some are "good at languages," and others bad; some 

 have a " good head for figures," and others not. E.\perts 

 in pedagogy might be able to tell us whether this is due 

 to some selective ability or inability. But that some persons 

 use .-ilgebra and the calculus with facility, and are bored 

 by geometry, while others have " no head for algebra," but 

 have an aptitude for geometrical methods, seems to be a 

 matter worthy of investigation by the mental philosopher. 



Not only has Mr. Larden used " analytical " in a some- 

 what restricted sense, but in this discussion he limits 

 " graphic methods " to " those methods that depend on 

 accurate drawing only, there being no calculation. ..." 

 I will give one example of what I mean by a graphical 

 7nethod in an educational course. The fundamental idea 

 of a differential coefficient is explained in the old text-books 

 purely by symbols. Persons with " no head for algebra " 

 find the greatest difficulty in grasping the idea. But draw 

 a curve of speeds on the black-board, and explain that a 

 tangent to it, or the slope at any point, gives the acceler- 

 ation or rate of increase. You need no accurate drawing, 

 no calculation, no algebra, but you give a perfectly clear 

 idea of a differential coefficient. 



It is, rather hard that those who are called calculus 

 dodgers cannot discuss the relative advantages of algebraical 

 and geometrical methods without being accused of writing 

 against mathematics or deprecatingly of mathematicians. 



Westminster, June 6. A. P. Trotter. 



Association of Economic Biologists. 



For some time past workers engaged upon various 

 problems connected with economic biology have felt the 

 need of some organisation whereby they could meet from 

 time to time to discuss these different problems with fellow- 

 workers so as to bring out suggestions and to prevent un- 

 necessary duplication of work, and generally to promote 

 and advance the economic side of biological science. 



With a view to the formation of such an association of 

 economic biologists, I have briefly discussed the matter 

 with a few fellow-workers, and I shall be pleased to receive 

 an expression of opinion or suggestions from any others. 



The idea at present in my mind is an association somewhat 

 on the lines of the American one, which would include and 

 welcome all investigators and teachers in economic biology 

 in its widest sense. 



Mr. Fred. V. Theobald (Wye) writes : — " Your suggestion 

 for an Association of Economic Biologists is most excellent. 



