i98 



NATURE 



[April 26, 1894 



as it opens up new possibilities of approaching- 

 difficulties now arising in certain quarters, as to the 

 exact interpretation of parts of the arthropod body where 

 ■similar fusion is effected. Messrs. Wilson and Martin 

 contribute a couple of papers on " The Muzzle of Orni- 

 thorhynchus," and inform us that the beak of that 

 animal is in life "no more horny than a dog's nose." 

 They show that Turner's " fibrous membrane " is really 

 a cart'laginous tract, and that the immense pre-nasal 

 cartilage is the inter-trabecular one of Parker, highly 

 specialised. Their observations on the " rod-like tactile 

 organs," which Poulton first described and discussed in 

 their exquisite bearings on the functions of end-organs 

 of the Pacinian type, appear on the whole unsatisfactory, 

 in consideration of their having worked upon fresh 

 material. Their illustrations are crude, and they do not 

 seem to have made the most of their preparations. 

 Then follows a paper by Mr. C. Hedley, on the aber- 

 rant gasteropod Parmacochlea, and one by Prof. Ralph 

 Tate on the " Geographical Relations of the Floras of 

 Norfolk and Lord Howe Islands," in which he concludes 

 that the latter are to be regarded as outliers of the New 

 Zealand region. Baron von Mueller contributes two 

 papers on systematic botany, and Mr. R. Etheridge,jun., 

 one, already alluded to, upon " Some Implements and 

 Weapons of the Alligator Tribe, Port Essington, North 

 Australia." The series closes with a monograph of 

 51 pages, by Mr. W. A. Cobb, on " Nematodes, mostly 

 Australian and Fijian," in which eighty-two species (half 

 of which are new, and many of which are European) are 

 worked out, in relation to a plan under which the unit of 

 measurement equals the i-iooth part of the worm's 

 length, and certain longitudinal and transverse measure- 

 ments, taken at points which mark the disposition of 

 leading organs and apertures, are ingeniously formulated 

 for ready comparison. 



Such is the scope of the volume, and we congratulate 

 the committee upon it. So far as the editor is con- 

 cerned, there is internal evidence of the great labour of 

 his task, and that its execution has been to him a labour 

 of love. When it is considered that during the com- 

 pilation of a work so costly and unremunerative, the 

 country lay under a sore financial depression, we earnestly 

 hope that the meagre list of subscribers announced 

 within its covers will be supplemented by a number 

 sufficient for adequate repayment. 



The illustrative plates are somewhat unequal in merit, 

 those of the Photoline Printing Company being in par- 

 ticular not a little crude and muzzy. We note, however, 

 with intense satisfaction, the work of a native litho- 

 grapher, Wendel by name. Anything more satisfacto ry 

 than his draughtsmanship it is difficult to conceive ; and 

 illustrations such as those numbering pi. xi., fig. 9, 

 and pi. xiv., fig. i, betoken, on his part, artistic feeling 

 {Geist) of a high order, and, on that of the printer, 

 manipulative skill worthy the highest encouragement. 

 For the "discovery" of this artist Prof. Spencer has to 

 be thanked ; and it is not a little irritating to us at home 

 that it should have remained for our antipodean confreres 

 to first reach ihat stmdard of excellence in scientific 

 ■illustration which, in association with the well-known 

 names of certain continental lithographers, has been so 

 long the admiration of the biological world. 

 NO. 1278, VOL. 49] 



The contents of the volume, when broadly estimated 

 in correlation with the work which the Australasian 

 biologists have during the last decade made public, 

 amply testifies to a determination on their part to leave 

 the study of histogenesis and the refinements of micro- 

 scopy to us at home, in preference for the monographino- 

 of their indigenous fauna and flora, along those broader 

 lines upon which the great problems to which they hold 

 the keys must be solved. The resolution is as wise as it 

 is noble on their part, and in adopting it they are un- 

 questionably furthering the foremost desires o f the 

 generous and far-sighted man whose pioneer's work they 

 have so successfully combined to memorialise. 



G. B. H. 



HARMONIC ANALYSIS. 

 An Elementary Treatise on Fourier's Series, and 

 Spherical, Cylindrical, and Ellipsoidal Harmonics, 

 with Applications to Problems in Mathematical Physics . 

 By W. E. Byerly, Ph.D., Professor of Mathematics 

 in Harvard University. (Boston, U.S.A. : Ginn and 

 Co.) 



THIS treatise contains, in an expanded form, the 

 subject-matter of a course of lectures by Prof. 

 Byerly, on the functions mentioned in the title. The 

 properties of the functions are developed, to a large 

 extent, by means of special examples of their application 

 to obtain solutions of problems involving the differential 

 equations of physics. The object of the treatise appears 

 to be rather to give examples of the practical applica- 

 tions of the functions, than to develop in detail their 

 analytical properties ; many important theoretical points 

 are accordingly passed over, the results of investigations 

 being in many cases merely stated. In the introductory 

 chapter the functions of Legendre and Bessel are intro- 

 duced by means of some of the simpler differential 

 equations of physics. As a matter of method, we think 

 it might have been better to have referred all the 

 functions to Laplace's equation in the first instance, 

 leaving the cases of the equations of heat, vibrations, 

 &c. for subsequent treatment ; thus, for example, the 

 circular and exponential functions, spherical harmonics, 

 and Bessel's functions should make their first appearance 

 in the normal forms, 



i.^ m-^-ti-z cos COS '^ COS , ti'"/ a\ 



e ■ mx . ■ ny, r ■ md) . P (cos 6], 



sm sm -^' =1" ^ - ^' 



sm 

 ^^'= cos 



m(j} . J (A'p), 



which satisfy the equation 



V'V = o. 



The least satisfactory part of the book appears to us 

 to be the treatment of Fourier's series in chapters ii. and 

 iii. ; it is neither desirable nor possible in an elementary 

 treatise to give a complete discussion of the various 

 points which arise in such a subject as the expansion of 

 arbitrarily given functions in series of circular functions, 

 but it is eminently desirable that it should be distinctly 

 pointed out whenever a result is obtained by a method 

 which falls short of demonstration, and the nature of the 

 assumptions made, should as far as possible be indicated. 

 If this is not done, the student is misled into thinking 



