October 31, 



•^95j 



NATURE 



659 



not, nor is it infallible ; but it is a praiseworthy attempt to 

 organise into one jjuiUi the teachers of a growing and most 

 important section of educational work. The labour involved in 

 getting together the facts which make up the contents must 

 have been immense, and it is to i)e hoped that, now the work 

 has been done, the support ret|uired to ensure the annual 

 publication of the directory will not be lacking. If the book 

 only makes teachers in technical .schools and institutes realise 

 that they are part of one organic whole, having for its object 

 Ihe extension of .scientific knowledge, it will accomplish a much- 

 desired end. 



The Report of the Technical Educational Committee of the 

 Berks County Council is optimistic, but it is not distinguished 

 by descriptions of any very noteworthy developments. Berk- 

 shire is an agricultural county, and that is tantamount to saying 

 that little encouragement is given to .scientific education. Such 

 counties are not willing to be taught much about principles ; 

 what they will tolerate, arc subjects like practical butter-making, 

 l.uindry-work, poultry-keeping, hedging, and hor.se-shoeing ; but 

 to attempt to teach agriculturists anything much beyond 

 manual dexterity, is to court opposition. However, the 

 Technical Education Committees are doing something to 

 educate the agricultural mind to a better appreciation of the 

 benefits to be derived from science, though it must be confessed 

 ihat the rate of progress is extremely slow. Berkshire, along 

 with Oxfordshire and Hampshire, contribute towards the main- 

 tenance of the Unis'ersity Extension College at Ref cling, and, 

 in recognition of the .satisfactorj' development of the agricultural 

 ilepartment of the college, the Board of Agriculture recently 

 granted a sum of £yxi, and the money could not have been 

 better bestowed. The various courses of study at the college 

 are well arranged, and valuable field experiments are carried on. 

 Hy paying over the sum of /'400 to the college, the Berkshire 

 Committee ensures efficient instruction for the students under 

 tlieir care, and that is a very important consideration, for the 

 supply of good teachers, competent to teach science as it should 

 be taught, is comparatively .small, to .say nothing of the labor- 

 atory accommodation essential for truly scientific instruction. 

 In spite of the facilities thus ofiered, the lectures in elementary 

 science arranged for teachers were not successful. It would be 

 a great pity if the Committee had to discontinue this part of their 

 work on account of the want of su]>port by the teacher for 

 whom the lectures are intended. The other ways in which the 

 Committee disposes of the funds allocated to technical education 

 are evening continuation classes, scholarships, dairying, farriery, 

 and bee-keeping. Aid is also given to classes in the principles 

 of agriculture, mensuration, botany, drawing, horticulture, 

 chemistry, mechanics as applied to agriculture, and to manual 

 instruction in woodwork and metalwork. 



The Brussels correspondent of the 7Y/««j reports that the elec- 

 trical and anatomical institutes founded by M. Ernest Solvay, and 

 )>resented ityhim and other donors to the University i)f Brussels, 

 were officially inaugurated on Monday, under the presidency of 

 the Burgomaster, a.ssisted by M. Graux, the Chancellor, and the 

 entire body of professors. Delegations from the English and 

 ("ontinental Universities have responded to the invitation of the 

 Hrussels University to take part in the series ol fetes organised 

 in celebration of the event. 



It was announced a few weeks ago that the Treasury has 

 thoughts of reinstating King's College, London, in the enjoy- 

 ment of its share of Ihe grants made to University Colleges. In 

 consequence of this decision, the Council of ifie College have 

 adopted a conscience clause as a standing regulation. 



SOCIETIES AND ACADEMIES. 

 London. 

 Physical Society, October 25. — Mr. Walter Baily, Vice- 

 President, in the chair. — Prof. J. Perry read a paper, by himself 

 and Mr. II. E. Hunt, on the development of arbitrary function.s. 

 During the discus.sion on Prof. Ilenrici's paper (.-Xpril 13, 

 1894), one of the authors described a graphical method of 

 developing any arbitrary function in a series of other normal 

 forms than sines and cosines, such as Bessel's or zonal spherical 

 harmonics. The method consisted in wrapping the curve which 

 represents the function round a specially shaped cylinder, not 

 circular, and projecting this curve on to a certain plane. Many 

 months were wasted in finding with great exactness a suflicient 

 number of coordinates of the trace of the cylinder suitable for a 



^O. 1357, VOL. 52] 



Zeroth Bessel development. The lalwur, however, was un- 

 necessary, since the coordinate most troublesome to calculate i.s 

 not really needed, the projection only taking place in one direc- 

 tion. To develop any arbitrary function of .r (say y) in normal 

 forms, the real difficulty consists in finding the value of an in- 

 tegral such as [" y. Q(a). dx where Q(jr) is some tabulatc-d 

 function. If now z is another tabulated function which is the 

 integral of Q (jr), the required integral is [yds. If the values 



for y for 25 equidistant values of x are known, from .r = o to 

 X = a. Let the corresponding values of c be tabulated, and let 

 a curve be drawn with the values of j as ordinales and the 

 values of; as abscissa' ; Ihe area between the axis of : and this 

 curve gives the value of the integral required. The authors give 

 four tables ctmtaining the abscissa- for the four first terms in the 

 development in Zeroth Bessels. They have tested the method 

 by applying it to the calculation of a known function in terms of 

 zonal spherical harmonics, and Ihe agreement l)ctween the 

 true value of the coefficients and those found is very satisfactory. 

 Prof. Henrici said the method was a new departure, since in the 

 place of an instrument of complicated design the authors only 

 used a planimeter and pencil and paper, and obtained the .same 

 degree of accuracy. The fact that the series employed to test 

 the method consisted of a finite number of terms seemed to him 

 an objection. Prof Karl Pearson had in a recent conversation 

 informed him of a method for the development of functions which 

 he (Prof Pearson) had recently discovered. This method was 

 not, however, so simple — at least in most cases — as that of Ihe 

 authors. Prof Minchin thought it would add to the intelli- 

 gibility of the paper if it were stated that the method was similar 

 to that employed when expanding in terms of a Fourier series 

 or in spherical harmonics. In these cases you have a function 

 which, when multiplied by other functions of different orders, 

 kills all the terms except one. draphic methods ought, in his 

 opinion, to be very much oftener employed, and he con- 

 sidered that there was no problem in physical mathematics 

 of which the solution could not be obtained by graphic 

 methods. He would also like to know if Prof. Perry 

 had obtained a graphic method of calculating Bessels. Mr. 

 Trotter agreed with Prof .Minchin as to the neglect of graphic 

 methods. He regretted that Prof. Perry did not continue to 

 consider the method as the projection from a Cylinder, as he had 

 found the method of wrapping curves round a cylinder most use- 

 ful. Prof Perry in his reply said he had adopted the expansion 

 they had employed, under the imjiression that the test was a 

 particularly severe one. He had not discovered a graphic 

 method of calculating Bessels. The reason they gave up the 

 cylinder was the immense labour involved in calculating the ^ 

 coordinates of the trace, which would afterwards be of no use 

 in the development of the function. — Mr. F. W. I^nchester read 

 a paper on the radial cursor, a new addition to the slide-rule. 

 The ordinary form of slide-rule enables calculations to be made 

 which involve mulliplication and division, also involution and 

 evolution where Ihe indices are integers. The radial cursor allows 

 of the solution of problems in which fractional indices occur ; 

 for example, in questions involving the adiabatic exfansion of a 

 gas, where an expression of the form /!<, = const, has to be 

 dealt with, and where 7 is not an integer, nor is it constant 

 for all gases. In this case it is necessary to provide some ready 

 means of dividing the scales on the rule and slider proportionally 

 to the value of 7, which corresponds to the division and multi- 

 plication of the respective logarithms of the quantities dealt 

 with in the proportion of the indices of p and v, i.e. I and 7. 

 This proportionate division of the scales is effected in the new 

 cur.sor by a radial index-arm which is arranged to swing about a 

 slud fixed to a sliding-bar running in guides at right angles to the 

 rule. All readings are taken at the [Joints of intersection of a 

 line on the radius arm and the edges of the slide. The distance 

 of the pivot, on which the radius arm turns, from the scale, and 

 therefore the value of the index employed, is re.id off on a scale 

 fixed to the transverse bar. Mr. C. V. Boys said thai owing to 

 the kindness of the author he had been able to try the cursor, 

 and had found it of great service in dealing with questions of 

 adiabatic expansion. The new addition to the slide-rule sufters 

 under the same disadvantage as the rule itself, namely that a 

 verbal or written description seems so very njuch more complex 

 than is the actual operation when using the rule. The author's 

 device might be described as an india-rubber slide-rule, for it 

 performed the function of a slide-rule in which Ihe graduations 



