August 23, 1894] 



NATURE 



407 



ject of importance was a discussion on integrators, harmonic 

 analysers and integraphs, and their application to physical and 

 engineering problems. A number of these were exhibited, both 

 models and working instruments, some of the latter being beau- 

 tiful specimens of Swiss workmanship. For the discussion an 

 hour and a half had been allowed : of this the opener, Prof. 

 Henrici, occupied the greater part, but did so to the entire 

 satisfaction of his audience. The subject had been discussed at 

 previous meetings by Sir Frederick Bramwell at Brighton, and 

 by the late Mr. Merrifield at Swansea ; Prof. Hele Shaw had also 

 read a paper on the subject before the Institute of Civil 

 Engineers. The first planimeter was invented by a Bavarian 

 engineer named Hermann. It was lost sight of, but was sub- 

 sequently reinvented in 1825 and 1S26, and from it our present 

 planimeiers are derived. Amsler invented his instrument in 

 1854, and first published an account of it in 1856. Planimeters 

 may be classified in two ways. As Prof. Hele Shaw subse- 

 quently remarked, it is natural for an engineer to classify instru- 

 .ments with reference to their mechanical action, and thus 

 planimeters may be divided into two classes, according as the 

 wheel does or does not slip. Prof. Henrici prefers a classifica- 

 tion depending upon the geometrical pioperties involved in the 

 action of the instrument. A planimeter measures the area 

 swept out by a line. The length of the line may either be fixed 

 or variable. Again, a line in a plane may either move or turn. 

 To obtain general areas we have a choice of two combinations 

 (for only special areas could be traced, e.g. by a line moving 

 parallel to itseK). The first class of planimeters depends upon 

 the motion of a line which can both turn and move parallel to 

 itself, but which remains of fixed length. The line takes the 

 form of a rod of fixed length, one end of which is jointed to 

 another rod so as to move on a circle about a fixed point (the 

 pole), while the other end is provided with a tracing-point 

 to be moved around the figure whose area is to be evalu- 

 ated. These planimeters can only be used to integra'e 

 around closed curves. It does not matter where the 

 wheel is placed along the rod, but its axis must be parallel to 

 the axis of the rod. This introduces one of the most serious 

 difficulties with which the maker has to contend. In Amsler's 

 planimeter the rod can only be used on one side, so that the 

 error is always in the same direction ; but an improved form 

 was exhibited in which the rod can be used on both sides, so that 

 this error is eliminated. Then there is the slipping error. 

 Maxwell drew attention to this, and was the first to propose 

 an instrument in which there was no slipping at all. There are 

 a number of planimeters in which the wheel, instead of rolling 

 on the paper, rolls on a prepared surface. There is always some 

 resistance to the motion of the wheel and counters, and this 

 increases the slipping. The error can be reduced to a mirimum 

 by diminishing as far as possible (i) the friction between the 

 paper and the wheel (as by using a prepared surface) ; (2) the 

 resistance to the motion of the wheel. In using the instrument 

 we should also avoid getting the instrument in such a position that 

 the wheel has to move much at right angles to its own plane, 

 for then the friction and slipping error is greatest. Amsler, in 

 his first paper (1856), fore.-hadowed many improvements which 

 have since been carried out ; and in his second paper (he only 

 published two), he described a planimeter depending upon the 

 action of a cylinder rolling on a sphere, in which there was no 

 slipping. Maxwell suggested two forms of instrument in which 

 slipping was altogether avoided ; tut they were never made. 

 The second class of planimeters depends upon the motion of a 

 line of variable length which moves without turning. They 

 give the value of definite integrals between any fixed limits, anil 

 may be called integraphs. Instruments of this type have been 

 devised by Lord Kelvin, Abdank-Abakanowilz, Vernon Boys, 

 and Conradi. To engmeers it is more important to be able to 

 integrate a curve than an expression ; and an integraph can give 

 the integral of a curve as a curve. Lord Kelvin and Boys 

 have shown how instruments may be made to integrate a 

 dilierential equation. The idea 01 a harmonic analyser was 

 given l)y .Vmsler in his first paper as early as 1S56, but Lord 

 Kelvin first actually constructed one. It has been of great 

 service in analysing tidal motion ; but it is bulky, and cannot be 

 carried about. Prof. Henrici has devised two others, one of 

 which will give five terms in the expansion according to Fourier's 

 theorem ol any curve. These analysers should prove of great 

 use to engineer^ and electricians, <'.^'. in investigating the action 

 of valve-gear and the behaviour of dynamos. In the discussion 

 which followed, Prof. Hele Shaw drew attention to the Hatchet 



NO. 1295. VOL. 50] 



planimeter as a most simple and efficient workshop instrument. 

 Prof. Boys explained why it was so much more difficult to con- 

 struct an instrument for differentiating than for integrating. An 

 automatic differentiator appeared at present to be an impossi- 

 bility. A person can differentiate with a machine ; but a 

 machine cannot of itself well differentiate. It is of the very 

 nature of an integraph to smooth over the irregularities of a 

 curve ; whereas a differentiator would exaggerate all the 

 irregularities of a curve. 



Mr. Arnulph Mallock followed with a note on the behaviour 

 of a rotating cylinder in a steady current. Lord Kelvin was in 

 his best British Association form when discussing the resistance 

 experienced by solids moving through fluid-;. As the time 

 approached for Mr. Hiram S. Maxim's paper on flight, the 

 audience grew to dimensions most easily explained by sup- 

 posing that an experimental demonstration in Keble Hall was 

 expected. 



.\fter Friday, on account of the large number of papers, the 

 Section had to split up into two or three departments sitting 

 simultaneously (and continuously, without any luncheon interval). 

 Only the more important physical pipers can be noticed here. 

 On Saturday, Prof. Osborne Reynolds described and illustrated 

 experimentally the successive stages in the motion of water pass- 

 ing under gradually increasing pressure through a verticil tube 

 constricted in the middle. At first the water leaves the con- 

 striction in the form of a narrow, steady jet. As the pressure 

 increases it fills the lower part of the tube, and eddies appear 

 below the constriction ; but the motion is still steady. The 

 third stage is that of turbulent motion. Finally, there is an 

 appearance as of air-bubbles at the constriction, accoinpanied 

 by a singing or hissing sound ; the water is now boiling under 

 diminished pressure. Prof. S. P. Lingley gave an account of 

 his recent researches on the infrared spectrum to an audience 

 most unwilling to allow him to stop, and rather impatient at 

 the manner in which his lantern slides were exhibited. The 

 President (Prof. Kucker) and Prof. Norman Lockyer heartily 

 congratulated Prof. Langley on the magnificent success of his 

 work, which will be fully described in a subsequent number of 

 Nature. Dr. E. Pringsheim followed with an account of his 

 new determination of the ratio ol the specific heats of certain 

 gases. 



The first paper on Monday was one by Dr. A. Schmidt, on a 

 new analytical representation of terrestrial magnetism. Prof. 

 Schuster followed with two papers : in one of these he examined 

 a suggested explanation of the secular variation of terrestrial 

 magnetism, and in the other he discussed the minimum current 

 which could be observed in a galvanometer of given dimensions 

 wound in various ways. Lord Rayleigh followed with three 

 papers. 



In the first of these he described experiments made by him 

 to determine the minimum current audible in the telephone. 

 The estimates previously put forward vary widely : Preece gives 

 6 ;; lo'"' ampere ; Tait, z x 10 '-, and De la Rue 1 x lO"* 

 ampere. Ferraris is the only experimenter who has given 

 satisfactory details of his experimental methods ; he founa that 

 the current diminished when the frequency increased, and that 

 a minimum current of 5 x 10"'' ampere was rc'iuire.l at a fre- 

 quency of 594. His experiments were made with a make-and- 

 break apparatus, which would give higher harmonics in addi- 

 tion to the stated frequencies. In Lord Rayleigh's experiments 

 electromotive forces of the harmonic type were produced by the 

 revolution of a magnet in the neighbourhood of an inductor 

 coil of known construction. The revolving magnet consisted 

 of 25 cm. of clock-spring driven, windmill fashion, by air 

 from an organ bellows. The magnetic moment of the magnet 

 was deduced from observations with a magnetometer. The 

 inductor coil was the one which had been used as the "sus- 

 pended coil " in the determination of the electro-chemical 

 equivalent of silver, and it was placed with its centre vertically 

 below that of the ma;net. From the known data the inducel 

 electromotive forces were calculated. The current was carried 

 to a distant part of the house through leads, and was varied by 

 introducing a resistance-box going up to 10,000 ohms ; the 

 adjustment of the sound could thus be made by the observer 

 at the telephone. Theory shows that the minimum 

 current required in a telephone .should be inversely .is the 

 square root of the resistance. Two telephones of the 

 Bell unipolar type were used : the data given below refer 

 to one which had a resistance of 70 ohms. When the 

 magnet was driven at full speed the frequency was 307, and 



