156 



NATURE 



[December 13, 1900 



of 



them happening by - = i, these quantities have to one 

 n 



another the ratios required. We then arrive at the true meaning 

 of the fraction which is said in mathematics to be the " proba- 

 bility " of a contingency ; and much confusion might be avoided 

 if we called the fraction, not the "probability," but the 

 " modulus of the evidence" and the so-called equally likely 

 cases not " equally likely " but " equi-evidential," or by some 

 more convenient name conveying the same idea. 



But it must be insisted that the above is only one way of 

 measuring the evidence, and is not applicable to all cases. In- 

 deed, the more important matters of daily life usually do not 

 admit of it, for there are qualitative differences in strength of 

 evidence which cannot really be measured quantitatively, and 

 that is why the application of mathematical probability to the 

 testimony of witnesses is so obviously futile. 



The solution of every mathematical problem in probability is 

 in the last resort only the finding of a modulus of evidence, in 

 the ratio of the part of the whole number of equi-evidential cases 

 which involve a given contingency, to the whole number of such 

 cases ; and with the finding of the modulus the strictly mathe- 

 matical work ends. Mathematics, as such, has nothing to do with 

 the inclination in our minds to expect the event for which the 

 modulus of evidence is greatest (or " the probability" greatest), 

 or the inclination, when some practical step has to be taken, to 

 act on the hypothesis that the event will happen for which the 

 evidence to us seems strong. 



Unfortunately, however, there is too often a tendency to con- 

 fuse the mathematical measure of the mere state of our minds 

 with the measure of something in reality ; and this produces 

 various mistakes — e.g. the inclination to expect that the 

 actual proportion of the occurrences of the event will tend to 

 conform to the proportion represented by the mathematical pro- 

 bability, i.e. conform to a formula of our ignorance. This is an 

 insidious fallacy, and we are not unlikely to fall into it in one 

 form when we have escaped it in another ; the mistake of 

 supposing the mathematical probability could be confirmed by 

 actual observation belongs to the head. The attempt to 

 regulate betting by mathematical probability is another instance 

 of the fallacy of confusing the subjective with the objective. 

 The truth is that an observed average may be made the basis of 

 a mathematical "probability" or modulus of evidence, by a 

 process which could easily be explained ; but though a " pro- 

 bability " may be based on an average, an average can never be 

 based on a " probabiUty." J. Cook Wilson, 



Instruments of Precision at the Paris Exhibition. 



I WAS glad to see your appreciative article upon the German 

 instruments of precision at the Paris Exhibition, in which you 

 refer, among other things, to the splendid catalogue which was 

 freely given away to any one who showed any interest and 

 desired to have a copy. 



As a member of the Jury of Class 15, I naturally was led to 

 duly appreciate both the German productions and their cata- 

 logue, and fearing that this valuable record might too soon 

 become inaccessible, I asked Dr, Drosten if he would send a 

 copy to the Science Library of the Victoria and Albert Museum, 

 so that it might be permanently available for many who might 

 wish to see it. This he most willingly did. 



If copies are becoming scarce, it would be more to the point 

 that public libraries attached to scientific institutions should have 

 them than that they should run the risk of being buried and lost 

 in private hands. C. V. Boys. 



A New Form of Coherer, 



During the past eighteen months I have been called upon 

 to demonstrate the principles of wireless telegraphy in connection 

 with my regular lecture courses, and now and then, while wire- 

 less telegraphy was still the latest scientific novelty, in popular 

 lectures. 



For the latter purpose it was necessary to have the receiving 

 apparatus as simple as was possible, compatible with a moderate 

 sensibility and regularity of action, 



I found the Marconi arrangement, consisting of the separate 

 instruments, coherer, relay and decohering devices, to have the 

 disadvantage, for my purpose at least, of requiring long and 

 careful adjustment each time the apparatus was set up. 



It occurred to me that if the functions of the three instru- 



NO. 1624, VOL. 63] 



ments could be performed by a single instrument, an easier 

 adjustment would result. 



This would, perhaps, be of no advantage in the case of a per- 

 manent set up, but would be of considerable advantage in 

 apparatus designed for the purpose of demonstration. 



By a slight modification, which need not be permanent, an 

 ordinary telegraph relay of moderate sensibility may be made 

 to serve the purpose of the coherer, relay and decoherer of the 

 Marconi arrangement. 



The ordinary telegraph relay is shown in the accompanying 

 sketch. 



M is the electromagnet, which in most cases is mounted so 

 that its distance from the armature, nn', can be varied by a slow- 

 motion screw, E and d are the main circuit, terminals, A and c 

 the terminals of the relay circuit, c is connected with the arma- 

 ture nn', and A is connected to the stop a when the instrument 

 is used as a relay. T is a screw connected to nn' by a spiral 

 by means of which the pressure of the armature on the stop b 

 may be varied. 



Usually the stop b is of hard rubber, and a and b may be 

 interchanged. If this interchange is made and if C is connected 

 with D, then the battery B will send a current through the 

 electromagnet M and the loose contact n'^. 



The tension in the spiral, s, and the position of the electro- 

 magnet may be adjusted so that no current flows, on account of 

 the very high resistance of the loose contact (coherer) n'*^. If 

 this resistance is lowered by electromagnetic radiations, then the 



current through the electromagnet rises and nn' is attracted 

 towards M and the circuit at n'3 is broken. The spiral s draws 

 nn' back into contact with b and the instrument is ready to 

 again respond to electromagnetic radiations. The adjustment 

 of M and T are easily made, and once made the coherer works 

 very steadily. 



The motion of nn' is too slight to be visible or to close an 

 auxiliary circuit with a sounder, but if a telephone, /, in series 

 with a condenser, c, is.put in parallel with the coherer (i.e. across 

 A c) the make and break of n'3 are clearly audible. 



If a " loud-speaking" telephone or a telephone with a mano- 

 metric flame are used, the make and break can be made audible 

 or visible to an audience. 



If the distance between sending and receiving stations should 

 make it necessary, c can be earthed and A connected with a 

 vertical wire. It is well to have the resistance of the electro- 

 magnet as low as is compatible with moderate sensibility in order 

 that the normal high resistance of the coherer shall form the 

 major part of the total resistance in series with the battery. 



In adjusting the contact n'3 it is convenient to set M and T 

 so that the armature nn' vibrates automatically, and then relieve 

 the tension in the spiral s until the automatic vibration just 

 ceases. 



When this adjustment is made, a "dot" signal from the send- 

 ing station gives a single ' ' tick " in the telephone — a dash 

 gives a series of ticks. 



I have never attempted to telegraph over a distance exceeding 



