May 28, 1908J 



NA TURE 



89 



this difficulty, it is found, can readily be overcome. All 

 measurements with alternate currents relate to mean values. 

 It is not necessary to make the instantaneous value of 

 ihe torque exerted on the moving system of the instru- 

 ment a measure of the simultaneous value of the quantity 

 tested, as, for instance, is the case with ordinary dynamo- 

 meters. All that is needed is proportionality between the 

 mean values. With the aid of this principle it can be 

 shown that the shunt magnet offers for instrument purposes 

 great advantages, one of these being that the density of 

 the air-gap flux, without loss of accuracy, can be increased 

 to a value far exceeding that obtainable in permanent 

 magnet instruments. 



The ordinary modes of analysis used for the solution of 

 alternate current problems rest upon several convenient 

 but inaccurate assumptions, such as sine law wave form, 

 proportionality of magnetic flux to magnetising current, 

 &c. Such methods can be used to give an approximate 

 explanation of known results, but are not adapted to pre- 

 dict precisely the action of a new type of instrument in 

 terms of ineasured data relating to its parts. In a paper 

 read before the Royal Society ' on January 16, a simple 

 form of analysis, previously pointed out by the present 

 writer, is further developed. This method is free from 



assumptions such as those mentioned. It rests upon the 

 theorem that each one of a number of known cyclic quanti- 

 ties, however different these may be in wave form, can be 

 expressed as a linear function of an equal number of other 

 cyclic quantities, the latter being such that the mean square 

 of each is unity, arid the mean product of any two is zero. 

 This theorem leads naturally to a vector method of re- 

 presentation, which in many cases closely approximates to 

 that usually adopted for alternate current investigations, 

 but there is the important difference that when the results 

 obtained are independent of assumptions such as sine law 

 wave form this fact can be proved, while if such in- 

 dependence does not hold good a superior limit can be 

 found to the error involved in results obtained by the 

 ordinary method. 



One of the instruments of which the behaviour has been 

 investigated theoretically and fully confirmed experiment- 

 ally is illustrated in Fig. i. The magnetic circuit consists 

 of a block of thin iron stampings shaped so as to have 

 only one narrow air gap, the section of which is increased 

 by suitably extending the poles. The field windings are 

 shown in section, and are liberally supplied with copper. 

 By this construction the ratio of resistance to impedance 

 is made small. The moving coil is rectangular, one side 

 turning in the air gap, the opposite side acting as an axis 

 perpendicular to the figure, and shown at o. The instru- 

 ment becomes a voltmeter if the moving coil is placed in 

 series with a condenser across the voltage applied to the 

 field coil. It becomes a wattmeter if the main current is 

 passed through an induction coil the secondary of which 



J " Alternate Current Measurement." By Dr. W. E. Sumpner. (Cotr.- 

 municattd by Prof. Prrry, F.R.S) 



NO. 2013, VOL. 78] 



contains a large resistance and the moving coil. If the 

 resistance of the field coil were zero, the fiux through the 

 core would simply depend on the applied voltage, whatever 

 the magnetic properties of the core ; and if this coil were 

 short-circuited the core flux could not be varied. The chief 

 points to be investigated were the effect of the actual 

 resistance of the field coil, the influence of the E.M.F. 

 induced by the field in the moving coil circuit, and the 

 precise meaning and influence of the self-inductance of the 

 moving coil. Exact formula have been established and 

 verified for all these effects, some of which may be illus- 

 ti-ated by the following tests. If the field coil be open- 

 circuited and a current be passed through the moving 

 coil, this will turn so as to enclose the greatest flux, bu^ 

 this position will not be oc because of the portion of the 

 flux crossing the air gap twice, this part being greatest 

 for the position oh. For feeble currents the resulting 

 position will be near ob, but will tend to approach oc for 

 larger currents, owing to the corresponding increase in 

 the permeability of the core. If, however, the field coil 

 be short-circuited, an alternating current through the 

 moving coil will invariably turn it to the position oh, 

 because such current cannot produce a flux through the 

 long limbs of the magnet. If the field coil be excited bv 

 an alternating voltage and the moving coil circuit be 

 closed through a small resistance, this coil, owing to its 

 self-inductance, will turn to oa so as to enclose the mini- 

 mum flux, while if under the same conditions the moving 

 coil circuit be closed through a condenser, the coil will 

 turn to oc so as to enclose the maximum flux. 



A thorough analysis of these effects, confirmed by actual 

 tests, shows that the instrument can be so constructed that 

 for most purposes its errors are negligibly small, and also 

 that it is possible to eliminate precisely these errors for 

 any specified frequency by using a special winding round 

 the magnet with its ends joined up to a condenser the 

 capacity of which is '."icrmined by the frequency and the 

 winding. None of the c-;-'.r> arise froin the variable mag- 

 netic properties of the core. In connection with alter- 

 nating current work, the voltage-controlled magnetic field 

 thus offers great advantages for investigating purposes. 



W. E. Sumpner. 



.V£ir LIGHTS ON THE ANTHROPOLOGY OF 



CALIFORNH. 

 T^HE anthropological department of the University of 

 California, thanks to Mrs. Hearst's munificent 

 endowment, is able to issue a further series of studies on 

 the native races of that State. The most voluminous 

 contribution is that of Mr. S. A. Barrett on the " Ethno- 

 geography of the Porno and Neighbouring Indians," a 

 group of tribes numbering at present about 1000 soul^. 

 and occupying the region known to geographers as the 

 Coast Range Mountains immediately north of San Fran- 

 cisco Bay, and running eastward to the Sacramento River. 

 These people are now partially civilised, and support them- 

 selves by farming and labour. But sufficient is known of 

 their primitive condition to show that they had no totemic 

 clans or groups, and that their tribal organisation was 

 weak, there being no chief in the commonly accepted 

 sense of the term. There was a sort of council of minor 

 chiefs presided over by a chief captain, whose authority 

 was strictly limited, and who was elected by the com- 

 munity. The inferior chiefs, on the other hand, held their 

 offices by hereditary right, and the succession passed from 

 one incumbent to the family of that sister who was nearest 

 to him in age, kinship and descent being in the female 

 line. 



In regard to culture, these people fall into three 

 divisions : — the ocean tribes, who depended for food upon 

 the fish and molluscs which abounded in the sea, and 

 derived the material for their food and clothing from the 

 redwood forests of the coastal districts; secondly, the 

 valley tribes, who occupied in severe weather round grass- 

 thatched houses, w'hile during the suminer thev wandered 

 along the streams and lived in temporary brush shelters, 

 but used no canoes, as the rivers are of inconsiderable 

 voluine ; lastly, the tribes of the inner lake region, who 

 built elliptical huts thatched with the tule rush, which 



