]V1ay 21, 1909] 



SCIENCE 



837 



Cn _ l/'l/Oa— l/fli 

 Ci ^ v' 1/a, — I/O, ' 



•where «„ Oa, 03, Oj, have been written for the four 

 impedances in the denominators above. 



While theoretically the method may be extended 

 to any number of harmonies, it is practically lim- 

 ited to two by the accuracy of readings and by the 

 labor of computation. Experiments in the analy- 

 sis of waves built up by combining the E.M.F.'s 

 of different machines, and also by the analysis of 

 E.M.F. waves of single generators, show that the 

 method is capable of an accuracy of two or three 

 per cent, of the fundamental. 



The method has the disadvantages of giving no 

 information of the phase relations, and of not 

 readily lending itself to the analysis of current 

 waves. The advantages are that it requires no 

 special apparatus; direct access to the generator, 

 or the use of synchronous motor, is not necessary; 

 and the accuracy is better than that of an oscillo- 

 graph, though not equal to that of a curve tracer. 



The Accurate Analysis of Alternating Current 



Waves: P. W. Geover. 



With the rapid development, in recent years, of 

 methods and apparatus for the tracing of alter- 

 nating current waves, the question of the conve- 

 nient analysis of the curves obtained has become 

 increasingly important. Although the well-known 

 method of Fourier is the most direct and accurate, 

 its employment seems to be quite generally re- 

 garded as too laborious for general use. This is 

 evidenced by the appearance of a number of graph- 

 ical and planimetrical methods, among which may 

 be mentioned those of Clifford, Fischer-Hinnen, 

 and Houston and Kennelly. All these modes of 

 procedure, however, labor under the disadvantage, 

 inherent in all graphical methods, of inaccuracy 

 where small quantities are involved, without any 

 saving of time over that required to derive the 

 values of an equal number of harmonies by the 

 Fournier analysis if the calculation be suitably 

 arranged. 



In 1897 Rosa simplified the calculation by the 

 use of a table from which the required products 

 of the ordinates by the sines of the angles could 

 be taken directly from a table. Using this, all the 

 odd harmonics up to and including the 15th can 

 be obtained in a little over an hour. 



S. P. Thompson^ showed that the work could be 

 still further shortened, (1) by grouping together 

 those ordinates which are to be multiplied by the 

 sines of the same angle, and (2) by dividing the 



' Electrician, May 5, 1905. 



half wave into an even number n of equal parts, 

 when the products divide themselves into comple- 

 mentary groups, so that the /tth and ( « — fc ) th 

 harmonics are found, respectively, by adding and 

 subtracting the sums of two groups of products. 

 He gave the complete scheme of calculation for 

 the two cases, to=6 and »= 12. The whole 

 analysis in the former case may be carried 

 through in ten minutes or even less. 



The electromotive force waves of alternators 

 with slotted armatures, however, often contain 

 the higher harmonics to an appreciable extent, 

 and these may greatly distort the form of the 

 current wave in circuits containing capacity. The 

 speaker has therefore developed the scheme of 

 calculation for the ease of 18 ordinates and has 

 prepared a table to facilitate the multiplications. 

 Such a table need include the ordinates up to 100 

 only, the fractional parts being found from the 

 same table by shifting the decimal point. Using 

 this method the amplitudes of all the harmonics 

 up to and including the 17th may be determined 

 in about half an hour with an accuracy and ease 

 not attainable by any graphical method. 



R. L. Fabis, 

 Secretary 



THE BIOLOGICAL SOCIETY OE WASHINGTON 



The 458th meeting was held April 3, 1909, with 

 President Palmer in the chair. Lantern slides 

 made by a novel application of well-known meth- 

 ods were shown upon the screen by Mr. A. A. 

 Doolittle. The silver is thoroughly removed from 

 plates, leaving only the gelatin film; from old, 

 unused or undeveloped plates by the usual hypo 

 bath, and from poor or waste negatives by the 

 reducing process with ferri-cyanide. On im- 

 mersing the thoroughly washed plate in blue print 

 solution for five minutes and subsequent drying 

 in the dark, they may be printed upon by contact 

 with negatives in the usual manner. They give 

 clear high lights and contrasting effects, desirable 

 qualities in lantern slides or transparencies. The 

 color is a pleasing semi-translucent blue. The 

 method is simple and can be used by the inex- 

 perienced. Beautiful window transparencies are 

 similarly made. 



The following communications were presented: 

 Classification of the True Fishes: Theodoee Gill. 



The speaker restricted the class Pisces to the 

 true fishes or Teleostomes, as he had done since 

 1873. Two of the best zoologists of Europe (Hu- 

 brecht, of Holland, and Regan, of the British 

 IMuseum) have recently come to the same con- 



