172 



SCIENCE. 



[N. S. Vol. XVI. No. 396. 



On the Complex Product of E.M.F., Cur- 

 rent and other Vectors: H. T. Eddy, Uni- 

 versity of Minnesota. 

 The rules which govern multiplication 

 and the other processes of ordinary algebra 

 are those of mere number in its arithmetical 

 sense. But algebra necessarily admits the 

 iise of complex numbers, to which arith- 

 metical processes, such as multiplication, 

 are perfectly applicable. Such complex 

 numbers used as factors are not physical 

 vectors, though they are frequently repre- 

 sented geometrically as quasi vectors. 



When a physical vector, such as a force 

 or a velocity, expressed in complex notation 

 is multiplied by a mere numerical complex, 

 the ordinary rules of algebra still hold. 

 But when we multiply together two phys- 

 ical vectors expressed in complex form in 

 order to obtain their product, the result 

 has a physical significance which imposes 

 laws of operation differing from those of 

 ordinary algebra, and the factors are found 

 to be non-commutative. The paper con- 

 tains a detailed comparison of the nature 

 of the two kinds of complex products, es- 

 pecially directed to the consideration of the 

 product of pairs of alternating vectors of 

 the same frequency, to show that the double 

 frequency of such products does not arise 

 in any way from the non-commutative char- 

 acter of the multiplication, as has been 

 sometimes assumed. 



Coefficients of Expansion bettceen. 0° and 

 —190° C: J. S. Shearer, Cornell Uni- 

 versity. 



The coefficients of expansion for a num- 

 ber of metals at low temperatures have 

 been measured by Dewar, using the method 

 of weighing in liquid air. The writer has 

 tried to get a method for the determination 

 of the linear coefficients between 0° and 

 —190° C. The method finally adopted 

 was based on the idea of the compensated 

 pendulum. By means of a combination of 



iron and cadmium, one end of the specimen 

 was held fixed, while the other operated an 

 optical lever. 



This paper will later be published in full 

 in the Physical Beview. 



A Set of Direct Current Dynamos ar- 

 ranged in Series for High Tension Work : 

 G. S. MoLER, Cornell University. 

 This paper describes, in detail, the instal- 

 lation at Cornell University of 24 small 

 500-volt dynamos connected in series. The 

 machines are separately excited and give 

 0.22 ampere of current under an E.M.F. 

 of 12,000 volts. This paper will later be 

 published in full elsewhere. 



Test of Liquid Air Plant at Cornell Uni- 

 versity: Frank Allen, Cornell Univer- 

 sity. 



This plant consists of an electric motor, 

 a compressor and a liquefier. 



The compressor is of the four-stage type 

 with air cylinders of about seven-, four-, 

 two-, and one-inch diameter and of eight- 

 inch stroke. Purified air is compressed by 

 this machine to a pressure of 2,700 pounds 

 per square inch. 



In order to accomplish this a 500-volt 

 electric motor of 30 horse-power is used, 

 which has an efficiency of 87.6 per cent. 



The apparatus used for liquefying air is 

 known as the Hampson Liquefier, from the 

 name of its English inventor." It works on 

 the principle discovered by Lord Kelvin 

 many years ago, that gases expanding from 

 a high pressure to a low become slightly 

 cooled. Air compressed to 2,700 pounds is 

 allowed to flow through coils of copper tub- 

 ing and issues at a low pressure from a 

 small valve. The cool air circulates among 

 the coils and cools the incoming air, which 

 in its turn expands, lowering its tempera- 

 ture still more. This process goes on con- 

 tinuously and in about five minutes the 



