418 



SCIENCE 



[N. S. Vol. XXVI. No. 665 



wire carrying a current is, as we know, tan- 

 gent to a circle through whose center the wire 

 passes at right angles, and is numerically 

 equal to 8C/a, where G is the current in ab- 

 solute units, and a the distance in centimeters 

 of the point from the axis of the wire. 



While the approximate direction of the force 

 is easily found experimentally, its numerical 

 value is determined only by integrating the 

 effects of all parts of the current. And since 

 the force is in a plane at right angles to the 

 wire, it is not an easy matter to make clear to 

 students beginning the subject why it is neces- 

 sary to consider parts of the wire off this plane. 



This is one of the many places where the 

 electron theory can be used to marked advan- 

 tage, and besides, if, as many believe, it is the 

 correct theory — or embraces a larger number 

 of facts than any other — then it should be 

 used both in this case and in all others. 



Let electrons, all moving in the same direc- 

 tion with the constant velocity V centimeters 

 per second, be uniformly distributed along a 

 straight wire, and let E be the total amount of 

 electricity per centimeter length of the wire. 

 Then, assuming the field of force from each 

 electron to be the same in all directions, that 

 is, moving slowly and undisturbed by other 

 electrons, the rate of change of induction, due 



Hence 



to the electricity at all parts of the wire, 

 through a circle at right angles to it of radius 

 a; or in other words, the work required to carry 

 a unit magnetic pole once around this circle 

 (see the figure) is given by the equation 



--=2 I -T- 25raFcose. 

 dt Jo r^ 



But COS. edl = rde, 1/r = cos &/a, andEV= C, 

 the current. 



dF_ 

 di ' 





coadde = 4-C, 



and therefore the force on a unit pole at any 

 point on the circumference of a circle of 

 radius a is 



4ttC_2C 



2ira a ' 



However, presumably the field due to each 

 electron is influenced by all others, and so in- 

 fluenced that it is confined to a plane at right 

 angles to the wire, but equal in every direc- 

 tion from it. From this it follows at once 

 that 



dF 



dt 



and 



= 'i^EV= 47rC, 



47rO_2C 



2-nra a ' 



According to this conception, which I believe 

 to be the correct one, the magnetic force at any 

 point is due entirely to that part of the current 

 nearest to this point; the more distant parts 

 having no direct effect whatever. But, of 

 course, as just explained, all electrons produce 

 their full effects indirectly by compressing 

 each other's fields into planes at right angles 

 to the wire. 



While the above contains nothing new in 

 physics, it is given because it, or some modifi- 

 cation of it, may be of use in the class-room. 

 W. J. Humphreys 



Mount Weatheb Obsebvatort, 

 Bltiemont, Va., 

 June, 1907 



REFLEX PROTECTIVE BEHAVIOR IN BUFO 

 VARIABILIS 



During the past year, while studying the 

 Opalinae parasitic in the recta of different 

 species of frogs and toads, I have had to kill 

 many of these batrachians. In each case the 

 backbone and spinal cord were cut behind the 

 head and the brain destroyed by " pithing " 

 with a needle. In this way Rana fusca, Bana 

 esculerda, Rana agilis, Bufo variahilis, Bom- 

 hinator ignexis, Bomhinator pachypus and 

 Hyla arborea have been killed. In all but 

 one of these species I find that, on cutting the 



