November 4, 1892. 



SCIENCE. 



259 



rents are induced in the iron, the energy-function of the magnetic 

 circuit follows the more general law : — 



H^TiB^" + eNB^, 

 where ff gives the loss of energy per cycle and cm', in absolute 

 units, iVis the frequency, or number of cycles per second, r; the 

 co-eflBcient of molecular friction or hysteresis, and e a co eflScient 

 of eddy currents. 



Herefrom the loss of power per cm* of iron, in Watts, is de- 

 rived, as 



W=NH X 10 



, iVBi-" + £ JV^ BM X 10 



Tbe next problem was now, to determine the energy-function 

 of the magnetic circuit for cyclic variations of magnetism be- 

 tween any two limits, B^ and B^, and to derive numerical values of 

 the CO efHcient of molecular friction, 7, for different magnetic 

 materials. 



In the meantime, it had been found by Kennelly (Transactions 

 of American Institute of Electrical Engineers, October, 1891) that 

 Frohlicb's formula of magnetic induction — 



B= g 



a + bH 



(where H is the magnetomotive force or field-intensity, a and b 

 constants), which had been abandoned already as inexact, holds 

 rigidly by a slight modification. Using not the whole magnetic 

 induction, B, but the " metallic-magnetic induction," L = B — H, 

 where H is the field-intensity, we find, that for infinitely large 

 field-intensities S, the metallic induction L approaches a finite 

 limiting value L^, and follows Frohlicb's formula: — 



a + aH 

 or, if we assume Ohm's Law for the magnetic circuit, 



P 

 where p is the magnetic resistance, or reluctance, it is 



p = aA-aH; 

 that is, the magnetic resistance is a linear function of tbe field- 

 intensity. 



On the hand of a large number of experimental determinations, 

 made by the electro dynamometer and by the magnetometer 

 method, comprising several thousands of readings, I was enabled 

 to communicate to the American Institute of Electrical En- 

 gineers at the meeting of September, 1893, the results: — 



1. The loss of energy by molecular-magnetic friction, per cycle 

 and cm*, for a cyclic variation of the magnetic induction between 

 the limiting values L^ and L.,, is expressed by tbe function — 



where L, and L^ most likely have to represent the metallic in- 

 duction L = B — H. 



When Foucault — or eddy — currents are present in the iron, 

 the energy-function of the magnetic circuit takes tbe more gen- 

 eral form — 



^-n^-3-7 ^'""K^Y-^) 



where the first term gives the energy converted into heat per cycle 

 ttnd cm* by true molecular friction, the last term the energy con- 

 verted into heat by Foucault currents. 



2. Beyond a minimum value of field-intensity, Hm, the metallic 

 magnetic resistance follows the linear law : — 



p = a -\- a H. 



3. Beyond this minimum value of field-intensity, Hm, all the 

 essential properties of magnetic materials can be expressed by 

 three constants: — 



a, the co-efficient of magnetic hardness; 

 ff, " " " " saturation; 



v. '' " " " hysteresis; 



or, instead of this, by the three constants : — 



ioo =-, the value of absolute (metallic) magnetic saturation. 



H-- 



H„ — —, the critical field- intensity, or that field intensity where 



half-saturation, — °?, would be reached, if the linear 



3 

 law of magnetic resistance held already for this field- 

 intensity H„, and 



H^ = ijL^^-", the maximum value of hysteretio loss, by means 



of the formulas : — 

 The equations of magnetic resistance, or reluctance — 



p = a + cH = ^'>+^ 



(corresponding to Ohm's Law in the electric circuit), and the en- 

 ergy-function — 



(corresponding to the energy- function of the electric circuit, 

 W=c^R). 



4. These equations hold for all kinds of iron and steel, for nickel, 

 cobalt, and magnetite, and most likely for the amalgams of iron, 

 that is, for all magnetic materials. 



5. In first approximation, the magnetic induction, B, and the 

 magnetic hysteresis, or molecular friction. H, depend upon the 

 magnetic field-intensity, H, by the law of probability of molecular 

 distances. 



6. Average values of magnetic constants are: — 

 For wrought-iron, soft cast-steel, and mitis metal — 



a = .38 X 10 a = .05.5 x 10~° 7 = .OOd [Hm = 9); 



for cast-iron and low-permeability cast-steel — 



a = 3xl0 a = .095xlO~ t? = .013 (iJm = 22); 



for soft welded-steel and medium-hard cast-steel of high permea- 

 bility — 



a = 1.7xl0~'' a = .06xl0~° i? = -02 (Hm = 50); 

 for glass-hard steel — 



a = 10 X 10~^ a = A X 10~' 7 = .07 (fl^m = 110), 

 October, 1892. 



THE APPARENT GROWTH OF GOLD. 



BT RICHARD BAMBS, JR., M.E. 



Of the many myths prevalent regarding gold, the greatest one 

 of all is its growth. Of course there are many interesting in- 

 stances where ancient worked-out galleries in mines are slowly 

 closing up by the incrustation process, so that space long ago ex- 

 cavated is being filled with an accumulation resulting from the 

 percolation of water through the ad jacent wall- rock. This water 

 has in chemical combination such minerals as iron, copper, sul- 

 phur, and the precious metals, which are deposited in the open 

 crevice, making for a second time a mineralized body which will 

 show by analysis the above named and many more minerals. In 

 fact, I have had this actual experience resultant on the examina- 

 tion of an old gold mine in Honduras, Central America, that had 

 been worked some time prior to any history we have of that 

 country. This circumstance gave to the natives the idea that 

 gold grew, and they so expressed themselves; while it seemed in 

 the case of one individual a transmutation idea had permeated 

 his head, for he explained that the green carbonate of copper was 

 undergoing a change into silver, while the silver in turn would 

 develop into gold. 



In India I found a caste of mining people who believed that 

 gold grew in the bottom of the large lakes situated in that coun- 

 try. They expressed no practical reason other than fairy-tale 

 superstitions. And even in this country there are converts to the 

 idea. I was much amused and interested some years ago to bear 

 an intelligent acquaintance maintain in strong and not altogether 

 religious terms that " the stuff grew and he knew it." His ex- 

 perience was based on the fact that in a certain pile of tailings, 

 resulting from the milling of heavy sulphuretted gold-ores, he 

 had treated at one time several tons with no result. Again, in 



