22 



NATURE 



[May 3, 1888 



(q -<r)§ and (q - r)h was made manifest in the unsuccessful 

 attempt to calculate the coefficient of (q - r)h. 

 It thus appears that the assumed law of the indices is the true 



one - , i , r 



It will be remembered that/, q, r, . . . . are the halves of 



the sharpened Hamiltonian Numbers E« + i, E«, E« - tf 



. , . . and that consequently the relation — 



Em CEh - 1) _ E„ + l (E M -, - i)(E«-i -2 ) + # 



1.2 1 . . 2 ... 3 



E«+i = i + : 



may be written in the form — 



2) 5(25 ■ 



l)(2J-2)(25-3) 



t(2t-l)(2t- 



2 • 3 

 ■2)(2/-3)(2/- 4 ) 



2 . 3 



• • 5 

 11(211 



l)(2U - 2)(2U - 3)(2U - 4)(2U - S) 



3-4-5 



(a) 



The comparison of this value of p with that given by (i) 

 furnishes an equation which, after several reductions have been 

 made in which special attention must be paid to the order of 

 the quantities under consideration, ultimately leads to the 

 determination of the values of A, B, C, . . . . in succession. 



"Physical Society7~April 14.— Sh el ford" Bidwell, F.R.S., 

 Vice-President, in the chair. — Mr. W. E. Sumpner read a paper 

 on the variation of the coefficients of induction. The author 

 pointed out that there are three ways of defining the coefficient 

 of self-induction of a circuit, expressed by the following 

 equations — 



(0 < = Li 2 



(2) N = L 2 C 



(3) T = iL,C»; 



where e = back E.M.F. due to change of current, C = current, 

 N = total induction through the circuit, and T the kinetic energy 

 of the circuit. If the medium be air, L 15 L 2 , and L 3 are identical, 

 but in the case cf iron this is no longer the case. When tho 

 curve of magnetization is given, their values, corresponding with 

 any value of C, can be easily determined by the above equations. 

 ■Maxwell's absolute method of measuring self-induction gives L 2 , 

 and by a modification due to Prof. Ayrton, where the current is 



C + C 



altered from C, to C, instead of from o to C = — K the 



2 



value of L obtained is approximately Lj, if C 2 - C 2 is small 

 compared with C. From the known character of the curves of 

 magnetization of iron, it is easily seen that the value of L 2 in- 

 creases with the current when the current is small, then becomes 

 nearly constant, and afterwards decreases. For an electro- 

 magnet having a horse : shoe core of best Swedish iron %' diameter 

 and 14" long, wound with 800 convolutions, the value of L z for 

 currents between '047 and "107 amp. was found to satisfy the 



• T A 



equation L 2 = - + '0425, where A ss current in amperes. A 



method of comparing self-induction with capacity is described, in 

 which the arm of a Wheatstone's bridge opposite the one con- 

 taining self-induction is shunted by a condenser of capacity K. 

 The bridge is balanced for steady currents, and the deflection, 6 lt 

 of the galvanometer observed on breaking the battery circuit. 

 1 is : : L 2 - Kps, where p and s are the resistances of the two 

 remaining arms of the bridge. The condenser is then disconnected, 

 and another swing, 6. 2 , obtained, on again breaking the battery 

 circuit. 2 is : : L«* 



1 L 2 - Kps ' 



or L = 



Kps. 



Further experiments were made on the electro-magnet when its 

 poles were joined by a piece of soft iron, the currents being 

 reversed. The resulting values of L 2 , 23, Jt), and p are given in 

 absolute measure, and from them the author deduces — 



L 2 = "05 + 3-9 A, jb= 210 + 720 % 



28 — 210 5ty + 720 |§ 2 , for values of A between # o6 and "9. 



The difficulties experienced in determining the induction co- 

 efficients for strong magnetizing forces produced by the testing 



current are de-cribed. They arise chiefly from the fact that in 

 order to obtain strong currents, the resistances must be small. 

 This makes the " time constant" large, and in order to obtain 

 the values of L in absolute measure, a ballistic galvanometer o( 

 very long period would be required. A method of calibrating a 

 galvanometer of comparatively short period to give approximate 

 results is described. Where the magnetizing force is produced 

 by an independent coil, no such difficulties present themselves. 

 Results obtained for the coefficients of self-induction of a 

 gramme armature (A type) for different currents round the field 

 magnets vary from T>2i8 for current .0 to '0117 for a current of 

 29 amperes. The value of L for a given point on the curve of 

 magnetization is not a definite quantity, but has always two or 

 more distinct values, depending on whether the magnetization is 

 increased or decreased by the test currents, and on the previous 

 history of the iron. That this must be the case is easily seen 

 from the curves obtained by Prof. Ewing in his "Experimental 

 Researches on Magnetism." The values of L corresponding to 

 the three sides of a small Ewing's cycle are denoted by 

 L/ (progressive coefficient), L r (return coefficient) and L<r (cyclic 

 coefficient). ~Lp is always the largest, whether the magnet- 

 ization be increased or decreased by the testing current. 

 Numerical values of L/> and L, c obtained from a Kapp 

 and Snell transformer are given. ~L C can be very accurately deter- 

 mined by Profs. Ayrton and Perry's secohmmeter, and some of 

 the results given in the paper were thus obtained. Having 

 given the curve of magnetization and that connecting impressed 

 E.M.F. and time, a simple graphical method is described for 

 drawing the current curve. Applying this to an alternating current 

 where the E. M. F. is a pure sine function of the time, it is shown 

 that the resulting current curve differs considerably from a nine 

 curve. The case of the rise of current in the magnet coils of a 

 dynamo excited by accumulators is also discussed, the derived 

 curves being in accordance with observation. In conclusion the 

 author pointed out that the time taken to discharge a condenser 

 through a given resistance may be decreased by adding self- 

 induction to the circuit, provided L is less than £KR-. When 

 L = iKR 2 , the discharge is completed in one-half the time 

 required when L = o. This may account for the remarkable 

 results observed by Dr. Lodge in his experiments on iron and 

 copper as lightning-conductors. — Mr. C. V. Boys described and 

 performed some experiments on soap-bubbles, and by their aid 

 demonstrated in a remarkable manner the phenomena of surface 

 tension, diffusion, and the magnetic properties of gases. By 

 blowing one bubble inside another, he showed that there is no 

 electrical force inside a closed conductor. A peculiar property 

 of soap-bubbles is their refusal to come into contact when 

 knocked against each other; they may receive violent shocks 

 and still remain separate. If, however, an electrified body be 

 brought in the vicinity, they immediately coalesce. So sensitive 

 are they to electrical attraction that a potential difference due 

 to one Leclanche cell between the two bubbles causes them t i 

 unite. They may thus serve as very delicate electroscopes. 

 Many other beautiful and extremely interesting experiments on 

 liquid films of different shapes were performed in a masterly 

 manner. 



Geological Society, April 11. — W. T. Blanford, F.R.S., 

 President, in the chair. — The following communications were 

 read : — On the lower beds of the Upper Cretaceous series in 

 Lincolnshire and Yorkshire, by W. Hill. — On the Cae Gwyn 

 Cave, North Wales, by Dr. Henry Hicks, F. R. S. ; with an ap- 

 pendix by C. E. De Ranee. The author gave an account of the 

 exploration of the cavern during the latter part of 1885, and during 

 1886-87. He considered that the results obtained during that 

 time proved conclusively that there was no foundation for the views 

 of those who contended that the drift which covered over the 

 entrance and extended into the cavern was remanie, but they 

 proved that the deposits which lay over the bone-earth were in 

 situ, and were identical with the normal glacial deposits of the 

 area. These deposits had once extended continuously across the 

 valley, and the cavern (400 feet above Ordnance datum) had 

 consequently been completely buried beneath them. The cave 

 must have been occupied by animals du»ing the formation of the 

 bone-earth, before any of the glacial deposits now found there 

 had accumulated, and a thick floor of stalagmite had covered this 

 "earth" before the cavern had been subjected to water-action. 

 This action had broken up the floor, and completely re-sorted the 

 materials, and added sandy and gravelly material to the deposits ; 

 this sand and gravel had been examined by Prof. Boyd Dawkins, 

 who found that it agreed in every particular with the glacial sand 



