June 4, 1874] 



NATURE 



97 



stance, there was on Dec. 18 a marked increase of resistance 

 ■when the magnet was first put on ; but on tlie afternoon of that 

 day the experiments were repeated, and there was no apparent in- 

 crease of resistance in this first effect. Next, with regard to the 

 average effect ; on Dec. 16, 17. and 18, this average effect of mag- 

 netism was a decrease of resistance. 



4. The experiments were resumed on Jan. 7, the arrangement 

 having remained untouched during the holidays. From this 

 date until Jan. 10 inclusive, the key was taken out before begin- 

 ning experiments in the morning; there A\'as no peculiar^/.?/ 

 effect ; while, on the other hand, an average effect denoting a de- 

 crease of resistance came out very prominently. On Jan. 12 

 and 13 the key was only taken out before magnetising, and on 

 these occasions the first effect denoting increased resistance was 

 sufficiently m.irked. 



Our method of procedure was varied in the above manner up 

 to Jan 27 ; and it was invariably found that whenever the key 

 was taken out before commencing experiments there was no 

 first effect ; but when it was kept in until before magnetising, 

 this first effect was sufficiently marked. These experiments con- 

 cur in proving that i\\tfust effect has some reference to the pre- 

 vious treatment of the wire, but they do not prove that it is at 

 the same time connected with the putting on of the m.ignetism. 

 To determine this point we made a set of experiments on Jan. 

 22, 26, and 27. When the current had become constant the 

 key was taken out, but the magnetism was not put on ; and on 

 these occasions there .vas no first effect of the current upon itself 

 in the direction of increased resistance, but rather in the oppo- 

 site direction. It thus appears that \X\t first effect which increases 

 the resistance has not only reference to the previous treatment of 

 the wire, but depends also en the magnetism being put on. 



This result is confirmed by experiments made previous to Dec. 

 12, in which the key was not taken out at all. For instance, we 

 have on Dec. 9 — ■ 



First off. On : First effect. Second off. 



O +54 -1-45 



We have hitherto only spoken"of the first effect obtained after 

 Jan. 7, we now come to the average effect. From [an. 7 to Jan. 

 27 inclusive, the magnetism was always put on in the same direc- 

 tion, and the a:vrage effect invariably denoted a decrease of 

 resistance when the magnetism was on. 



5. On Jan. 2S the magnetism was reversed ; the effect during 

 this day was very irregular. On Jan. 29, 30, 31, Feb. 2, the 

 key was left in until before magnetisation. The first effect was 

 now extremely large, but it was suspected that during these ex- 

 perim.ents the contact of the key was not very good. 



On Jan. 29 the average effect denoted a decrease of resistance, 

 but on Jan. 30, 31, Feb. 2, 4, 6, the average effect denoted an 

 increase of resistance. 



6. From Feb. 6 until Feb. 11 the wires were left broken ; on 

 Feb. 1 1 there was a very slight first effect in the direction of in- 

 creased resistance, and a slight average tffect in the direction of 

 decreased resistance. On Feb. 12 a mercury interrupter was 

 used instead of a metal key, both the wires being broken by it, 

 and its use was continued until Feb. 18. The interrupter was 

 left in over night, and the current was only broken before mag- 

 netisation, but no first effect was observed. 



From Feb. 19 to Feb. 26 ore wire only was broken by the 

 fluid interruptor, nevertheless there was no first effect. 



On Feb. 12, when the fluid interruptor was first employed, 

 there was a very small averai;e effect in the direction of increased 

 resistance ; but in all the experiments afterwards this average 

 f^ff/ was in the direction of decreased resistance. The magne- 

 tism had been in one direction from Jan. 28, but during the 

 experiment of Feb. 25 it was reversed and retained in this con- 

 dition through the experiment of ¥eh. 26 without appearing to 

 affect the results. 



7. From these experiments we may perhaps conclude as fol- 

 lows : — 



In the first place there is a first effect in the direction of in- 

 creased resistance which appears to have reference to three 

 tilings, namely, the previous state of the wire, the solidity of the 

 circuit, and its magnetisation. 



In the stceiid flace we have an average effect, of which the 

 normal state appears to denote a decreased resistance while 

 the magnetism is on, without reference to the direction of the 

 magnetism. 



In the lliirii place, when in a solid circuit the direction of the 

 magnetism has been recently changed, there appears to be a 

 temporary reversal of the average effect, which appears at first 



as an increase of resistance. Besides the evidence heiein de- 

 tailed, we have o'her evidence in favour of the third conclusion ; 

 for in some preliminary experiments, in which we frequently 

 reversed the poles, we found an increase of resistance when the 

 magnetism was on. 



We are led to conclude, from other experiments besides these, 

 that the effect of the magnetism is not merely confined to the 

 part of the copper wire wound round the pules, but is propa- 

 gated all along the wire. On Dec. 2, for instance, the current 

 was passed through the wire, the galvanometer being joined as 

 a secondary circuit. The main current was therefore measured. 



The deflections were as follows : — 



297 



297 



off 



300 



off 

 on 



off 



This shows an average strengthening of the current equal to 

 about 1-200 part of the whole. Were this strengthening due 

 merely to the change of resistance of that part of the wire wound 

 round the poles, the effect as measured by the much more deli- 

 cate arrangement of Wheatstone's bridge would be much larger 

 than was actually observed. 



9. Allusion was made in Article 7 to some preliminary experi- 

 ments in which increased resistance was observed when the 

 magnetism was put on alternately in different directions. Simi- 

 lar experiments were made, giving the same result with a piece 

 of coke and graphite which were between the poles of the 

 magnet. 



10. We have also some evidence that a copper wire, one end 

 of which is wound round the pole of the magnet, changes its 

 position in the electromotive series. Two copper wires were 

 dipped into dilute nitric acid and connected with the galvano- 

 meter. A weak current passed through the galvanometer owing 

 to a slight difference in the copper wires, one of which was also 

 connected with the copper wire wound round the magnet. 

 When the magnet was on, the current as a rule changed in in- 

 tensity; but the effect was small, and the difficulty of having 

 two copper wires which, when joined together and dipped into 

 nitric acid, give a current sufficiently weak and constant, pre- 

 vented us from getting any decided results. 



1 1. In conclusion we have to state that we regard these results 

 which we have ventured to bring before the Royal Society as 

 preliminary, the correctness of which will, we trust, be con- 

 firmed by the further experiments which it is our intention to 

 make. 



Mathematical Society, Thursday, May 14. — Dr. Hirst, 

 president, in the chair. — The president having vacated the chair 

 gave an account of his paper On the correlation of two planes. 

 "A correlation is said to be established between two planes, 

 when their points and right lines are so associated that to each 

 point in one of the planes, and to each line passing through that 

 point, respectively correspond, in the other plane, cite line and 

 one point in that line." It was first shown that eight conditions 

 are necessary and sufficient for the establishment of a correlation 

 between two planes : and in the next place it was shown that the 

 problem of determining a correlation between two planes which 

 shall satisfy any eight given conditions is susceptible in general 

 of a finite number of solutions. Systems of correlation were then 

 considered : as also the origin and nature of exceptional correla- 

 tions. Relations were next established I^etween the charac- 

 teristics and singularities of any system of correlations. An 

 enumeration and classification of the fundamental systems 

 of correlations were then made and illustrated by reference 

 to a table in which the systems were arranged in mx groups. 

 Dr. Hirst also touched upon the number and nature of exceptional 

 coiTelations in the fundamental systems. A talile was exhibited 

 showing the number of correlations satisfying eight elementary con- 

 ditions. If a points in one plane have given polais in the other ; /3 

 right lines in the first plane have given poles in the second ; 7 points 

 and S lines in each plane have given conjugates in the other plane, 

 then (k;S-. 5) is termed the signature of the system of correlations 

 satisfying the above conditions. We see that the systems of 

 correlations corresponding to the signatures (0^76) and (j8a75)are 

 identical. The following two theorems are generalisations of the 

 results arrived at : — (I.) In a .system of correlations (0)870), the 

 curve of the class [a;8(7+i)5] which reprcf';i t,^ eilhfr ol two 

 conjugate points ./j, ./;, breaks up into the uther, together with 

 a point on each of the singular lines associated with ti.ose which 

 pass through the foi mer. The multiplicity of ^^ on the representa- 



