April 6, 1883.] 



♦ KNOWLEDGE ♦ 



20; 



It is not always, however, that we wish to measure the 

 conditions of a wire of uniform structure and thickness 

 throughout. Were it so, we might in many instances 

 answer our purpose, at least approximately, by simple 

 linear measurement But let us suppose, for example, 

 that, in Fig. 2, A B is a line four miles long, of which the 

 first mile, A D, has only one-third the specific conductivity 

 of the remaining three miles of thicker wire. In other 



tarth 



Earth 



Fig. 2. 



•words, letting the resistance of A B be 30 Ohms, then the 

 lengths D E, E F, and F B each offer but 10 Ohms, and will, 

 therefore, together offer 30 Ohms. The point J) is thus in 

 the centre of the resistance — that is, there are 30 Ohms 

 resistance on each side of it. The potential at D should 

 therefore be half of what it is at A. The fall throughout 

 the wire is that illustrated by the line or lines 

 G H B. This fall from A to D is there shown to be 

 same as the fall from D to B, — a wire three times the 

 length of A D, but offering only the same amount 

 of resistance to the current, and giving the current, in 

 fact, an equal amount of work to perform in tra- 

 versing it. J K is another line of four miles, three of 

 which, J to N, ofi'er, at ID Ohms per mile, a total resist- 

 ance of 30 Ohms ; while the fourth mile, N K, being of 

 proportionately smaller wire, offers 30 Ohms. N therefore 

 is in the centre of the resistance offered by J K, and the 

 potential at N will be half that at J, as is indicated by the 

 vertical line N O being half the length of J T. NO is 

 necessarily equal to D H, and consequently a galvanometer 

 inserted between D and N is not affected. Similarly P is 

 midway between D and B ; so also is Q between N and 

 K. P R is equal to Q S ; therefore the potentials at P and 

 Q are the same, and, as a consequence, no current would 

 flow through a galvanometer connecting P Q. 



Analysing these different experiments, we conclude that 

 (granting tirst that where two points are of the same 

 potential no current will flow between them, and that if 

 there is no cun-ent there can be no effect exerted upon a 

 galvanometer placed between those points) : — 



1. Potential may be represented by longer or shorter 

 lines drawn at right angles to the wire. 



2. The fall of potential may be represented by inclined 

 lines connecting the free ends of the vertical lines above 

 referred to. 



3. In a wire of uniform quality and size, the fall is 

 uniform throughout, and may be represented by one 

 straight inclined line. 



4. In a wire of \aryLng quality or size, the fall will be 

 variable, and will vary directly as the resistance of the 

 different parts. 



5. If in two similar wires of unequal length, or in any 



two wires of unequal resistance, we connect a point a 

 certain distance (measured in Ohms) along one line, to a 

 point on the other line at the same proportionate resistance- 

 distance from its terminals, there will bo the same potential 

 at the extremities of the connecting wire, and no current 

 will flow through it 



Summing up these deductions, it will be apparent that 

 (referring to "Electrical Measurement — VIII," Fig. 2, 

 Knowledoe, No. G8) : - 



6. When we have succeeded in bringing the galvano- 

 meter permanently to rest (whether the battery circuit is 

 completed or not), we have effected a balance in which the 

 proportion A bears to the unknown resistance D is the 

 same as the proportion between B and E. We may, 

 therefore, express the proportion as a simple rule of three 

 sum : — 



B :E :: A : D or B : A :: E : D 

 To take an example, let A offer 100 Ohms, and B 10 Ohms. 

 Then, supposing we get a balance when E offers ."lOO Ohms, 

 the problem \i ill work out thus : — 



B : A :: E : D 

 that is, 10 : 100 :: 500 : 5,000 

 5,000 Ohms is, therefore, the resistance of the line or 

 coil D. 



For our readers (with three small but known resistances) 

 to apply this to the manufacture of a resistance coil, 

 ranging up to 400 Ohms (or higher, if necessary), is not 

 diaicult 



Where only a small resistance is required — such, for 

 instance, as •! of an Ohm — it is advisable to join side by 

 side a number of wires offering a higher resistance. A 

 .short length of No. 3.5 or 3G copper wire offers, say, 4 of 

 an Ohm. Two such pieces of wire coiled together will offer 

 only 2, and four pieces only "1 of an Ohm. Such an 

 arrangement will be found much more satisfactory. In 

 coils ranging up to about 10 Ohms, thin copper wire may 

 bo used. German silver wire should be resorted to for 

 coils of higher resistance, because of the high resistance of 

 that metal as compared with copper. 



We must, however, defer our observations on the com- 

 pletion of a convenient set of " Bridge " apparatus until 

 our next article. 



PERIODS OF THE AURORA. 



MR. SOPHUS TROMHOLT contributes a paper in 

 Danish to the Meteorological Society of Denmark 

 on the above subject, and M. T. Terby, of Lou vain, gives 

 an account of it in Ciel et Tern', Feb. 15, 1883, from which 

 we extract the following particulars. 



Discussing reports of auroras seen at Godthaab, in South 

 Greenland (64" 11' N. lat, 54° C long W. of Paris), Mr. 

 Tromliolt observes that they show a totally different state 

 of things from what occurs in lower Latitudes. Wolf, of 

 Zurich, says not only is there no parallelism, but, on the 

 contrary, an almost diametrical opposition between the 

 frequency of auroras and of sun-spots in the above reports. 

 Observations by Rudolph, at Jacobshavn, Greenland, show 

 that the maximum of auroras follows two years after 

 minimum of sun-spots, and that the following minimum 

 arrives almost in the same epoch as the highest point in 

 the sun-spot curve. Bloch's observations at Godthaab, 

 though too short to be conclusive, indicate that the number 

 of northern auroras reaches a high figure near the epoch of 

 minimum sun-spots, and that the number diminishes as 

 the spots increase. Observations at Iviktut, Greenland, 

 from 1875 to 1880, and at Stykkisholm, Iceland, show 



