since there is a preponderance of land in the northern hemisphere, and the currents are always towards the positions of greatest atom-density, that they will flow out of the northern parts and, after circulating, enter into the southern parts. This is uniformly taken to be the direction of the earth's currents in my hydrodynamical theory of magnetism. Accordingly the positions of greatest efflux and influx, although they cannot be far distant from the earth's poles, will be partly dependent on the distribution of land and water. It is thus consistent with the theory to find that in the northern hemisphere there are two positions of maximum intensity-one, which at present appears to be the principal one, in a high latitude of the North-American continent, and the other a little north of the Asiatic continent. There is not the same geographical reason for two positions of maximum influx in the southern hemisphere; and, in fact, observation has hitherto only determined that, if there be two, they cannot be far apart. Hence the theory at once accounts for the circumstance that, of all positions on the earth's surface, the magnetic intensity is greatest in the neighbourhood of the south pole. For the total influx is necessarily equal to the total efflux; and consequently the influx is intensified in that quarter, either because there is but one position of maximum intensity, or, if there be two, because they are near each other. The foregoing comparisons of the theory with facts of observation are confirmatory of the view taken of the nature and source of terrestrial magnetism. It will be seen that this theory attributes the generation of terrestrial magnetic streams altogether to impulses given to the æther by the earth's atoms in motion, and that it would be much corroborated by any independent evidence of the actuality of this action between atoms and the æther. Now it happens that such evidence is obtainable by reference to the explanation of certain phenomena of aberration, which I have given in the Number of the Philosophical Magazine for April 1872, inasmuch as that explanation depends on an impulsive atomic action of the very same kind as that which has been under consideration, as will appear from the following argument. The aberration of light is simply due to the circumstance that whereas the pointing of a telescope, as instrumentally determined, is in the direction of the straight line joining the optical centre of the object-glass, or object-mirror, and a certain fixed point in the field of view, the actual course of a ray from the first point to the other deviates from that line by reason of the earth's movement in the interval occupied by the passage of the ray. The deviation is in the direction towards which the earth is moving; and its angular amount is measured by the ratio of the earth's velocity, resolved perpendicularly to the line of pointing, to the velocity of light. Now the communication above cited contains an account of experiments made with telescopes the tubes of which were partly filled with a transparent fluid, the object of this arrangement being to ascertain what effect would thereby be produced on the amount of aberration. I confess that I fully expected, on account of the longer time occupied by the passage of the light between the two points owing to the retardation caused by the fluid column, that the amount of aberration would by this means be increased. But two independent sets of experiments, one by M. Hoek with the telescope pointed to a terrestrial object, and the other by the Astronomer Royal with the telescope directed to y Draconis, have proved conclusively that the passage of the light through the fluid column does not sensibly alter the amount of aberration. By parity of reasoning the aberration is unaffected by transmission of the rays through the lenses of the telescope. At the end of the aforesaid communication I have endeavoured to account for these facts theoretically, but not quite successfully. The following amended explanation may, I think, be considered to be satisfactory. The rate of propagation of any disturbance of the æther being supposed to be a in free æther, that within a medium whose re a fractive index is μ is Hence the mean retardation of the rate of propagation by the reaction of the atoms is a ( (1–2), which, μ if a2 represent the elasticity of the æther, may be supposed to be due to a retarding force represented by ao(1 − 1)*. Conceive the propagation to take place along the line of pointing of a telescope in the tube of which there is a fluid column of refractive index μ, and let the telescope be carried by the earth's motion with a velocity the projection of which transverse to the line of pointing is V. Hence the æther will be continually impelled by the atoms of the fluid in the transverse direction proportionally to that resolved part of the earth's velocity. Like impulses will be produced by the part resolved along the line of pointing; but as these, as far as regards aberration, would only give rise to small quantities of the second order, they may be left out of account. It has been already argued above that the disturbance of the æther produced by the motion of translation of the earth is steady motion of such kind that it is always quam proxime the same at the same position relative to the earth's centre. Hence the disturbance is propagated in space at the rate of the earth's motion; and any mutual action between the æther and the atoms is propagated at the same rate. Consequently the rate of propagation resolved transversely to the line of pointing is the velocity V. Now since, as we have seen, when the independent rate of propagation is a, the mutual action between the æther and the 2 atoms of the fluid column is represented by ao(1-1), it fol 2 lows, analogously, that when the independent rate of propagation is V, the mutual action between the æther and the atoms of the same fluid is V2 (1. This amount of apparent elasticity corresponds to a rate of propagation equal to V (1 − 1) μ in the transverse direction. Combining this with the rate of propaga tion a μ in the line of pointing, the result is an aberration from that line the angular measure of which is the ratio of V (1 − 1) a V to or (-1). By comparing the direction of the earth's μ' a motion with the direction of the propagation of light towards the earth, it will be seen that this aberration is from the quarter towards which the earth is moving, the ray being, as it were, dragged towards that quarter while it traverses the part of its course from the optical centre of the telescope to the field of view, which lies within the fluid column. Relatively, therefore, to the usual mode of estimating aberration, this amount is negative. V The instrumental aberration, as is known, is, apart from the effect of the passage of the light through any medium in the telescope-tube. For a medium of refractive index μ this ratio Τμ is altered to on account of the rate of propagation in the a medium being to that in vacuum in the ratio of 1 to μ. As the sign of this aberration is positive, the total aberration is Τμ a V a V (μ-1), or which is independent of μ. Since the same reasoning applies to any portion of a given medium, and therefore to the whole of each medium, it follows, conformably with experience, that the amount of aberration is unaffected by the transmission of the light through any number of transparent media contained within the telescope-tube. I cannot forbear remarking in conclusion, since the same mutual action between the atoms of a substance and the æther has u = been adduced to explain two such different phenomena as the amount of aberration under the circumstances above detailed, and the existence of terrestrial magnetic currents, that I am justified in regarding this coincidence as corroborative of the truth of both explanations. Cambridge, November 17, 1873. IV. On Wheatstone's Bridge. By R. S. BROUGH, Assistant IN Na paper by Mr. Heaviside, published in the Philosophical Magazine of February 1873, "On the best Arrangement of Wheatstone's Bridge for measuring a given resistance," two equations are given (the author's Nos. 1 and 2) to express generally the strength of the current flowing through the galvanometer before balance is established. These equations are incorrect, and they should respectively stand as follows:- (ad-bc)E (a+c)(b+d)e+(a+b+c+d)ef+(a+b) (c+d)f+cd(a+b)+ab(c+ d) } {a+b+c+d From the latter equation the best resistance for the galvanometer near balance can be at once deduced; for near balance {4664 may be neglected against the re a+b+c+d mainder of the denominator of the right-hand member of the equation, and then we have for a maximum of u√e: Obviously the question of the best resistance of the galvanometer is only independent of the resistance of the battery (so long at least as this is a quantity of relatively finite magnitude) when balance is nearly established, and is not so generally (i. e. away from balance as well as at balance) as Mr. Heaviside's equations would imply. It is to be observed, however, that to proceed directly to find the resistance of the galvanometer which makes its magnetic effect a maximum at balance (when no current passes through * Communicated by the Author. the galvanometer) is a merely mathematical problem destitute of physical meaning. Clearly the proper procedure is first to prove that there exists a general maximum when balance is not established, dependent on the resistances of the four branches and on the resistance of the battery, and then to find to what condition this converges as we approach balance and becomes equal when we reach balance. From the second of the above equations we find that the general maximum is given by E= (a+b) (c+d) + (ad-bc)2 a+b+c+d (a+b+c+d) { (a+c) (b+d)+(a+b+c+d)f}' which, as balance is approached, rapidly converges towards the condition This is the general useful solution, since it is only near balance that it is of practical importance that the condition of maximum sensibility should be fulfilled; and we notice that it is independent of the battery resistance. The resistance of the battery has been supposed to be of finite magnitude compared with the other resistances in the bridge. If, however, the resistance of the battery be indefinitely large compared with the sum of the four resistances in the bridge, then the condition holds universally, i. e. is independent of whether balance is nearly established or not. (Such a case could, of course, only occur in the physical laboratory.) Again, if the battery resistance be indefinitely small compared with the sum of the four resistances in the bridge (as in measuring the "insulation" of a well-insulated telegraph-wire), we see that the condition is universally true, i. e. is independent of whether balance is nearly established or not. Of course when balance is nearly established the two conditions become identical. Bridges for testing telegraph-lines are almost invariably wrongly arranged. It can be proved that when the galvano * See Clerk Maxwell's Electricity and Magnetism,' Art. 348. |