IV. Investigation of the possible Errors. Since is always small and can be determined very accurately, and the last factor does not differ greatly from unity, if we bear in mind moreover that λ2 is always small in comparison with 72, in investigating the possible errors we may take the approximate expression w= 32 ST2 to K AB 1. The principal share of the uncertainty must be ascribed to the horizontal component of the earth's magnetic force T, the percentage error of which affects the resistance in a twofold degree. The difficulty of accurately determining this element (a difficulty which is no doubt in general underrated) makes it essential that the observations should be carried out in a very completely equipped magnetic observatory. It is evident also that the variations of the earth's magnetism must be taken into account; for the horizontal intensity varies with us to the extent of about per cent.; so that, without observing the variation-apparatus, an error of 1 per cent. might arise in the calculation of the resistance. The observatory of Göttingen without doubt answers to the requirements of the case more completely than any other place, inasmuch as the arrangements that have been carried out there by Weber for determining the horizontal intensity far surpass, in delicacy and convenience, those in use elsewhere. The greatest sources of error in the absolute measurement unquestionably lie in the determination of the moment of inertia and the measurement of distances; in long series of observations of variations the change in the magnetism of the bifilar needle also introduces difficulties that are not inconsiderable. Essential improvements have been effected affecting precisely these points. The distances to be measured are solely those between the suspending fibres of magnets, and therefore can be determined with the utmost accuracy. The weights for determining the moment of inertia are more firmly connected with the magnetometer; they * In practice, √2+λ2 can always be taken as =; and so long as A is not great, we have as a close approximation (in the present case, for instance, within 0.05 per cent.) (A2+B')2 ( 1+2 2'). 2 Phil. Mag. S. 4. Vol. 47. No. 312. April 1874. X cause the same strain on the suspending-thread in all the observations, and likewise admit of very accurate measurement of the distance between them. Finally, the bifilar magnetometer is supplied with a Weber's auxiliary needle*. I had myself the gratification of using these arrangements for the first time in their entirety, while determining the terrestrialmagnetic elements at Göttingen in 1867, and of convincing myself of their excellence. During these determinations, and in a subsequent series, I acquired an accurate knowledge of the constants of the instruments and sufficient practice in their use. While referring to the next section for the observations themselves, I will adduce here two pairs of determinations of intensity, from each of which variations in the terrestrial magnetism are eliminated, and which can therefore be directly compared. The following are these values:— 1867, with an interval of sixteen days, 1·83960 and 1·83849; difference 0.00011. 1869, with an interval of three days, 1.83860 and 183832; difference 0.00028. = = Expressed in terms of the whole, these differences amount to 0.00006 and 0.00015. But the error arising from the moment of inertia and the measurements of distance is not included in these differences; hence for the possible error AT of the horizontal intensity we may take about ten times the above amount -that is AT = ± 1 1000 2. The moment of inertia K of the astatic pair of needles was determined by two different methods. One of them gave K=1,135,700,000; and the other, which was not quite free from objection, 1,132,800,000. We will assign to the former determination the weight two, and assume as the error AK the deviation of the two determinations from the mean—that is, 3. The inductor-surface S is the only magnitude which I have not measured myself. It was determined by Weber when he constructed the inductor; he measured the length of the wire by coiling it upon a large wheel about 3 metres in diametert. It was moreover controlled by measuring the individual windings. I put the possible error 4. The time of vibration to amounted to about 34.4 seconds. * Abhandl. d. Götting. Gesellsch. d. Wissensch. vol. vi. (1855). ↑ Abh. der Gött. Ges. 1853, page 53 of the separate impression. The greatest difference which occurred between values which ought to agree with each other amounted to 0.018 second. Hence the error assumed is 5. Lastly, the arcs of vibration A and B may each include an error in reading of ±0.2 millim., which observations, to be afterwards communicated, will probably show to be too high. Now, measured in divisions of the scale, A=370 millims., B=225 millims. ; and therefore =0.50. A B =1.64, λ= log nat 1.64 If we express the errors produced in w by the separate errors AT, AS,... by Awr, Aws,..., we have It will be observed that the ratio of A to B is just of such a kind that a small error in A has no influence. If we were to add together the whole of the errors in the most Δω unfavourable sense, the total error would be =±0.0067, or พ per cent. The mean error to be feared in the case of a single determination, or the root of the sum of the squares, amounts to ±0.0033, or about per cent. The error of observation in the comparison with Siemens's standard need not be considered; for it does not exceed 0.0001. In order to eliminate the alteration due to change of temperature, the influence of which cannot be directly determined in large masses of wire, one comparison was made at the beginning of each set of observations, and another at the end. As the temperature of the air changed but little during the time of observation, this method is in any case adequate. The question arises whether the supposition made in the differential equation (page 302) is correct, namely that the coefficient of sensitiveness q of the galvanometer is constant, or, in other words, that the damping-ratio is independent of the amplitude of the swing. In reference to the instruments the question may be thus stated:-Is the multiplier so broad that a lateral displacement of the needles such as occurs in the vibrations does not alter the moment of rotation which a current in the multiplier exerts upon the needles? The question could be easily decided. The horizontal component of the terrestrial magnetism made the largest are equal to about 3°; if the damping in these vibrations were already less than in very small ones, its amount must considerably decrease if recoil-observations were made with the vertical component as the inducing force, in which case the are of vibration amounts to 7°. Observation gave :— Large arc =3°, ratio of damping =1·74430 Hence if the induction were executed with the vertical component, a correction would be necessary in our galvanometer which would amount to a quarter of a division in the smaller arc. As the correction must be proportional to the square of the amplitude, it can from this be calculated that for the horizontal component it must amount to about 4000, a magnitude so small that it is not worth while to determine it accurately. In the sequel no regard is paid to it. As regards the induction on each other of the short currents arising and ceasing in the terrestrial inductor, brief consideration will show that it can exert no appreciable influence on the deflections; for the extra current which accompanies the principal current causes no change in the velocity imparted, but exhibits its influence solely in a sudden displacement of the needle, as I have shown elsewhere*. From the observations there given we cannot estimate the extra current at more than 1.5 division; and that produces an error of at most 0·01 division in our larger arc A, which may well be neglected. The actual agreement of the three measurements given below quite satisfies expectation. It will be found that they differ respectively from the mean values by 0·14, 004, and 0.11 per cent., which would correspond to a "probable error" in the result of 0.05 per cent. In this indeed are not contained the • Pogg. Ann. vol. cxlii. p. 422. errors of the moment of inertia and of the inductor surface-nor those of the intensity of the earth's magnetism, except so far as concerns variations in this magnitude. On the other hand, I have assumed sixfold the above amount as the error. I by no means maintain that with such a limit of error all that is desirable is accomplished; but without constructing entirely new instruments, and without erecting special buildings, it would be for the present difficult to exceed this limit. It must moreover be considered that an alteration of per cent. in the conductivity of the ordinary metals is produced by an alteration of 1° in temperature. [To be continued.] XXXVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 229.] June 19, 1873.-William Spottiswoode, M.A., Treasurer and VicePresident, in the Chair. HE following communication was read :— THE "On the Action of Electricity on Gases.-No. II. On the Electric Decomposition of Carbonic-Acid Gas." By Sir B. C. Brodie, Bart., D.C.L., F.R.S. In my previous experiments the maximum amount of ozone obtained by the action of electricity upon pure oxygen passed through the induction-tube of W. Siemens was about 20 per cent., an amount which, under the conditions of the experiment, could not be exceeded. It occurred to me as possible to replace the 80 per cent. of oxygen unaffected by the action of the electricity by an indifferent gas, and thus to effect the complete conversion of oxygen into ozone. This idea was the starting-point of the following investigation. When pure and dry carbonic-acid gas is subjected in the induction-tube to the electric action, a certain proportion of the gas is decomposed into carbonic oxide and oxygen, a portion of which appears in the form of ozone. The presence of this ozone may be detected by its odour and the characteristic oxidations produced by it. It was a point of fundamental importance to determine whether the ozone thus generated was the same in kind as that formed by the action of electricity on pure oxygen, and whether the oxidations referred to were exclusively due to it; for it was quite conceivable that under the peculiar circumstances of the experiment other substances capable of producing similar oxidizing effects might be formed. Now, in the investigation before referred to, I had discovered certain quantitative reactions of ozone by which this substance is discriminated from all other known gases, and by which its presence may be detected and its quantity estimated. The electrized carbonic-acid gas was examined by the aid of these re actions. |