had to this circumstance, formula (E) obtains a higher numerical value than (F). From this it follows that the vertical component of the induction-force at the astronomic pole is less than at the point for which formula (E) holds good. If in formula (C) we make 1=90+34, we obtain the sought force for a point t' situated at 56° latitude counted from d. Formula (C) is in this way transformed into the following: kM(r sin 34°+p sin 17°)p sin 51° (2+p2-2rp cos 51°)* + kM(r sin 34°-p sin 17°)p sin 51° (+p2+2rp cos 51°) (G) Formula (G) having a higher numerical value than (E), the point at which the vertical component of the induction-force will be the same as at the point t must be at a higher latitude than t'. From this it follows that the aforesaid annular zone will cut the plane in question at a point t" situated between the astronomic pole and t'. Thus the zone presenting the greatest frequency of aurora boreales must be at a higher latitude in Europe and Asia than in North America. W [To be continued.] XLIX. On the Laws of Chemical Change.-Part I. HILE studying chemistry under Prof. Mills, I was much struck by the want of knowledge concerning the laws regulating the amount of change which chemically active bodies undergo in a given time, and in what manner the rate of change is influenced by heat, electricity, &c. Many cases of change have been investigated and represented graphically; but, as far as I am aware, no theory has been given confirmed by experiment whereby, the temperature and amount of active bodies undergoing change being known, the amount of remaining energy at any time can be calculated. The nearest approach to such a theory was given by Messrs. Harcourt and Esson in the Phil. Trans.' for 1867, where they showed that for the case of hydric peroxide reacting on hydric iodide, H2O2+2 HI=2 H2O+I2, the amount of change was proportional to the amount of acting substance, considering hydric peroxide as the active body. * Communicated by the Author. A thorough investigation on this point might lead to many interesting facts in science, and a clearer insight might be gained into molecular action. For instance, by a comparison of the rates of change at different temperatures, all other conditions being the same, the necessary data could be obtained to deduce the law of temperature, and so find the point at which no action could take place; or, again, if analogous compounds, such as the sulphates, nitrates, chlorides, &c., have an accelerating or retarding effect on the change, their "equivalence" might be determined or compared-that is to say, whether K, SO4, or 174 parts by weight of potassic sulphate, can perform the same amount of work as Na, SO4, or 142 parts of sodic sulphate. The cases of chemical change selected for investigation would require to be under complete control, to allow of the determination of the amount of change up to any period of time, as it might so happen that the intervals of time between two observations would require to be equal in order to calculate the necessary constants required by theory. The methods of determining the remaining energy should be accurate and speedy. When two bodies A and B undergo change and produce a third, C, which does not take an active part in the change, it will doubtless, by its mere presence, if not removed from the sphere of action, either accelerate or more probably retard the change taking place; and if this effect be great, supposing C not capable of being removed immediately it is formed, a mathematical statement of the change would not be possible, as the influence of C could not be determined. If, however, the rate of change is so little influenced by the presence of C that it may be neglected, a theory of the action can easily be formed as a guide to the experimentalist. The experiments detailed in this paper were made merely to see how far the following theory of chemical energy is correct, neglecting all retarding or accelerating effects of the compounds produced during the action. By an inspection of the results, it will be evident that this influence cannot be very large. Suppose two bodies in solution which are capable of reacting on each other to form new inactive compounds, and the action taking place be expressed by an equation in terms of the time and the amounts of remaining active bodies at that time, on the hypothesis that the amount of change in an finitely small space of time is proportional to the product of the remaining active bodies at that time. Let A and B be inde the initial values of the bodies, a and ẞ the amounts of A and B that have already undergone change up to time t, and let Sa be the amount of A acted on in time &t; then, by the above hypothesis, Suppose, further, that the amounts of A and B are chemically equivalent (that is to say, they are just sufficient to render each other inactive), then the ratio A a 1 call this, and equation (1) becomes Sa=kv(A—a)3St. (2) Replacing A-a by y, the amount of A that remains un or, writing it in the more convenient form, b=y(a+t), (3) (4) being the equation to an equilateral hyperbola with axis t for asymptote. The influence of temperature and the non-equivalence of A and B I will consider further on, after I show how far experiment agrees with this theory. Experiments. In the first experiments made, not knowing how the rate of change was influenced by heat, I took every care to keep the temperature of the water-bath perfectly constant; but in spite of every attention, the fluctuations were about ±1° C. This, I afterwards found, could not introduce any considerable error. The flasks containing the experimental solutions were submerged in the bath, and were never removed during the experiment. The solutions were freely exposed to the air, as it was found, after repeated trials, that atmospheric oxygen had not any perceptible influence on them during the time the experiments lasted. The active bodies used were (1) a solution of ferrous sulphate containing an indefinite amount of hydric sulphate, and (2) a solution of potassic chlorate, the strengths of which were accurately known. For the determination of the iron, a dilute solution of potassic permanganate was employed, the absolute strength of which was never determined, as the experiments were wholly relative. For the experiments made to find the influence of temperature on the rate of change it was necessary to express the different solutions of permanganate in terms of one standard, this being equivalent to using the same solution for all the experiments. For measuring the solutions, 10-cubic-centim. and 50cubic-centim. burettes were employed; the errors of calibration were so small that they were in every case neglected. Experiment 1.-There were taken 100 cubic centims. ferrous sulphate solution containing 5772 gram ferrous iron with an indefinite amount of hydric sulphate, 10 cubic centims. potassic chlorate containing 2104 grm., and 200 cubic centims. water total volume 310 cubic centims. 5772 grm. iron is equivalent to 2105 grm. KClO3, by the equation KClO3+6 Fe0= KCl+3 Fe2 03. All the solutions were immersed in the water-bath until they had acquired the necessary temperature before mixing, the iron solution being first run into the water, then the potassic chlorate, and the whole well shaken. After standing in the bath five minutes, 10 cubic centims. were withdrawn as rapidly as possible, run into a small flask containing about 20 cubic centims. of water, to partially stop the action going on by the dilution, and the remaining iron determined by means of the permanganate, the whole operation occupying less than one minute. The time was always noted just when the iron solution withdrawn had run out the pipette. As an excess of permanganate had always to be added to see the tint, 02 cubic centim. was deducted from the reading of the burette for the coloration; but in many cases no such deduction was made. When the iron to be determined was small, 20 or 30 cubic centims. were withdrawn for titration. The following Table contains the results of this experiment: the numbers under " permanganate calculated" are calculated by theory from the observed times, and those under "time calculated" from the permanganate found-the permanganate found, or y, being the number of cubic centims. required for 10 cubic centims. of the experimental solution. for Taking the first two observations to calculate the constants y(a+t)=b, we get a='133-84, b=1338.4. Experiment 2.-The solutions employed were 50 cubic centims. ferrous sulphate (equal to 9847 grm. Fe), 10 cubic centims. potassic chlorate containing 3593 grm. KClO3, and 400 cubic centims. water: total volume 460 cubic centims. The following Table contains the results of this experiment. Taking the second and third observations for the constants a and b, the equation is y(222.8+1)=2512.1. Permanganate, in cubic centims. Time, in minutes. |