§ 31. In a previous paragraph (29) the loaded dynamic frame (fig. 38) for one position of a direct-acting horizontal steam-engine has been described, and the mode of drawing that frame explained, on the assumption that the loads La, Lb, Lc, Ld, are known: it was stated that these loads had been calculated for one particular engine. The present paper gives the varying effort which this engine is capable of exerting at each part of its stroke with given pressures (both constant and varying) in the cylinder, and given constant velocities of the crank-axle. The same calculations show the efficiency of the engine at each part of the stroke, and its total efficiency under the same circumstances. This problem has, it is believed, never hitherto been solved so as to take into account all the circumstances of mass, weight, and friction.

§ 32. No pains has been taken in the choice of the particular example. The object of the paper is not so much to draw general conclusions as to all steam-engines—which, indeed, differ too much in arrangement to make this feasible—as to show how, by a method of no great complexity, full information can be obtained as to any particular engine or class of engines.

The following paper contains the results of an inquiry which has occupied me at intervals for somewhere about ten years. It was carried out in part at the expense of the British Association, and I have already reported results to that body in 1869 and 1871. But these provisional reports referred to very short ranges of temperature only, and the experiments were made with faulty thermometers, for which I had not the corrections which had been carefully determined by Welsh at Kew.

The inquiry arose from my desire to extend to other metals the very beautiful and original method which Principal Forbes devised, and which the state of his health prevented him from applying to any substance but iron. Forbes' experiments gave a result so very remarkable, and (as it seemed to me) so theoretically suggestive, that I wished to extend them to other pure metals, and also, in one or two cases at least, to alloys.

I believe that Principal Forbes had at least two reasons for undertaking his investigations:—(1.) When he commenced his inquiry, there was no really accurate or trustworthy determination of the absolute conductivity of any body whatever for heat. (2.) FORBES had himself, in 1833 and subsequent years, pointed out a very remarkable analogy between the conducting powers of metals for electricity and for heat, and had shown that these were almost precisely proportional to one another—that is to say, that the list of the average relative conductivities of different metals for electricity differed, from that of their relative conductivities with regard to heat, certainly not more than did the several electric lists furnished by different experimenters, and certainly less than the corresponding thermal lists. Hence it was natural to suppose that temperature might have a marked effect on thermal conductivity, as it was known to have such an effect on electric conductivity.

After having for many years felt with Professor Tait the want of a word “to express the Availability for work of the heat in a given magazine, a term for that possession the waste of which is called Dissipation” I now suggest the word Motivity to supply this want.

In my paper on the “Restoration of Energy from an Unequally Heated Space,” published in the Philosophical Magazine for January 1853, I gave the following expression for the amount of “mechanical energy” derivable from a body B, given with its different parts at different temperatures, by the equalisation of its temperature throughout to one common temperature T, by means of perfect thermodynamic engines,—

where t denotes the temperature of any point x, y, z of the body; c the thermal capacity of the body's substance at that point and that temperature; J, Joule's equivalent; and μ, Carnot's function of the temperature t.

The permanent record obtained with Mr T. A. Edison's phonograph has afforded a new opportunity of investigating the nature of spoken sounds, and the method which this invention placed at our disposal appears to us to possess several important advantages.

This method consists in obtaining a magnified transcript on paper of the indentations impressed by spoken vowels on the tinfoil of the phonograph, and then subjecting the periodic wave-forms thus obtained to harmonic analysis.

The curves as drawn in ink on paper represent to a large scale the surface of a longitudinal section of the tinfoil made along the centre of the furrow impressed by the pricker of the phonograph. The forms impressed on the tinfoil depend essentially on the movement which a particle of air performs when the given sound is being uttered, and the harmonic constituents of each period of the continuous wave-form indicate the relative proportions in which the prime tone and its harmonics are present in the sound.

We thus obtain what may be called a harmonic analysis of the vowel sounds.

Colours and colour sensations are much referred to still by double-star observers, who make use of a most extensive range of names, and differ widely from each other, in describing the many different tints which they claim to recognise by simple eye-observation in those interesting objects.

Material coloured shades, generally in glass, are also of daily use in both terrestrial and nautical astronomy, in decreasing or qualifying the intensity of sun's, moon's, and other rays; while special varieties of such media are still being inquired after for acting, if possible, with improvement of, rather than detriment to, the nicest definition of the optical instruments concerned.

And again coloured glasses have been latterly demanded, which should allow only the strictest mono-chromatic light to pass through them in one or another particular grade of the spectrum,—so as to allow, as one example only, the solar red-prominences to be plainly and broadly observed, without the usual spectroscopic draw-back of having to look at them through the narrowest of slits.

The object of the present paper is to show how, by graphic methods, we may find the relation between the effort exerted at one part of a machine in motion, and the resistance overcome at another part; the solution found is rigorous for all motions in one plane, and takes count of the friction, weight, and inertia of the parts. It also takes into account the stiffness of ropes or belts.

The paper shows that we may represent any machine, at any given instant, by a frame of links, the stresses in which are identical with the pressures at the joints of the machine. This self-strained frame is called the dynamic frame of the machine, and may be so drawn as to represent the machine either rigorously, taking into account friction, weight, inertia, and rigidity, or approximately, omitting some of the conditions under which the machine works.

Moreover, it is shown that for all machines (in which the motions can be represented as in one plane), the dynamic frame is of one type, either simple or compounded. The dynamic analysis of machinery into parts represented by this simple frame is believed by the author to be novel. It is consistent with the kinematic analysis of Reuleaux.

Most common oils and fats are mixtures of ethereal salts, termed glycerides or glyceric ethers, formed from glycerine and acids of the fatty, the oleic, and other allied series.

Of the methods employed for the decomposition of oils and fats, the following are the most usual:—

1. 1. Distillation of the oil or fat; those which yield volatile acids, such as the acetins, butyrins, &c., may be more or less distilled without decomposition; but those which yield fixed acids, e.g., palmitin, olein, &c., are almost wholly decomposed by a heat of 300° C., yielding acrolein, numerous hydrocarbons, &c.

2. 2. Distillation with dilute sulphuric acid, by which the volatile acids are separated from the non-volatile.

3. 3. Distillation in a current of superheated steam, when the glycerides are decomposed, the fatty acids being liberated.

4. 4. Saponification; oils and fats are decomposed by caustic alkalies into glycerine and a soap, the soap, when boiled with dilute sulphuric or hydrochloric acid, being decomposed into a sulphate or chloride of the alkali employed and the fatty acid set free.