STRENGTH OF GLOBES AND CYLINDERS; BY S. MARSDEN.

47

EXPERIMENTS TO DETERMINE THE COMPARATIVE STRENGTH OF GLOBES AND CYLINDERS OF THE SAME DIAMETER AND THICKNESS OF SIDES (WITH SPECIMENS OF EACH). By SAMUEL MARSDEN, of St. Louis, Mo.

[ABSTRACT.]

FOR the above purpose, I had patterns and core boxes made suitable for moulding globes and cylinders four inches internal diameter and inch thickness of sides. The cylinders were made with globular ends, eleven inches in total length. For the purpose of enabling the moulder to place the core as near the centre of the mould as possible, short pipes were cast to opposite ends of both cylinders and globes, their centres coinciding with the axis of the cylinders and poles of the globes. Through these pipes the cores were extracted; afterwards a pipe belonging to each was filled with solder, and to the pipe, on the opposite end, a small piece of gas pipe was attached with a plumber joint so as to form a connection with an hydraulic testing machine. From the same pots of melted lead there were cast four cylinders and four globes, and a number of specimens in the centre, 1 inch at each end and 3 inches long, for the purpose of ascertaining the tensile strength of the metal of which the globes and cylinders were composed. Finally four of these pieces were reduced with a file to × inch in the middle. The upper ends were secured to a trestle the lower to a scale and weighted until torn asunder, breaking with 303 lbs., after being subject to that weight less than one minute each, showing a remarkable uniformity of strength in the lead.

The strength of a cylinder being as its diameter and tensile strength of its sides. Let t represent the tensile strength of 1 inch long on one side, t 2 will represent the tensile strength of 1 inch long on each opposite side of the diameter, D the diameter in inches, P the bursting pressure. t2

D

=

1214

For a general formula we have P. Substituting their values, in the present case we have by experiment 303 lbs. the tensile strength of inch long. Hence= lbs. P 303 lbs. as the theoretic bursting pressure of our cylinders, and twice this amount for the bursting pressure of our globes. Ex

D

4

perimentally we find them to burst with the amounts tabulated

In only one instance out of eight, do we find the actual strength to coincide nearly with the theoretical. The discrepancies are due to imperfections in the manufacture of the globes and cylinders. The patterns and core boxes appear to have been as near perfection as can be desired. The placing of the core in the centre of the mould and retaining it there while the metal is run is almost impossible. In view of the above facts it is folly to assume that a given globe or cylinder will stand practically the amount of pressure indicated by theory even if the material from which they are made be of a uniform tensile strength.

HISTORIC NOTES ON COSMIC PHYSIOLOGY.

of Montreal.

[ABSTRACT.]

By T. STERRY HUNT,

THE author began by insisting that general physiology, as the philosophy of material nature, is co-extensive with general physiography, in which sense it was employed by the best writers up to the first years of this century. In the abridgments of the Philosophical Transactions of the Royal Society up to 1700 and 1720,

the chief division is into Mathematical and Physiological subjects, the latter including the phenomena of the three kingdoms of nature. There is a physiology not only of animals and plants, but of the inorganic world, and from terrestrial physiology we rise to a conception of the physiology of the Cosmos or material universe, a subject which from the earliest times has attracted the attention of philosophers. One of the most evident of the problems thus presented is that of interstellar space and its relations to our earth and its gaseous envelope. After noticing the views of the ancient Greeks, the author referred to the discovery by Alhazen of the refraction of light, from the phenomena of which the Arab philosopher attempted to fix the limit of the terrestrial atmosphere. He then noticed the similar attempts of later observers, and adverted to the well-known hypothesis of Wollaston, who endeavored to assign thereto an absolute limit on grounds which are inadmissible. He adverted to various views as to the so-called ether of space, which Newton thought must include exhalations from celestial bodies, and noticed the hypothesis of Grove, that the mediam for the transmission of radiant energy through space is but a more attenuated form of the matter which constitutes the gaseous envelopes of the earth and other celestial bodies, between which, through this medium, Grove, like Newton, supposed material interchanges to take place. The suggestion of Arago as to the possibility of determining the density of the rare matter of interstellar space was noticed, as well as that of Sir William Thomson, who has even attempted to fix the minimum density of the luminiferous medium, which he, like Grove, conceives may be a rarified extension of the terrestrial atmosphere. W. Mattieu Williams, adopting the hypothesis of the atmospheric nature of the interstellary matter, has attempted to show how the sun in its course through space may condense this matter with the evolution of heat, and thus replenish the solar fires. From this ether also, by a stoichiogenic process, the various chemical species are perhaps generated.

The author has endeavored to approach the study of interstellary matter from a wholly different side. From a consideration of the chemical and geological changes of which we have evidence in the earth's crust since the beginning of life on the planet, it is clear that great quantities of carbonic dioxide have become fixed, partly in the form of carbon, with evolution of oxygen, and partly

as carbonates-equal in the aggregate to 200 atmospheres or more. This enormous volume, it is held, must have come from outer space to supply the gradual absorption of the gas from the atmosphere; while by a reverse process of diffusion, the great amount of liberated oxygen may have been got rid of, and the equilibrium of the atmosphere in this way maintained. The consequences, both meteorological and geological, of this process, were discussed by the author in 1878, and more fully in 1880, in an essay on "The Chemical and Geological Relations of the Atmosphere," in the American Journal of Science. As a further contribution to these views, the author proceeded to show that Sir Isaac Newton not only held to the presence in interstellar space of exhalations from the sun, the earth, the fixed stars and the tails of comets, which he supposed to become diffused and to form part of the ether, but even suggested that this ethereal matter is the solar fuel, and essential to planetary life. From a consideration of the processes of vegetable growth and decay Newton arrived at the conclusion that elements from interstellar space, brought by gravity within the terrestrial atmosphere, serve to nourish vegetation, and by its decay are converted into solid substances. In this way are, according to him, generated not only combustible (sulphureous) bodies, but calcareous and other stones, whereby the mass of the planet is augmented. These views, put forward in Newton's "Hypothesis Concerning Light and Color," in 1675, and in the Queries to the Optics, are more definitely enunciated in Propositions 41 and 42 of Book III of the Principia.

SYMMETRICAL METHOD OF ELIMINATION IN SIMPLE EQUATIONS, BY THE USE OF SOME OF THE PRINCIPLES OF DETERMINANTS. By JAMES D. WARNER, of Brooklyn, N. Y.

[ABSTRACT.]

THE general principle of forming a determinant from the coefficients, and another by substitution of the independent terms. for the coefficients of any one of the unknown quantities, for finding the value of the unknown by dividing the value of the latter determinant by the value of the first, will not be exempli

fied, being in all books on determinants, and having been given already by some authors of algebra. It is thought that a long explanation of the method of multiplication might be omitted, if a rule specifying direction were given. The following is suggested, viz. :-after placing the known quantities in rows as directed, i. e., forming the determinant, multiply each term of a row or column by all the other terms, so that if a line were drawn through the factors it would always be in a diagonal direction. The sign is to be changed for each change in direction from the positive. It is immaterial which direction is assumed for the positive direction; but the direction downward and to the right is generally taken for the positive direction.

There is a principle of determinants by which the same value is obtained, if we take the sum of the two determinants obtained by dividing into parts the terms of a row or column. By this principle we may resolve a row or column of either determinant into two parts, by taking one term from each of the others in a column or row, and then obtain the value by taking the sum of the prod ucts of each of the remainders, taken as a first minor, into its reciprocal, and the common part into the sum of these reciprocals. In practice, it is best to place that column first which contains the unknown which is to be first obtained.

Take the sum of the two products obtained by multiplying the difference of terms of each column into that term of the other column which is in the same row as the subtrahend. The subtraction in each example must always be in the same direction, and