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(ur. t.). The ovary (ov.) is seen to lie partly beneath but mainly above the intestine; the median opening of the oviduct (ovd.) being indicated by the arrow between the third and fourth pair of legs. Attention should be called to the eversible coxal sacs (c. g.), of which there are eleven pairs situated at the base of the legs of each pair; the sac is largest and most developed in the middle of the body and is a convoluted tube which makes three turns. The silk gland (s. gl.) at the end of the body is large, its direct opening situated at the end of the cercus, while the gland itself extends as far forward as the third segment from the end of the body. The brain and nerve-cord are large and thick, much as in Pauropus. The dorsal vessel, fat body, rectal glands and the salivary glands are not represented.

There is in Scolopendrella a mixture of Diplopod and Thysanuran characters, the former the more primitive and predominating. My original idea that it is a Thysanuran is certainly a mistaken one. The Symphyla evidently forms a group by itself, and I am inclined to agree with Pocock and with Kingsley that it should for the present be associated with Pauropods and Diplopods. Yet were it not for the anterior position of the genital opening we should regard it as the representative of a group from which the insects have descended.

The Symphyla is evidently a much less primitive group than the Pauropoda and Diplopoda, as proved by the single genital opening and the Thysanuran characters it possesses. It would seem as if it had already begun to diverge from the Diplopod stem, and was becoming modified in the direction of the Thysanura.1 It is a true composite or prophetic type which has persisted from very early paleozoic times, and we may well imagine that there once existed a form intermediate between it and the Thysanura in which the genital outlet had moved back to the position it holds in Chilopods and insects. As I state in my Text-Book of Entomology, certainly Scolopendrella is the only extant Arthropod which, with the

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1 The thysanurous characters and the fact that it has but a single pair of legs to a segment (unless, as Schmidt suggests, the parapodia "represent the vestiges of a second pair of legs and correspond to the hinder pair of limbs of the primary double segment," thus indicating I would add the diplopod origin of Scolopen drella) appear to indicate that it is a form which has become considerably detached from the Diplopod stem, and has gone part way towards the incoming Thysanura. Campodea also possesses these so-called " "parapodia."

sole exception of the anteriorly situated genital opening, fulfills the conditions required of an ancestor of Thysanura, and through them of the winged insects" (p. 22). Meanwhile, until the embryology of this form is thoroughly worked out and compared with that of the Diplopods on the one hand, and Campodea, as treated by Uzel, on the other, we must be content to let the Symphyla remain provisionally associated with the Diplopoda in the phylum Meropoda.

Phylum IV. PROTRACHEATA. Class Malacopoda. The arthropodan features of Peripatus are discussed in my Text-Book of Entomology (p. 9). Its nature as the probable ancestor of the Chilopoda is, notwithstanding the immense gap between it and Chilopods and insects, such as to still compel us to suppose that it resembles the probable progenitor of the Chilopods and of the insects. It would be difficult to know what better to do with it. It certainly cannot be placed among the Annelids, or in any other Arthropodan phylum, and it is with little doubt a very ancient type which has persisted from perhaps early paleozoic times.

Phylum V. ENTOMOPTERA. Class Chilopoda and class Insecta (Hexapoda). While the Chilopoda are the nearest allies of the Insects, there is certainly a wide gap between them, and there are no structures in insects which unmistakably point to their origin from Chilopods, although Uzel in his account of the embryology of Campodea shows that in some respects it develops like Geophilus. At present, however, we are in the dark as to the origin of the thysanurous Synaptera from any form, unless we invoke a Scolopendrella-like ancestor in which the genital opening has moved back to a position homologous with that of Peripatus, Chilopods and insects.

The combination of Chilopoda and Insecta as here given is a new one,' and for the Phylum, as we limit it, a new name seems necessary. As the Chilopods are a quite subordinate group, and the great mass of the orders is composed of winged forms, I have ventured to propose the term Entomoptera to cover this great group of Arthropodous animals, reserving the name Insecta for the class which has always borne that name. Each of the phyla as here limited appears, judging from their structure and what we know of their development, to represent distinct and independent lines of development, and are submitted for consideration by zoologists. It

1 The Antennata of Lang comprises all the Myriopoda and the Insects.

may at least be claimed that the breaking up of the Arthropoda into more definite, well-circumscribed groups will lead to greater exactitude and definiteness when referring to them.

After this article was completed I discovered that A. C. Oudemans as early as 1886 thus expressed his views as to the naturalness of the Arthropoda: "It is desirable that the group of Arthropoda should be given up. The groups of Acaroidea, Arachnoidea, Crustacea, Pantopoda, Onychophora, and Insecta are independent of each other, and should, therefore, be treated separately in the manuals. The very complicated structure would then become clearer to the student. A comparison of the groups with each. can best take place afterwards and not beforehand " (7. c., p. 20). The following diagram will roughly indicate the different Phyla and the principal classes into which they are divided. It should be observed that the Annelidan ancestors of any of these five Phyla probably had few trunk-segments, being probably primitive Trochozoa with parapodia already developed.

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THE PRINCIPLE OF LEAST WORK IN MECHANICS AND ITS USE IN INVESTIGATIONS REGARDING

THE ETHER OF SPACE.

BY MANSFIELD MERRIMAN.

(Read April 2, 1903.)

The principle of least work has been extensively used in applied mechanics since 1879, when it was first formally stated and established by Castigliano. Previous to that time, various authors had discussed the principles of least action, of least constraint, and of least resistance, and had applied them in the solution of special problems. The principle of least work, however, is capable of more definite statement and demonstration than the other minimum laws, and its range of application in statical investigations on elastic structures is wide, while it has been found to be of great practical value to civil engineers.

When a structure like a bridge truss contains members sufficient to prevent distortion of its panels and no more, the stresses in these members due to given loads can be readily computed by the principles of rigid statics, the members in this case being called necessary ones. If there be superfluous members, however, rigid statics cannot determine the stresses, since the number of unknown stresses is greater than the number of statical conditions. In this case the structure is said to be statically indeterminate, and the principle of least work must be applied. This principle asserts that the stresses under consideration have such values that the potential stress energy stored in all the members of the structure shall be a minimum. If there be stresses under consideration and m statical conditions, the remaining n-m conditions are expressed by nm equations, which are deduced by equating to zero the derivatives of the expression for the total stored energy, these being the conditions that render this energy a minimum.

As a simple example the case of a rectangular table with four legs may be considered, it being required to find the stresses in these legs due to single load placed on the table in a given position. This is a statically indeterminate problem, since rigid statics furnishes but three conditions, and the solution cannot be made if the legs are rigid. The legs are, however, really elastic and each one is shortened in supporting the load, the stress in each leg multiplied by the amount of shortening being proportional to the stored

energy in it. The amount of shortening is, moreover, proportional to the stress, if the elastic limit of the material be not exceeded. Accordingly, the stress energy in the four legs due to the given load is proportional to the sum of the squares of the four stresses, and this sum is to be made a minimum. This condition, in connection with the three statical ones, enables the four stresses due to the load to be readily determined for any given position of that load, and that these stresses actually occur is easily verified by experi

ment.

A close analysis of the principle of least work as applied to any framed structure will show that its applicability and its validity depend upon the fact that the longitudinal deformation of any member is proportional to the stress upon it. This law of elasticity, commonly known as Hooke's law, is closely true for the materials used in engineering structures, provided the elastic limit be not exceeded. In all cases of the design of structures it is intended that this limit shall not be surpassed, and hence the principle of least work may be used with confidence and success in computations of stresses in statically indeterminate trusses.

It is sometimes asserted that the principle of least work is a statement of a general law of nature which is obeyed not only by materials under stress but by animate beings. While it may be true that men and animals endeavor to perform their tasks in the way most economical of effort, this analogy has no bearing upon the demonstration of the principle of least work. For this demonstration rests upon the theorem of virtual velocities, the formula for the stored stress energy being the integral of that of virtual velocities. On analyzing this proof it is seen that the integration is rendered possible by the fact that the deformation of each member is assumed to be proportional to the stress upon it. This assumption indeed is the same as that of the superposition of forces, for it supposes each stress to produce its effects independently of the existence of other stresses. The theorem of virtual velocities applies to all cases of equilibrium, but its integral form does not give the principle of least work unless Hooke's law of elasticity is fulfilled. This principle, therefore, is of limited application in mechanics, and it states no general law of nature.

In the method of least squares the conditions and rules for finding the most probable values of observed quantities are derived from the principle that the sum of the squares of the residual errors

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