methods might also be adopted for the determination of C. Suppose for instance two points were known, at which the vibratory wave arrived at the same instant, then, if we bisected the line joining these two points, and drew another line perpendicular to it through the point of bisection, the latter line would pass through C, assuming always the spherical form of the general vibratory wave. In some cases also, as in those of earthquakes in the neighbourhood of insulated volcanos, circumstances may indicate, antecedently to any instrumental observations, the approximate position of the point in question. C being determined, the determination of the depth CO of the centre of disturbance, by the formula (B.) (art. 43) would require the values of the horizontal velocity (v) of the wave, and of its absolute velocity (V). For the determination of v, two instruments would be necessary merely to record the exact times of the initial shock at two places, which ought to be situated as nearly as should be convenient on the same line through C. They ought not to be too near C, because the variation of horizontal velocity would there be very rapid; nor ought they to be so far removed from that point that the angle 0 (fig. 13) should approximate too near to a right angle, because the difference between v and V would then be so small that a small error in the determination of either would vitiate the result given by the formula. I have already indicated (art. 40) how the absolute velocity of propagation (V) might be determined if we could ascertain the coefficients of elasticity of a number of rocks similar to those which may be presumed to constitute the portions of the earth's crust through which earthquake vibrations are propagated. And here I would again remark on the insufficiency of attending only to the coefficient of linear expansion; that of cubical expansion must also be determined. We might also determine V by observing the horizontal velocity at such a distance from the origin of the motion, that the horizontal and absolute velocities of propagation might be considered as approximately equal, and in the present imperfect state of our knowledge respecting the velocity with which vibratory motions are propagated through solid masses, this would probably be the best way of determining the quantity in question. In a region surrounding an active volcano, it is probable that a sensitive instrument would detect a great number of slight earthquake shocks which would pass entirely unnoticed without some special means of observation; and if, moreover, the volcano should be an insulated one, like Vesuvius for example, we should have a case in which, as already remarked, the position of the point above denoted by C, might be considered as very approximately known, assuming the shocks to originate in the interior of the volcanic mountain. Such a region will naturally suggest itself as one in which we should best commence our instrumental observations, and soonest ascertain the capabilities of our instruments. With the assumption just mentioned respecting the origin of the vibratory wave, the only essential requisite of the instruments used would be that they should note accurately the instant of the initial shock at the respective stations chosen as above mentioned for the determination of v and V; without the above assumption, it would also be requisite that the instruments should indicate the horizontal direction of the initial vibration. This latter requisite belongs. I believe, to several instruments already invented; in fact, the determination of the horizontal direction of vibration is manifestly a much more simple problem than that of the absolute direction. The period and amplitude of vibration would not be at all necessary. I am not aware that any self-registering instrument has yet been constructed with the power of recording the exact instant of a shock. With out this requisite, however, no instrument can have the slightest value for the purposes here contemplated. In the methods above suggested, the horizontal direction of propagation is alone required; but if V, and V, could be determined with sufficient accuracy by means of the coefficients of linear and cubical expansion, the formula (d.) (art. 43) would give immediately the position of O by a single observation, provided our instrument could determine the time denoted by T, and the absolute direction of propagation of the wave within the earth. This direction will coincide with that of the normal vibrations of the wave arriving first at any point within the earth; but it should be observed that the particles situated at the surface will not generally vibrate in the same direction as those within the vibrating mass. Consequently, supposing we had an instrument with the above-mentioned requisites, it would be necessary, for the object here proposed, to place it at a certain depth below the surface of the earth; and here again the interference of the wave reflected back from the surface into the interior mass, with the incident wave, would render the observations useless, unless the instrument were placed at a sufficient depth. Let this depth=h, and let 0 denote the angle of incidence, as in figure 13; then it is easily shown that the interval of time between the arrival of the 2a cos 0 incident and reflected waves at the point of observation = Now, V1 since the sounds usually resulting from these vibrations are continuous sounds, so many vibrations must take place in a second, that if the instrument were placed, for instance, in a mine at the depth of a few hundred feet, several complete vibrations of the incident wave might be completed at the point of observation before the arrival of the reflected wave; and if the instrument should be capable of recording the absolute direction of these initial vibrations, independently of the subsequent ones due to the combined effects of the two waves, the absolute direction of propagation of the wave in the interior of the terrestrial mass would be determined as required. The The advantage of this method would consist in its requiring only a single instrumental observation; but the exactness with which the observation must be made, and the few localities in which the instrument could be placed at the requisite depth, must necessarily render the method comparatively useless for the general determination of the depths of volcanic foci. I have entered into this brief discussion of it to indicate the precautions which would be required in the adoption of any method depending on the determination of the absolute direction of vibration within the vibrating mass. methods above indicated, depending on the horizonal direction of vibration, will probably be found far more simple in application, and far more deserving of confidence. We may remark, however, that the determination of the absolute directions of vibration, if it was found practicable in any one locality at a sufficient depth below the surface, would be highly interesting on account of the experimental knowledge it would afford of the characters of vibratory motions propagated through solid media. It may also be remarked, that though we could not for this purpose avail ourselves of similar determinations made upon the surface of the vibrating mass, these latter might also give results affording interesting tests of theory; and, moreover, in giving the vertical as well as the horizontal parts of the superficial vibrations, they would afford us a knowledge of one of the essential elements of earthquake movements considered with reference to their disturbing and dislocating effects on objects placed on the earth's surface and subjected to their influence. 93 Report on the Microscopic Structure of Shells. Part II. (Continued from Report for 1844, p. 24.) Introductory Remarks. In my former Report I gave an account of the principal varieties of elementary structure, which had presented themselves to me during a minute and extensive examination of the shells of Mollusks; and I described the peculiar combinations and arrangements of these elements, which are characteristic of the following groups of Bivalves, namely, the Brachiopoda, the Placunidæ, Ostracea, Pectinida, Margaritaceae and Nayadea. On the present occasion I shall enter into similar details in regard to the remaining families of the Lamellibranchiata; and shall state the results of my inquiries into the structure of the shells of the Gasteropoda and Cephalopoda. These last are, however, chiefly of a negative character. Before proceeding, however, to this continuation of my former Report, I shall make a few additions to the facts contained in it, as to the structure of the shell in certain of the groups therein described, which have resulted from the continuation of my inquiries into their organic peculiarities. I. Observations Supplemental to former Report. 57. Brachiopoda.-When drawing attention (§ 41) to the very remarkable system of perforations presented by the shells of certain species of Terebratula and allied genera, I was obliged to express my ignorance of the relation which these passages have to the structure and economy of the animal; not having had at that time the opportunity of examining a shell, the animal of which had been preserved in situ. This opportunity, however, by the kindness of Mr. Cuming and Mr. MacAndrew, I have since enjoyed; and I can now communicate the results of my inquiries, which, though not fully satisfactory, will be found, I think, to possess much interest. 58. The species on which my observations have been made, are the T. australis, and the T. caput serpentis (?) lately discovered to be a native of our own seas. When a thin portion of a shell of either of these (and probably therefore of any of the perforated species of Terebratula) which has been preserved with the animal in spirit, is ground down from the inner side, so as to leave the outer surface unchanged, it will be seen that each perforation in the shell is covered-in by an oval membranous disc, whose texture appears very firm (fig. 1). When a thin section thus made is exposed to the action of dilute acid, so as to remove from it the calcareous matter, it will be seen that these discs are connected together by a layer of very pellucid membrane, in which no distinct structure can be made out (fig. 2); this membrane, differing as it does from the membranous basis of the interior layers of the shell, is probably to be regarded in the light of an epidermis. When a portion of the shell, not reduced in thickness, is completely decalcified by immersion in dilute acid, and the menbranous residuum is then examined, a very remarkable structure presents itself, such as is found in no shells of the Lamellibranchiate Bivalves. Attached to the membranous films are a series of tubular appendages, corresponding in diameter to the perforations in the shell, and arranged at the same distances (fig. 3). The free extremities of these appendages are much larger than those by which they are attached to the membrane, and have distinct cæcal terminations, which appear by the straightness of their border to have been flattened against the discs that closed the orifices of the perforations in the shell. Indeed in some instances these discs have remained adherent to them, when the shell-membranes were torn asunder; and are seen edgeways, as in fig. 3, a. There can be no doubt, therefore, that these membranous cæca occupied, in the living animal, the perforations already described as penetrating the shell from one surface to the other. This will be still more evident on reference to fig. 39 of my former report; in which it will be seen how exactly the shape of the cæca corresponds with that of the perforations, when the latter are laid open lengthways by a section of the shell perpendicular to its surface. The lower margin of that figure corresponds with the outer surface of the shell, and the diameter of the perforations is seen to be there greatly increased. With regard to the office of these cæca, however, I am unable as yet to give any distinct explanation. Their contents are of a brown granular character, in which I have recognised distinct cells (fig. 4), such as are to be met with in the tubuli and follicles of ordinary glands; and their whole aspect satisfies me that they must be regarded as possessing a glandular character. I have not been able, however, to discover the nature or destination of their secretion *. The internal orifices of the perforations obviously constitute the outlets of the cæca; but there does not appear to be any system of tubes or canals for collecting the matters poured out from them, each cæcum having its distinct and independent termination on the internal surface of the shell. Although the unusual degree of adhesion between the mantle and the shells of Terebratulæ, first noticed by Professor Owen, formerly led me to suspect that the mantle might send prolongations into the perforations of the shell, I have not been able to discover any vestige of such. On the contrary, it has appeared to me that the mantle, which is a nearly homogeneous membrane where not traversed by vessels, is simply applied to the internal orifices of the cæca, and continued over them; no trace of any connection with them being visible when it is detached from the shell. I may mention, however, that I have found the surface of the mantle in contact with the shell to be scattered over with minute cells, corresponding in size and aspect with those contained in the cæcal tubes (fig. 4, a). 59. The physiological purpose of this curious structure, therefore, is at present a mystery; but there can be little doubt that it is a very important one in the œconomy of the animal, when we see the shell thus rendered subservient to the special protection of these cæcal appendages. And there is evidently strong reason for regarding the presence or absence of the perforations in the shell as a character of greater value in the subdivision of the genus Terebratula and its allies, than those more trivial indications furnished by the external conformation of the shell, which seem to have little to do with the structure or œconomy of its inhabitant. I am very happy to find this opinion sanctioned by so high an authority on the classification of the Brachiopoda as Mr. Morris, who has laid great stress on the presence or absence of these perforations, as exactly corresponding with characters derived from the relation of the foramen to the deltoidal areat. And I am quite content to accept his correction of an error into which I had fallen (through an accidental disarrangement of my sections) in the classification * Should I, however, be ever fortunate enough to have the opportunity of examining a fresh specimen, I shall be able to form a better idea of the former than is possible from specimens preserved in spirit. + See his paper on the subdivision of the genus Terebratula, in the Journal of the Geological Society, vol. ii. p. 382. of species under the two heads of "perforated" and "not perforated," which I gave in my former report (§ 42); Ter. coarctata and Ter. subrotunda being perforated, whilst Ter. acuta is not perforated. 60. Placunida.-As the "prismatic cellular structure" appeared to be peculiarly characteristic of the group of shells with the lobes of the mantle completely divided-presenting itself most typically in the Margaritacea, and in a subordinate degree in the Ostraceae on the one hand and the Unionidæ on the other-I could not readily account for its apparently complete absence in the shells of this family. I have since ascertained, however, that a very thin but distinct layer of it may sometimes be traced on the exterior of Anomia ephippium (fig. 7); and I am disposed from analogy to believe that it is constantly formed in the first instance, but is subsequently more or less completely worn away. Since my former Report, I have also examined a specimen of Placunanomia; and have found that whilst its general texture closely resembles that of its congeners, there is one part of the shell-that which bears the muscular impression and surrounds the passage for the socalled bony attachment-which has a more solid and less laminated character, and is made up of a distinct cellular structure. The "bony attachment" of Anomia and Placunanomia differs entirely in structure from the shell to which it belongs; I have not been able, however, to satisfy myself fully in regard to the plan of its formation, and I therefore refrain from now attempting to describe it. I may state, however, that it has nothing in common with true bone in its texture, save the large proportion of animal matter which it contains. 61. Pectinida. For the reason just stated, I have always been on the outlook for indications of the prismatic cellular structure on the exterior of the shells of this group also; but I had not succeeded in distinctly tracing them at the time of my former Report. I was disposed to account for this by supposing that the first-formed or external portions of the shelly layers are usually abraded, perhaps in consequence of the comparatively active movements of these animals. My expectation has been in some degree justified by the discovery of a thin but beautifully distinct layer of this substance on the exterior of Pecten nobilis, as represented in fig. 6. I would suggest it to those who may have the opportunity of prosecuting the inquiry, to examine the shells of very young Pectens, which may be usually viewed by transmitted light without any preparation. 62. Margaritaceae.-In describing the prismatic cellular structure, as it is presented in the shell of Pinna and its allies, I drew attention (§ 11) to the transverse markings which are seen upon the membranous walls of the prismatic cells, and also upon the calcareous prisms which they enclose, when these two elements of the structure are obtained in a separate form. And I stated my reasons (§§ 12, 13) for not assenting to the interpretation of this appearance offered by Mr. Bowerbank, who regards these striæ as indicative of the presence of tubes; but for considering them as produced by a simple thickening of the cell-membrane, at the points where successive layers of flat epithelium-cells have coalesced in piles, so as to make up the long prismatic cells or tubes which characterize the fully-formed shell substance. Since that time I have made repeated and careful examinations into this question; and I have now to present what I believe to be demonstrative evidence of the correctness of the view which I had taken. Amongst the various species of Pinna which I have examined, the Pinna rudis is most remarkable for the large quantity of animal matter interposed between the linings of contiguous cells, and also for the clearness and strength of the transverse markings on their walls. In making vertical sections of its decal |