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affected organs, and increasing in bulk by an inherent growth.' Our readers will perceive that Dr. Farre restricts the meaning of the term tumour nearly as Mr. Abernethy had done, to swellings which arise from some new production that made no part of the original structure of the body. The first genus of the order consists of the tubera, which are defined to be tumours of a cellular structure and fungous nature, producing, in general, remarkable elevations on the surfaces of the affected parts. Two species only are described, the tubera circumscripta and the tubera diffusa.
The following character is given of the former :
Their colour inclines to a yellowish white, they elevate the peritoneal tunic of the liver, and their projecting surfaces, slightly variegated with red vessels, deviate from a regular swell by a peculiar indentation at or near their centres, which are perfectly white and opaque. They vary much in size, which depends on the duration of each tuber; for at its first appearance it is very minute, but during its growth it assumes the character above described, and at its maturity exceeds an inch in its diameter. They adhere intimately to the liver, and their figure is well defined. In the interstices of the tubera, the liver is paler and more flabby, its cohesion is weaker than natural, and slight effusions of blood are sometimes found. They commonly remain distinct at the surface of the liver, but internally they ultimately coalesce, and form immense morbid masses which pervade its substance. The patient often lives until the mass occupies the greatest part of the abdomen, and the natural structure of the liver is nearly supplanted. They possess so close a cellular structure, that the section of them, at first view, appears solid and inorganic; but on the edge of the knife, by which they have been dissevered, an opaque white fluid, of the consistence of cream, is left, and a fresh portion of this fluid is gathered on it at each time that it is repassed over the surface of the section. Their cellular structure becomes more apparent after long maceration.'
In conjunction with the character, we shall quote the author's account of the symptoms:
The patient suffers pain in the region of the liver, languor, loss of appetite, and cough; but until the liver, by the growth of the tubera, descends below the hypochondria, a distinct judgment of the case cannot be formed: then the functions of the alimentary canal are more impaired, the body wastes, and the enlargement of the liver, its hardness, and remarkable irregularity of surface, may be distinguished through the parietes of the abdomen. In the advanced stage the patient is distressed by its enormous bulk, the respiration is oppressed, the bowels are prone to diarrhoea. Neither jaundice nor serous effusion into the peritoneum are symptomatic of this disease: they may be conjoined, but it is an accidental circumstance, rather than a ne cessary consequence,'
Two cases of this disease are related, in which we find an ample account of the symptoms before death, and of the appearances on dissection, accompanied by apparently a very characteristic engraving. Dr. Farre observes that what he calls tubera circumscripta have been named by Dr. Baillie the large white tubercle of the liver, and that this anatomist considers it as of a scrofulous nature. Dr. F., however, ventures to dissent from this high authority, both as to the name and his opinion of the disease; thus stating his reasons with respect to this latter point: First, the tubera circumscripta are distinctly allied to the tubera diffusa, which unquestionably fall under the tribe of fungous diseases. Secondly, the tubera circumscripta differ from the tubera strumosa in their character and termination.'
The character and symptoms of the second species of tuber, the diffusum, are thus stated;
These tumours not only pervade the substance of the liver in a distinct or in a confluent form, but also appear at its surface, elevating more or less its peritoneal tunic. They rise from the surface of the liver with a more gradual and uniform swell than the tubera circumscripta, and are, in different subjects, of various figures, sizes, colours, and consistence, often pulpy. No texture seems to escape the ravages of this fungus. It appears indifferently in all the viscera, in the cellular membrane, and even in the bones.
Symptoms. These vary in proportion to the varied seats of the disease: the diagnosis, therefore, must depend on one of the circumstances from which its name is derived, viz. its dispersion through many textures of the body. But when this disease affects the liver in particular, then the symptoms will not materially vary from those which accompany the tubera circumscripta.'
Two cases here also are detailed, which are to be regarded as specimens of the disease under its most usual form; and afterIward, in the second number, we enter on its varieties. These are said to be too numerous to be all particularly noticed but Dr. Farre selects some of the most remarkable of them, in which the character, symptoms, and appearances on dissection are given, with the usual appendage of engravings. We shall not follow Dr. F. through these varieties, because we have already afforded a sufficient specimen of his manner of describing diseases. We have no means of determining the plan which will be pursued in the remaining numbers: but enough is published to enable us to speak very favourably of the talents of Dr. Farre as an accurate narrator of cases, a diligent examiner of morbid parts, and a correct discriminator between the different shades of disease. The engravings are remarkably beautiful, and very expressive,
ART. XIII. ATreatise on Mechanics; intended as an Introduction to the Study of Natural Philosophy. By the Rev. B. Bridge, B.D. F.R.S. Professor of Mathematics and Natural Philosophy in the East-India College. Il. Is. Boards. Cadell and Davies. 1814.
HE contents of this work appeared about two years since, in two volumes, under the title of "An Introduction to the Study of Natural Philosophy:" but the author's attention having been called, a few months after its appearance, to an error in the solution of a problem in the latter part of the performance, he has been induced to reprint the pages which contained that error, and a few other pages in different parts of both volumes, in all about 40, and to re-publish the whole as two volumes combined in one under the different title, viz. A Treatise on Mechanics. To this change of title, however, we should have objected, because many of the purchasers of the "Introduction" in its original form may thus be led to consider the present as a distinct treatise, and to incur the expence of a second purchase. We think, also, that the author has not been sufficiently explicit in his advertisement, which has very much the appearance of a preface to a second edition. He says;
This work had been published some months, when the author's attention was called to an error in the solution of the Problem at page 185., Part IV. This mistake is now corrected; and the principle of the solution of the Problem as it stands at present will be found to agree with that by which it is solved in Simson's Miscel laneous Tracts, page 131., Ed. 1757. In the revision of the work, some further corrections and alterations have been made. The substance of the notes, which were annexed to the end of Part II., are now introduced into the text; and a new form has been given to the First Lecture. The work is still divided into four parts.'
We would not be supposed to insinuate that the Professor entertained the idea of deceiving his readers by any ambiguity, but we acknowlege that we were ourselves deceived till we had recourse to the former volumes, and made the requisite comparison.
Having said thus much with regard to the "questionable shape" of the volume, we shall state the nature of its contents, which cannot be done better than in the author's own words:
• Part I. relates to the Rectilinear Motion of Bodies both by Impulse and Gravity; the Composition and Resolution of Motion, with the Solution of the Problem for resolving any Number of Forces into the direction of Three Axes at Right Angles to each other; the Method of finding the Center of Gravity of a Body or System of Bodies; the Motion of the common Center of Gravity of a System; the Collision of Hard and Elastic Bodies; and the Motion of Projectiles.
The first Three Lectures of Part II. contain the Doctrine of Equilibrium, as applied to the Mechanical Powers; the Fourth relates to the Pressure and Tension of Cords, including the Construction of the Funicular Polygon and Catenary. The last Lecture comprehends the common Theory for estimating the Strength, Stress, and Pressure of Beams.
· Part III. commences with the Motion of Bodies over Inclined Planes and Pulleys; and then proceeds to the Rotatory and Vibratory Motion of Bodies about a Fixed Axis; with the Investigation of the Centers of Gyration, Oscillation, Percussion, and Spontaneous Rotation of a Body or System of Bodies. In this part of the work will also be found some plain Theorems for ascertaining the Maximum Effects of Machinery.
Part IV. contains Three Lectures upon Miscellaneous Subjects; such as, the Descent of Bodies over Pulleys by Variable Forces; the Vibration of Cords; the Oscillations of Bodies in Circular and Cycloidal Arcs; the Angular Motion of Bodies suspended from the Arms of a Straight Lever, &c. &c.; and concludes with the Method of finding the actual Time and Velocity of a Falling Body, on supposition that the Force of Gravity varies inversely as the square of the distance from the Earth's center."
Such are the subjects which Mr. Bridge undertakes to illustrate but we do not think that the manner in which he has performed his task is such as we might have expected from a professor of mathematics in the 19th century. We have before stated our opinion with regard to the introduction of diagrams in mathematical treatises, by which it will appear that we do not object to avail ourselves of their assistance whenever they have an obvious tendency to illustrate the subject under discussion: but we are persuaded that the eight figures, which the author has given to explain the laws of accelerated motion, are not only unnecessary but injurious. The same may be said with regard to the chapter of projectiles, which is made to occupy thirty-five pages, and to require thirteen complicated figures; whereas the whole of the matter that it contains, or at least all the results deduced from it, might have been investigated in four pages, with every necessary explanation for the most unexperienced reader; and the same prolixity of detail and unnecessary display of diagrams pervade the whole performance.
This, however, we are sorry to say, is not the only fault which we have to allege against the present, treatise; since it contains, with many ambiguities and imperfect demonstrations, some palpable inaccuracies. Thus at page 363. we have the following example:
What is the greatest weight which may be rolled down an oak plank 20 feet long, 18 inches broad, 3 inches thick, and inclined to
the horizon in an L of 60°, without breaking it; the weight of the plank not being taken into the consideration?
To find the weight which this plank would sustain at its middle B x D' bx d point when placed horizontally, we have S: LXW 1xw" ::
20X IX to
•. W'= 4860lbs. ; but the strength of a plane horizon in an L of 60°: its strength when placed horizontally rad. cos. 603,.. the inclined plank would sustain 8 W or 38880lbs. about 17 tons at its middle point; consequently as the stress at this point is the greatest, a weight of 174 tons might be rolled down without breaking it.'
Now, the whole of this operation, as well as the preceding investigations on which it rests, is founded in error, and contrary both to theory and practice. That the stress on the plank varies as the cosine, we admit : but not that the strength increases as the square of the cosine. The latter is theoretically true when a beam is fixed in a wall at one end, so as to render the fracture vertical, but in no other case; and the inference which the author has drawn is therefore totally erroneous as applied to his example: as is also the investigation whence he has deduced it. It is obvious, in the case which he has supposed, that the fracture would take place perpendicularly to the face of the plank, the same as if it were placed horizontally; consequently, the strength is the same: it will therefore only bear double the weight in the former position that it will bear in the latter, and not eight times; and this double weight is not sustained from any increase of strength, but from a decrease of pressure or stress.
The most commendable part of this performance is the judicious selection of examples given at the end of each chapter, as exercises for the student; a plan which is not commonly adopted by authors on mechanics, although it is very advanthe present case, they are certainly arranged in the most eligible manner, and are well calculated to answer the intended purpose of illustration. The problems beginning at page 20., vol. ii., on the descent of bodies under different circumstances, are also neatly demonstrated; and, though they are, as the author justly observes, rather matters of curiosity than of practical utility, the simplicity of their demonstrations cannot fail of rendering them interesting to a mathematical student.
tageous in books intended for tuition. fi
Mr. Bridge's Mathematical Lectures were noticed in our Ixixth Vol., p. 204, Number for October 1812.