No abstract

SUMMARYIn any mesh, rules exist that interrelate the number of internal and external sides, vertices, etc. and the total number of elements. These are given explicitly for plane meshes of triangles and quadrilaterals, and for solid meshes of tetrahedra and cuboidal elements. The method is quite general and discovers all such independent rules that exist. Thus, for a plane mesh of T elements having internal and Vb boundary vertices and Si internal and Sl, boundary sides, thenwhere H is the number of internal boundaries (holes) there might be. For solid meshes, these twodimensional equations relating elements to sides generalize to T = .i(Fb+ 2 6 ) (for cuboid elements)where there are 4, boundary and 6 internal faces. Unfortunately, there is no direct generalization of the two-dimensional equations relating vertices and elements: it is only possible to do this by including the E i internal and El, boundary edges:(for cuboid elements) T = BEb+Ei-V i + H -h -1 (for tetrahedral elements) where there are H through holes and h cavities.

BOOK REVIEWS597 and numerical integration. These two texts are, in most respects, similar but describe more sophisticated software for use on a personal computer. The emphasis is on computer programs, user interfaces (for the Apple and IBM) and program operations, with a brief description of numerical techniques.The two books differ only in the example computer programs written specifically for the Apple and IBM PC computers (they are referred to henceforth as 'the book). The text consists of eight chapters: on interpolation, complex arithmetic, vector and matrix operations, solution of simultaneous equations, solution of equations, integration, differential equations, and curve fitting. Each chapter contains a number of computer codes, with a total of about twenty.The details of each computer code are contained in the program listing, followed by a program description and program operation with example menus, user inputs and program outputs. The listings are clear, with an abundance of comment statements to assist the reader. The program description includes details of the tasks performed by each subroutine, and all input and output variables are defined. There follows a detailed explanation of how to run the program; this is obviously specific to the Apple and IBM PC computers. The details of the programs, subroutines, and user input and output provide a model format for program documentation and can be recommended to all writers of software.Details of the numerical methods discussed in the book are kept to a minimum. The reader is referred to the abundance of books which discuss in depth the question of numerical analysis.From the elementary nature of the numerical routines, the book is clearly aimed at the non-numerical specialist who is interested in results rather than methods. To achieve success the details and explanations of the methods should be particularly good.However, I found the text to contain numerous typing errors and in some cases misleading explanations of basic concepts. Certainly the standard of proof-reading does not approach the level expected of a textbook. There are numerous errors with subscripts and superscripts, brackets in equations are occasionaly missing, there are simple arithmetic mistakes in the solution to problems, and throughout the abbreviation for logarithm is given as 'ln'. But of more concern are misleading statements, of which there are several. To take a particularly bad example, the errors contained in the discussion on how to form the product of two matrices destroy the explanation.The issue of clarity is not helped by a rather strange mixture of typefaces. The diagrams are printed in a style I found uncomfortable to the eye, and the typeface for the program descriptions and operations is difficult to read and not conducive to continued concentration.Many of the errors are obvious and can be immediately corrected, but one cannot help wondering if there are similar types of errors in the program listings. If so, the unsuspecting user of the software will have a frustr...

I. The development of religious institutions and beliefs may be logical or real.1. Logical development is the explication of the content of a notion. Nothing new is added; it is like the opening of a closed hand. Such a development is consistent with the static, or mediæval, conception of the world, and is not unknown to the older theologians. In this sense of the word many of them would admit a development—e.g. of the Papacy, of Transubstantiation, of Sacramental Confession, of the devotion to the Blessed Virgin—from the less formally complete teaching and practice of an earlier age. But there is no process, they would maintain, in the notion; the change is not in the notion but in us. This proviso is essential. The full powers of the modern Papacy, we are taught, were conferred by Christ on Peter; and the Syllabus of 1907, in condemning the proposition that the apostle was ignorant that this was so, appears to reject the principle even of logical development—of which it would be truer to say that it is tolerated than that it is approved of, by the official Church. Pius X carried this identity of dogma back into the legendary age of the Old Testament, attributing a knowledge of the Immaculate Conception of the Virgin—defined in 1854—to the Hebrew patriarchs. Noah, he says, contemplates this mystery in the ark; Moses meditated upon it before the bush that burned in Horeb; David when he danced before the ark of the covenant. This is the language of a formal Encyclical (February, 1904), not the devout play of a pious imagination sporting over the sacred text.

HARVARD THEOLOGICAL REVIEW America is to be told, then the hasty and blunt verdict upon it by Charles Hodge-"atheism"-the explanatory advocation by Asa Gray, and the general hospitality towards it which was shown by Congregationalists, are of the first importance. But of these Dr. McGiffert says nothing. And it would seem as though it were not an unprofitable line of historical investigation to discuss why Congregationalists were as hospitable as they were. It would then appear that in the long development of "the New England Theology," technically so called, and in the Unitarian movement, Congregationalists had learned these great and liberating things-that the Calvinistic theology of Geneva was not final and authoritative, that much could be learned from adversaries, that the fundamental elements of religion are vital, spiritual processes (see N. W. Taylor, long anterior to Ritschl), and that progress in theology is to be expected and labored for. These were the preparation for evolution and biblical criticism, and for the dynamic rather than the static view of the universe. We hope the book will pass to a second edition, and that Dr. McGiffert will extend his view to the fields suggested, and to others, and give us thus a still more vital history of the actual growth of our American system of thought, now in process of rapid development among us.