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PROSPECTUS

OF

A NEW CALCULUS,

CALLED,

FOR THE SAKE OF DISTINCTION,

THE POTENTIAL CALCULUS,

Which is applicable to all those Questions that are considered by Writers on the Fluxionary, and Differential and Integral Calculus; and is demonstrated on Principles purely Analytical; being independent of Prime and Ultimate Ratios, Fluxions and Fluents, Differentials and Integrals.

BY W. GRISENTHWAITE.

THE very extensive application of the Doctrine of Fluxions to questions intimately connected with the business of life, and the very important place it holds in Mathematical Science, render it desirable that the Principles upon which the Doctrine is founded, should be rigidly demonstrable, in order that the conclusions drawn from it may be satisfactory. The nascence and evanascence of quantity, upon which it has hitherto been established, are considerations not only beyond the reach of human speculation, but are almost entirely unconnected with mathematical research: and the subsistence of rationality independently of quantity, is an incomprehensible refinement upon the subtility of Metaphysics. In the work, of which this is a brief notice, will be explained, whence the errors of the Fluxional and Differential Calculus arose, and the fallacy of the reasoning by which they have been

perpetuated. Some fundamental errors in the Differential and Integral Calculus, as modified by LA GRANGE, and taught by the French Mathematicians, will also be pointed out; and, as incidental to the Work, the received opinion concerning the vis inertia of matter, and the "status quiescendi" of Sir ISAAC NEWTON will be exploded. From the New View of this part of Mechanical Philosophy, several important and curious conclusions will be deduced. The Work will also contain the application of a new method of demonstrating the truths of the Fluxional Calculus, independently of Prime and Ultimate ratios-Nascent and Evanescent quantitiesFluxions and Fluents-Differentials and Integrals; and the Author believes, that a student who has passed through an Algebraical course of reading, will find his progress by this method uninterrupted by difficulties, which he has constantly to encounter on the very threshold of the Fluxionary and Differential Calculus. In the course of the Work, the New Theory will be applied to the Rectification of Curves-to the Determination of the Radii of Curvature-to Involutes, and Evolutes-Contrary Flexure of Curves-to Questions de maximis et minimis

Logarithms—to finding the Centres of Gravity— Gyration-Oscillation and Percussion of Bodies, and to several interesting Physico-Mathematical Problems-in the course of which will be explained the nature of the questions that admit of a Fluxionary consideration, and the manner of considering them.

The New Theory will also exhibit a view of the Integral Calculus which may become of considerable utility in the integration of differential expressions.

By the same Author.

A NEW THEORY OF AGRICULTURE, in which the Nature of Soils, Crops, and Manures, is explained; many prevailing Prejudices are exploded; and the application of Bones, Gypsum, Lime, Chalk, &c. is determined on Scientific Principles. Second Edition.

For writing the New Theory of Agriculture, the author received at an Agricultural Meeting at Holkham, in Norfolk, a handsome piece of Plate, from T. W. Coke, Esq. M. P. on which is inscribed "NEW THEORY OF AGRICULTURE."

"It has been also thought, that Salts are favourable to vegetation only in proportion as they hasten the putrefaction of vegetable substances contained in the soil, or attract the humidity of the air. But sulphate of lime is not deliquescent; and if its action consist merely in accelerating putrefaction, why is its beneficial effect confined but to a small number of plants? Grisenthwaite's New Theory of Agriculture answers this question, by stating, that as in the principal grain crops which interest the agriculturist, there exists a particular saline substance peculiar to each, so if we turn our attention to the clover and turnips, we shall still find the same discrimination."

Loudon's Encyclopædia of Gardening, p. 162.

"Grisenthwaite conjectures, that in many cases in which the blight and mildew attack corn crops, it may be for want of the peculiar food requisite for perfecting the grain."

Loudon.

"A rotation of crops is unnecessary, according to Grisenthwaite; and in a strict chemical sense, what he asserts cannot be denied. His theory is a refinement on the common idea of the uses of a rotation; but by giving some details of the constituent parts of certain grains, and certain manures, he has presented it in a more clear and striking point of view than has hitherto been done. To apply the Theory in every case, the constituent parts of all manures and of all plants must be known."

Loudon.

"That wheat may be grown many years on the same soil by the use of animal manures, or such as contain gluten, Grisenthwaite's Theory would justify us in believing chemically.”

Loudon.

"There are reasons sufficiently strong, Grisenthwaite observes, to discourage the practice of allowing dung heaps to ferment and rot without interruption."

Loudon.

"On the subject of Gypsum, Mr. G. has entered into an explanation of the subject chemically, and encouraged hope of success. He had probably repeated the experiments of Sir H. Davy upon Clover, and also upon Sainfoin, &c.; and it struck his ingenious and scientific mind, that there must be manures that act specifically, and can benefit only certain vegetables. What he has since written has sufficiently proved the fact."

Editor of the Farmers' Journal, in a communication to the
Norwich Mercury.

"It is to be hoped that Mr. G. will proceed with these investigations, which are so interesting to the theory of Agriculture, and which may ultimately be of considerable benefit to its practice."

Editor of the Farmers' Journal.

A REFUTATION of every Argument brought against the Truth of Christianity, and Revealed Religion, by THOMAS PAINE, in the First Part of his Work, called "The Age of Reason."

"I did not think it necessary, in the former editions, to mention any names of authors: but as Mr. Taylor, in his Syntagma, makes a mighty vaunting of this omission, I shall specify a few. Grotius, Leland, Paley, and Chalmers, in their works on the general evidences of Christianity; the Second Part of Baxter's Saints' Everlasting Rest, and his Reasons of the Christian Religion; Ditton, Sherlock, West, and Michaelis, on the Resurrection of Jesus; Douglas's Criterion of Miracles. To this list many other impartial and judicious treatises might be added, but surely these are enough. I must, however, mention one work, which is by no means known as its merits deserve, having been published in a remote country town: this is "A Refutation of every Argument brought against the Truth of Christianity and Revealed Religion, by Thomas Paine, in the First Part of his Work called the Age of Reason: by W. Grisenthwaite.

Extract from the Rev. Dr. Pye Smith's “ Answer" to the
Rev. Robert Taylor.

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