NEW SYSTEM

OF

MENTAL ARITHMETIC;

BY THE ACQUIREMENT OF WHICH ALL NUMERICAL QUESTIONS
MAY BE PROMPTLY ANSWERED WITHOUT
TO PEN OR PENCIL.

RECOURSE

IN THE FORMER PART WILL BE FOUND

EXAMPLES

OF

THE GREAT UTILITY OF FRACTIONS

IN THE FORMATION AND PROVING OF RULES,

WITH THEIR APPLICATION TO MENTAL CALCULATION

AND, IN THE LATTER,

AN ENTIRELY NOVEL METHOD

OF

REDUCING THE LARGEST SUMS OF MONEY, WEIGHTS, MEASURES,
TIME, AND SPACE, TO THEIR LOWEST DENOMINATIONS,

BY MEANS OF

ORIGINAL QUADRANTAL RATIONALE ;

ALSO, A MODE OF PERFORMING

INVOLUTION AND EVOLUTION BY A NEW PROCESS.

BY DANIEL HARRISON.

LONDON:

PRINTED FOR THE AUTHOR, AND SOLD BY HENRY HARRIS,
21, GREAT ALIE STREET, GOODMAN'S FIELDS;

AND BY ALL BOOKSELLERS.

MDCCCXXXVII.

TO THE

MOST NOBLE

THE

MARQUESS OF LANSDOWNE, K. C. B.

&c. &c.

MY LORD,

I TENDER you my sincere and grateful acknowledgements for permitting me to dedicate this Work to your Lordship; and I trust that the public will see reason to own and attest, that such influential patronage has not been unworthily bestowed. Let me not be charged with abusing your generosity, if I take this opportunity of laying before your Lordship a brief history of myself, and, of the publication here ushered into the world. The obscurity of my situation seems to warrant, and to justify, the measure; whilst the character of the book, whatever be its merits, will, from such a narrative, be more justly appreciated.

In the ardour and enterprize of youth I volunteered to serve, as a substitute, in the Second Somerset Militia. From thence I enlisted, in 1811, into the 9th Regiment of Infantry, and was immediately promoted to the rank of Serjeant.

I was present at several of the most signal engagements in the Peninsular War; at Salamanca, Burgos, Vittoria, St. Sebastian, Invasion of France, Bayonne, &c.

I accompanied the Regiment to America ; and from thence to France, on the return of Bonaparte from Elba. In 1817, I was discharged, in consequence of a reduction in the forces; and, because of a deafness contracted by the severity of the service.

own

My military career was both arduous and dangerous; yet, unhappily, it was too short to entitle me to a pension. Thus thrown entirely upon my resources for procuring a livelihood, I have devoted the subsequent part of my life to a daily school, in Bath; and, amidst the toils of this laborious and ill-paid occupation, I have prosecuted the inquiries, and matured the system, exhibited in the following pages.

V

After having faithfully served my King and Country in the Field of Battle, I now humbly proffer the best services I have at command towards the instruction and benefit of my fellow-men, in that branch of scientific knowledge, to which I am devotedly attached.

I have every confidence that both your Lordship and the public will view, with approbation, the motives by which I am actuated; consider with candour, the circumstances under which I have laboured and estimate, with justice, the merit of my production.

With unfeigned gratitude and respect,

I am,

MY LORD,

Your deeply obliged and most

obedient humble servant,

DANIEL HARRISON.

Bath, January, 1837.