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POPULAR SCIENCE REVIEW.
HITTING THE MARK; OR, CANNON-BALLS AND
THEIR STRIKING VELOCITY.
By G. WEST ROYSTON-PIGOTT, M.A., M.D., CANTAB. M.R.C.P.,
LATE FELLOW OF ST. PETER'S COLLEGE, CAMBRIDGE, AND FELLOW OF THE CAMBRIDGE PHILOSOPHICAL, THE ROYAL ASTRONOMICAL,
AND MICROSCOPICAL SOCIETIES, AUTHOR OF "THE HARROGATE SPAs."
spatched at fine conveying ordere he has a chance
TVERY few years, we are now accustomed to hear of cam
U paigns on a most stupendous scale being fought, lost or won, in a great measure by superiority of modern artillery. The nation which has the best field-gun and can strike the most rapid, overwhelming, and hard-hitting blows at long range, demoralises the foe before he has a chance to hit again. Electricity for conveying orders, and explosive missiles despatched at fabulous distances, enable concentric masses to annihilate the enemy, innocent of such resources of the modern art of killing the greatest number in the least possible time.
SOLFERINO, SADOWA, and SEDAN hissed a sad sarcasm, from the vainglorious vanquished, whilst Europe rang with sympathetic echoes, trembling at the fall of embattled hosts, destroyed for lack of knowledge. Yet the philosophy of projectiles seems only just now beginning to be understood. A practical working knowledge of the effective energy of shot hitting a distant mark is of more importance now than ever. In face of the European dramas so recently played out before our eyes, the question of striking energy, or distant velocity, is now of supreme, it may be hereafter of tremendous interest, as involving the very destinies of the country.
Here is a question of apparent simplicity which our artillerists could not recently solve.
If a 9-inch 250 lb. cannon-ball strikes an object 200 feet distant with a velocity of 1,400 feet per second (1,400 f. s.),
VOL. X.-30. XXXVIII.
what loss of velocity would be effected by the resistance of the air upon its reaching an iron-clad vessel a mile distant ?
To fire cannon-balls with a given charge and ascertain their time of flight and range, or perhaps their penetrating power at short ranges; and to “time” the fuze of a bursting charge, were the chief points formerly attended to.
Attempts had been made, indeed, with considerable success, to ascertain one velocity for each ball striking a ballistic pendulum, which, upon receiving the shock of the striking ball, vibrated through a measurable arc.
Even this solution was sufficiently difficult to have engaged the powers of Robins, Hutton, Didion, and Helié. So late as 1865 the latter confesses (" Traité de Balistique"): “ Les solutions les plus avancées laissent encore fort à désirer. L'exposé de ce qui a été fait montrera du moins ce qu'il reste à faire” (p. 2).
There still remains, however, a great desideratum—a complete system which shall enable the scientific artillerist to answer any question respecting the motion and behaviour of a shot after it has left the cannon's mouth at any point of its path. Such results should also be immediately practicable by those who are without the scientific knowledge on which such results have been obtained. “ Applied science,” the master idea of the age, would, in the case of artillery students, receive a striking illustration: and thus literally connect the Government with technical education. The general reader will understand the remarkable difficulties encountered in prosecuting this research, by presenting to him a short résumé of the history of this engrossing question.
Nearly the whole system of theoretic modern gunnery is founded on Hutton's “ Mathematical Course” (H. died 1807). Hutton's celebrated experiments with the ballistic pendulum were published by the Royal Society in their Transactions in 1778, nearly one hundred years ago : these experiments had an important influence.*
* Several European Governments took up the question. The chief theatre of them was Metz in 1839-40, where an extensive system was developed under the direction of MM. Piobert, Morin, and Didion, with a large instrument constructed on the English plan. In 1855, a large ballistic pendulum was constructed at Elswick for the English government, at the cost of several thousand pounds, which has not hitherto been even used, for shortly afterwards Navez's electro-ballistic instrument was imported from Belgium, which appeared to give correct initial velocities. But when the mathematicians began to cross-question its results, they found that no law of resistance of the air at various points of the ball's path could be deduced from its use. Since 1866 Benton's electro-ballistic machine with two pen
In a languid melancholy way we have been arriving (for a reward of 200 years' study of this question) at an inkling of the real state of the case. In gunnery our parabolic theory was all wrong. It was fancied, somehow, first of all that the resistance of the air had little power as against shot. Sir Isaac Newton and Dr. Halley were both of this opinion. Robins states (“Gunnery,” Preface), that a musket-ball at an elevation of 45° should range seventeen miles in vacuo, yet it only flies half a mile! *
The great honour of mastering the complicated difficulties attending the determination of successive velocities at different points of the flight, and calculating the laws of the resistance of the air from experiments made upon a large scale, is unquestionably due to our fellow-countryman, Professor Bashforth. This gentleman, apparently from the tenour of the Report, received little approval or encouragement from the official mind.
The English public will no doubt appreciate these labours, and it is a matter of congratulation that such men as Professors Adams and Stokes have undertaken the onerous task of pronouncing their verdict upon researches as profound as they were spontaneous. An elaborate Report is now published replete with results of the highest importance to the future defensive power of this country.f Quoting from this report we read :
dulums, under the name of Leur's, and another by Boulenge, which give only one velocity, have been much used in this country and on the Continent. Sir Charles Wheatstone, F.R.S., and Breguet, also designed instruments for measuring successive velocities, but no information is extant upon their experimental success. At Paris, in 1867, Schultz's instrument was also exhibited with a similar intention and no result.
* The resistance of the air in the case just mentioned reduces the range to a space thirty-four times less than a vacuum range.
Hutton's law assigned it to be a function of the velocity added to its square (av + bv).
Didion at a function of the velocity added to the cube (bv + cv3).
bu? + dv4. What is very remarkable is that Hutton and Piobert (whose laws have been commonly employed) deduced very different laws from the same experiments.
For further information on this point see “ Description of a Chronograph, adapted for Measuring the varying Velocity of a Body in Motion through the Air, and other Purposes.” London: Bell & Daldy.
† Report on Experiments made with the Bashforth Chronograph for determining the Resistance of the Air to the Motion of Projectiles (p. 169). Printed by Eyre & Spottiswoode, November 1870, for Her Majesty's Stationery Office.