"A QUARTETTE OF MATHEMATICAL GYMNASTS. "
This is a pretty devastating review of the work of four mathematicians/engineers that
appeared in the Scientific American on May 6, 1867:
The article concludes:
“We have a few other mathematical acrobats on our list,
but as their summersaults were turned on another stage, we
will not mention them at the present time, but we hope be-
fore long to place them before the readers of the Scientific
American. We will briefly observe, however, that one of
them is not a thousand miles from the Navy Department, and
he is still, we believe, accumulating figures with extraordi-
nary cunning and industry.”
It is pretty cutthroat beginning-to-end:
"The errors which have lately been made in calculating the
power of projectiles, the resistance of armor plates, and the
force of steam vessels when used as rams, seem to indicate
that a knowledge of first principles is more necessary for a
correct appreciation of mechanical problems than any amount
of abstract mathematical skill..."
The scientific gentlemen whose errors on the subjects al- luded to, it is intended at this time to point out, are Captain Noble ; Professor Daniel Treadwell, late of Harvard Universi- ty ; one of the Shoeyburyness scientific reporters, and Rear Admiral Louis M. Goldsborough, of the U. S. Navy. The curious blunder of Captain Noble, of her Britannic Majesty's Service, the famous artillery calculator, in comput- ing the dynamic force of the fifteen-inch shot, has a parallel, in point of inaccuracy, in a late error (which will presently be referred to) of another Shoeburyness mathematician in calcu- lating the resistance of a certain iron-clad target, and also in the blunders committed by Professor Treadwell in his calcu- lation on the fifteen-inch gun. Captain Noble, it will be re- membered, made the following error in his calculation of the power of the fifteen-inch shot. Referring to page 80 of his report, the result of his calculations is stated as follows, viz.: That with a " 50-pound charge and a 484-pound shot an initial velocity of 1,070 feet per second will be the result." This is equivalent to a force represented by 8,658,760 pounds raised one foot high, which divided by 50 gives only 173,175 foot- pounds as the energy exerted by each pound of powder. We are sorry to say that Professor Treadwell has blundered still more than Captain Noble in his speculations on the ca- pacity of the fifteen-inch American gun. In Vol. VII. of the Proceedings' of the American Academy of Arts and Sciences, we find the following statement in a communication from Professor Treadwell, read by Prof essor Winlock, viz, that the fifteen-inch gun with a projectile of " 315 pounds" weight and a charge of " 50 pounds" of powder an " initial velocity of 1,118 feet per second" is obtained, which is equal to a " force in pounds raised one foot high, 6,057,950." Referring to the results of trials before alluded to, it will be remembered that 50 pounds of powder projected a 450- pound shot with no less a velocity than 1,214 feet per second, which is equal to 10,328,400 foot-pounds, or 4,276,450 more foot-pounds, or nearly double the vis viva stated by the Pro- fessor. And in order to show still further to what extent he has underrated the real power of the gun, it is only necessary to repeat that with a proper charge the gun imparts an energy to its shot of no less than 17,145,310 foot-pounds, as tested by more than a hundred discharges from one single gun, as before stated. In the same communication we find the following put down as the performance of the Armstrong wrought-iron coil gun : "Weight of shot 600 pounds," " charge of powder 100 pounds," "initial velocity 1,400 feet," "force" of shot "in pounds raised one foot high, 18,375,000." According to these statements a pound of powder in the 15-inch only exerts a force of 123,039 foot-pounds, while the late Shoeburyness trials show that this piece actually exerts a force of 206,567 foot-pounds ; thus the Professor underrates the American gun to the enormous extent of 83,537 foot-pounds for each pound of powder employed, a degree of blundering quite inexcusa- ble in one who undertakes to teach the American Academy of Arts and Sciences. The enormous friction of the rifle shot and the absence of friction in the 15-inch shot, should have suggested to the Professor that his calculations must be erro- neous. Again, the 100 pounds which he puts as the charge in the Armstrong gun has only been used on one or two occasions ; 70 pounds was called the service charge, and even that ruined the gun in a very short time, and the last one tested burst at the sixth fire with but 70 pounds. In a word, the English themselves admit this gun to be a dead failure. But with this charge, i. e. 70 pounds, and a 511-pound projectile, an in- itial velocity of only 1,250 is obtained ; hence the force of the shot is equal to 12,500,000 foot-pounds, or only 178,528 foot- pounds against nearly 207,000 for the 15-inch. While Professor Treadwell has overstated the power of the abortive 13'2-inch English wrought-iron coil gun, he has as we have shown understated the power of the American 15-inch cast-iron gun in the ratio of 6,051,950 foot-pounds to 17,145,- 310 foot-pounds, that is, he has underestimated its capacity nearly three-fold! In looking through Professor Treadwell's paper, an expla- nation which seems to account for these astounding blunders may be found in the fact that the document in question is in- tended as an argument in favor of the coil system of con- structing cannon, his patent system. On this point it will be enough to say that the Armstrong coil system, which the Professor crowns with unearned laurels, is utterly unable to meet the strains put on heavy ordnance ; in short, it is a complete failure, and is so acknowledged in England by the fact of its abandonment for a simpler system. The Armstrong system is now admitted to be founded on erroneous mechani- cal principles. Much more remains to be said on this point, but we pass on to the next candidate, the Shoeyburyness scientific reporter. And with respect to the blunder made by this official in his calculations on the resisting power of an iron target, we cannot do better than quote from the London Army and Navy Ga- zette of August 24th. The Gazette, after giving its views of the self-satisfied air of the Shoeyburyness ordnance and select committee men, says : " There is, we see by the pages of the leading journal, a recent and rather remarkable illustration of the utter fallaciousness of the calculations at Shoebury- ness, which the scientific officers would have done better to have kept to themselves. It was considered desirable to test the power of the American system of laminated plates as com- pared with that of solid plates. One target was composed of a solid 7-inch plate, one of two 3|-inch plates, and one of three 2J-inch plates, bolted together." We are told that "the ratios of resistance under the 'em- pirical rule' ought to have been 49, 24, and 16 respectively. The result was ludicrously at variance with the empirical rule, and is represented in the proportion of 61, 57, and 52 respectively." It is not likely that any comments can add to the force of the teachings of such a result. The blunder to which we now call attention, in point of ignorance of principles, is entitled to cap the monument of blunders whose base and shaft is formed by the others which we have already mentioned. It is the extraordinary hal- lucination of no less a mathematician than Admiral Golds- borough with regard to the smashing or punching power of rams. The Admiral's fallacious reasoning deserves to be pointed out at the present time, from the fact that he still clings to an error which, if he has any conception of the sub- ject, he must have seen long since. In his report to the Secretary of the Navy in 1864, the Ad miral strongly advocates the employment of rams for the protection of harbors, unprovided with guns, which he says " are detrimental to unity of purpose." This view he at- tempts to sustain by the absurd statement that a ram weigh- ing 10,080,000 pounds, moving at the rate of 15 knots an hour or 25 feet per second, " is equal in point of shock" to a.ball of iron weighing 252,000 pounds striking with a velocity of 1,000 feet per second. This ball is 10 feet 2f inches in diameter. The striking force of the ram is measured by its equivalent of a little over 100,000,000 of foot-pounds, while the striking force of the 10 feet 2f inches ball is measured by no less than 3,906,000,000 foot-pounds. In other words, the Admiral, by not understanding the fact that the comparative " shocks " of the impact of moving masses are measured, not directly as theirvelocities, but as the squares of their velocities, has com- mitted the ludicrous blunder of exaggerating the power of his ram nearly forty fold. The Admiral's ramming theories appear to have been con- ceived while he was in command of the naval force in Hamp- ton Roads opposed to the Merrimac, and while that iron-clad was nightly haunting his dreams. The official delivery of these theories was formally announced with the ceremony due to a royal birth, in the report to the Secretary referred to. We have a few other mathematical acrobats on our list, but as their summersaults were turned on another stage, we will not mention them at the present time, but we hope be- fore long to place them before the readers of the Scientific American. We will briefly observe, however, that one of them is not a thousand miles from the Navy Department, and he is still, we believe, accumulating figures with extraordi- nary cunning and industry.
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