Familiar lectures on scientific subjects / by Sir John F.W. Herschel.

  • John Frederick William Herschel
Date:
1866
Catalogue details

Licence: Public Domain Mark

Credit: Familiar lectures on scientific subjects / by Sir John F.W. Herschel. Source: Wellcome Collection.

    522/530 (page 506)
    (10.) The same principles apply of course equally to rifle-shooting as to archery, provided the target aimed at be circular. If rectangular, and especially if an elon- gated rectangle, the same formulae will not apply; and the appropriate formulae would be necessarily much more complex and their results proportionably more difficult of calculation. This is a strong argument for the use of circular targets : for, though for the mere decision ot the order of merit in a distribution of prizes almost any impartial rule, rough and readily applicable, may suffice, the same cannot be said when the object is to obtain a true numerical measure of the national skill in the use of that great weapon : for which purpose it is highly desirable that the data afforded by our rifle prize meet- ings should be preserved, collected, and reduced syste- matically. NOTE. Demonstration of the formula in § (2.) and (3.) The probability of committing the specific error r (all errors pre- senting equal facility for their commission] is proportional to E (—£r-), the characteristic sign E being used to denote the expo- nential or anti-logarithmic function ; and k being some certain con- stant to be determined or eliminated. And in the case of aiming at the central point of a circular target, the degree of facility afforded for the commission of a lineal error r, no matter in what direction, is proportional to 2irr, the circumference of a circle of that radius, or, simply to r: so that the probability of planting a shot some- where on the circtimference of that circle is measured by r. E (—for), and therefore the probability of making a hit anywhere within its area is proportional iofrdr. E (—kr1) taken between the limits o and r. Representing certainty therefore by i ; this probability (which we have denoted by H in the foregoing pages) will be ex-