JOURNAL

OF THE

UNITED STATES ARTILLERY.

VOL. VIII. No. 3.

NOVEMBER-DECEMBER, 1897. WHOLE NO. 29.

THE WELDON RANGE FINDER, ITS USE AND ITS THEORY.

In the field some such device as this is of great assistance to light artillery. To be of great service in the field a range finder must have to a reasonable degree the following qualifications:

1. Portability; 2. Durability; 3. Accuracy; 4. Adaptability to accidents of the ground; 5. Simplicity of manipulation; 6. Stability; 7. As far as possible the instrument should combine the best characteristics of all classes of range finders, with as few as possible of the objectionable ones, the purpose of the range finder being kept in view.

The Weldon is essentially a field range finder. It is meant for rapid and usefully accurate range firing.

It possesses the first two (portability and durability) of the above requisites to a satisfactory degree, weighing only four ounces and may be carried in the vest pocket; and also being strongly constructed of metal with crown glass prisms, and having a metal cover and on the outside of this a thick leather

case.

As to accuracy, the requisite degree of this must be determined. by the method of fire. If the firing is to be done assuming that the range finder is absolutely correct in its results, then it is necessary that a more accurate range finder than this or any other field range finder known to the writer be used; but if a means is desired of promptly finding the range with close approximation for a first shot in "bracketing" the target, this range finder will be useful.

In regard to the use of range finders, Colonel John I. Rodgers, 5th Artillery, says:

"The range finder is of assistance in eliminating the great errors which may arise in estimating distances. With a reliable

instrument and skilful takers the distance measured should be taken to govern the elevation for the first shot."

It is to be noticed that this indicates that the range finder is to be used no further for that target. If used further the range finder is a fruitful source of error, as the deterioration of powder, state of the air with reference to moisture and other conditions modify the accuracy of the range-table under the circum

stances.

Elsewhere, Colonel Rodgers states, "Range finders should not be made use of when the range is easy or the target of a transitory nature, such as advancing infantry."

From the above it will be seen that a range ascertained within 3% of the correct distance is of material assistance; and it is fair to presume that a reasonable time will be allowed the range party in which to make the observation.

The error of this instrument under average conditions is less than 3% of the correct value.

As two points, one seen directily and the other by reflection and refraction, may be made to coincide in this instrument by making the axis of the prism perpendicular to the plane of the eye, the point whose distance is required, and the direction point, it is easily seen that no instrument could well be more adaptable to varieties of ground than this.

Its simplicity of manipulation may be shown by the statement that, at present, every non-commissioned officer and several privates (these enumerated being the only ones instructed in its use), in this battery (E, 1st Artillery) is capable of making an estimate of distance with it, within 3% of the truth.

Its stability is self-evident. The angles of the prisms are fixed and can be changed only by re-grinding. Should they become detached from fastenings (highly improbable) each prism may still be used for its original purpose.

It is not adjustable and is the more accurate on that account. This range-finder belongs to that class of telemeters having a fixed parallax and a base proportional to the measured distance. It may also be said to have to a certain degree the advantages of those telemeters which have a variable parallax, since the combinations of prisms give different parallaxes corresponding, each to a different proportional base, (5, 30, 25).

The instrument referred to is the range finder of semi-cylindrical shape when closed and having three prisms of glass (arranged one above the other) having the following measuring angles :

74° 53′ 15′′

tan-1 50. tan-1 4.

3d or lowest... The first is used in order to establish the direction of the base for an assumed starting point. The second used in connection with the first establishes an angle at the other end of the proportional base, the tangent of which is 50, the ratio of the range to the base. The third, whose use will be shown later, facilitates measurement and shortening the base, the ground being uneven. The principles on which this instrument depends are shown as follows:

It is desired to show that in any right prism with a triangular base, ABC, the prism being composed of any substance forming a transparent isotropic medium, if used in the manner prescribed for the Weldon Range Finder prisms (to be shown later) the angle between the incident and emergent rays will be constant for that prism and equal to the face angle of the prism, provided that the face angle, (A), is twice as large as one (C) of the other angles; that the side (BC) opposite the face angle is silvered and that the angle made by the refracted ray DE with the normal to that face (AC) of the prism included between the angles A and C (already referred to) is greater than the critical angle for that medium.

Fig. 1 represents any cross-section (of the right prism of Fig. 2), that is parallel to the plane C'A'B', the ray lying entirely within that plane of cross-section. In Fig. 2 such plane is roughly represented by the same letters used in Fig. 1.

In Fig. 1, IDEFGO represents the course of the refracted ray; ID represents the direction of the direct ray from the eye to the

relative index of the medium of the prism, with reference to that of the surrounding medium (air, say).

Though so drawn in the figures, ID is not necessarily parallel to BC, as will appear from the general nature of the discussion.

No restriction is placed upon the direction of ID save that it shall lie in the plane ABC and shall have such direction that the refracted ray shall strike AC and AB consecutively within the limits of the prism, and make with the normal to AC at the point of incidence (E, say) an angle less than the critical angle, that angle being (in this instance) sin

Let the value of A, the face angle, be represented by 2a, and that of C by a = A.

It is evident that a 60° theoretically; and, practically, it has a maximum value of 45°.

It is desired to show that A = OPD', under the conditions of the proposition. O and I are points of the ray exterior to the prism and on different sides of it.

'being that

Before going further it is well to note that V being the velocity of transmission of light in the outer medium and of the material of the prism,

Now, from optics we know that ( being the angle made by ID with the normal to AB, and ', e,, and " being as indicated in Fig. 1) the following is true:

sin sin y' and