US2646253A

US2646253A - Directional drilling

Info

Publication number: US2646253A
Application number: US136533A
Authority: US
Inventors: Daniel S Johnston
Original assignee: Signal Oil and Gas Co
Current assignee: Signal Oil and Gas Co
Priority date: 1950-01-03
Filing date: 1950-01-03
Publication date: 1953-07-21
Anticipated expiration: 1970-07-21

Description

n rnv nr July 21, 1953 Filed Jan. 3, 1950 D. S. JOHNSTON DIRECTIONAL DRILLING DHN/EL 5 4 Sheets-Sheet l INVENTOR.

. JoH/vs TON y 1953 D. s. JOHNSTON 2,646,253

DIRECTIONAL DRILLING Filed Jan. 5, 1950 4 Sheets-Sheet 2 N VEN TO R. DHNIEL 5. HMSTON y 1, 1953 D. s. JOHNSTON 2,646,253

DIRECTIONAL DRILLING Filed Jan. 5, 1950 4 Sheets-Sheet 3 INVENTOR. .DHNIEL 5. zkH/vsm/v flrrozaivay.

July 21, 1953 D. s. JOHNSTON 2,646,253

DIRECTIONAL DRILLING Filed Jan. 5, 1950 4 Sheets-Sheet 4' DEN/EL S JOHNSTON flTTaRNEy.

.called azimuthal deviation.

Patented July 21, 1953 DIRECTIONAL DRILLING Daniel S. Johnston, Rolling Hills, Califi, assignor to Signal Oil and Gas Company, Los Angeles, Caliil, a corporation of Delaware Application January 3, 1950, Serial No. 136,533

This application is a continuation-in-part of Serial No. 642,080, filed-January 18, 1946, now

abandoned.

This invention relates to a method of drilling directional deviated bore holes in the earth, particularly deviated bore-holes drilled in the earth forproduction of petroleum. Thesebore holes are characterized by the fact that their course in the earth is in a direction otherthan vertical, and thus-their axes are directed insuch manner that they make an angle with the vertical called Vertical deviation andv are directed in the azimuthal plane. This direction, referred to as north or 0 azimuth, in the azimuthal plane is In drilling parlance the vertical deviation is also called drift and the azimuthal deviation is also called the direction or deviation of the bore hole.

In drilling a deviated bore hole, it is the present practice to direct thebore hole to pass in a large arcuate path to a desired point in a target formation. Thus, the course of the well results in the axis having an increasing vertical deviation or drift as the bore is advanced. This procedure is termed .building or increasing drift angle. The rate of increase of drift and the maximum desirable angle of drift is determined by a number of considerations; Among the most important and controlling isthe slenderness ratio of the mechanical system of easing, drill pipe, and also the phenomenon of key seating.

As a practical matter, the maximum rate of increase of drift usually employed in commer- 4 Glaiins. (o 255+L6).

cial practice is about 34per hundred feet of bore hole and the usual "maximum deviation found desirable 'is about 60-70. These limits are dependent upon and are determined by the physical characteristics of the" bore hole and the size and character of casing and drill tubing employed in drilling wells. Ordinarily, for conventional tubing and casing the practical limit is as indicated; The frictional resistance to the introduction of casing in holes'of much greater degree of curvature, or greater total deviation, is excessively large and largely impractical.

It is frequently conventional practice to start 2 built may be at some distance from the target. It is then conventional to continue the bore in a straight course at a constant drift angle.

It is frequently desirable to end the bore hole as a'vertical bore. This is desirable, in order to space the bore holes for efficient drainage of the formations. When penetrating a formation at an angle to the vertical, the bore hole intervals at the top of the formation will, in practi ally all cases, be different from. the bottom of the formation. If they are spaced for efficient drainage at the top or bottom, the spacing at-the other end of the formation will beineflicient since the bore holes in going through the formationv will in practically all such cases make an angle with each other. Y

Where there is a plurality of oil horizons separated by non-pro'ductive zones, it is usually desirable to penetrate the zones at a predetermined position of the structure for. maximum efficiency. of production. Since in the usual case the variousoilproducing horizons have similar dips and strikes, it may be that if the course of the bore is inclined to the vertical, the bore hole Will penetrate at diflerent'positions' of the structure. Sinca'as is frequently necessary, it may be desirable to finish the hole to produce from selected formations, the position of the bore hole may be unfavorable at the selected zone. A vertical bore obviates these difficulties.

The reverse bend created bythe decreasing of drift angle in any of the above cases increases the hazard or key seating, since the conditions for key seating are aggravated in such circumstances.

V 'It is thus necessary in drilling a deviated bore I hole to build and decrease angles during the course of the bore hole.

As a practicalmatter, it is desirable ideally to drill the bore hole so that its bent or curved axis traverses as nearly as possible a plane, hereafter called" the target plane, which intersects the Well locationand the point where it is desired to reach in the formation in which the bore hole is'to be bottomed, i. e., thetarget point in the target sand. This makes not only for minimum length'of hole, but also reduces difficulties in" drilling.

It is, however, asa practical matter, impossible co-maintain the azimuthal direction of the bore hole in the desired plane; The bore hole wanders to the left of the desired. plane (1. e. develops left deviation) or to the right of the desired plane (develops right deviaton) in an unpredictable manner; left and right being here and elsewhere defined in relation to a fictitious observer at the bottom of the bore looking in the direction which the axis of the bore is to progress. The direction and degree of deviation depends upon a very large number of factors and the effect of such factors is unpredictable. Whether the hole will deviate to the right or left will depend upon one or all or a combination of the following factors: The type of drilling bit, that is, its design, whether it is a roller bit or a drag bit; if a roller bit, on the number of rollers and their sharpness; whether or not a reamer is used, and if a reamer is used, on the number of reamers and sharpness thereof, and on its design; on the length, size, and stiifness of the drill bit and drill collar placed between the reamer and bit, and above the reamer; the size and type of drill pipe string, the size of the bore hole, the relative amount of cased and uncased hole, inclination and degree of curvature of the bore; type and condition and circulation rate of the mud, the weight placed on the drilling bit, the R. P. M. of the drill bit, the lithology, bedding, dip, and strike of the formation.

Variations in any one or in combination of these factors will change the direction of the bore hole in an unpredictable manner. The prior art has thus, in order to control and predict the direction of a bore hole, relied on the setting of directionally oriented whipstock. A directional e whipstock is a Wedge which has the diameter of the bore hole and weighs from 1 to 2 tons. It is set in the bore hole by means of pipe and turned in the direction so that the face of the whipstock is in the desired direction. Special drills, such as knuckle jointed drills, may be employed. When the hole has been deviated, the whipstock is removed and reintroduced when the direction must again be corrected. The difficulty of setting and running whipstock, particularly in deep holes, creates a serious hazard in oil wells. The danger. is great that the whipstock will wedge in the key seats or other portions of the bore holes. If this should occur, there is no way to dislodge and recover the whipstock, and the hole must be abandoned or the whipstock side-tracked. The cost of running a whipstock, even when the operation proceeds without, diff culty, is great and if the whipstocks must be run with any degree of frequency, the costs may be prohibitively large.

As a result of experience in the drilling of a large number of directionally deviated wells, I have deviseda drilling method whereby I may control the. direction and degree of deviation of a bore hole drilled at an angle to the vertical, i. e., a directionally deviated well, in a predictable manner without the use of whipstocks.

As is well known, all bore holes for production of petroleum are drilled by clockwise rotation of a drill string. This results from the fact that all tool joints and coupling used in the making up of a drill string have right-hand threads and the direction of rotation is clockwise since a counter-clockwise rotation of the drill string may unscrew the couplings and result in parting of the drill string.

My invention may be summarized as follows: In drilling non-vertical wells, the control of the building or dropping of drift angle is obtained by mounting a guide above the drill and using drill collars of desired weight between the guide and the drill and by adjusting the compression or tension in the drill pipe above the guide, so that on rotation in one'direction, either clockwise or counter-clockwise, the deviation is in one direction (left or right deviation) and this direction of deviation may be reversed or the degree of de* viation in one direction diminished by the simple expedient of reversing the direction of rotation of the drill while maintaining the above controls. The ability to drill counter-clockwise as well as clockwise arises from the use of tool joints which will not separate on rotation in either direction.

This invention will be further described in con. nection with the drawings, in which Fig. 1 illustrates somewhat schematically a directionally drilled well according to my invention;

Fig. 2 is a view in part section of one form of tool joint suitable for the drilling method of my invention;

Fig. 3 is a part section on line 3-3 of Fig. 2;

Fig. 4 is an enlarged detail of the end of the drilling string shown in Fig. 1 when the drill pipe is in compression;

Fig. 5 is a section taken on line 5-5 of Fig. 4;

Fig. 6 is a section taken on line 66 of Fig. 4;

Fig. '7 is a section taken on line of Fig. 4;

Fig. dis a section similar to Fig. 6;

Fig. 9 is a section similar to Fig. '7;

Fig. 10 is a detail of the lower end of Fig. 1 with the drill pipe in tension;

Fig. 11 is a part section on line llll of Fig. 10;

Fig.

12 is a section on line l2l2 of Fig. 10; 13 is a section on line l3|3 of Fig. 10;

Fig. 14 is a section similar to Fig. 12;

Fig. 15 is a section similar to Fig. 13.

The drilling equipment employed at the well head is conventional with the exception of the mechanism of reversal of rotation of the rotary table and the use of tool joints which will not unscrew on rotation in either direction. I employ such tool joints wherever a joint is necessary in the drill string. I also provide, above the drill, a guide which is of the gage of the hole to act as a fulcrum point, and I mount drill collars between said guide and said drill.

In Fig. 1 the conventional derrick l is mounted on the well site fioor 2 over a cellar 3 in which is set. surface casing with the usual well head equipment such as mud discharge pipe 4 discharging into mud collecting trough 5. The drill ipe is rotated via the conventional kelly 6, rotated by the rotary. Usually the rotary is rotated clockwise by means of some source of motive power. I, however, introduce between the driving engine 9 and the, rotary table a reversing mechanism such as a reversing gear box. Such reversing gear boxes, while. not employed with drilling engines, are conventional pieces of equipment and any one of the commercially available units capable of transmitting the horsepower necessary for the drilling operation may be employed. The kelly is connected to the drill pipe [2 and the swivel it by tool joints H to be more fully described below. The drill pipe I2 is made up of sections 13, as is conventional, but I also employ tool joints I I to be described below.

The drill pipe carries near its lower end a collar M of desired length and stiffness as described below and a guide I5 carrying rollers id of gage equal to the gage of the bore hole. The guide may be of many forms. Such guides have been used in drilling for centering purposes and other purposes heretofore. A suitable guide may be a conventional reamer such as is used in drilling of oil wells. The reamer cutters may be employed as the roller IE or the reamer cutters may be replaced by smooth rollers of the contour of the cutters. Below the guide I5, I may position another drill collar between the guide tation.

when

and the drill 118. All connections between the drill "pipe sections 13, collars Hi, and guide 15 and drill collars i1 and "between drill collars i l -and bit i8 may be of the form of the tool joints II "which will not separaterirrespective of the direction .of rotation of thedrill'string.

The drill string is supported as conventional 'o'n hook i9 which engages the'eye of the swivel I and 'is supported on the block"2il'and on drilling lines 2! which pass over the crown-block 22 and is wound on a drum as is conventional. Conventional power and other -equipment for operation of the line'aretused, as will be under pipe and through the tool joints in the 'drill bit up the "annulus betweenthe drill'pipei'i and bore holeZ'i' "and out the-pipe 4 tothepit '23 'system'whereby I may rotate the drill-in either i a clockwise or a "counter-clockwise direction. This, as stated, requires a'tool'joint which'will not separate 'irrespectiveof the direction of "ro and m ll. SJPatentNO. 2,485,763. One suitable form is illustrated herein in Figs. 2 and 3., The box 2? andpin 28 of the tool'joints H are connected by a screw thread 29. The .boX

andpin are' eitherscrewv "threaded,welded to orformed integrally with thedrill pipe section i2. 1 The external" sleeve '35 is sli'dably fitted over the "outside Wall 'of'the'box and the pi1'1 and I "carriesan internal shouldertlwhich is seated onthe end sii'of th'e'pin"28. Afga'sk'et 33 maybe "provided *between shoulder-3i and the End 32. The sleeve iifi'is s'crewedtdthe' exterior wallof 1 the box by means 'of screw'threads'"it'd-which are of 'an opposite hand to the screws connecting the box and pins to eachother andto'the pipe sections i3. Thus, if these *are-rightmanded threads the threads-t4 are left handed. Thisponstructio'n.

- drift; thatis, by proper drilling techniques, I

canbuild or decrease or maintain drift angle. Thusthe course of the borehole-inthe vertical plane is established.- I also am able todirect the deviation and degree of. deviation right and left of the vertical plane and thus can direct "the c'ourse'oi the bore hole 'iri'its azimuthal plane.

The building of drift "angle is illustrated "in "Fig-"4. After the hole has been" -drille'd"'ver-- *tically' through the unconsolidatedformationan "oriented whipstoch is set to establish -the origi-,,

" nal dir-ec'tion; of the bore holeat an angle and direction required-to reach -the ultimate target.

- 5 This-is conventional 1 procedure *andi-well unders'tood in this art.

'recourseto whipstocks. The real purposeof setting a whipstock in my method isto ,-dev.e1op

a non-vertical bore,and any other method-other than the settingof a whipstock ior thispurpos will also be suitable for the purposes of :my

method.

' Fig.4 illustrates-sucks. non-verticalzbore. use the drill astring described above. The roller drill bit It isseparated'from the guide .;lf4;iby means of arelativelyshort-collar. iThef-length of the collar depends upon therateof. build-11D f drift angle desired; the length .and ;size 10f drill pipe and the degree of compressive :force exerted, as described above, :and also on .other factors. Experience has shown that for rates of drift angle build-up of up to :34 per 1100' and for A. P. I. drill tubing .of 4% 0. D. the

drill collars may be from.-2 to the choicebeing directed in'the mannerdescri-bed below.

The drill pipe is loaded so as toplacetherdrill pipe in compression. This, as will'beunderstood by those'skilled in'the art, consists of 'placingithe drill lines in such degree'of tension thataportion orall of the weight of. the drill pipei'flrests on the drill i8. Due to the inclination .of the 7 hole and the fact that the drill pipe is incom- E'may employ any type of such joint, for'eaample, the tool joint 'disclosedin applicaltion Serial No."642,079 "filed January 18, 1945,

pression, the drill pipe will be bowed and-rest on the bottom of the hole,-as illustrated in .=l.f ig.- 4'.

The guide f ulcruming at 16 willtend todift the drill so as to be directedin an upwardidirection illustrated by the line A. "The magnitude of the upward force depends uponthe in-. clination of the hole,the compression-0f the drill "pipe, and the length of the drill-collar, andother factors described above.

Figs. 10-13 illustrate the effect of placing the drill pipe in tension. By employing long drill collars H and placing the drilling lines in tensionto equal'the weight of the drilltube-down to the fulcrum point, the drill pipe may be placed in tension while the drill collar I! is placed in compression. This procedure is identical to that,

employed in drilling vertical wells for controlling the weight on the drill and will be well ,understood'by those-skilled in this art.

As will beseen from Fig. l0, the net'result of the tension in the drill pipe and the'weight'of the drill pipeandtheslant of the bore hole results in a net component which bows-the pipe against the upper-side of the bore hole. =Because of the fulcrum point 15, the drill is directeddownward, as is shown by line B. The magnitude of this force depend upon factors similar to that described for force-A. Y

When I employ the above expedients for building, maintaining, or reducing drift angle, em-

ploying conventional drill strings-and rotary equipment universally now "employed and which may be used only-With clockwise, i. e., right-hand rotation'of the drill string, I'introduce, dependent upon whether the drill stringis in compres- Er'om this point on, 'I' 'may-c'ontinue#the drill-.375

tation. The effectof this is a f0rce-G,=i-ndicated by thearrow on Fig. 6-,to cause the bit-to fulcrum :tQthe-left; as indicated by o on' F ig. 5. The net result: ofalthisifulcruming candstheo upward force illustrated in Fig. 4' is a force component D illus- -trated=1-in Fig'=.-..7.; ItT-willbe-seenthat the righthand rotation reduces the rate of drift build-up and causes a left-hand deviating tendency to be introduced. It will also be noted that the resultant D, that is, the resultant angular deviation, is less than that which would have been obtained if no deviating force was introduced; that is, the deviating force tends to decrease building a drift angle, 7

It willalso be'noted that sincethe resultant force of A and the force C depend on the magnitude of the compression for any given set of drilling conditions, an effort to increase the drift angle by loading the pipe will increase the magnitude of the drift variation.

I do not wish to be understood to say that the right-hand rotation of a pipe with the pipe in compression will necessarily cause a left-hand deviation of the drill, since many of the factors listed above may overcome this left-hand deviation factor and actually deviate the drill to the right. However, I have found that, admitting that these other factors may in such cases have a right-hand deviating effect, the right-hand rotation superimposes on these factors a left-hand I deviating tendency which may reduce, cancel out, -or overcome these factors, depending upon the .situation' There is no way of predicting what 'the outcome will be. conditions and the rotation of the drill pipe is unpredictable.

The effect of any set of {A similar situation exists when the drill pipe iis in tension. The right-hand rotation of the pipe causes. it to ride down the left-hand wall of the bore (as indicated by the arrow H, see Fig. 12) to take a position determined by the tension, weight, ;rigi:lity, and speed of rotation. The fulcruining action licenses a force to be exerted to the right, as illustratedat E (see Fig. 11). The resultant of this force E and the fulcruming force B is a force F which introduces a right-hand deviation tendency and reduces the rate of drift angle decrease tendency, resulting from force B alone.

The effect of these forces is also unpredictable as is the case with the drill pipe in compression.-

ploying right-hand or clockwise rotation has taught that the only possible course of procedure is one of trial and error. Thus if I wish to drill so as to increase drift angle, I employ the drill pipe in compression with a relatively short drill collar, as described above and drill ahead. After drilling a short distance, for example, 30 feet, I survey the bore hole by any of the standard surveying techniques to determine the vertical deviation and the azimuthal direction of the drilled section.

If the result of the survey indicates that the rate of build-upof drift angle is insufiiciently great, then additional weight may be placed on the bit by reducing the tension in the drilling lines. This increases the compressive force on the drill pipe. The drill pipe may be removed from the hole and a shorter drill collar i! may be introduced to increase the leverage ratio. If the rate of build-up of drift angle is too great then the weight of the drill pipe on the drill is reduced to reduce the degree of compression.

In caseswhere the build-up of angle is largely I influenced by lithological considerations, the drill highly hazardous.

8 pipe may be placed in tension to introduce, as will be described below, mechanical downward components to overcome the tendency of the drill to travel up the structure.

After drilling a short distance I again survey the bore hole and if the drift angle is not correct, I may employ the expedients described above to establish the correct drift angle. But the effect of these factors on the direction of deviation is unpredictable.

Thus, if I rotate in one direction, I may build, maintain or reduce drift angle but the direction of the bore hole is unpredictable. Generally it may be said that with clockwise rotation the tendency of the bore hole when increasing drift angle or maintaining drift angle is to the left, and while decreasing drift angle to the right, as explained above, but whether it will go to the right or left or the rate of such drift depend on multitudinous factors and is unpredictable.

One is thus forced to the expedient of setting Whipstocks or by the laborious procedure of trial and error varying the factors, of which, as stated above, there are some twenty or more, to find the conditions whereby the bore may be drilled at the desired drift and direction. This means is so uncertain that whipstocks are reset where direction control or variation is required. The setting of whipstocks is costly even at shallow depth, For depths in excess of about 6000', the setting of whipstocks is not only time-consuming, but The danger of stickin of whipstocks which are of full hole gage is very great and if once stuck, the bore may have to be abandoned.

My drilling method employs a simple expedient for solving this dilemma. Whenever, either during drift increase, drift maintenance, or drift decrease, a survey of the bore hole shows that the bore hole is drifting in an undesired direction or at an undesired rate in the desired direction, I reverse the direction of rotation of the drill string. By so doing I counter the tendency of the drill to move in the direction in which it is going by imposing a force which tends to direct it in an opposite direction. The reversal of rotation imposes a deviation in a direction opposed to the original deviation, which may be equal to or lesser or greater than the original rate of deviation. In each case the actual deviation is a lesser or diminished deviation, and this term lesser, i. e., diminished, is used in an algebraic sense as including an equal, lesser, or opposite direction of deviation, whereby the deviation is reduced to zero, reduced in amount, but not in direction, or an opposite deviation is induced, i. e., a left deviation, if the deviation was originally right, is thus obtained.

To control the angle, 1. e., deviation and direction, I place the pipe in axial stress, either compression or tension, and rotate the pipe either counter-clockwise or clockwise, depending on the direction of the stress, i. e., whether it is in tension or compression. Whenever it is desired to increase the tendency of the drill to deviate to the left or oppose the tendency to move to the right, I place the drill pipe in compression and rotate the drill pipe to the right-hand or place the pipe in tension and rotate to the left, i. e., counterclockwise. Whenever it is desired to increase the tendency of the drill to deviate to the right or oppose its tendency to move to the left, I place the drillpipe in compression and rotate the drill pipe to the left or counter-clockwise or place the drill pipe in tension and rotate to the .posite side of the bore hole with a fulcruming force G, as shown in Figs. 8, 9, and the direction.

of the force D will be at 90 to the force D and its tendency will be a right tendency rather than a left tendency. t

In like manner, the reversal of rotation in the case illustrated in Fig. 12, with the drill pipe in tension on the left, with a fulcruming force in the direction of the arrow H, will move the drill pipe to the opposite side of the bore hole, as shown in Fig. 14, with a fulcruming force in the direction of the arrow H, resulting in a net compression F which is at 90 to the component F and resulting in a left deviating tendency rather than in a right deviating tendency.

From the above considerations and explanations" of the underlying principles of my new drilling technique, those skilled in the art will know how to apply my new drilling technique.

Generally stated, my invention includes a rotary drilling technique whereby a bore hole is advanced in a direction and at a desired angle to the vertical and astring of drill pipe is rotated in a bore hole having an angle inclined to the vertical in which the drill pipe is under an axial force, which may be either a compressive or a tensive force, and the lower end of the drill pipe e 10 tion and reversing the direction of said rotation and thereby altering'the azimuthal direction of said drill.

2. A method of drilling deviated bore holes which comprises advancing a drill string which includes a drill pipe and a drill, in an inclined bore hole, fulcruming said drill string in a said bore hole at a zone in said drill string above said drill, placing said drill string above and below said fulcrum zone in compression, rotatlng said drill string in one direction and advancing said drill in one azimuthal direction and reversing the direction of rotation of said drill string and advancing said drill in an altered azimuthal direction.

3. A method of drilling deviated bore holes which ccrnprl es advancing a drill string which includes a drill pipe and a drill, in an inclined bore hole, fulcruming said drill string in said bore hole at a zone in said drill string above said drill, placing said drill string above and below said fulcrumv zone in compression rotating said drill string in one direction and advancing said drill in one azimuthal direction, thereafter placing the drill string adjacent to the above said zone in tension, and reversing the direction of rotation of said drill string and advancing said drill in an altered azimuthal direction.

4. A method of drilling deviated bore holes which comprises advancing a drill string which includes a drill pipe and a drill in an inclined bore hole, fulcrurning said drill string in said bore hole at a zone in said drill string above said drill, placing the drill string adjacent to and above the said zone in axial tension and the drill string below said zone and adjacent said drill in axial compression, rotating said drill string in one direction and advancing said drill is fulcrum'ed against the wall of the bore hole at a point adjacent the drill,,rotatin'g the drillin one direction whilecircul'ating mud through the drill pipe and bore hole, advancing the bore hole by advancing the drill into the earth for a material distance, surveying thebore hole, and if the direction of deviation is in'an undesired direction, reversing the direction of rotation, and, if desired, also changing the magnitude and direction of theaxial'force, and drilling ahead, surveying the bore hole in order to determine the direction of the bore hole and by control of the direction and degree of the axial force and the direction of rotation when added to the conventional technique of rotary drilling, I may obtain and control the course of the bore hole.

I claim: 1 r

1. A method of drilling deviated bore holes Which comprises advancing a drill string, which includes a drill pipe and a drill, in an inclined bore hole, fulcruming said drill string in said bore hole at a zone in said drill string above said drill, placing an axial stress in said drill string adjacent to and above said fulcrum zone, and placing said drill string below said zone and adjacent said drill in compression, rotating said drill string and advancing said drill in one azimuthal direc- 'in an azimuthal direction, thereafter placing the drill string adjacent to and above said zone in axial compression and reversing the direction of rotation of said drillstring and advancing said drill in an altered azimuthal direction.

DANIEL s. JOHNSTON.

References Cited in the file of this patent UNITED STATES PATENTS OTHER REFERENCES I Rotary Drilling HandbookJ. E. Brantly4th edition, 1948, pp. 242-246.