THE SHAPES OF BEACH PEBBLES. 

By CHEsTER K. WENTWORT:H. 

PURPOSE OF THE STUDY. 

There is much confusion in geologic literature as to the shapes of fluvial and beach 

pebbles and the differences between them, if 

differences exist. Though the contrary has 

been asserted, most geologists who have 

written on the subject appear to hold the view 

that beach pebbles are generally flatter than 

river pebbles, having discoid, lozenge-shaped, 

ellipsoid, or oval forms. 1 It is asserted by 

some that these forms are produced by pushing of the rock fragments to and fro by the 

waves. 2 Others have considered that the 

shapes of the original fragments and the in-' 

·herent structure of the rock are dominant in 

determining the shapes of beach pebbles,3 and 

with this view the writer is in accord. That 

beach pebbles, even those composed of massive 

igneous roc~s, ·are commonly of ·a flattened 

oval form seems certain, as has been stated 

elsewhere/ but this fact is probably to be 

attributed to the development of such forms 

from original flat fragments or from rocks of 

schistose structure or to the segregation of 

such forms under the peculiar action of the 

waves, rather than to their production by a 

specialized wave abrasion. 

Though many opinions on the subject have 

been expressed, no one, so far as known to the 

writer, has made any quantitative test of the 

deyelopment of such shapes on a beach. -It 

was the writer's good fortune during the summer of 1921 to visit two localitjes on the Atlantic coast of New England where pebbles are 

1 Sue$, E., Der Boden der Stadt Wien, pp. 64, 65, 1882 (quoted from 

Grabau, A. W., Principles of stratigraphy, p. 595; 1913). 

Hoernes, R., Gerolle und Geschiebe: K.·k. geol. Reichsanstalt Verh. 

No.12, pp. 42etseq., 1911 (quoted from Grabau, A. W., op. cit.,'p. S95). 

Cole, G. A. J., Roc~s and their origins, p. 71, Cambridge Univ. Press, 

1912. 

Trowbridge, A. C., Classification of common sediments: Jour. Geology, 

vol. 22, p. 435, 1914. 

Stephenson, L. W., The Coastal Plain of N or.th Carolina: North Carolina Geol. and Econ. Survey, vol. 3, pp. 274-275, 1912. 

Geikie, A., Textbook of geology, vol. 1, p. 569, 1903. 

2 Suess, E., op. cit. Hoernes, R., op. cit. Cole, G. A. J., op. cit. 

a Grabau, A. W., Principles of stratigraphy, pp. 715-716, 1913. 

Dunn, E. J., Pebbles, p. 7, Sydney, G. Robertson & Co., 1911. 

• Wentworth, C. K., Quantitative studies of the shapes ofpebbles(unpublished thesis, Iowa St ate Univ.). 

being produced by wa.ve abrasion of igneous 

rock in place. At these localities he measured 

more than 300 pebbles with the hope of obtaining evidence that would be conclusive, at least 

so far as these localities are concerned. The 

results obtained are presented on the following 

pages. It is the writer's hope that geologists 

acquainted with localities where similar m.easurements might be made or where conditions 

of wave abrasion are especially effective or 

peculiar will refer him to such places. 

BEACH CONDITIONS. 

The ·first locality visited was at the south 

extremity of Nantasket Beach, at the point 

shown on the topographic map of the Boston 

Bay quadrangle under the · capital A of "Atlantic." Here, on the east side of the point, is 

a beach about 200 feet in length which is com--

posed of material ~anging from sand to blocks 

and boulders a foot or more in diameter. At 

each end the beach is terminated by low promontories of the local light-green to gray igneous 

rock, which is included in the Mattapan volcanic complex as m~pped by Emerson. 5 The 

greater part of the' gravel of the beach is derived from the adjacent outcrops, which show, 

however, great variations in type within short 

distances, includmg some pyroclastic and sedimentary derivatives of the igneous rock. In 

addition to the local rock there is a considerable admixture of pebbles of granite, porphyry, 

breccia, felsite, and many other kinds of igneous 

rock from other parts of eastern Massachusetts 

which have been transported by glacial ice, 

by streams, and by shore currents. The 

general character of the beach gravel is shown 

in Plate XXVI. The conditions of abrasion 

at this point are those of a pocket beach. The 

tides rise and fall, shifting the zone of abrasion 

by several feet in ;height and about 75 to 100 

feet horizontally. Storm waves break high 

over the north-south beach ridge and both adjacent rock promontories. Gravel is not trailsported to any extent .from the beach, either 

5 Emerson, B. K., U.S. Geol. Survey Bull. 597, p. 200,1917. 

75 
76 SHORTER CONTRJBUTIONS TO GENERAL GEOLOGY, 1922. 

alongshore or out to deep water, and remains 

indefinitely in the zone of effective abrasion. 

The coast at this place trends northwest, and 

the beach is exposed to the full force of waves 

from the northeast, but not so much to those 

from south of east. 

The site of the second series of measurements 

was the rocky shore at· the en trance to New 

Haven Harbor, near Fort Hale, Conn. Here, 

for a distance of several hundred feet, is~ wavecut cliff and abrasion platform cut in the end of 

a north-south ridge of Triassic trap that 

reaches the shore. Along the cliff and strewn 

in both directions on the beach is considerable 

gravel composed of trap from the local exposure. This gravel extends only a few hundred feet in each direction, giving way to sand 

and finer materials. Mingled with the trap 

pebbles of the gravel are a few pebbles and 

larger pieces from the glacial till that overlies 

the bedrock at the top of the cliff and is exposed 

lower down along the adjacent parts of the 

shore. These are readiiy identified by inspection. The general character of the shore and 

gravel at this point is shown in Plate XXVII. 

On this beach wave actiqn is far less effective 

as an agent of abrasion than at N antasket. 

Not only are the waves in this part of Long 

Island Sound less violent than those of the 

Atlantic Ocean at N antasket, but the pebbles 

here are not confined in a pocket beach. 

METHODS OF .MEASUREMENT. 

Three diameters mutually at right angles 

were ~easured for each pebble with a steel 

tape. The radius of curvature of the sharpest 

edge of each was measured with the convexity 

gage described elsewhere.6 All measurements 

were in millimeters. The data ,were recorded 

~ several grou~s as follows: 

Nantasket: Pebbles. 

A: Random selection, all materials.... .. ........ 61 

B. Miscellaneous rock types : 

Quartzite .................... . . . .... 20 

Red porphyry ............ · __ .. .. .. . .. 20 

Black porphyry. . .. . .. .. .. .. .. .. .. .. 10 

LABORATORY DETERMINATIONS. 

The relative resistance of the local rocks at 

the two beaches was determined by an abrasion test in. the tumbling mill. Four pebbles 

of each rock were ground at one end on a lap 

to a sharp 90° edge. They were then subjected to abrasion in the mill for a total distance of about 80 miles. Measurements of the 

convexity of the prepared edge were made at 

intervals, and the resulting data were used in 

comparing the durability of the two types of 

rock. 

COMPUTATIONS. 

Computations were made as follows for each 

pebble: · 

Mean diameter/ computed approximately by 

the formula D=vD'D"D"' where D', D", 

and D"' are the length, breadth, and thickness as measured in the field. 

. r t 2r 1 h . . th . Roundness ratiO, R = D , w ere 1'1 Is e 

radius of curvature in millimeters of the 

sharpest edge and R is the mean radius of the 

pebble. 

D' +D" Flat!less ratio, 2D"' or the av,erage of the 

length and breadth divided by the thickness. 

All these values were computed to two significant figures by the use of graphic charts. 

Further description of these ratios and methods 

of computation has been given elsewhere·. 

8 

RESULTS. 

·The results of the measurements are plotted 

on the graphs of figures· 5 to 10. The variations of the roundness ratios are so great that 

for practical considerations it seems better to 

average these ratios by subgroups. These 

averages were made as described ·below, and 

the subgroups are indicated by the large dots 

in figure 5 and hy all the dots in figures 6 to 10, 

where the number of pebbles represented by 

each dot is shown by the small accompanying 

figures. In the subgroups marked X under 

1 The writer's use of the term "mean diameter" is open to the objec- Granite ................... .. ........ 10 

C. Local volcanic rock ....... ~ .. . ... · ......... . 

201 

Fort Hale: 

tion that in the use of the approximate formula given above the true 

60 value of the arithmetic mean of all diameters (the ideal concept of the 

80 term) is not derived. Tp.e writer does not consider the objection to be 

serious, for it applies in varying degree to all physical constants that 

are based on empirical data. It is customary to speak of the values 

derived for these constants as the theoretical constants themselves, and 

the common practice seems not to be unduly confusii:J.g. . Therefore, in 

the following pages where the term ''mean diameter'' is use«, the actual 

numerical values are understood to be approximations to the true arithmetical mean of all diameters. 

· D. Local trap .......................... ~ ....... 101 

6 Wentworth, C. K., Quantitative studies of the shapes of pebbles 

(unpublished .thesis, Iowa State Univ.), p. 61, 1921. See also Wentworth, C. K., The shapes of pebbles: U. S. Geol. Survey Bull. 730, pp. 

91-114, 1922. 

s Wentworth, C. K., The shapes of pebbles: U.S. Geol. Survey Bull. 

730, pp. 91-114, 1922. 
U. S . GEOLOGICAL SURVEY PROFESSIONAL PAPER 131 PLATE XXVI 

A. GRAVEL IN POCKET BEACH SOUTH OF NANTASKET, MASS. 

B. GRAVEL AND JOINTED ROCK OF PROMONTORY SOUTH OF NANTASKET, MASS. 

C. ROLLER-SHAPED COBBLES IN TWO STAGES OF FORMATION, POCKET BEACH SOUTH OF 

NANTASKET, MASS. 
U . S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 13-1 PLATE XXVII 

A. BEACH AT FORT HALE, CONN. 

The cliff in the middle distance is the source of pebble material. 

B. NEAR VIEW OF CLIFF OF JOINTED TRAP AND LANDWARD EDGE OF ABRASION PLATFORM 

AT FORT HALE, CONN. 
THE SHAPES OF BEACH PEBBLESi 

6 

5 

4 

D'+D" 

·2i)i' 

3 

2 

0 .2 l'j 

R 

.3 .5 

FiGURE 5.-Graph showing flatness ratios ~· j/?," (ordinate) and roundness ratios .!:!. (abscissa) of 61 pebbles of group A at Nantasket, Mass. R I, 

Large dots show average positions for subgroups of pebbles. (See 

fig. 6.) 

"Method of computing averages" in the fol-

. · . D' + D" 

loWing table the values of. 2D"' for all the 

pebbles of .the subgroup were averaged arithmetically for the ordinate, _and the mean of 

the limits of~ for the subgroup was used for 

abscissa. In the subgroups marked Y the 

D' +D'' . values of 2 D"' were averaged similarly for 

the ordinate and the values of ~ for all the 

pebbles of the subgroup were averaged arithmetically for the abscissa. Method X was 

used for the subgroups in which values of ~ 

were fairly uniformly and thickly distributed; 

method Y was used for subgroups in which a 

few erratic points needed to be averaged. 

The subgroup limits were chosen to avoid as 

far as possible .very small subgroups or very 

great differences in the number of pebbles in 

adjacent subgroups. No data were rejected, 

and every measurement taken in the field is 

represented ~ the averages here presented. 

o~~~~~-~.~~~~~~~~.2~~~~~~.3~~~~~~4 

li 

R 

FIGURE 6.-Graph showing flatness and roundness of 61 ·pebbles of group A. The flatness ratio D' +DD" is plotted as the ordinate and . 2 "' ' 

the roundness ratio~ as the .abscissa. For simplicity, the pebbles are ar;anged in subgroups, and each large dot shows the mean position of 

the nmnber of pebbles indicated by the small figures. It is apparent that as the roundness increases the flatness decreases. 
78 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1922. 

o~~~~~_L~~~~~_L.2~~~~~~3~~-r~~~.4~ 

r; ..... 

R" 

FIGURE 7.-Graph showing flatness and roundness ratios of pebbles of ~o~p B. ' :Fo~ ~~Jm.lation, figUre~, 

14 

o~~~~~~-~~~~~~~~.2~~~~~~-3~ ~~~~~-~~ 

. l'j 

"R 

FIGURE 8.-Graph showing flatness and roundness ratios of pebbles of group C. For explanation, see figure 6. 

4 

~ 

3 

4 

41 D'+D" 20'" 2 

0 .2 

_!i 

R 

•:::1 

-~~ 

.3 

I 

ra 10 -~ 

FIGURE 9.-Graph showing flatness and roundness ratios of pebbles of groups A, B, ~d C combined. For explanation, seefigure6, 

... ,_. ., 

3 I 

I 

I 

• 

2 14.3 

0'+0" 

---zow 

r-+- -+- -· 

0 

Ia 

~4 

f.- ~ 

14 

l'j 

R' 

~t: 

.2 .3 

FIGURE 10.-Graph showing flatness and roundness ratios of pe~bles of group D. For explanation, see figure 6 • 
THE SHAPES OF BEACH PEBBLES. 79 

Method of computing averages for; subgroups. 

Method 

Sub- Tt --ofcomGraph. Group. puting. group. Ii aver-

' ages. 

--

{ 

1 0.01-0.05 

} X 

Figures 5 and 6, five 2 . 06- . 10 

large dots at left ... A 3 .11- .15 

4 .16- . 20 

5 . 21- . 25 

Figures 5 and 6, 

large dot at right .. A · 6 .26 and y 

Figure 7, all dolE • ...I over 

u . 06- .15 

} B .16- . 25 X . 26- . 35 . 36-.45 

{11 . 01- . 15 

} Figure 8, all dots .... c 12 .16- . 25 X 13 . 26- . 35 

14 . 36- . 45 

15 . 01- . 05 

16 . 06- . 10 

17 . 11- .15 

18- .16- . 20 . Figure 9, all dots .... A,B,C 19 . 21- . 25 X 

20 . 26- . 30 

21 . 31- . 35 

22 . 36- . 40 

23 . 41- ·. 45 

Figure 10, four dots r4 . 02- . 05 

} X 

25 . 06- . 09 at left ............. D 26 .10- . 14 

27 .15- .19 

Figure 10, <lot at 

right. ............ D 28 . 20- . 45 y 

Roundness and flatness ratios of pebbles. 

Group A, figures 5 and 6. 

Subgroup. r1 D'+D" Abscissa and ordiflate. R 2D"' 

0.01 2.7 . 05 2.2 . 03 3. 6 

.03 3.0 

.03 4. 1 Method X, abscissa 0.03; .05 3.8 1 .... ······ .05 4. 6 ordinate (32.3+9) 3.59. 

.05 3.4 

.03 4.9 

32.3 

1

.07 3.9 . 07 2.7 . 09 2.9 . 08 6.5 . 08 1.8 

.10 6.3 . 06 5.2 . 06 2.5 Method X, abscissa 0. 08; 2 •.... ·-· .. .10 3.0 . 09 2. 1 ordinate (4~.0+14) 3.50. 

. 07 5.5 . 09 2.0 . 09 2.0 . 06 2.6 I 

J 

49.0 

Roundness and flatness ratios of pebbles-Continued. 

Group A, figures 5 and 6-Continued. 

Subgroup. 

3 .......... 

4 •......... 

5 ... - ···--· 

6.- .... ~ ... -

r1 

Ii 

0. 12 ' .12 

.11 

.12 

.11 

.12 

.12 

.12 

.11 

.15 

.12 

.13 

.11 

.17 

.19 

.18 

.19 

.18 

.19 

. 20 

.19 

.17 

. 22 

. 22 

. 21 

. 24 

. 25 

. 25 

. 24 

. 28 

. 26 

. 32 

. 40 

.40 

. 50 

. 30 

. 36 

. 38 --

3.20 

0.13 

. 08 

.09 

.14 

. 09 

.13 

7......... . 09 

. 13 

.11 

.14 

.15 

D'+D" Abscissa and ordinate. 

2D"' 

3.1 

1.7 

3.4 

5.0 

1.5 

4.0 

3.5 

2.2 Method X, abscissa 0.13; 

2. 5 ordinate (35.5+13) 2.73. 

2.2 

2.0 

2. 9 

1.5 

35. 5 

2. 9 

5. 5 

3.0 

5.0 

2.0 

2.5 Method X, abscissa 0.18, 

1.4 ordinate (25.2+9) 2.80 

1.2 

1.7 

25.2 

2.5 

2. 8 

2.0 

2.1 

1. 6 Method X, abscissa 0.23 

2.4 ordinate (1.4.9+7) 2.13 • 1.5 

14.9 

2. 5 

2.5 

1.9 

1.3 

2.2 Method Y, abscissa (3.20 

1.2 +9) 0.355; ordinate 

1.9 (16.7+9) 1.86 . 1.3 

1.9 ---- 16. 7 

Group B, figure 7. 

1.3 

1.9 

1.7 

1.4 

1.8 

1.5 

3. 2 Method X, abscissa 0.105; 

2. 2 ordinate (19.7+11) 1.79 • 1.8 

1.6 

1.3 

. 19.7 

PROPERTY OF U. S. BUREAU OF MINES 

-
t ' 

80 SHORTER CONTRJBUTIONS TO GENERAL GEOLOGY, 192~. 

Roundness and flatness ratios of pebbles-Continued. 

Group B, figure 7--Continued. 

Subgroup. 

8 : ........ 

9 .... ····· 

10 ......... 

r1 

'R 

0. 19 

. 25 

. 23 

. 21 

. 22 

. 23 

. 24 

.18 

.19 

. 25 

.18 

.16 

. 20 

.19 

.16 

.19 

. 25 

. 23 

. 22 

.16 

. 21 

. 22 

. 32 

. 26 

. 34 

. 30 

. 26 

. 26 

. 26 

. 34 

. 28 

. 32 

. 30 

. 26 

. 26 

. 32 

. 28 

. 26 

. 30 

. 32 

. 32 

. 28 

. 45 

. 40 

. 38 

. 42 

. 40 

. 45 

. 45 

. 03 

. 02 

1

0.05 

11.~·-····· :zg 

. 02 

. 04 

D'+D" Abscissa and ordinate. 2D"' 

.. 1.7 

2.0 \ 

2.1 

2.6 

2.2 

1.2 

1.4 

1. 6 

1. 9 

1.2 

1.5 

1.6 Method A, abscissa 0.205; 1.6 

1.2 ordinate (37 .4-+-22) 1. 70. 

1.2 

1.8 

1.4 

2.2 

1.2 

1. 9 

2. 0 

1.9 

37.4 

2.0 

1.4 

1.5 

1.5 

,__ 6 

1.8 

1. 8 

1.8 

1.7 

1.8 

1. 6 Method X, abscissa 0.305; 

2.0 ordinate (32.5-i-20) 1.63 . 1.9 

1.8 

1.4 

1. 7 

1.1 

1.1 

1.5 

1.5 

32.5 

1. 3 

1.5 

1.4 Method X, abscissa 0.405; 1.3 

1.2 ordinate (9.9-+-7) 1.41. 

1. 6 

1.6 

9. 9 

Group C, figure 8. 

2.5 

2.0 

2.3 

3.2 

3.3 

3.8 

3. 4 . 

Roundness andfla.tness ratios of pebbles-Continued. 

Group C, figure 8-Continued. 

Subgroup. _rl D'+D" Abscissa and ordinate. 'R 2D'" 

0.05 3.2 . 13 2.2 . 08 1.8 

.13 2.2 

.14 3. 1 . 07 4. 7 

.10 1. 2 . 12 2. 2 

.10 2.4 . 15 2. 1 

.10 1.5 

.15 1. 7 . 08 3.9 

.12 2. 6 . 08 2.3 

11.-Contd. .14 3. 1 Method X, abscdssa 0. 08; 

.12 2.2 ordinate (102.7-r-36) 2.85. 

.14 7. 1 

.15 3. 3 

.14 3.0 . 10 2. 7 . .14 3. 7 

. 07 3.4 . 09 2.4 . 08 2.3 

. 09 3. 9 

.11 3; 7 

. 08 2.0 

.13 2.2 

102. 7 

.16 2.2 

.16 1.2 

. 25 . 4.3 . 22 2.5 

.16 1. 7 . 20 4.0 

.16 1.8 

.18 2.8 . 20 1.8 . 22 3. 5 

.17 1.9 . 21 4.5 . 24 2.5 

.18 5.3 .·18 2. 1 . 23 1.8 

.17 1. 7 . 22 1.7 Method X, abscissa 0.205; 

12 ........... . 22 1.7 ordinate (90.5-+-34) 2.66. 

. 16 1.9 . 18 2.3 . 23 1.3 

.17 3. 1 

.19 2.0 . 16 2. 7 . 19 5. 5 ·' . 25 3.2 

.18 2.5 . 20 2.8 

.18 3.2 . 25 2.0 

.16 2.3 

.17 3.5 

.17 3.2 

90.5 

82 SHORTER CONTRJBlfTIONS TO GENERAL GEOLOGY, 1922. 

Roundness and flatness ratios of pebbles-Continued. 

Group D, figlire 10-Continued. 

Subgroup. TI D'+D" Abscissa and ordinate. R 2D'" 

0. 15 1.4 

.17 2.9 

.19 2.2 . 19 1.2 

.16 1.8 ~ 16 1. 7 

.15 3. 2 M~thod X, abscissa 0.17; 27 ........... .15 1. 2 . 18 3. 1 ordinate (23.7~12) 1.97. 

. 17 1. 1 

.16 2.5 

.16 1.4 

23. 7 

. 23 1. 7 : 30 2. 7 l . 20 2.2 . 45 1. 8 Method Y, abscissa 2.17~ . 34 2.0 28 ..... . ..... . 20 1. 6 8) 0.27l; ordinate 15.4~ 

. 24 1.9 8) 1.92. 

. 21 1.5 

2. 17 15.4 

It is evident that in each one of the five 

groups of pebbles 'the flatness and roundness 

of edges stand in inverse relation-that is, the 

more rounded the edges the less fiat the pebbles. 

It is valid to assume that the pebbles with 

rounder edges have been longer affected by 

wave action than those with sharper edges. 

The former, which have been on the beach 

longer, are less fiat than the latter, which have 

been a shorter time on the beach and are nearer 

to their original shape. It ·is · conclusively 

proved that at these two beaches the pebbles 

become less fiat as abrasion proceeds and that 

any predominance of fiat, discoid forms is to be 

attributed to the flatness of the original fragments resulting from the. current processes of 

disruption. Likewise the rather common rollershaped cobbles and pebbles are the result of the 

rounding and smoothing of original elongate 

fragments, as suggested by the series shown in 

Plate XXVI, 0, and evidence that these shapes 

are the result of any special sort of abrasion or 

:rp.otion was not seen by the writer. 

The data are insufficient to warrant drawing 

ideal curves correlating the diminution of 

flatness with the increase of roundness, but the 

definite trend described above is established 

for the two localities visited. In figures 11 and 

12 are shown diagrammatically the average 

shapes of the extreme pebble subgroups at the 

two localities with regard to both the flatness 

and the roundness. In each of ·these figures 

the flatness and roundness shown in the upper 

and lower diagrams are those of the subgroups 

f cl 

I 

I 

I 

b 

!-<--------~-----a-----------:-_, 

I 

I 

FIGURE H.-Diagrams showing average flatness and roundness of most 

angular and most rounded subgroups of pebbles of group C at Nantasket, Mass. Top diagram represents these values for the average of 

the 36 pebbles of the left-hand subgroup of figure 8. Bottom diagram 

represents these values for the two pebbles of the right-hand subgroup 

of figure 8. 

a D'+D" . b= 2D'" 

Sizes are arbitrary, but dimensions show true flatness and roundn.ess 

ratios as indicated in the equation above. 

represented by the dots at the extreme left and 

extreme right of figures 8 and 10, respectively~ 

It will be noted that the N antasket material 

yields flatter original fragme~ts than that at 

Fort. Hale;· This is a result of factors related 

to the structure of the rocks and the processes 

I c I 

I 

I 

b 

I . ------r--------a -------- 1 • 

l 

I 

b 

I 

--~--:------ a--- ,..-- 1 

I 

FIGURE 12.-Diagrams showing average flatness and roundness of m(JSt 

angular and most rounded supgroups of pebbies of group D at Fort 

Hale, Conn. Top diagram represents these values for the average of the 

43 pebbles of the left-hand subgroup of figure 10. Bottom diagram rep- · 

resents these values for the 8 pebbles of the right-hand subgroup of 

figure 10. Notation same as in figure 11. 

and conditions of disruption. The writer has 

not yet made a study of this important aspect 

qf the problem. 

Comparisons of the average roundness of the 

several groups follow. All the pebbles of 
THE SHAPES 0:1!.., BEACH PEBBLES. 83 

group B ·and some of those of group A are at of abrasion that those at Fort Hale have rean unknown distance from their source, and ceived. The ratio is a result of two factorslittle can be said about them except that they the violence of wave action and the effectiveare rounder as a whole than those of groups ness of retention of the same pebbles in the 

C and D shown in figures 8 and 10. Between zone of wave action. 

those · of groups C and D an interesting com- Although the writer has ventured to exparison can be made. The pebbles of group C. press the ratios in numerical form, he does not 

are much rounder and indicate more travel or wish to convey any false impression as to their 

abrasion than those of group D. On compar- accuracy. He is aware, probably more clearly 

ing the average roundness of the two groups than the read({r, of, the extreme complexity of 

on the basis of his previous studies of the rela- the problem, which involves a large number of 

tion between abrasion and the roundness unknown factors. The figures given are beratio 9 the writer finds that the pebbles of lieved to be within 25 per cent of the truth, 

group C (N antasket) indicate greater wear by and it is hoped they may provoke more accuabrasion than · those of group D (Fort Hale) in rate and extensive investigation. 

the approximate ratio of 3.4 to 1. It was 

found by abrasion tests, however, that the 

N antasket rock requires much more abrasion 

to produce a given degree of rounding th~n the 

Fort Hale rock. The ratio is approximately 5. 

On multiplying this ratio by the ratio given 

above, we find that the ave:rage pebble at Nantasket represents about 17 times the amount · 

9 Wentworth, C. K., The shapes of pebbles: U. S. Geol. Survey Bull. 

730, pp. 91-114, 1922. 

ACKNOWLEDGMENTS. 

In conclusion, acknowledgment is due to Dr. 

J. B. Woodworth, of Harvard University, for 

his kindness in guiding the writer to the Nantasket Beach locality and for his advice and 

comment dliring two days of field work on 

the Massachusetts coast; and to Mr. J. S .. 

Brown, of the United States Geological Survey, 

who suggested the Fort Hale locality. 

I