This arti­cle is from the British Print­er mag­a­zine of 1961.  The research was con­duct­ed for PATRA: The Print­ing and Allied Trades’ Research Asso­ci­a­tion.

The pro­por­tions of char­ac­ters mak­ing up a fount of type should be such that by the time one char­ac­ter is exhaust­ed as lit­tle as pos­si­ble of the oth­ers remains in the case. A fur­ther require­ment is that any char­ac­ter in the fount has the same chance of being exhaust­ed first and still leave a near­ly emp­ty case. If this is achieved then the print­er will effect sav­ings in the amount of type stocked in the cas­es and also in the expen­sive reorder­ing of indi­vid­ual char­ac­ters to make up his defi­cien­cies. This arti­cle presents the results of the first sys­tem­at­ic study of type fount pro­por­tions and a new scheme is pro­posed which it is believed will ful­fil the above require­ments, as far as it is prac­ti­ca­ble.

Such a study may seem a lit­tle belat­ed, but hand-set work still remains an impor­tant part of print­ing. It is esti­mat­ed, for exam­ple, that the fount schemes pro­posed in this arti­cle will effect at least a 10 per cent sav­ing of dead met­al in the case which to the indus­try rep­re­sents many thou­sands of tons of type met­al. Fur­ther­more, as the kind of work which is now hand-set has become some­what sta­bilised the fount pro­por­tions pro­posed should remain effec­tive for many years to come.

The ori­gin of type fount pro­por­tions, even in recent times, is rather obscure and this seems large­ly because the respon­si­bil­i­ty for sup­ply is con­fined to rel­a­tive­ly few peo­ple. It is cer­tain, how­ev­er, that as ear­ly as the begin­ning of the six­teenth cen­tu­ry some account was being tak­en of the vari­a­tion in usage of the var­i­ous char­ac­ters since the most fre­quent­ly used char­ac­ters were placed at the front of the case. A more pos­i­tive exam­ple is giv­en by Mox­on’s low­er­case, which appeared in 1683, and which has remained vir­tu­al­ly unchanged to this day. The lay of this case is such that the vol­ume of the type com­part­ments is rough­ly pro­por­tion­al to the fre­quen­cy of usage.

Some of the books on print­ing which were pro­duced in the nine­teenth cen­tu­ry con­tain tables of bills of founts, but unfor­tu­nate­ly they rarely men­tion how these pro­por­tions were deter­mined. It is true that the only sat­is­fac­to­ry way in which to arrive at suit­able pro­por­tions is to count the fre­quen­cy of occur­rence of char­ac­ters in a piece of work that has been hand-set. Pre­sum­ably most of them were deter­mined in this way but with­out a knowl­edge of the nature of the work cho­sen, the valid­i­ty of the results can­not be judged. One of the few records that do exist of a count illus­trates this point. The count, which is attrib­uted to the Caslon Foundry, was made by enu­mer­at­ing the num­ber of let­ters used in set­ting a lengthy debate in the House of Com­mons where it was assumed that ​‘the best and most com­pre­hen­sive Eng­lish would be spo­ken’. The valid­i­ty of this count can be ques­tioned on two points, first­ly that the fre­quen­cies of the spo­ken word vary from the writ­ten word and, sec­ond­ly, the sam­ple was not typ­i­cal of the Eng­lish being set at that time.

It is record­ed that ​‘the pro­por­tions of almost every type­founder failed lam­en­ta­bly to give sat­is­fac­tion’. Such fail­ures seem part­ly due to the use of biased sam­ples on which to base the pro­por­tions and part­ly to the fact that, at a time when all the work was hand-set, small vari­a­tions in the style of the work would have a large effect on the char­ac­ters required. The work of Dick­ens, for exam­ple, would quick­ly emp­ty the case of vow­els, where­as Macaulay’s style had a sim­i­lar effect on con­so­nants. No fount pro­por­tion scheme could rea­son­ably be expect­ed to cope with that type of vari­a­tion.

At the present time the copy that is hand-set from roman and ital­ic types may be broad­ly classed as job­bing work, and it gives rise to rather dif­fer­ent prob­lems than those fac­ing the old type­founder. This change in the char­ac­ter of the work, which was brought about by the wide­spread use of type­set­ting machines, has led type­founders to mod­i­fy the old pro­por­tions by ​‘expe­ri­ence’ in order ​‘to meet the needs of the cus­tomer’. It might be expect­ed that since most type­founders are cater­ing for the same type of work their expe­ri­ence would have led them to the same pro­por­tions. In fact, for some char­ac­ters there are wide vari­a­tions between the var­i­ous pro­por­tion schemes in use today.

It should be not­ed at this stage that the present work was not under­tak­en as an aca­d­e­m­ic exer­cise but the need for it was sug­gest­ed by a type­founder. Sub­se­quent enquiries amongst print­ers con­firmed this and their main com­plaint was that cur­rent­ly used pro­por­tions gave rise to short­ages of the most com­mon­ly used char­ac­ters (in par­tic­u­lar, e, r, s and t) while the least used char­ac­ters built-up in the case. The rea­son for this hap­pen­ing will become appar­ent lat­er.

Before the main results are dis­cussed it is essen­tial to realise the main types of vari­a­tion that will affect the type pro­por­tions required to set a piece of job­bing work. There are three of these:

1. Work-type Vari­a­tion
   Hol­i­day brochures pro­vide a good exam­ple of work-type vari­a­tion since in these a con­sis­tent part of the hand-set work are the names of hotels. Con­se­quent­ly, the fre­quent occur­rence of the word ​‘HOTEL’ means that a high­er pro­por­tion of the char­ac­ters H, O, T, E, and L will be required than is nor­mal­ly found. This type of vari­a­tion is inher­ent in the work.
2. Job Vari­a­tion
   A parish mag­a­zine, for exam­ple, nor­mal­ly con­tains a large num­ber of dis­played adver­tise­ments for the par­tic­u­lar town it serves. The fre­quent occur­rence of the town’s name will again upset the nor­mal pro­por­tions of char­ac­ters. This vari­a­tion is inher­ent in the job, rather than the type of work, as the char­ac­ters most seri­ous­ly affect­ed will vary from town to town, ie from job to job. Fur­ther­more, with this type of vari­a­tion if a num­ber of such jobs are under­tak­en for dif­fer­ent towns then the like­li­hood of upset­ting the nor­mal pro­por­tions is reduced. On the oth­er hand, with work-type vari­a­tion the pro­por­tions become more seri­ous­ly affect­ed as more jobs of the same type are under­tak­en.
3. Sam­pling Vari­a­tion
   The two types of vari­a­tion denned above will upset any fount pro­por­tion scheme and this fact must be recog­nised by print­ers and catered for by sep­a­rate­ly order­ing more of the char­ac­ters affect­ed. There is, how­ev­er, a third type of vari­a­tion which is always present and must be tak­en into account to the fount pro­por­tion scheme itself, This is called ​‘sam­pling’ vari­a­tion and because of its impor­tance it is dis­cussed in detail.

The foun­da­tion of any type fount scheme is that char­ac­ters occur in fixed pro­por­tions, but the essen­tial point is that the pro­por­tions can only be con­sid­ered as fixed for a large num­ber of char­ac­ters.

To illus­trate this state­ment, sup­pose that a piece of set­ting con­sists of 100 lines and each line has 50 low­er­case let­ters. If there is no work-type or job vari­a­tion present then about 200 d’s would be used in the set­ting. This is 4 per cent of the low­er­case alpha­bet which is the nor­mal pro­por­tion for d, that is, what is expect­ed to occur in a large sam­ple of char­ac­ters such as the 5000 used in this sup­posed set­ting. If each of the 100 lines is now tak­en sep­a­rate­ly as small sam­ples of 50 char­ac­ters then there will not be 4 per cent, or two d’s in each line. There will be a num­ber of lines that do not con­tain any d’s and it is quite pos­si­ble that one line will con­tain as many as sev­en or eight. This illus­trates sam­pling vari­a­tion and shows that if only small amounts are set then a wide vari­a­tion in usage is expect­ed.

Refer­ring still to the above exam­ple, if the occur­rence of a d‑and the same can be argued for any char­ac­ter — is a pure­ly ran­dom process then the prob­a­bil­i­ty of obtain­ing 0, 1, 2 etc of them in any of the lines is giv­en by the 1st, 2nd, 3rd … terms of the bino­mi­al expan­sion (0.04+0.96)⁵⁰. The results of this cal­cu­la­tion are shown graph­i­cal­ly by the full line in Fig­ure 1, where it can be seen that with 100 lines some 13 would be expect­ed to have no d’s, 27 have one d, 27 have two d’s and so on. The dot­ted line in Fig­ure 1 shows the prob­a­bil­i­ties for sam­ples of 25 char­ac­ters, and the curve becomes more dis­tort­ed and shows that the chance of get­ting a wider vari­a­tion from the expect­ed one d increas­es. Con­verse­ly, as the size of the sam­ple is increased, so the curve becomes more sym­met­ri­cal with its peak over the true pro­por­tion and the spread of the curve (the vari­a­tion) get­ting small­er. A fur­ther fact, which is not Illus­trat­ed here, is that a char­ac­ter such as e, which has a high­er pro­por­tion­al occur­rence (13.4 per cent) will have a tow­er per­cent­age vari­a­tion for the same sam­ple size. The val­ue of these cal­cu­la­tions to this study is that for a fount of a giv­en size the num­ber that is like­ly to occur for each be found.

The cal­cu­la­tions are based, how­ev­er, on the assump­tion that the occur­rence of a char­ac­ter is a ran­dom process that is, its occur­rence is inde­pen­dent of the char­ac­ters pre­vi­ous­ly set. This is clear­ly not the case when it is known that for 58 per cent of the times that d occurs r does so after n or e and that it does not nor­mal­ly fol­low let­ters such as c, h and j. In order to deter­mine how this depen­den­cy would affect the cal­cu­la­tions, a num­ber of tests were car­ried out and it was found that for the present pur­pose of type fount pro­por­tions, the effect would be neg­li­gi­ble. This means that the sta­tis­ti­cal mod­el out­lined above can be used to pre­dict what vari­a­tion is expect­ed to occur under var­i­ous cir­cum­stances and so place type fount pro­por­tions on a more pre­cise basis than has hith­er­to been pos­si­ble.

As men­tioned ear­li­er, the only way is which it is pos­si­ble to deter­mine the pro­por­tion of char­ac­ters is by count­ing their occur­rence and using this to pre­dict future require­ments. It is impor­tant when mak­ing a count to select sam­ples of work which tru­ly rep­re­sent the type of work being hand-set at the present time and so reduce the num­ber of char­ac­ters to be count­ed to a rea­son­able lev­el.

To devel­op the new scheme sam­ples of hand-set work were obtained from twen­ty-five ran­dom­ly-select­ed print­ing firms, which includ­ed job­bing print­ers, mag­a­zine print­ers and a provin­cial news­pa­per. In all, 92,000 char­ac­ters (exclud­ing spaces) were count­ed from 350 sep­a­rate jobs. In order that job and work-type vari­a­tions could be exam­ined more close­ly these items of work were regrouped into eighty-eight class­es con­tain­ing jobs of a very sim­i­lar nature and fur­ther regrouped into fif­teen broad class­es of work. These fif­teen work-type groups includ­ed forms, enter­tain­ment hand­bills, and a vari­ety of dis­played adver­tise­ments spe­cif­ic to var­i­ous sub­jects such as motor­ing, office equip­ment, chem­i­cal engi­neer­ing and shop ser­vices. The char­ac­ters were also sub­di­vid­ed into com­po­si­tion and dis­play sizes, the lat­ter being char­ac­ters of 14 pt and above.

Clear­ly, if an exam­i­na­tion of the var­i­ous items of work showed great dif­fer­ences from one anoth­er, there would be no val­ue in alter­ing the cur­rent­ly used pro­por­tions. It so hap­pened, how­ev­er, that sam­pling vari­a­tion was the vari­a­tion of great­est impor­tance. Oth­er types of vari­a­tion did occur infre­quent­ly as expect­ed: for exam­ple, with low­er­case a, two jobs that were found to show oth­er vari­a­tions were a danc­ing acad­e­my prospec­tus and a bal­let pro­gramme. Some vari­a­tions were not quite so obvi­ous, such as the work-type vari­a­tion shown by low­er­case b which was not found so fre­quent­ly as expect­ed in dis­played adver­tise­ments for shop ser­vices. The gen­er­al remits of this work do show, how­ev­er, that a type fount scheme which would suit most print­ers is entire­ly prac­ti­ca­ble.

The basis of the new scheme is the sta­tis­ti­cal mod­el pre­vi­ous­ly dis­cussed. Sim­ply inter­pret­ed this means that the less fre­quent­ly used char­ac­ters need to be strength­ened more than the com­mon­ly occult­ing ones and the exact amount of strength­en­ing can be deter­mined math­e­mat­i­cal­ly. The cur­rent­ly used schemes also strength­en the less fre­quent­ly used char­ac­ters but they do so irre­spec­tive of the size of the fount and this pro­duces excess­es of these char­ac­ters. By real­is­ing that when the size of the fount is increased the pro­por­tions should get clos­er to the actu­al pro­por­tions found from the count­ing the scheme pro­posed here will meet require­ments of type fount pro­por­tions out­lined in the intro­duc­tion. An abridged ver­sion of the new founts, togeth­er with the actu­al pro­por­tions found is giv­en in Table I for both low­er­case and cap­i­tals. Table II shows the actu­al pro­por­tions found for fig­ures and points.

LOWERCASE FOUNTS
Sort	% Found	Size of Fount
a	8.1	10	20	30	40	50	75	100	150
b	1.3	3	5	7	9	11	16	21	29
c	3.4	5	10	15	19	24	36	48	67
d	4.1	6	12	17	22	28	41	56	80
e	13.4	15	30	46	63	80	119	160	236
f	1.5	3	5	8	10	12	18	23	33
g	1.7	3	6	9	11	13	20	26	37
h	3.3	5	10	15	19	23	34	46	67
i	6.7	9	18	26	35	43	62	86	125
j	0.1	2	4	5	6	6	6	6	6
k	0.7	3	5	6	6	7	10	13	18
l	4.9	7	14	20	26	32	48	65	93
m	2.3	4	8	11	14	17	25	34	48
n	7.7	10	20	29	38	48	71	96	141
o	8.3	10	20	30	40	50	75	102	151
p	2.3	4	8	11	14	17	24	34	47
q	0.2	3	4	5	6	6	6	6	8
r	7.9	10	20	29	39	49	72	98	146
s	6.9	9	18	25	34	43	62	86	124
t	7.7	10	20	29	39	49	71	98	142
u	3.1	5	10	14	18	22	32	44	62
v	0.9	3	5	6	7	8	11	15	22
w	1	3	5	6	8	9	12	17	24
x	0.2	3	4	5	6	6	6	6	9
y	2	4	8	10	13	16	22	31	46
z	0.1	2	3	4	5	6	6	6	6
ff	0.1	2	3	4	4	6	6	6	6
fi	0.1	2	3	4	4	6	6	6	6
fl	0.05	2	3	3	4	5	6	6	6
ffi	0.05	2	3	3	4	5	6	6	6
ffl	0	1	2	2	3	5	6	6	6

CAP FOUNTS
Sort	% Found	Size of Fount
A	7.5	10	20	30	40	50	75	100	150
B	2	4	7	10	14	17	25	33	46
C	5	7	14	21	28	35	53	70	104
D	4.4	7	13	19	26	32	45	65	90
E	1.1	13	26	38	52	65	98	134	188
F	2.1	4	8	11	14	17	26	34	44
G	2.3	4	8	12	16	19	27	36	51
H	3.3	6	11	15	20	25	37	50	70
I	5.9	8	16	24	32	40	60	81	117
J	0.5	3	4	6	7	7	8	11	16
K	0.7	3	5	7	8	8	11	14	20
L	5.3	8	15	22	30	37	55	74	109
M	3.4	6	11	16	21	26	38	50	72
N	6.9	9	19	28	38	47	69	94	136
O	6.7	8	18	27	36	45	68	92	132
P	3.2	5	10	15	20	24	36	48	68
Q	0.3	3	4	6	6	6	6	7	10
R	7.3	10	20	29	39	49	72	98	145
S	8	10	21	31	42	53	79	107	161
T	7.9	10	21	31	42	53	79	107	161
U	2.4	4	8	12	16	19	28	37	53
V	1.1	3	5	7	9	11	16	20	25
W	2.1	4	8	11	14	17	25	34	44
X	0.2	3	4	5	6	6	6	6	9
Y	1.5	3	6	8	12	14	19	26	38
Z	0.1	3	4	5	6	6	6	6	6

ACTUAL PROPORTIONS OF FIGURES AND POINTS
Fig­ures, etc.	%	Points, etc.	%
1	8.4	.	29
2	4.6	,	14.5
3	3.5	:	3.3
4	2.7	;	0.2
5	3.4	’	3.2
6	3.2	-	3.9
7	2.2	?	0.3
8	1.8	!	0.2
9	3.3	&	1.4
0	6.4	(	3.4
�	1.1	Total	100

Table I is based on com­po­si­tion sizes but com­par­i­son of these pro­por­tions with those obtained for dis­play sizes showed that there was lit­tle jus­ti­fi­ca­tion for sug­gest­ing sep­a­rate pro­por­tions for the two groups. The main dif­fer­ences found were that cap­i­tals I and L occurred rather more fre­quent­ly in the dis­play sizes.

The quan­ti­ty of type ordered from a type­founder varies con­sid­er­ably; it may be a five-pound fount for a spe­cial job or it may be suf­fi­cient to fill a case. So that the print­er will get the max­i­mum ben­e­fit from the new founts two pro­por­tion tables have been pre­pared. For orders less than the equiv­a­lent of 160a or I60A, which con­tain few­er than 2,000 char­ac­ters a ​‘pre­lim­i­nary fount’ is used which is the weight­ed sys­tem shown in Table I. For orders exceed­ing this quan­ti­ty, and where the effects of sam­pling vari­a­tion become small, the type is sup­plied from a ​‘con­tin­u­a­tion fount’ in which the num­ber of char­ac­ters are in direct pro­por­tion to those found from the count­ing. This refine­ment, which has again been devised to give a more uni­form usage from the case, will not com­pli­cate the order­ing of type from the point of view of the print­er.

Anoth­er aspect stud­ied was the ratio of the num­ber of low­er­case char­ac­ters to the num­ber of cap­i­tals in a com­plete fount. At present a 5lb fount of job­bing type con­tains 2½ lb of low­er­case and 2½ lb of cap­i­tals, fig­ures and points. This weight rela­tion­ship auto­mat­i­cal­ly fix­es the numer­i­cal ratio and those in cur­rent use have about 1.9 low­er­case for every cap­i­tal. It was found, how­ev­er, that a ratio of 1.5 low­er­case to one cap­i­tal would bet­ter suit the major­i­ty of print­ers and to achieve this future founts would have to be made up of 2¼ lb of low­er­case and 2¾ lb of cap­i­tals, fig­ures and points. Oth­er ratios incor­po­rat­ed into the new scheme are that the most suit­able ratio for cap­i­tals to fig­ures and points is 3.8 to 1 and that of points to fig­ures is 1.5 to 1. The lat­ter two ratios do vary con­sid­er­ably with the size of the type and those sug­gest­ed here are again the ones that would suit most print­ers.

There were many oth­er aspects of this work which had to be dis­cussed and stud­ied but because of their lim­it­ed inter­est they are not men­tioned here. Nev­er­the­less they were impor­tant in order to make the new scheme eas­i­ly work­able for the type­founder and also accept­able to the type user.

As quite a few firms car­ry out hand-set­ting and cor­rect­ing of machine-set work from the same case it was nec­es­sary to make a fur­ther study in order to deter­mine whether the fount scheme above would be quick­ly upset by such a prac­tice. In oth­er words, are the pro­por­tions obtained for hand-set­ting founts suit­able for cor­rec­tions founts? Eleven main rea­sons for cor­rec­tions were list­ed and while some of these (bat­ters, miss­ing words, wrong fount, etc) would require pro­por­tions almost iden­ti­cal to those found for job­bing work, there were oth­ers which depend­ed on the human ele­ment and machine capa­bil­i­ties. Because of the lat­ter, no pre­cise pro­por­tions are pos­si­ble and the require­ments will vary from firm to firm accord­ing to the abil­i­ty of the oper­a­tors and the type of work being pro­duced. One major require­ment of a cor­rec­tions fount is that it must be of such a size as to with­stand sud­den demands made upon it as are called for by repeat­ed mis-spelling of a word, a dirty matrix, or the replace­ment of one of the alpha­bet in the die-case by a more fre­quent­ly occur­ring sort. If this require­ment is met, then, from counts of the fre­quen­cy of occur­rence of char­ac­ters requir­ing cor­rec­tions the hand-set scheme pro­duced here will prove to be quite sat­is­fac­to­ry under most cir­cum­stances.

For sug­gest­ing the prob­lem and pro­vid­ing ini­tial evi­dence of its exis­tence, I am grate­ful to Messrs San­type Lim­it­ed. I wish espe­cial­ly to thank their for­mer Man­ag­ing Direc­tor, H. F. W. Cory, for his valu­able help on the prac­ti­cal prob­lems asso­ci­at­ed with the work.

This arti­cle from the British Print­er mag­a­zine dur­ing 1961