BA Small Screws Committee
2nd Report, 1884

British Association for the Advancement of Science.
Report of the Fifty-Fourth Meeting of the British Association for the Advancement of Science; held at Montreal in August and September 1884.
London: John Murray, 1855.
Pages 287-293.

Sir William Thomson, the future Lord Kelvin, has joined the committee.

Second Report of the Committee, consisting of Sir Joseph Whitworth, Sir W. Thomson, Sir F. J. Bramwell, Mr. A. Stroh, Mr. Beck, Mr. W. H. Preece, Mr. E. Compton, Mr. E. Rigg (Secretary), Mr. A. Le Neve Foster, Mr. Latimer Clark, Mr. H. Trueman Wood, and Mr. Buckney, appointed for the purpose of determining a gauge for the manufacture of the various small screws used in telegraphic and electrical apparatus, in clockwork, and for other analogous purposes:¹

1. Since the presentation of its first report on a gauge for small screws at the meeting of the Association held in 1882 at Southampton, this Committee has further examined into the recommendations there made, with the result that they have now to propose some important modifications, the general effect of which will, it is felt, be to materially facilitate the introduction of the system.

2. The want of unanimity on the part of the Committee referred to in paragraph 7 of that report, arose mainly on the question as to whether the inch or millimetre should be taken as a unit of measurement. It is evident that if either is rigidly adhered to, and in any way employed in the nomenclature of the screws, as for example, in specifying the diameter, pitch, or threads per inch or per mm., the same dimensions could not be expressed in whole numbers in the other unit, and thus a material obstacle would be at once introduced to its adoption.

3. It should be pointed out, however, that it has hitherto been the common practice to designate such small screws as the Committee alone is considering, not by any specific dimension, but by a number, which as a rule, is arbitrarily chosen and does not of itself form a guide to the size of the screw. Considering, then, that the unit of measurement is only indirectly connected with the subject of a screw-gauge, the Committee has felt that the two units might be reconciled so far as relates to such a subject, and that thus one important difficulty would be removed.

4. The manner in which the series of screws adopted lately by Swiss manufacturers is correlated has been sufficiently explained in the previous report, and very full explanations are given in the two original pamphlets to which reference is there made.² The diameter (D) is related to the pitch (P) by the formula D = 6P6/5, (1) all measurements being in millimetres, and P having successively the values 1 (or 0.90) mm.; 0.9¹ mm.; 0.9² mm.; 0.93 mm .… 0.9n mm.

Thus n, the index, becomes a convenient designating number for the screw, and the formula (1) may be expressed D = 6 (0.9n)6/5, where P = 0.9n.

5. The pitch of any screw can be at once ascertained from its designating number by raising 0.9 to the power indicated by that number; and from this pitch the diameter is directly deducible by the formula (1), so that the number (n) given in the first column of the table, by which a screw is known, is intimately related to all its dimensions.

No. Nominal Dimensions
in Thousandths of an Inch
Absolute Dimensions
in Millimetres.
Diameter. Pitch. Threads
per Inch.
Diameter. Pitch.
I. II. III. IV. V. VI.
25 102.8353 0.25 0.072
24113.1 317 0.29 0.080
23133.5 285 0.33 0.089
22153.9 259 0.37 0.098
2117 4.3 231 0.42 0.11
2019 4.7 212 0.48 0.12
1921 5.5 181 0.54 0.14
1824 5.9 169 0.62 0.15
1727 6.7 149 0.70 0.17
1631 7.5 134 0.79 0.19
1535 8.3 121 0.90 0.21
1439 9.1 110 1.0 0.23
1344 9.8 101 1.2 0.25
125111.0 90.7 1.3 0.28
1159 12.2 81.9 1.5 u.31
106713.872.61.7 0.35
97515.465.11.9 0.39
88616.959.12.2 0.43
79818.952.92.5 0.48
611020.9 47.9 2.8 0.53
512623.2 43.03.2 0.59
414226.038.53.6 0.66
316128.734.84.1 0.73
218531.931.44.7 0.81
120935.4 28.2 5.3 0.90

6. It is evident that, by taking the exact successive powers of 0.9 for the pitch, complex numbers would soon be arrived at. Such dimensions would, however, involve a degree of accuracy which is hardly attainable in practice, and it may be shown that, with two significant figures employed throughout to express the pitch, the degree of accuracy likely to be attained in screws of the kind under consideration is reached. Relying on this fact, the series of pitches given in column VI.3 is arrived at for screws ranging from .236-in. to the smallest in use, 0.01-in. in diameter, in place of the mathematically exact series obtained by raising 0.9 to successively higher powers.4 And this is the series which the committee recommends for adoption.

7. Viewing the numbers thus obtained in the first place merely as a graduated series of pitches, and ignoring the unit of measurement, it may be admitted that the series of powers of 0.9 from which they are deduced is perhaps as good a one as can be suggested for the purpose, and it is found to very closely correspond with experience. Thus, column VI., which gives the nearest approximation to this series that is practically required, is well adapted for such a system of screws. It is to be observed that in selecting a series of pitches there are three simple alternatives to choose from— (1) To have a constant arithmetical difference between successive pitches, in which case either the pitches of small screws would differ by too great an amount, or those of the larger screws by too small an amount; or (2) to divide the entire range into sets, in each of which the differences are constant. The third alternative is to take successive powers of some other simple fraction, for example, 0.8, but such a series would not so well correspond with the screws most generally employed.

8. Accepting this series, it may, however, be urged that it should be based on some aliquot part of an inch rather than on the millimetre. But any advantages to be gained by such a modification are inappreciable, for an examination of the numbers at once shows that they are, for the most part, awkward fractions of a millimetre, and the metric system of measurement thus enjoys no advantage in this respect over that based on the inch. From the point of view of interchangeability, however, of screws to be manufactured in this country and on the Continent, it is essential that the same basis of measurement of the pitch be everywhere adopted, because, having agreed upon only two significant figures on one basis, terminable decimals are obtained, but such terminable decimals could not be accurately expressed by two significant figures. on the other basis of measurement.

9. Again, it is to be remembered that the use of metric measurement to designate the pitch need not inconvenience English manufacturers who are desirous of cutting the screws in their lathes. For, as has recently been pointed out by Mr. Bosanquet,5 it is easy to cut a thread, whose pitch differs from one millimetre by an amount which may for all ordinary purposes be neglected (1/155300th), with a guide-screw based on the inch by the addition of a wheel of 127 teeth, and thus the series here recommended could, on the rare occasions that it became necessary, be originated on any screw-cutting lathe provided with the requisite wheels. But the Committee do not consider it needful to specially contemplate facility in the originating of the threads, as the screws under consideration are made in a plate or by the aid of dies, and manufacturers on a large scale would be provided with a special lathe for the purpose.

10. Whether the inch or millimetre is adopted as a unit of measurement, the series of pitches for these small screws becomes an ideal rarely attained in practice, for with screws tapped in a plate, or even with dies, the exact pitch aimed at will often not be attained; neither is it safe to assume that two screws, tapped in corresponding holes in different plates, will have precisely the same number of threads per inch. This is especially the case with the smaller screws, as may be proved by accurately measuring the pitches of several tapped in holes that are nominally alike.

11. The fact here stated affords a reason against extending the practice of designating screws by their number of threads per inch, already sometimes resorted to in the case of large screws, to the screws now under discussion. It is found that screws, nominally alike, frequently differ in this respect by as much as five or even ten threads in the inch, nor need this occasion surprise when it is remembered that the screw-plates employed must expand to varying extents in the hardening, that the hole is often not more than three or four threads deep, and that the pressure applied by hand must vary considerably. Such a nomenclature would thus involve the use of inconveniently high numbers to express a minute degree of accuracy but seldom attained, while they convey but little real information, since mere examination would not enable anyone to distinguish between, say, a screw of 169 and 181 threads per inch.

12. The series of diameters must next be considered. Before the formula D = 6P6/5 was adopted, it was ascertained by the minute examination of about 140 small screws that the series very closely corresponds with those recognised as good in the trade, and the screws made in the new plates, known as Filières Suisses, which the Committee have had an opportunity of examining, appear to them to be well proportioned in this respect. The series of diameters, like the pitches, are expressed by two significant figures in each case, as the values for D deduced from the formula (1) are necessarily indeterminate in most cases. These diameters are given in millimetres in column V., and their nearest equivalent in thousandths of an inch in column II. As the committee considers that these screws are well-proportioned as regards pitch and diameter, and approves the formula (1) being taken as a basis, it is led to recommend this series of diameters being adopted in conjunction with the pitches already discussed. It has been suggested to the Committee that the introduction of such a system into general use in this country might be facilitated by punching against each hole in the screwplate, side by side with the designating number, as given in column I., the approximate diameter of the screw made in it as expressed in thousandths of an inch (column II.), as these numbers would convey a meaning to English workmen more definite than the numbers in column I. or column V. The committee sees no serious objection to such a course; but it should be remembered that screws have hitherto always been recognised by a number seldom higher than twenty-five, and it may be questioned whether any substantial advantage is gained by substituting such high figures as are involved in the expression of the diameters.

13. It will be seen that the series here recommended gives twenty-six screws for the range from ¼-in. to the smallest in use. Comparing this number with those of two of the best systems commonly met with— namely, the Latard (Perrelet et Martin) and Bourgeaux plates, we find that:

For a range of 21 sizes of watch screws on the Latard plate, this gives ... ... 15

For a range of 23 sizes of watch screws on the Bourgeaux plate, this gives ... ... 17

For a range of 36 sizes of clock screws on the Latard plate, this gives ... ... 23

The entire series is thus less than that of well-established plates, and cannot, therefore, be considered greater than the requirements of practice demand; while the fact that the watchmakers (who probably require the most extensive assortment of screws) in Switzerland have accepted it, confirms the committee in its opinion that the series is not deficient in this respect.

14. It remains to consider the form of thread. There are so many practical points to be taken into consideration in discussing such a question that it becomes specially useless to rely much on theory for guidance; and the divergence observable among the forms adopted by different manufacturers is thus very great.

The most important points to be bome in mind in its selection are:—

(1) The threads must be easily cut with the class of screw-cutting tackle ordinarily met with in workshops.

(2) The strength of the threads on the male and female screws must be so correlated that the liability of either to strip is a minimum.

(3) The resistance of the core to torsional stress when force is applied in rotating the screw must be a maximum.

(4) The friction should be as small as possible, in order to reduce wear.

15. In regard to the first of the above conditions, it is to be observed that very many of the screws considered by the Committee are usually made by means of a plate in which are round, tapped holes. Such a hole forms a thread by causing the metal to ‘flow’ from a space towards a thread, and its action is obviously of quite a different character from the cutting action of dies or of a chasing tool. In the case of plates with notched holes the cutting and squeezing actions are combined.

16. As bearing on the second condition, it is evident that, as the strength of the threads depends so essentially on the materials of which the screw and nut are made, and these are very varied, no precise and invariable rule is obtainable. If strength were the only point to be considered, a purely triangular form without any rounding would be the best, contact being assumed to take place over the entire surface. But in practice it is impossible to secure such perfect contact, and it becomes needful to round off the crests from all the threads; and this rounding is all the more necessary as the screws are smaller, and irregularities in the manufacture become relatively more marked. This modification is also necessary in view of condition (1) already considered.

17. The third point—namely, the resistance of the core to torsional stress—is determined primarily by the depth of thread. If the sectional area of the ring cut away is less than that of the core, the probability of the latter breaking across may be regarded as approximately equal to that of the threads stripping; but it is impossible to maintain a constant ratio, as such a condition would require the thread to be so fine, in the case of small screws, that there would be no sufficient hold in the nut. Thus in the very smallest screws (those that are below .030-in. in diameter) the ratio area of core/sectional area of thread is less than 1, and it gradually increases till a proportion of between 2 and 3 is attained.

18. Condition (4) is evidently best satisfied by a square thread. Such a form is, however, impracticable in the case of the small screws under consideration, but it is obviously approximated to according as the angle of a triangular thread is made less and the rounding greater.

19. The angles that have been adopted in practice show, as might be expected, considerable variation. On the one hand an angle of 60° is rarely exceeded, the thread being thus derived from the equilateral triangle, and, on the other hand, 45° may be taken as the lower limit.

20. The depth of a thread is evidently a function both of its angle and of the amount of rounding at the top and bottom. It may conveniently be expressed as a fraction of the pitch (taken as unity). In the case of the small screws in general use the mean value of the depth thus expressed is found to be 0.563, the maximum being 0.771, and the mimimum 0.311. It is evident that any increase in the depth beyond what is essential will materially and needlessly increase the difficulty of manufacture when a screw-plate is used; at the same time the depth must not be too much reduced, on account of the greater tendency of the thread to strip. It is further important that the additional torsion involved in cutting a deep thread, which materially increases the risk of tearing the metal across, should not be lost sight of.

21. The Committee, after comparing together a large number of different forms of thread, some of which are in actual use, while others have only been suggested, were much tempted to recommend the Whitworth thread for adoption by the British Association, because it is so well known in this country, and experience has proved indisputably that it is excellent when employed for engineers' bolts, &c. But, as appears from sections 16 and 18, in the case of small screws the tendency should rather be to increase the rounding on account of the difficulties of manufacture, and the depth of the Whitworth thread is 0.64 of the pitch, which is considerably in excess of 0.563, the average adopted in practice. The Whitworth thread is, moreover, characterised by a greater angle than is usual in small screws.

The whitworth thread form, endorsed in the first report, is abandoned.
  In the Swiss system, screws larger than 6 mm in diameter had a thread form (Steinlen's) that differed from the one for smaller screws.

22. The advisability of modifying the form of thread of small screws, as compared with those of greater diameter, is fully recognised by the Swiss Committee, their thread for the former having an angle of 47½°, while that for the latter is 53°, nearly the same as that of the Whitworth thread. In the case of small screws made in the Filière Suisse the crest of each thread is rounded off with a radius equal to 1/6th the pitch, and the hollow with 1/5th the pitch. The actual depth is 0.60 the pitch, somewhat less than in the Whitworth thread.

23. While approving the general form of thread here described, this committee could not but feel that the difference in the roundings (1/6th at top and 1/5th at the bottom) was unnecessary. Looking, moreover, to the fact that very many of the screws of the sizes now under consideration are for electrical and telegraphic instruments, and, therefore, may be of brass, and that, with such dimensions, it is impossible for the eye to ascertain whether a given screw satisfies the required conditions in regard to such small differences between the crest and hollow of the thread, the committee feels that an equal rounding (2/11ths of the pitch) at the top and bottom would be preferable. This would maintain the angle of thread and the depth the same—namely, 47½° and 3/5ths of the pitch respectively.

24. Having now discussed the three main points that require to be considered in any system of screws—namely, the pitches, diameters, and form of thread, it seems desirable to enumerate briefly the recommendations at which the Committee has arrived. These are:

(1) That the series of diameters for screws from 1/100th in. to ¼ in. be that given in millimetres in column V., the nearest thousandths of an inch being given in column II.; these diameters being the series calculated by making P, in the formula D = 6P6/5, having in succession the following values:

1 (or 0.90) mm.; 0.9¹ mm.; 0.9² mm.; 0.93 mm.; … 0.9n mm
Only two significant figures are taken to represent the diameters.

(2) That the pitches of these screws be the above gradually decreasing series, each pitch being 9/10ths of its predecessor, but that only two significant figures be used in their expression. The series thus obtained is given in column VI.

(3) That in view of the desirability of securing a system of small screws—international in its character—English manufacturers of screws, screw-plates, &c., adopt the exact pitches given in millimetres in column VI., which, as we explained in par. 9, can, if required, be originated on an English lathe. Further, in view of the fact that small screws and screw-plates, while nominally alike, will not unfrequently differ considerably as regards their number of threads per inch, the practice of designating such screws by their number of threads per inch should not be adopted. For reference, however, the approximate number of threads per inch, as calculated from the pitch given in column VI., are given in column IV.

(4) That the designating numbers given in column I., being the indices of the powers to which 0.9 is raised to obtain the pitch, be punched against each hole in the screw-plate, and that, if thought desirable, its diameter in thousandths of an inch (column II.) might be punched side by side with this number.

25. In his Systèmatique des vis Horlogères, Prof. Thury has done for the small screws used by watch, clock, and scientific instrument makers what was done forty years ago by Sir J. Whitworth for the larger screws used by engineers; and like the admirable system introduced by the latter, the scheme here advocated is based on the data obtained by measuring the several dimensions of many screws accepted by practical men as being well-proportioned.

26. The Committee has had an opportunity of examining both screws and screw-plates (for the smaller screws) made on this system, which it is convinced will satisfy all the demands of practice. The Committee, can, therefore, confidently recommend its adoption by the British Association, subject to the slight modification discussed in par. 23; and it feels that an important incidental advantage would be the support it would at once receive on the Continent, and the consequent increased rapidity with which it might be expected to come into general use; for it cannot be doubted that its recognition by so important a body as the British Association would have considerable influence in establishing the system abroad.

[The recommendation for the appointment of this Committee having failed to reach the Committee of Recommendations at Southport in time to allow of its sanction by the General Committee, the Council at their meeting on November 6th, 1883, requested the Committee to continue their labours, and undertook to recommend to the General Committee at Montreal that this report be printed among the Reports.]

Original footnotes

[Numbering has not been retained since the original pagination has not.]

1. See Report of the Council presented to the General Committee at Montreal.
[where it states (page lxv):
“The Council have been informed that, through an inadvertence, the resolution of the Sectional Committee recommending the reappointment of the Committee on Screw Gauges was not transmitted to the Secretary in time to be considered by the Committee of Recommendations, and so did not receive the sanction of the General Committee. The Council, having regard to the importance of the work carried on by that Committee, have requested them, through their Secretary, to continue their labours and make a report as if duly appointed. The Council ask that this action of theirs be sanctioned, and that the above-named report be received and printed among the reports of the committees duly appointed.”]

2. Systèmatique des vis Horlogères, by Prof. M. Thury, Geneva, 1878. Notice sur le Système des vis de la Filère Suisse, Geneva, 1880, by the same author,

3. It may be incidentally pointed out here that this series comprises two screws, with pitches of 1 mm. and 0.25 mm, which would be serviceable for micrometers.

4. Sir Joseph Whitworth’s gauge, in general use, ends at ¼-in., where this commences.

5. Phil. Mag. (Fifth Series), vol. xv. pp. 217, 438.

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