# Miscellaneous Papers on Mechanical Subjects/A Paper on Standard Decimal Measures of Length

STANDARD DECIMAL MEASURES OF LENGTH.
Manchester, 1857.
In the address which I had the honour of delivering before the Members of this Institution at the Glasgow Meeting last year, I briefly alluded to the beneficial results which would follow the application of the decimal system to our weights and measures, referring more particularly to the latter. In compliance with the wish expressed by several members of the Council, I propose in the present paper to bring this important subject more prominently under the notice of the members, confining myself, however, to its practical bearing on mechanical operations, without discussing different systems of notation, which I leave to other and abler hands.
I have long been convinced that great and rapid progress would be made in many branches of the mechanical arts if the decimal system of ​measures could be generally introduced. To state the case broadly, instead of our engineers and machinists thinking in eighths, sixteenths and thirty-seconds of an inch, it is desirable that they should think and speak in tenths, hundredths, and thousandths. I can assure those who have been accustomed to the fractional system that the change to the more perfect decimal one is easy of attainment, and, when once made, it will from its usefulness and convenience amply repay any trouble which may have attended its acquirement. In the manufacture of my standard gauges of size, the workmen measure to the 1-20,000th of an inch, and these measures are as familiar and appreciable as those of any larger dimensions. It will therefore be at once conceded that the only scale of measurement which can be used for such small sizes and proportionally small differences must be a decimal one, as any other would be productive of insurmountable difficulty, if not of utter confusion.
When the sizes of the fitting parts of machines are determined by sight from the lines on a scale or a two-foot rule, such nicety of measurement is out of the question; and as long as they are made on that system, the progress of improvement will be retarded. My experience has satisfied me that no system of measurement depending on the power of sight is suitable for ​obtaining the size of the working parts of machines. Where exact size or good fitting is required, the sense of touch is far more to be depended upon. I make standards of size by a system of measurement depending for its accuracy upon the sense of touch; and use an instrument provided with a mechanical multiplier, by which a space is presented to the eye many thousand times greater in extent than is the case where the distance is directly measured by sight only.
With truth of surface, that never-failing element of success, as the basis of operation, we are enabled to measure with exactitude; and there is no difficulty in making parts of machines to fit one another with any degree of nicety: but, when we wish to express correctly by the common fractional system very minute measurements, our ideas are cramped and hampered by an inconvenient and often confused system of notation. What exact motion can any man have of such a size as “a bare sixteenth” or “a full thirty-second;” and what inconvenient results may ensue from the different notions of different workmen as to the value of these terms. A scale of notation that may have suited the old system of manufacture has been left behind, I am happy to say, as the present age has improved on the past; and our improvement has created a want ​which necessity urges us to supply without delay. In the production of duplicate parts of machinery, correct measurement is indispensable to ensure good work: and if, as is the case, we are able to measure with all the accuracy and nicety that can be required, we surely ought at once to adopt a system of notation which will properly represent our measurements.
As an illustration of the importance of very small differences of size, I have brought an internal gauge having a cylindrical aperture ·5770 inch diameter, and two external gauges or solid cylinders, one being ·5769 inch, and the other ·5770 inch diameter. The latter is 1-10,000th of an inch larger than the former, and fits tightly in the internal gauge when both are clean and dry; while the smaller ·5769 inch gauge is so loose in it as to appear not to fit at all These gauges are finished with great care, and are made true after being casehardened. They are so hard that nothing but the diamond will cut them, except the grinding process to which they have been subjected. The effect of applying a drop of fine oil to the surfaces of these gauges is very remarkable. It will be observed that the fit of the larger cylinder becomes more easy, while that of the smaller becomes more tight. These results show the necessity of proper lubrication. In the case of the external gauge ·5770 ​inch diameter, the external and internal gauges are so near in size that the one does not go through the other when dry, and if pressed in, there would be danger of the surface particles of the one becoming imbedded in or among those of the other, which I have seen happen, and then no amount of force will separate them: but with a small quantity of oil on their surfaces, they move easily and smoothly. In the case of the external gauge ·5769 inch diameter, which is 1-10,000th of an inch smaller in diameter than the internal gauge, a space of half that quantity is left between the surfaces; this becomes filled with the oil, and hence the tighter fitting which is experienced.
It is therefore obvious both to the eye and the touch, that the difference between these two cylinders of 1-10,000th of an inch is an appreciable and important quantity; and what is now required is a method which shall express systematically and without confusion a scale applicable to such minute differences and measurements: it should be based on a uniform principle which will accustom the workman to speak of his measures as aggregates of very small differences; and when a good workman becomes familiar with such sizes as 1-1000th and 1-10,000th of an inch, he will not rest satisfied until he can work with corresponding accuracy. He will also be ​able to judge of their effect under different circumstances, and know how much to allow in the fitting parts of a machine, according to their relative importance and the treatment they are likely to receive at the hands of the attendant. For instance, the cylinder of the moving headstock of a lathe requires as good a fit as possible; but in practice it is found that the cylinder must be ·0005 inch or 1-2000th of an inch too small, because it frequently happens that machinery is not kept in a proper state of cleanliness, or from motives of false economy is lubricated with bad oil. These are two evils which are productive of great mischief. The abrasion caused by accumulated dust and grit produces increased wear and tear, and soon injures the surfaces in contact; while bad oil becomes sticky and rancid, and spoils the working of a good fit.
And here let me state what I think is the proper definition of a good fit. A tight fit is not necessarily a good one; but when the surfaces are true, and a proper allowance is made in the size of the parts working together, then a good fit is obtained. What constitutes a proper allowance or difference in size depends on the nature of the case, and the treatment which the machinery will meet with. In machinery supplied to establishments using rape oil ​there must be greater allowance and looseness in the fits than would be requisite if better oil, as sperm oil, were used, I need scarcely say how much more advisable it is to have the more accurate fit and use the best oil, than to have a loose fit and use the inferior oil, which causing more friction consumes greater power.
Again, a good workman acquires by experience an intuitive knowledge of the allowances in size which are requisite in various cases; and if a suitable decimal system of notation be adopted, there will be no difficulty, with the power of measurement we now possess, in registering minute differences; and so the knowledge gained by the experienced workman may be imparted to others in precise terms, which to the young beginner will be of invaluable service. Much important information may by these means be stored up, and at any time reference can be made to the experience of the past, which will then run no risk of being lost through disuse, inattention, or other causes.
The deterioration of templates or patterns of size, from their becoming worn or altered in process of time, is productive of great inconvenience, as many of us perhaps have experienced. For when an original standard was thus altered, it was irretrievably lost, because there were no means of ascertaining and recording the exact ​measure. It is of great importance to the manufacturer who makes parts of machines in large quantities to have the means of referring to an accurate fixed measure: it will enable him to reproduce at any time a facsimile of what he has once made, and so preserve a system of sizes of the fitting parts unaltered. The greatest care should be taken to make standards of size correctly at first, and to preserve them unaltered. Errors in the standards are not only propagated in the copies, but are superadded to the errors in the workmanship, which will occur in the course of manufacture; and this is especially likely to occur in cases where one manufacturer supplies parts of machines for the use of another.
My argument is shortly this:—If we had a better system of notation for our measures, in which small differences in size were expressed in terms conveying their value to the mind, the importance of minute and accurate measurements would become more familiar, more appreciated, and more generally applied. Many operations would by that means be more easily and effectually performed, and in some cases greater safety will be the result. Take for instance the present method of proving guns, which are proved by firing them with a considerable charge of powder and shot. If the barrel ​stands the proof without manifest injury, it is passed as a good one, while it may in the very process of proof have received such permanent injury as to render it highly dangerous for use. How much better it would be after proving the barrel to measure it, and ascertain accurately if any, and what, permanent alteration had taken place, and retain or reject it accordingly. This would be substituting an exact and satisfactory system for an uncertain and dubious trial; but, inasmuch as the degrees of alteration will be various, and the differences in their measurement very minute, a better system of notation with the improved mode of measuring is required, to enable this and other similarly useful applications to be made.
After careful thought and a comparison of different scales, I have come to the conclusion that the scale for standards of size given in the accompanying Table is the one I would recommend to be adopted. I have endeavoured to arrange one which would be easily intelligible to the ordinary workman, and that would in every possible case coincide with the old system, so as not to cause more expense in altering the present sizes than may be absolutely necessary. I am perfectly aware that other scales may be devised more complete and more advantageous in many respects, if we were now prepared not merely to ​revolutionise, but to abandon what has been manufactured and is now in use. But would not that be going too far? As long as the machines already made are in existence, the sizes of their parts cannot be abandoned; and these considerations have induced me to propose a scale which shall combine the greatest possible advantages with the least possible change.
It would be desirable that those establishments which may decide upon adopting the decimal scale should introduce rules having the inch divided into tenths and their subdivisions, which would soon become as familiar to the workman as the eighth scale he now uses.
The scale proposed for the wire-gauge commences with the smallest size and increases by thousandths of an inch up to half an inch. Contrary to the custom usually adopted in marking the wire-gauge, I have called the smallest size No. 1, being 1-1000th of an inch, No. 2 being 2-1000ths of an inch, and so on; increasing up to No. 20 by 1-1000th of an inch between each number; from No. 20 to 40 by 2-1000ths; from No. 40 to No. 100 by 5-1000ths of an inch. I propose therefore to suppress the use of the numbers of designation which have been hitherto employed for the various wire-gauges, and simply call the sizes by their expressive ​numbers in thousandths of an inch, as shown in the accompanying table of wire-gauges; a change which will, I think, render the new scale easily intelligible and convenient for use. ​
MR WHITWORTH'S PROPOSED DECIMAL SCALE. :
| STANDARDS OF SIZE. | STANDARDS OF SIZE. | STANDARDS OF SIZE. | WIRE-GAUGE. | WIRE-GAUGE. | WIRE-GAUGE. | WIRE-GAUGE. | WIRE-GAUGE. | WIRE-GAUGE. | WIRE-GAUGE. |
| Proposed Standards of Size for Taps and Dies. | Proposed Standards of Size for Taps and Dies. | Proposed Standards of Size for Taps and Dies. | Standard Wire-Gauge. | Standard Wire-Gauge. | Old Birmingham Wire-Gauge. | Old Lancashire Wire-Gauge. | Old Metal of Plate-Gauge. | Old Needle Wire-Gauge. | Old Music Wire-Gauge. |
| No. of Screw Threads per Inch. | Old Sizes. | New Standard of Size. Decimals of an Inch. | Value of each No. in Decimals of and Inch. | New Nos. of Gauge. Thousandths of and Inch. | Old Nos. of Gauge corresponding to New Nos. | Old Nos. of Gauge corresponding to New Nos. | Old Nos. of Gauge corresponding to New Nos. | Old Nos. of Gauge corresponding to New Nos. | Old Nos. of Gauge corresponding to New Nos. |
| 48 | | ·100 | ·001 | 1 | | | | | |
| 40 | ⅛ | ·125 | ·002 | 2 | | | | | |
| 32 | | ·150 | ·003 | 3 | | | | | |
| 24 | | ·175 | ·004 | 4 | 36 | | 1 | 19 | |
| 24 | | ·200 | ·005 | 5 | 35 | | 2 | 18 | |
| 24 | | ·225 | ·006 | 6 | .. | | .. | .. | |
| 20 | ¼ | ·250 | ·007 | 7 | 34 | | .. | 17 | |
| 20 | | ·275 | ·008 | 8 | 33 | | 3 | 16 | |
| 18 | | ·300 | ·009 | 9 | 32 | | .. | 15 | |
| 18 | | ·325 | ·010 | 10 | 31 | | 4 | 14 | |
| 18 | | ·350 | ·011 | 11 | .. | .. | .. | .. | |
| 16 | ⅜ | ·375 | ·012 | 12 | 30 | .. | 5 | 13 | |
| 16 | | ·400 | ·013 | 13 | 29 | 80 | 6 | 12 | |
| 14 | | ·425 | ·014 | 14 | 28 | 79 | .. | 11 | |
| 14 | | ·450 | ·015 | 15 | .. | 78 | 7 | .. | |
| 14 | | ·475 | ·016 | 16 | 27 | 77 | 8 | 10 | |
| 12 | ½ | ·500 | ·017 | 17 | .. | .. | .. | .. | |
| 12 | | ·525 | ·018 | 18 | 26 | 76 | .. | 9 | 6 |
| 12 | | ·550 | ·019 | 19 | .. | 75 | 9 | .. | 7 |
| 12 | | ·575 | ·020 | 20 | 25 | .. | .. | 8 | 8 |
| 12 | | ·600 | ·022 | 22 | 24 | 74 | .. | 7 | 10 |
| 11 | ⅝ | ·625 | ·024 | 24 | 23 | 72 | 10 | 6 | 12 |
| 11 | | ·650 | ·026 | 26 | .. | 71 | .. | .. | 13 |
| 11 | | ·675 | ·028 | 28 | 22 | 70 | 11 | 5 | 14 |
| 11 | | ·700 | ·030 | 30 | .. | 68 | .. | .. | 15 ​ |
| 10 | ¾ | ·750 | ·032 | 32 | 21 | 66 | .. | 4 | 15 |
| 10 | | ·800 | ·034 | 34 | .. | 64 | 12 | .. | 17 |
| 9 | ⅞ | ·875 | ·036 | 36 | 20 | 62 | 13 | 3 | 18 |
| 9 | | ·900 | ·038 | 38 | .. | 61 | .. | 19 | |
| 8 | 1 | 1·000 | ·040 | 40 | 19* | 59 | 14 | 2* | 20* |
| 7 | 1⅛ | 1·125 | ·045 | 45 | .. | 56 | 15* | 1 | |
| 7 | 1¼ | 1·250 | ·050 | 50 | 18 | 55 | 16 | | |
| 6 | 1⅜ | 1·375 | ·055 | 55 | .. | 54 | 17* | | |
| 6 | 1½ | 1·500 | ·060 | 60 | 17* | 52 | 18 | | |
| 5 | 1⅝ | 1·625 | ·065 | 65 | 16 | 51 | 19 | | |
| 5 | 1¾ | 1·750 | ·070 | 70 | 15* | 49 | 21* | | |
| 4½ | 1⅞ | 1·875 | ·075 | 75 | .. | 47 | 22 | | |
| 4½ | 2 | 2·000 | ·080 | 80 | .. | 45 | 24* | | |
| 4½ | 2⅛ | 2·125 | ·085 | 85 | 14* | 43 | .. | | |
| 4 | 2¼ | 2·250 | ·090 | 90 | .. | 42 | .. | | |
| 4 | 2⅜ | 2·375 | ·095 | 95 | 13 | 41 | 25 | | |
| 4 | 2½ | 2·500 | ·100 | 100 | .. | 38 | 26** | | |
| 4 | 2⅝ | 2·625 | ·110 | 110 | 12 | 34 | 27** | | |
| 3½ | 2¾ | 2·750 | ·120 | 120 | 11 | 31* | 28 | | |
| 3½ | 2⅞ | 2·875 | ·135 | 135 | 10 | 29 | 31* | | |
| 3½ | 3 | 3·000 | ·150 | 150 | 9* | 23 | 34* | | |
| 3¼ | 3¼ | 3·250 | ·165 | 165 | 8 | 19 | 36 | | |
| 3¼ | 3½ | 3·500 | ·180 | 180 | 7 | 13 | | | |
| 3 | 3¾ | 3·750 | ·200 | 200 | 6** | 5 | | | |
| 3 | 4 | 4·000 | ·220 | 220 | 5 | 2 | | | |
| 2⅞ | 4¼ | 4·250 | ·240 | 240 | 4* | C | | | |
| 2⅞ | 4½ | 4·500 | ·260 | 260 | 3 | G | | | |
| 2¾ | 4¾ | 4·750 | ·280 | 280 | 2** | K | | | |
| 2¾ | 5 | 5·000 | ·300 | 300 | 1 | N* | | | |
| 2⅝ | 5¼ | 5·250 | ·325 | 325 | .. | P* | | | |
| 2⅝ | 5½ | 5·500 | ·350 | 350 | .. | S* | | | |
| 2½ | 5¾ | 5·750 | ·375 | 375 | 00** | V* | | | |
| 2½ | 6 | 6·000 | ·400 | 400 | .. | X** | | | |
| | | | ·425 | 425 | 000 | | | | |
| | | | ·450 | 450 | 0000** | | | | |
| | | | ·475 | 475 | | | | | |
| | | | ·500 | 500 | Note.—These Nos. correspond exactly or within ·001 inch with the new proposed Nos., except those marked *, which are within ·002 inch, and those marked **, which are beyond ·002 inch. | Note.—These Nos. correspond exactly or within ·001 inch with the new proposed Nos., except those marked *, which are within ·002 inch, and those marked **, which are beyond ·002 inch. | Note.—These Nos. correspond exactly or within ·001 inch with the new proposed Nos., except those marked *, which are within ·002 inch, and those marked **, which are beyond ·002 inch. | Note.—These Nos. correspond exactly or within ·001 inch with the new proposed Nos., except those marked *, which are within ·002 inch, and those marked **, which are beyond ·002 inch. | Note.—These Nos. correspond exactly or within ·001 inch with the new proposed Nos., except those marked *, which are within ·002 inch, and those marked **, which are beyond ·002 inch. |