THE PRATT & WHITNEY Co, STANDARDS OF LENGTH AND THEIR PRACTICAL APPLICATION. A RESUME COVERING THE METHODS EMPLOYED FOR THE PRO- DUCTION OF STANDARD GAUGES. TO INSURE UNIFORMITY AND INTERCHANGEABILITY IN EVERY DEPARTMENT OF MANUFACTURES, INCLUDING THE REPORTS OF PROFESSOR WM. A. ROGERS; THE COMMITTEE ON STANDARDS AND GAUGES, AMERICAN SOCIETY OF MECHANICAL ENGINEERS; THE COMMITTEE OF THE MASTER CAR-BUILDERS' ASSOCIATION; AND INCLUD- ING ALSO THE REPORT OF THE SPECIAL COMMITTEE APPOINTED BY THE FRANKLIN INSTITUTE, APRIL, 1864. Edited by GEORGE M. BOND, M.E. PUBLISHED BY THE PRATT & ^S^osiTiisrE Hartford, Conn., U. S. A. 1887. THE CASE, LOCKWOOD & BRAINARD Co., PRINTERS, HARTFORD. CON* QC niO OUR FRIENDS, wrp r]ave given us trjeir eqcouragerqent during trje progress of th[e work of establishing a staqdard for gauge dimensions, aqd to all wr|O appreciate tP|e advantages resulting frorq practical uqifornr|ity iq lesseqing tf]e cost of maqufactures, this col- lectioq of reports aqd data is respectfully dedicated by THE PRATT & WHITNEY COMPANY. M323716 EEPOKT OF PEOFESSOE WM. A. EOGEES. THE PRATT & WHITNEY Co., Gentlemen:- I communicate herewith the results of my investigation of the units of length upon which your system of gauges depends. In the preliminary discussion of this question with you, cer- tain considerations were urged by which we should be governed in the construction and adoption of standards of length for prac- tical use in mechanical operations. In iny letter of May 26, 1880, these were enumerated as follows : First. For ,the yard as a standard unit, the material employed should be an alloy known as Baily's metal, composed of 16 parts of copper, 2J parts of tin, and 1 part of zinc, since this is the composition of the Imperial Yard of Great Britain, to which final reference will be made, and of the standard yard, " Bronze 11 " of the United States Bureau of Weights and Measures. Second. The particular standard yard or yards constructed should be referred to one of the two yards named, and not to any copy in the hands of a private person. This standard of reference ought to be within easy access, in order that compari- sons with it may be made at stated intervals for the purpose of ascertaining whether a constant relation between the two units is maintained. Since the latter consideration would prevent a direct reference to the Imperial Yard No. 1, I strongly urge the importance of referring the proposed standard yard, which you have empowered me to construct, directly to " Bronze 11." This standard is not a legal standard in the sense that it has been authorized as such by an act of Congress, but since it has been in actual use for many years, and since it will, without doubt, receive a legal authorization in the near future, this objection has but little practical force. By the adoption of "Bronze 11," as the direct standard of reference, the ultimate reference to the Imperial Yard will be secured, since the relation between these standards has already been tlie subject of four distinct investigations. When "Bronze 11 " was presented to the United States in 1856, it was stated to be standard at 61.79 Fahr. It was, therefore, about one seven - thousandth of an inch too long. This relation was the result of the comparisons made at the time the standards were constructed. Two subsequent investigations of this relation have been made by Professor Ililgard and Mr. Chaney, the Warden of the Im- perial Standards, giving substantially identical results ; and for many years it has been assumed that "Bronze 11" is 88 mil- lion ths of an inch shorter than the Imperial Yard at 62 Fahr. An investigation by Mr. Charles S. Peirce, however, made in 1883, reduces this relation to 22 millionths of an inch. Whether this apparent variation in length is real, will doubtless be de- termined by future investigations, but the deviation will not be of any practical account within the limits which you require in your system of gauges. Admitting a doubt in the value of the relation as great as one ten-thousandth of an inch, the propor- tional part for six inches would be only one sixty-thousandth of an inch. Third. Since your gauges are made of tempered steel it will be necessary to construct one standard of this material in order that a direct comparison of the gauges with the standard may be made without regard to the question of temperature. Fourth. Since there are no reliable observations which deter- mine the behavior of tempered steel under variations of tempera- ture when compared with the same metal untempered, it will be necessary to have a standard yard upon annealed steel. Fifth. On account of the difficulty of maintaining a plane surface upon a bar of the dimensions described, it will be advisa- ble to construct a short standard for ordinary use in the con- struction and comparison of your gauges, in which the warping of the graduated surface by flexure may be neglected. Since this line standard will be the real basis upon which your system of gauges rests, the subdivisions of the total length should be such that any fractional part thereof may be readily and easily obtained. In the machine-shop practice of this country, there is not, at the present time, any extensive demand for units of length expressed in the metric system. Since, however, this system is 3 largely adopted in scientific investigations, it will be desirable to construct a standard meter and to obtain the correct subdivisions of the same. In order to avoid the confusion resulting from the fact that the Imperial Yard is standard at 62 Fahr., and that the meter is standard at Centigrade, the metric unit should be traced upon the same metal as the yard. If we could neglect this requirement, the bar for the meter should properly be of platinum, and it should have the same form and dimensions as the Metre des Archives, the legal standard of France, and now adopted as the basis of the prototypes constructed for the Inter- national Bureau of Weights and Measures. The great cost of platinum would preclude the use of this metal, and the same con- sideration would prevent the use of platinum-indium, the alloy of which the prototypes are made. Since, however, the Inter- national Bureau has every appliance for comparing standards of different material at any temperature required, it does not seem necessary to limit the standard meter to any particular material or dimensions. Therefore, as the yard and the meter will be represented upon the same bar, there is no reason why they should not be standard at the same temperature. The tempera- ture adopted will be 62. Fahrenheit. The fulfillment of the requirements stated above involves the following operations : (a) The direct comparison of the yard upon the bronze bars with "Bronze 11," and with the Imperial Yard indirectly, through the medium of the standards which have been compared with it. These standards are, a steel yard belonging to the writer which was compared with the Imperial Yard in January, 1880, by Mr. Chaney the Warden of the Standards; a combined line-measure yard, and line-measure meter upon brass, and an end-measure yard belonging to the Stevens Institute, kindly loaned to the writer by President Morton, both of which were also compared with the Imperial Yard by Mr. Chaney. As a further check, the comparison will be made with an end- measure steel yard, purchased by the writer of Sir Joseph Whit- worth & Co. It was supposed to be standard at 62 Fahr., although no statement to this effect by the maker has been received. For the meter, the comparisons will be made with a meter upon a copper bar of the form adopted by the International Bureau of Weights and Measures. This bar was traced for the writer from the working meter of the Conservatoire des Arts et Metiers, by M. Tresca, at 2 o'clock on the morning of February 6, 1880. It is signed by M. Tresca, by his son G-. Tresca, who executed the transfer, and, at the request of M. Tresca, by myself also, since I made one of the series of comparisons with the original, after the transfer. From the official report of M. Tresca it appears that this meter is 118.9 mikrons longer than the Metre des Archives at 13. 7 Centigrade, a mikron being equal to s^bo- inch, or ordinarily, with sufficient exactness,, 030 do- inch. The meter will also be compared with the meter upon brass belonging to the Stevens Institute, which has been compared directly with the Prototype of the International Bureau of Weights and Measures. A further comparison will be made with an end-measure meter of steel, purchased by the writer of the celebrated mechanician, M. Froment of Paris, and declared to be 8.43 mikrons longer than the Metre des Archives at Centigrade. (b) In order to make these comparisons, it will be necessary to determine with the greatest care the amount of the change in length of each standard thus compared for each degree of temperature. This quantity is usually designated the coefficient of expansion. It varies according to the metal employed. (c) Having the standard line-measure yard and line-measure meter with their subdivisions traced upon the same bar, it will be necessary to ascertain the relative errors of these subdivisions with the utmost precision. Then, applying the proper correc- tions for these relative errors to the proportional error of the total length, we shall have the absolute correction for any sub- division thus investigated at the adopted temperature. (d) A similar investigation must be made of the correction for total length and for errors of subdivision of the short steel line-measure referred to under division five. This comparison may be made with any selected subdivision of the same length upon the different standard yards. DESCRIPTION OF COMPARATORS. For a description of the two comparators with which this investigation was made, the reader is referred to a paper by the writer entitled " Studies in Metrology," published in the Pro- ceedings of the American Academy of Arts and Sciences, vol. xxiii, p. 287, et seq. DESCRIPTION OF STANDARD BARS. The four bars prepared for end and line-measure standards are described as follows : P. & W.j has the same composition, form, and dimensions as P. & W. 2 Polished gold plugs are inserted at the bottom of wells sunk in the bar to the depth of half an inch at intervals of 12 inches. P. & W. 2 is a bar of cast bronze 41 inches long, 1 inch wide, and 1 inch deep. It is composed of 16 parts of copper, 2 parts of tin, and 1 part of zinc. Platinum-indium plugs, T V of an inch in diameter, are inserted flush with the surface at the points indicated in Fig. 1. FIG. 1. P. & W. 3 is a bar of tempered steel 40 inches long, 1^ inches deep, and f of an inch wide. This bar is designed both for line- measure and end-measure standards. The shape is shown in Fig. 2. r- FIG. 2. The upper surface is polished for receiving the graduations. P. & W. 4 is an annealed bar of steel. It has the same form and nearly the same dimensions as P. & "W 3 . Instead of a plane surface, however, tempered steel plugs are inserted at points cor- responding to those in P. & W. 3 and five decimeter plugs are inserted in the second half meter. 6 P. & W. 5 is a tempered steel bar 6 inches long, and -J inch in cross section. The space of 4 inches is laid off upon this bar, with subdivisions which will be hereafter described (page 43). It gives me pleasure to say that these bars came from your establishment in admirable condition for receiving the gradua- tions. The surfaces of P. & W M and of P. & W. 2 were found to be practically parallel. The depth of the bars is so nearly the same, that one can be substituted for the other under the micro- scope of the comparator without requiring any change in focus. When placed upon a plane surface every part of the upper surface was found to remain in focus during a movement of the microscope carriage over the entire length. In all of these bars, however, it was found to be necessary to provide for the variations in the length of the standard unit pro- duced by the warping of the upper surfaces, occasioned by the flexure of the bars themselves whenever they do not rest upon a perfectly plane surface. This is accomplished by supporting the bars at two points placed at a distance from the center equal to half the length of the bar divided by the square root of 3. If the supports are moved nearer to the center of the bar the upper surface becomes more convex and the lower surface more con- cave. If they are placed nearer the ends, the reverse effect takes place. According to the investigations of Airy, Clarke, and others, the least effect of a warped surface in producing a change in the length of the whole unit will take place when the supports are placed at the neutral points whose distance apart should be Length of bar. V n* l in which n represents the number of supports. Aside from the neutralization of the effect of the flexure of the bar by the location of the points of support, this method of two supports has a decided advantage over the support upon a supposed plane surface, from the fact that although the bar may be ordinarily kept in a vertical position, whenever it is placed upon its supports at the neutral points it will fall into an invari- able plane within a very short time. As an illustration of the necessity of attention to the question of change of length through flexure, it may be stated that the deviation in the length of the yard upon P. & W. 2 , when the supports are placed at the extreme ends of the bar, is over one thousandth of an inch. If the defining lines are traced in the neutral plane of the bar, the effect of flexure will be practically eliminated. Hence in P. & W.j the yard is traced upon the polished surfaces of gold plugs inserted in the bottom of wells sunk to the middle of the bar. This form has certain advantages for standards in which the total length is the main consideration, but it has the decided disadvantage of requiring the use of an objective of low power; besides, only the larger subdivisions of the entire unit can be obtained. But there is a very simple way of avoiding the effect of flexure upon surface graduations. As the writer has nowhere seen an account of the method which he has found very successful in practice, it will be briefly described. The bed of the comparator is first carefully leveled up. A shallow pan containing a thin layer of mercury is placed upon the surface of the bed-plate and extends its entire length. The microscope, after being focussed directly upon the surface of mercury at one end, is then carried along the ways to the other end. If the surface of the mercury remains in focus at every point, the microscope plate moves in an invariable plane. By a movement of the flexure screws the bed plate can be easily and quickly adjusted so that this condition will be satisfied. As a further test Messrs. Alvan Clark & Sons have prepared for me a bar having nearly an optically plane surface when sup- ported at the neutral points. It is always found that when the bed-plate has been Adjusted to the mercury surface, every point of the surface of this test-bar also remains in focus. Having made sure that the microscope plate moves in an in- variable plane, we have only to stone the plugs which receive the graduations until they are in the same focal plane ; the bar mean- while resting upon its supports at the neutral points. It is obvious that whenever the bar is supported at these points the polished surface of the plugs will always fall into the same plane, unless a permanent "set" should take place, of which there is no present evidence. 8 CONSTRUCTION OF STANDARDS. Since it is desirable that the final standard shall have as small errors as possible, the plan was adopted of tracing upon P. & W. a provisional yard in order that its relation to "Bronze 11" might be obtained. With the corrections thus obtained, P. & W.j could be constructed independently of the variations of tempera- ture. Then, having prepared the surface of P. & W. 2 anew, P. & "W.j could be made available in laying off the final yard upon this bar. Professor Hilgard, Superintendent of the Bureau of Weights and Measures, kindly offered to undertake the final comparisons with " Bronze 11." He also placed at my disposal the various standards of the Bureau. It seemed necessary to transfer my comparator to Washington, in order that the standards in my pos- session might be compared with the standards of the Bureau under the same conditions as would exist in the subsequent comparisons at Cambridge. Inasmuch as the comparator of the Bureau is what is known as a vertical comparator, in which the graduated surface is in a vertical plane when the bar is placed in a horizontal position for comparison, while in all of my comparisons the graduated sur- face is in a horizontal plane, it seemed desirable to accept the facilities which the Bureau so kindly offered. In a subsequent paper I shall enter into a critical examination of the relative advantages of these two forms of comparators, employing data which the new comparator has furnished, since in this instrument the two forms are interchangeable. My present impression is decidedly in favor of the vertical form. It is to be remarked in this connection that the vertical comparator recently described by Professor Wild, of the Central Physical Observatory of St. Petersburg, was anticipated by the Lane comparator at Wash- ington, which has been in actual use for several years. Having traced upon P. & W. 2 a provisional yard in the man- ner already described, the bar was sent to Washington for com- parison with " Bronze 11." According to the report of Professor Hilgard, this yard was found to be 25 millionths of an inch longer than " Bronze 11." Since " Bronze 11 " is 88 millionths of an inch shorter than the Imperial Yard, this provisional yard was therefore 63 millionths of an inch shorter than the Imperial 9 Yard. Of course this very close agreement was, to a certain ex- tent, accidental. Having this standard as a basis, it was now possible to disre- gard in a large measure the question of temperature in the trans- fers to P. & W.j and from P. & W. t back to P. & W a . In making these transfers an attempt was made to make P. & W. 3 equal to the Imperial Yard No. 1, and to make P. & W. x equal to " Bronze 11." In P. & W.j there are several groups of three, four, and five lines each. As it was necessary to employ a special device in tracing the lines at the bottom of the wells, which could only be tested by actually ruling the lines, it was found necessary to ex- periment upon the surfaces of the gold plugs. The defining lines of this yard are the middle lines of the group of five lines nearest the inner edge of the plugs. (Fig. 3, p. 24.) In P. & W. 2 there are three lines on each plug, ruled at intervals of one thousandth of an inch. The middle lines are taken as the defining lines. The temperature of the comparing-room having been brought as near to 62 as possible, the yard, with the same subdivisions as on P. & W.j and P. & W. 2 was then transferred to the sur- face of P. & W 8 . Simultaneously with these transfers, the defining lines of the meter at 62 Fahr. were drawn by making the length 168.3 mikrons longer than the Tresca meter. In grinding the end-measures to length, I have employed, with good success, the very simple device furnished me by you for the purpose. Bar P. & W. 3 was originally left by your work- men only a trifle longer than the normal length, so that it was found necessary to carry the grinding beyond the normal length in order to make the end faces parallel. In this way both the yard and the meter were made too short by an appreciable amount. Inasmuch as the end-measures are useful only as orig- inal standards of comparison, a slight error is of no account, provided it is known with certainty and is constant. The precautions required in grinding to the correct length at a given temperature are so many that considerable labor is in- volved in the operation. The required length is first brought to within about one thousandth of an inch. During this operation a nearly constant temperature is maintained by the immersion of 10 both the comparing and the compared bars in the same liquid. When the bars are taken from the liquid and compared in air, one is liable to be deceived by an apparent change in their lengths, due to the unequal effect of evaporation upon the two bars. Unless the bars have the same shape this action is very noticeable. On this account alone, a leeway of y-J^ of an inch is none too great. A series of comparisons in air is now made with the standard extending over a period of from ten to fifteen days, and under temperatures ranging as far below and as far above 62 as pos- sible. The correction thus obtained is taken as the basis of the estimate of the amount which may safely be taken off in the next operation. Usually two or three operations will be found necessary before the true limit is reached, each requiring an in- vestigation of the relation between the comparing and the com- pared bars. When, however, the relative coefficient of expan- sion between the two bars is known, three or four days will be sufficient for each series of comparisons. On the 21st of January, 1881, comparator No. 1, belonging to the writer, was shipped to Washington, the temporary bed-plate for mounting it having been previously forwarded from your establishment. On the evening of the same day, I started for the same des- tination, taking with me the Tresca meter and bars P. & W M P. & W. 2 and P. & W 3 . Arriving at Washington on the 23d instant, everything was found to be in readiness for the work of comparison. My comparator was assigned to room 96, in which a pretty steady high temperature could be maintained. The comparisons which the Bureau were to undertake with the Lane comparator were committed to the care of Assistant Edwin Smith. It was arranged by Professor Hilgard that I should make alternate readings of the microscopes with Mr. Smith. With this exception, all the operations of comparison were conducted by Mr. Smith. Indeed, a knowledge of the results obtained was purposely avoided during the work, from the fear that the readings might be affected by this knowledge. The comparisons of P. & W. 2 with " Bronze 11 " occupied three days, from three to four series being taken each day at intervals of about two hours. The comparison of P. & W.j with " Bronze 11 11" also occupied three days, the order of observations and con- ditions of temperature being nearly the same as with P. & W 2 . During the afternoon of January 29th my comparator was removed to the Observatory, a nearly isolated small brick build- ing, which served an admirable purpose for comparisons at a low temperature. Two vacant transit piers gave a very steady sup- port to the comparator. Bars P. & W. 3 and the Tresca meter were at the same time removed to the building and placed in position for comparison. From this time till the afternoon of February 2d a very steady, low temperature was maintained in the building. During Jan- uary 30th, 31st, and a part of February 1st, comparisons were made between these bars. During the afternoon of January 31st "Bronze 11 ", P. & W.j and P. & W. 2 were removed to the Ob- servatory and placed in position for comparison ; the comparisons of these bars upon the Lane comparator having now been com- pleted. During February 1st and February 2d these bars were compared by Mr. Smith and myself, according to a scheme simi- lar to that observed with the vertical comparator. At 4 o'clock in the afternoon of February 2d the comparator and all the bars were again removed to room 96, in which the temperature was now not far from 62 Fahr. During February 4th, 6th, and 7th especial attention was given to the comparisons between " Bronze 11 ", P. & W.j and P. & \V. 2 with reference to the determination of their relative coefficients of expansion. After my return from Washington an extended series of com- parisons was made between meter P. & W. t and the Tresca meter T%; between the end-meter P. & W. 3 and the Froment meter designated (Rj)*; between yard and meter P. & W.j and the line- yard and meter of P. & W. 3 ; between yard P. & "W.j and the Whitworth yard (W.), and between (W.), P. & W. 3 and P. & W. 4 ; both for the yard and the meter. COEFFICIENTS OF EXPANSION. In order to transfer the standard yard from the bronze bar to a bar of any other metal, it is necessary to know either the abso- lute coefficient of expansion of the normal bar, or the relative expansion of the two bars compared. The relative coefficients of expansion between the several bars may be obtained from the * See pages 289-293, Proc. American Academy. 12 comparisons themselves. It is therefore necessary to obtain the absolute coefficient of at least one of the bars. At the International Bureau of Weights and Measures, and at the Standards office in London, comparisons are for the most part made at air temperatures. At Washington, however, the preference is given to liquid contacts, the bars to be compared being immersed in flowing glycerine. After considerable experi- ence with both methods, I am still in doubt which is capable of the most accurate results. In the operations connected with the construction and verification of standard gauges, however, you unquestionably require air contacts. I have therefore deter- mined the coefficients under these conditions. At the outset of this investigation a difficulty was encountered which at first appeared insurmountable with the means of con- trolling temperature at my command. In comparing the Tresca bar T a 2 which has a small mass, with P. & W. 2 which has a mass several times greater, it was found that the slightest change in temperature would change their relative lengths by an amount far greater than that due to the coefficient of expansion between them. I add one or two examples : On one occasion after the bars had remained at the nearly constant temperature of 78 for several hours, one of the windows of the comparing room was opened for thirty seconds and then closed again. The tempera- ture of the outside air was 20. The two bars were then com- pared again, the operation requiring about forty seconds. Dur- ing this time T a 2 had lost on P. & W. 2 no less than 468 mil- lionths of an inch. Under the normal condition of the two bars P. & W. 2 should have shortened faster than T a 2 under the sup- position that both had the same form and the same mass. As another illustration, I take the comparison of P. & W. 3 with T a 2 made February 24, 1881. These bars have as their relative coefficient 130 millionths of an inch for each degree Fahrenheit. The temperature of the comparing room had been maintained at 82 for several hours. The temperature of the outside air was about 25. In the column of P. & W. 3 minus T a 2 , are given the number of millionths of an inch which T a 2 had gained over P. & W. 3 at the times given. Both windows of the cornparing-room were opened wide at 3 hours, 55 minutes, seconds. Thermometer. (P. &W. 8 )-(T 2 ) o div. 78.0 +1672 68.0 + 5105 59.4 +4413 - 60.4 + 4057 60.7 +3723 64.9 58 64.8 76 63.9 63 62.2 73 60.6 136 57.2 132 13 Time. h. m. s. 3 55 35 3 57 15 3 58 45 410 4 2 35 4 12 45 4 14 45 4 17 5 4 20 15 4 26 25 4 28 5 It will be seen from the above that in 35 seconds T a 2 fell behind P. & W. 3 no less than 1672 millionths of an inch, that within two minutes the maximum deviation took place and that after this time P. & W. 3 continued to shorten faster than T a 2 but with a rapidly diminishing ratio of decrease. Suppose I place a bar of glass of large mass which has a very low coefficient of expansion upon the comparator, and place beside it a narrow and deep bar of zinc which has a very high coefficient of expansion. Suppose a steady low tempera- ture has been maintained in the comparing-room for a sufficient length of time for each bar to settle to its normal length at a given constant temperature. Under these conditions I suddenly introduce into the comparing-room a volume of heated air and maintain as nearly as possible a constant supply. The effect of this change of temperature upon the bars will be nearly as follows: . (1) Within ten minutes the zinc bar will increase in length by the total amount due to the change in temperature, and any further slight changes in temperature in the surrounding air will produce their normal effect in from five to eight minutes. (2) The heat will penetrate the glass bar very slowly, probably in nearly parallel waves. Ten or fifteen minutes will elapse be- fore any change of length will be noticeable. From this point the changes which occur will be very irregular, ^specially if there are changes in the temperature of the surrounding air. While that portion of the heat which has been already absorbed is doing its work the changes in the temperature of the surrounding air will produce their effect upon the outside portions of the bar. 14 These pulsations will go on in waves of constantly diminishing amplitude until there is an equilibrium of temperature between all the parts of the bar. It is impossible to predict in any assumed case the length of time required for a condition of equilibrium between the zinc and the glass bars. In general, the greater the range of tem- perature and the greater the fluctuations during the passage from one extreme to the other, the longer will be the time required for the restoration of the equilibrium. It cannot be safely placed at less than four hours. All of my observations show that the changes in the length of a bar under a varying temperature are due to two causes. (a) The direct action of heat upon the surfaces of the bar. (b) The action of heat already absorbed in the body of the bar and w r hich is not indicated by the ordinary thermometer. The amount of this absorbed heat will be a direct function of the conductive power of the metal and the mass of the bar. Changes of considerable magnitude have been repeatedly ob- served in the relative lengths of two bars having a large mass, notwithstanding the fact that the reading of the thermometer placed upon the surface of the bar remained constant during the continuation of the observations. The influence of mass in retarding the action of temperature has one compensation. If the standard bars having the shape and size of " Bronze 11 " are kept in a room from which direct sunlight is excluded, and in which a nearly constant temperature is maintained, the presence of the observer will have no effect upon comparisons if they do not occupy over fifteen or twenty minutes. During this time the bars may be handled, almost with impunity, if the hands are protected. The general law under which these variations take place may be stated as follows : The time required by bars of different metals to assume their normal length under great changes of temperature, is a function of their shape and mass. Further observations in this direction are needed, but the time required seems to vary from twenty-five minutes for the copper (Tresca) meter to four and a half hours for the bronze bars. In these observations the ordinary practice of placing the ther- mometer upon the upper surface of the bar compared has been 15 followed. At London, the thermometers rest upon the surface of the bar measured, but shields of the same metal are placed over the bulbs. At Paris, the same plan is followed, except that no shields are used. At Washington shields are used, but they are not made of the same material as the bars. Whenever a nearly constant 'temperature can be maintained, as is the case at Paris, the thermometers indicate nearly the temperature of the bar upon which they are placed. But it must be borne in mind that the thermometer indicates only its own temperature. Whenever a sudden change of tem- perature is indicated, it cannot be inferred that there is a corre- sponding change in the length of the bar to which it is attached. Many experiments have been made during the last three years for the purpose of determining within what limits small changes of temperature in the com paring-room can be neglected in the comparison of standards. When the observer first enters the comparing-room at Cambridge, where the temperature is consid- erably below the normal temperature of his person, the thermom- eter will usually indicate an increase of temperature amounting to 0.5 within five minutes. What ivill be the effect of this increase in changing the length of the bar within the same limits of time ? Here, again, the effect will be a function of the shape and the mass of the bar. The writer has at the present time strips of steel and of aluminum forty inches long, one inch wide, and four one thousandths of an inch thick, mounted horizontally upon the comparator. These strips are placed side by side, a very narrow space intervening. They are fastened at one end, and are kept taut by springs attached to the other end. It is obvious that the relative positions of the two parts of a line drawn across the face of the strips at a given temperature will indicate the relative varia- tions in the length of the strips under varying temperatures. These variations are measured under the microscope of the com- parator. Under this arrangement the strips become a metal thermometer. It has been found that very slight changes in temperature are practically registered instantaneously by the change in the posi- tion of the two lines. When the air in the room is set in motion by swinging the door of the comparing-room, the corresponding swaying of the lines back and forth furnishes a beautiful illustra- 16 tion of the instantaneous effect of a change of temperature upon a body having a large surface area and a very small mass. In this case it is impossible to make the reading of the micrometer of the microscope before the effect of the presence of the observer will be visible. When we pass to the Tresca standard, which has a large sur- face area and a small mass, experiment has shown conclusively that the effect of the presence of the observer can be neglected for about three minutes. In the case of standards having the shape and mass of P. & W. 2 , i. e., a cross section of 1 inch, or even a cross section of 1-J- X i inches, it has been found that the presence of the observer in the comparing-room can be neglected for fifteen minutes, provided there is no direct contact between the person of the observer and the bar. When there is a direct contact through the hands, continuing, e. g., for one minute, there will be an instan- taneous change in length, especially if there is moisture on the hands, but if no other contacts are made, there will be no visible shortening of the bar for five minutes, and the total dissipation of the heat stored in the bar by the contact w r ill require from twenty to twenty -five minutes. If a shield of thick writing paper is used the bar can be handled without producing any visible effect, at least for several minutes. The practical conclusion to be drawn from these observations is : first, that all comparisons of standards should be completed before the presence of the ob- server can produce any effect in changing the length ; and second, that no further comparisons should be made until the small amount of heat which, though imperceptible at the time, has in reality been imparted to the bars, has been merged in the general temperature of the entire mass. In general, all comparisons have been completed within ten minutes, and at least four hours have been allowed to intervene between the comparisons. Several other necessary precautions have been taken in relation to the temperature. First. The number of comparisons at equal distances below and above 62 have been made as nearly equal as possible, thus elim- inating to a certain extent at 62, the effect of errors introduced through the temperature. Second. Although the reading of a thermometer may seem to be stationary, it in reality has a drift, either up or down, which 17 may be ascertained by subsequent readings. It lias been my aim to obtain, in every series of comparisons, nearly an equal number of cases of upward and downward drifts. It should be said here, the reading of the thermometer adopted is always that which is taken w T hen the observer first enters the com paring-room. Third. It has been found that this elimination of errors for drifts of short period is not perfectly effected, but that there are drifts of long period which are functions of the season of the year. The effect of errors produced by this cause, is impercepti- ble except by the comparison of long series of observations made at opposite seasons of the year. The delay in completing this report has been occasioned by the necessity of continuing com- parisons of this character. It is believed that the results to be given hereafter in this report are practically free from errors of the nature indicated. I notice at this point one other precaution which must always be taken against a very fruitful source of error. I refer to the error introduced through an imperfect determination of the focal distance of the objective of the microscope in making the com- parisons. With heavy lines, having rounded edges, it is well nigh impossible to focus upon the defining lines twice alike. The error which may be introduced in this way may be as great as -g-J-Q-u of an inch in a yard. The most effective remedy against this difficulty is the selection of a very fine scratch upon the sur- face for the determination of the proper focus. The correct focal distance can be found from fine lines much more accurately than from coarse ones. It is obvious, in view of what has been said, that observations for the determination of the coefficients of expansion have a de- finite value only when the bars reach a state of absolute rest under a constant temperature, and when all the precautions above described have been taken. Three series of determinations of the absolute coefficient of expansion of P. & W. 2 and of T have been made. In the first series a normal bar was kept in the clock-room of the Observatory, in which the temperature rarely varied more than 1 or 2 during twenty-four hours. At an early morning hour, this bar was carried into the cornparing-room and compared with the bar whose coefficient was required. The time required 18 to make the comparison was usually about forty seconds. After the comparison, the normal bar was immediately returned to the clock-room. In the second series, P. & W. a was immersed in water, at a temperature varying between 32 and 90 Fahrenheit. The common unit of comparison was the constant distance between the stops of the comparator. While the results obtained by this method, from observations on the same day, were found to have a close agreement, the results obtained on different days were very discordant. It was found to be impossible to maintain at the same temperature, the entire mass of the water surrounding the bar. A new method of maintaining the entire mass of a liquid at a constant temperature has been recently introduced at Paris and London with success. Doubtless very accordant results will be obtained from this method, but after all, immersion in a liquid is not the normal condition in which standards are used in ordinary practice, and therefore the coefficient obtained in this way does not represent the conditions which are the most likely to occur in daily experience. The coefficient of expansion ought to be obtained under the ordinary conditions under which the standard is used in measurements of length. It is believed that the difficulties inherent in the methods described, are overcome in the third method adopted. An end- measure bar of steel was mounted in a metal box in such a manner that there was freedom of motion, longitudinally, under variations of temperature. The ends of the bar were of hardened steel. They project beyond the ends of the box about one-fourth of an inch. This box, filled with ice and water which covered the bar to the depth of about five inches, was supported upon the bed of the comparator in such a manner that one end of the bar was in contact with a fixed stop attached firmly to the bed plate. A corresponding stop was attached to the carriage which carries the microscope. Meter P. & W. 2 was mounted permanently upon the bed of the comparator in a line parallel with the stops, and was adjusted for parallelism with respect to the microscope carriage in both vertical and horizontal planes. The observations proceed in the following order : (a) After the movable and the fixed stops have been brought 19 into contact, the microscope is adjusted upon the initial defining line at one end of the meter. The microscope carriage is then moved forward far enough to allow the box containing the end- meter in melting ice, to be placed in position against the fixed stop. The movable stop is then brought into contact with the other end of the bar by a movement of the carriage. If the two bars have the same length, the micrometer line of the microscope should fall upon the defining line of the meter at this end. Whatever the relation existing between the length of the two standards, the difference is measured with the micrometer screw. The ice-box is then removed and the observation is not repeated until the required conditions which relate to temperature are fulfilled. It will be seen that whatever the temperature of the com par ing-room, the line-measure standard is referred to a con- stant unit of length. Hence, the difference in the length of the standards at known temperatures, divided by the difference of the corrected readings of the thermometer will give the absolute co- efficient of expansion for the bronze bar. The absolute coefficient's of three bars have been determined in the manner above described, viz.: P. & W. 2 , the Coast Sur- vey meter designated C. S., and the Tresca meter T. For the low temperatures nearly all the observations were made a little before sunrise ; the windows of the comparing-room having been left open during the night. For the high temperatures, a gas stove was used to maintain a constant supply of heat. It was found to be possible to keep the temperature of the comparing-room at about 80 for several days with an extreme variation not exceed- ing one or two degrees. The observations upon the bar T extend from February 7, 1883, to May 8, 1883; those upon bar C. S. from February 12, to May 18, 1883, and those upon P. & W. 2 from February 12, to May 8, 1883. The details of these observations are given in the Proceedings of the American Academy, pp. 371-380. It will be sufficient to give here the results of the groups of observations made near the temperature 32 and 62 Fahr., as shown on page 377 etseq. The comparisons for each group have all been reduced to 32 and 62 by means of the provisional relative coefficients previously found between the standards and the steel bar S in melting ice. The 20 results are expressed in divisions of the micrometer, 1 division being = 0.504/4= 0,000020 inch. Standards whose coefficients are to be determined. T b = Tresca Meter. C. S. = Stevens Institute Meter. P. & W. 2 = Pratt & Whitney Meter. Provisional relative coefficients. Coefficient = 33.18 div. " =34.63 " =34.00 DETERMINATION OF THE ABSOLUTE COEFFICIENTS OF ME- TERS T, C. S., AND R 2 , FROM THE NORMAL VALUES FOR AND 16. 67. METER T b i. Date. (r- 0) S T b i Means by at 32. Groups. Date. (16. 67 r} S T*i at 62.0 Means by Groups. 1883. o div. div. 1883. o div. dir. Feb. 7 + 1.76 + 60.7 Feb. 11 + 3.20 -476.9 7 + 3.83 + 57.8 19 7.86 480.4 7 + 7.60 + 59.6 25 + 9.09 473.2 8 4.30 + 65.1 25 + 8.36 469.6 8 + 1.46 + 53.8 +59.4 26 5.70 475.6 475.1 9 4.54 + 61.3 Mar. 3 2.66 476.8 12 -1.78 + 61.4 Apr. 15 2.74 472.6 12 2.96 + 59.5 17 + 4.42 474.9 12 0.79 + 59.0 18 + 7.53 472.9 13 + 1.69 + 62.2 +60.7 19 + 8.03 474.6 474.4 13 + 0.12 + 60.8 20 1.29 475.3 13 + 3.26 + 65.2 24 3.80 471.6 14 . 6.50 + 56.5 25 3.37 478.4 15 + 5.82 + 57.5 26 4.59 474.7 16 + 0.78 + 61.0 +60.2 27 + 7.65 475.8 475.2 20 1.92 + 57.0 27 + 0.30 475.3 25 + 2.96 + 63.0 28 1.87 473.9 27 6.71 + 63.1 29 + 1.32 473.1 27 + 2.91 + 61.5 29 + 0.66 475.1 28 3.47 + 63.1 +61.5 30 + 0.79 474.4 474.4 28 0.22 + 63.0 30 1.09 475.0 28 0.71 + 63.5 May 1 1.01 472.5 Mar. 1 + 3.64 + 62.1 1 + 0.11 476.4 4 0.35 + 59.2 2 + 7.95 475.1 5 4.38 + 66.7 +62.9 4 1.40 467.4 -473.3 5 1.18 + 65.6 4 1.49 469.9 Apr. 22 + 4.57 + 59.9 4 3.45 470.8 23 + 5.97 + 60.9 6 + 0.20 472.2 24 + 6.02 + 59.5 7 + 8.75 476.8 25 + 5.67 + 60.1 +61.2 8 + 3.80 473.6 472.7 21 METER C. S. Date. (T 0) S T b i Means by (167 r) at 32. Groups. S T b i Mean* by at 62. Groups. 1883. div. div. 1883. o div. div. Feb. 12 6. 14 + 483. 2 Feb. 26 5. 29 85.7 12 1. 15 + 488. 8 Mar. 3 2. 60 95.8 13 + 4. 69 + 490. Apr. 18 + 7. 82 89.4 13 7. 76 + 488.3 19 6. 21 92.0 14 4. 87 + 490. 2 +488.1 20 - 1 - 12 93 .6 91.3 15 + 6.14 + 481. 3 21 0. 12 96 .8 16 -1.44 [+473 71 22 7. 81 97 .8 20 25 2. + 1 96 75 [+476.7] + 490.4 25 25 3. 4 72 15 89 91 .3 .4 27 + 0.67 [+475. 4] +485.8 28 2 04 93 .1 98.7 28 2 58 + 488.7 May 1 0.02 88 .1 28 1 .07 + 487.4 2 1.42 98.8 28 11 + 487.1 2 2.32 96.7 28 .80 + 486 5 2 2.48 91 .0 28 2.33 + 485.0 +486.9 S 1.80 99 .0 94.7 28 8 76 + 484.0 3 1 15 97 .5 28 + 3 .13 + 487 .2 3 1 .54 88.8 Mar. 1 + 5 .65 + 482.5 4 1.68 96.7 4 8 .06 + 484.4 6 + 17 86 .1 4 4 .40 + 493.6 +486.3 6 79 96 .3 6 .04 91 .3 92.8 4 .89 + 484.8 19 + 6 .70 + 482.7 Apr. 22 + 4.07 + 482 .2 23 + 5 .79 + 485.8 23 + 5 .88 + 487.3 +484.6 24 + 5 .77 + 485 .1 25 + 2 .23 + 485 .4 26 + 1 .54 + 479.0 i 27 + 4 .97 + 485 .9 May 2 + 7 .55 + 477 .0 +482.6 Date. o-- S METER I 5 P.&W.g Means by at32.0 Groups. 12 >. & w. 2 Date. (1667 r) S P.&W at 62.0 .oMeansby Groups. 1883. o div. div. 1883. div. Feb. 13 + .58 + 431 .9 Feb. 11 + 3.66 135 4 12 i .31 + 429 .4 25 + 8 .19 131. 5 13 + 1 .52 + 421 .4 26 3 .79 [152. 1] 14 + 1 .81 + 437 26 4 .36 135. 15 + 4 .89 + 433 4 +430.6 Mar. 31 2 .57 126. 132.0 16 2 .28 + 419 2 May 4 1 .38 124. 9 16 + 3 .65 + 427 9 4 3 .11 136. 5 27 + 3 .17 + 429 6 4 3 .27 135. 4 27 + 2 .05 + 444 2 6 + .15 135. 6 28 4 .35 + 427 7 +429.7 8 + 3 .75 143. 3 135.1 Mar. 2 + 4 .27 + 427. 9 3 + 3 .25 + 432. 4 7 + 8.25 + 426. 6 +429.0 Collecting results, we have - For0 C. Forl6'.67. a = + 61.0 div. = + 30.7 p. a = 474.2 div. = 2.39.1 p Whence b + 32.10 div. = + 16.18 p For S - C. S. a = + 488.7 div. = + 246.3 p a = 93.1 div. = 46.9 p Whence b = -f 34.90 div. = -f 17.59 p ForS P. & W. a a = -f 429.8 div. = -f- 216.6 p a = 133.6 div. = 67.3 p Whence 5 = -f- 33.80 div. = -j-17.04^ We have therefore, from these absolute coefficients, the follow- ing relative values : From Whence for S-T S-C.S. s_p. & w. 2 T-C.S. T-P. & W. 2 C.S.-P. & W., r=-f 16.18 /i =+17.59^ $=+17.04,1 I +1.41 p 5= +0.86^ 1= 0.55/1 23 Combining these values with the relative values found from the observations with the universal comparator, we have finally the following values for the absolute coefficients : Standards. Coeff. for 1 Meter. Coeff. for 1 Yard. T + 16.18 fi -fH.SO/i C.S. 1 !^ 9 1^17.60 16.09 = I*.UP "21 17.27 17.04 These results are nearly identical with those found for T and P. & W. 2 by the methods described on page 18. They were as follows : For T, coefficient = 16. 56 p For P. & W. 8 , coefficient = 17.55 p Since the publication of this paper, the report of Dr. Pernet of the International Bureau, giving the determination of the co- efficient of the bar C. S., and of a bar identical in form and assumed to be identical in composition with the Tresca bar T b , has been received. The following are the results of the various determinations of the coefficient for each degree Centigrade. The number of units given represents the number of units of variation in 100 millions. Standard Bar. No. of units in 100 millions. Observer. T. 1642 Benoit. T. 1618 Rogers. C. S. 1771 Benoit. C. S. 1760 Rogers. P. &W. 2 1717 Rogers. Comparing the results for the bar of metal C. S. we find a dif- ference of only 11 parts irf 100 millions. In forming an estimate of the reality of these values, it should be borne in mind that they are the results of observations made at different times, by different observers, neither observer having any knowledge of the results obtained by the other, with comparators of widely dif- ferent forms of construction, by different methods x)f compari- son, and with thermometers which have never been directly compared. Ill the discussion of the absolute lengths of the yards and meters, P. & W.j P. & W. a P. & W., and P. & W. 4 at 62 Fahr., reference is made to the paper in the Proceedings of the American Academy above quoted for a full account of the obser- vations which are there given in detail. Only the general results will be given in this report. The bar here described as P. ifc AV. 2 is there designated R 2 a2 . The official report of Professor Hil- gard, however, relating to the comparison of the yards P. & W.j and P. & W. a will be given in full. It is as follows : U. S. COAST AND GEODETIC SURVEY OFFICE, WASHINGTON, February 4, 1881. PROF. J. E. HILGARD, Assistant in Charge U. S. Coast and Geodetic Survey Office. Dear Sir, The following report on the comparisons of Bronze Yards P. & W. Nos. 1 and 2 with the British Bronze Yard No. 11, is respectfully submitted. These two bars were brought to the office on Jan. 21st by Prof. Wm. A. Rogers, who gives the following description of them : "P. & W. No. 1 is a bronze bar of the same composition, shape, and dimensions as the British Bronze Yard No. 11. The defining lines are ruled on gold plugs in wells one-half inch in diameter and half the depth of the bar. There are four wells in this bar, the subdivisions of the yard into feet being traced on the plugs in the middle wells. The defining end lines, which have been compared with the British Bronze Yard No. 11, are the middle lines of the groups forming short chords with the cir- cles marking the junction of the gold plugs with the bronze. There is no defining cross line. The settings are made on the middle points of the chords. There are four other groups of lines on this bar, but they have not been used in these compari- sons. The appearance of the tracings is as follows : Lines on gold plug of bronze yard P. and W. No. 1. The initial point of measurement is at the end on which the stamp P. & W. No. 1 is engraved. The middle line of group marked* is the initial FIG. 3. point of measurement. 25 P. & W. No. 2 is a bronze bar of the same composition as P. & W. No. 1. It is 41 inches long, 1 inch wide, and 1 inch deep. Platinum-indium plugs are inserted in the bar, as shown in the following sketch : FIG. 4. ab be = cd =1 foot. aa! a^ etc., 1 inch. deli = c^d 3 etc., Clinch. a f 1 meter at 62 F. There are three defining lines traced on each plug. The com- parisons with the British Bronze Yard No. 11 were made with the middle lines on plugs a and d. A cross line at right angles to the tracings runs the whole length of the bar. The point a is taken as the initial point of measurement. The comparisons were made on the "line and end comparator," in room No. 6 of the Coast and Geodetic Survey Office. The British Yard Bronze, No. 11, had been on the comparator about two weeks, and in the afternoon of January 21st the bar P. & W. No. 1 was also placed on the comparator. On January 22d com- parisons wwe made by Smith alone, and on January 24th and 25th by both Rogers and Smith. After these comparisons were finished, bar P. & W. No. 2 was put on the comparator in the place of P. & W. No. 1, and compared with No. 11 on January 26th, 27th, and 28th, by both Rogers and Smith. In this comparator the microscopes are horizontal, and the bars are placed with the defining lines vertical. No. 11 was supported at its neutral points upon fixed supports. P. & W. Nos. 1 and 2 were placed upon the carriage having a horizontal motion No. 1 being supported at points seven inches from each end, and No. 2 at points seven inches from the a end and ten and a half inches from the f end. In each comparison each bar was in position twice, at one time making one reading and at the other two readings, each reading being the mean of two pointings, so that in the following tables of results each result is the mean of six pointings at each end of each bar. Such a comparison was made in from ten to thirteen minutes. 26 The two Fahrenheit ("Green") thermometers, Nos. 9 and 12, were used No. 9 being attached to the British Yard Bronze No. 11, and No. 12 to the P. & W. bar. The corrections to these thermometers at the temperature at which the comparisons were made are No. 9= 4-0. 03 No. 12 = + 0.00 On the following pages are given the results of these comparisons : Results of comparisons of Bronze Yard P. & W. No. 1 with British Yard Bronze No. 11: Date. 1881. January 22, January 24, January 25, Smith, Rogers, A. M. 9.35 11.26 P.M. 1.18 2.14 A.M. 9.30 10.38 11.51 P. M. 1.21 3.12 A. M. 9.31 11.09 P. M. 1.12 3.08 Temp. F. DEGREES. 62.45 62.10 61.60 61.40 57.10 57.05 56.90 57.00 57.10 57.70 57.55 57.65 57.70 58.71 57.33 B. Y. B. No. 11. P. & W. B. No. 1. SMITH. INCH. -.000079 120 038 120 -.000190 173 151 135 227 -.000163 199 168 125 -.000145 ROGERS. .000170 087 108 209 .000170 162 098 085 .000136 Giving Rogers' result two-thirds weight, we have At 58. 18 F. No. 11 P. & W. No. 1 = .000141 inch. * Imperial yard - No. 11 = +.000088 inch. Imperial yard P. & W. No. 1 = .000053 inch. * Report of 1877; App. No. 12, page 5. 27 Results of comparisons of Bronze Yard P. & W. No. 2 with British Yard Bronze No. 11: Date. 1881. A. M. January 26, 9.49 11.21 P. M. 1.28 3.11 A. M. January 27, 9.39 11.24 P. M. 1.23 3.10 A. M. January 28, 9.36 11.22 P. M. 12.36 2.16 Smith, Rogers, Temp. F. 56.20 56.16 56.20 56.35 55.90 55.55 55.10 54.60 52.00 51.75 51.30 51.30 54.37 54.98 B. Y. B. No. 11. SMITH. ; 0001 16 .000114 +.000004 000060 + .000063 .000002 .000140 .000133 .000064 .000041 .000018 +.000015 .000050 P. & W. B. No. 2. ROGERS. .000100 .000089 + .000022 .000084 +.000052 .000014 .000125 .000098 .000072 .000041 -.000055 At 54.70 F. No. 11 P. & W. No. 2 = ' .000052 inch. * Imperial yard - No. 11, = +.000088 inch. Imperial yard P. & W. No. 2 = +.000036 inch. * Report of 1877; App. No. 12, page 5. Respectfully yours, EDWIN SMITH, Assistant U. S. Coast and Greodetic Survey. Report approved, J. E. HILGARD, Assistant in Charge Inspector U. S. Standard Weights and Measures. According to this report, P. & W. t is 53 millionths of an inch longer than the Imperial Yard, and P. & W. 2 is 36 millionths of an inch shorter than the Imperial Yard at 62. Fahr., assuming that "Bronze 11," P. & W Bl and P. & W. a have the same coef- ficient of expansion. 28 The following are the results obtained from the observations made by Mr. Smith and myself at Washington, with my comparator : Date. Observer. Temperature. minus P. & W. i Feb. 1, R, 34.0 0.000155 inch. 1, S., 34.0 0.000166 4, R., 60.8 0.000154 6, R., 62.7 0.000106 7, R., 62.2 0.000052 Hence, P. & W. j 0.000127 inch = " Bronze 11." " Bronze 11 " + 0.000088 = Imperial Yard = Y. and P. &W.j Date. Observer. Feb. 1, R, 1, R., 1, R-, 1, R., 2, R, 2, S., 4, R., 7, R, Hence, P. & W. 2 -0.000027 inch = "Bronze 11." ' ' Bronze 1 1" + 0. 000088 = Y. and P. & W. 2 + 0.000061 inch = Y. Combining these results and assigning equal weights to each, we have 0.000039 0.000039 inch -vr Temperature. "Bronze 11," minus P. & W. 2 31.2 0.000039 inch. 31.2 4- 0.000028 35.6 0.000002 35.6 0.000083 30.9 0.000014 30.9 0.000030 60.9 0.000075 62.2 0.000059 P. & W. , + &000088 +_000006n L 2 J Or, finally, P. & W.i 0.000046 inch = Y. P. & W. 8 +0.000048 inch = Y. Before proceeding with the discussion of the comparisons made subsequently to my return from Washington, the details of the comparisons of the Yard C. S. with the Imperial Yard made by Mr. Chaney, and of the meter C. S. with the Metre des Archives made by Dr. Benoit at the International Bureau, will be given. 29 The following; relations for the Yard are taken from Mr. Cha- ney's report : Series. 1 2 3 4 Whence, 1 division = 0.0000319 inch. Observer. Chaney, Rogers, Chaney, Rogers, Y C. S. 24.03 div. 30.18 26.96 24.83 Temperature. 5780 58.25 58.55 58.65 C. S. +0.00080 inch = Y. Or, the Coast Survey Yard is 80 hundred-thousandths of an inch too short at 62.0 Fahr. The following are the equations of condition formed from the comparisons of the meter C. S. with Type I of the International Bureau, quoted from the report of Dr. Fernet : No. Obv's. C. S. minus Type I. Weight. V. 5 x+ 1.2617 = 374. 52 p 1.5 +.1.17 p. 4 aj+ 1.2727 = 375.07 1.5 +0.52 3 x+ 1.2997 = 373.95 1.5 +1.39 6 x+ 1.4247 = 373.64 1.5 +0.57 7 x + 1.4907 = 373.56 1.5 +0.05 17 x+ 6.1547= 331.52 1.0 0.27 14 x+ 6.1577 = 330.02 1.0 +1.20 18 x+ 6.1617 = 331.76 1.0 0.57 19 x+ 6.1707 = 332.11 1.0 1.00 13 x+ 6.1887 = 333.40 1.0 2.46 15 x + 6.1937 = 330.70 1.0 +0.20 16 x+ 6.2067 = 331.30 1.0 0.52 20 x+ 6.2337 = 332.97 1.0 1.43 12 x+ 6.2497 = 333.06 1.0 2.67 11 x+ 6.2717 = 331.65 1.0 1.46 10 x+ 6.3287 = 330.53 1.0 0.86 21 x+ 6.3377 = 330.49 1.0 0.90 9 x+ 6.4657 = 328.71 1.0 0.28 8 x+ 6.4837 = 327.40 1.0 +0.86 2 a? + 11.5647 = 279.97 1.0 +2.15 1 x + 11.9017 = 276.41 1.0 +2.65 Whence, C. S. Type I = 389.14^ 0.43// From the known relation between Type I, and the Metre des Archives A, the following relation was obtained for the tempera- ture C., viz. : C. S. +310.7// = A. The coefficient of expansion at 62 = 17. 71 p in 1 meter for each degree Centigrade 30 The meter C. S. is therefore 310.7 mikrons too short at 32 Fahr. Employing the coefficient determined by Benoit in the reduc- tion from 32.0 to 62.0 Fahr., we have for 62.0, C. S. +15.5/4=: A. Or, C. S. is 15.4 mikrons too short at 62 Q .0. The following are the relations between the meter T% and the Metre des Archives A, at 32.0 and 62.0 respectively : At 32 At 62 T% + 102.8// = A. T a s 167.0," = A. The Tresca meter T a s is therefore 102.8 mikrons too short at 32.0, and 167.0 mikrons too long at 62.0. COMPARISON BETWEEN METEKS T AND P. & W. 2 a 2. Two series of comparisons between these standards were insti- tuted, one Aeries with Comparator No. 1, and the other with the Universal Comparator. In the iirst series two microscopes attached to the carriage were used. The bars were placed at a distance 2 x centimeters apart, and observations were made for the positions -f x and x. For x = + 3.0 cm. At 62. F. T 8 P. & W. 8 a 2. + 164.0/Z + 163.8 + 159.2 + 158.5 + 166.9 + 159.6 + 153.3 + 150.0 + 152.5 + 152.3 + 165.2 + 163.7 + 161.7 + 158.8 + 159.7 + 160.5 + 161.1 + 162.6 Date. 1881. (r 62.0)F. T a 2 P. & W. s ' Feb. 14 + 24.1 + 177. 7 ti 15 + 23.5 + 177.2 16 12.2 + 152.2 17 --13. 2 + 151.0 20 + 32.5 + 185.4 21 + 22.2 + 172.2 22 13.7 + 145.5 23 13.7 + 142.8 Mar. 16 8.9 + 147.5 23 13.6 + 144.6 24 9.7 + 154.0 25 + 26.8 + 178.9 29 11.8 + 155.0 30 13.2 + 151.3 31 -15.4 + 151.0 Apr. 3 + 29.3 + 187.2 8 + 6.9 + 165.0 10 + 8:9 + 167.6 Feb. 24 25 Mar. 11 13 14 15 16 16.3 +35.9 + 4.8 +23.1 +19.6 +22.4 9.0 31 For #= 3.0 cm. + 165. 5 p + 197.8 + 174.7 + 183.6 + 186.1 + 189.3 + 163.2 + 177.4 + 172.0 + 170.5 + 175.3 + 176.6 + 163.7 We have, therefore, R' For x = + 3.0 cm. = + 159.7 p. X 3.0 cm. = + 172.9 p. Mean = + 166.3 p. With the Universal Comparator. EQUATIONS OF CONDITION BETWEEN T a 2 AND P. & W. 3 a a (With 1-inch objective.) 1 div. = 0.440 u Date. 1882. T a 2 P. & W. 2 Apr. 26 + 401. 5 div. 27 + 396.8 28 + 391.7 30 + 392.3 May 3 + 393.9 12 + 380.0 20 + 372.8 23 + 375.2 At 62 F. (r 62)F. T a 2 P.&W. 2 a 2. No. Obs. a 16.306 + 380.1 div. 3 a 13.41 6 + 379.2 4 a 12.156 + 375.8 5 a 10.476 + 378.6 5 a 9.426 + 381.6 5 a 1.246 + 378.4 3 a + 2.98 6 + 376.7 3 a + 4.646 + 381.3 3 Normal Equations. + 3104.2=+ 8. 00 a 55.376 Whence, 6 = - 1.31 div. = 0.58 p 22062.0 = 55.37 a +823.306 Whence, a =+ 378.9 div. = + 166.0 p Combining the results obtained from the two comparators, we find: T a 2 --P & W 8 2 _ 1 66.3 p + 166.0 p_ "2 c\ ' j* Since T a 2 167.^= A. We have : Or: p. & W. 2 a 2 0.9 n = A. Meter P. & W. 2 a 2 is 0.9 mikron too long at 62.0 Fahr. S2 A more extended series of comparisons between between T a s, C. S., and P. & W. 2 *2, and also the steel standard Ii n both for meter and the yard, was made in 1883. The details are given on pp. 362-371, proceedings of the American Academy. Only the results for the normal temperatures C. and 16. 67 C. are given here. The columns A, represent the deviations of the observed relations from the mean value derived from the entire series. 33 COMPARISON OF METERS T a 2. T'-i, R^, R^s, AND YARDS Date. Y 61 .0 ' ** y A A M si i u rs aS A A M fe I* pf A A 1883. March 22 1.93 1.30 0.25 + 2.27 + 0.92 1 + 6.40 1 + 1.05 ! 0.38 1 + 1.25 + 0.07 0.14 + 4.51 + 12.58 +10.34 + 6.98 + 14.68 +14.58 + 15.02 +14.75 +1446 + 1454 +14.43 +14.66 + 14.84 + 14.58 + 14.49 + 14.27 + 14.41 + 1464 + 14.76 +14.79 + 14.80 + 14.99 +19.18 + 17.59 + 17.07 + 17.07 + 17.23 + 17.8(5 + 17.89 + 18.04 + 17.87 + 17.97 + 18.1(5 + 18.03 r. 26... nl 1... r. 10... y 18... y 23... y 29... le 4. . . le 26. . . le 28. . . div. -13.8 13.6 15.8 -15.5 14.1 13.1 15.4 15.2 13.3 15.6 -14.9 14.8 13.8 14 1 div. +1.8 +2.0 -0.2 +0.1 + 1.5 +2.5 +0.2 + 0.4 +2.3 0.0 + 0.7 + 0.8 + 1.8 + 1.5 +3.0 +2.0 1.0 + 1.3 -1.7 0.3 +0.6 0.7 0.8 1.0 1.2 1.5 +0.4 2.8 -2.1 -2.4 1.1 1.1 1.1 0.4 0.6 +0.6 0.5 -1.7 i 14 0.9 +0.5 + 1.7 + 1.0 1.0 2.4 + 1.05 1+1.09 +1.5? +0.17 0.61 1.64 0.85 0.77 0.03 P +0.8 +0.9 0.1 +0.0 +0.7 + 1.1 +01 +0.2 + 1.0 +0.0 +0.3 + 0.4 +0.8 +0.7 + 1.3 +0.9 04 +0.6 0.7 01 +0.3 0:3 -04 0.4 0.5 0.7 +0.3 1.2 0.9 1.1 0.5 0.5 0.5 -02 -0.3 +0.3 0.2 0.7 0.6 0.4 i+0.2 +0.7 +0.4 0.4 1.1 +0.46 : + 0.48 +0.51 +0.07 ! 0.27 0.72 0.37 0.35 0.01 div. div. /" div. div. P 23 25 ! 25 26 28 29 ... 30 30 .... April 1 2 ... ;:;;;; 3 8 9 10 ... 12.6 13.6 16.6 14.3 17.3 15.9 15.0 16.3 16.4 16.6 16.8 17.1 15.2 18.4 17.7 18.0 16.7 16.7 16.7 16.0 16.2 15.0 16.1 17.3 17.0 16.5 15.1 13.9 14.6 -16.6 18.0 14.56 14.52 14.04 15.44 16.22 17.25 164(3 16.3S 15.64 May 14 9.8 7.2 58 -8.4 6.7 8.0 7.8 -97 8.9 8.7 8.0 8.2 -7.7 8.4 7.3 -8.9 8.7 9.7 6.7 7.6 6.3 8.7 -6.5 7.7 9.5 7.1 6.7 -8.4 -9.9 7.9 i 1.8 +0.8 +2.2 0.4 +1.3 0.0 +0.2 1.7 0.9 0.7 0.0 0.2 +0.3 0.4 +0.7 -0.9 0.7 1.7 +1.3 +0.4 + 1.7 0.7 +1.5 +03 1.5 +0.9 +1.3 0.4 1.9 +0.1 -0.8 +0.3 +1.0 0.2 +06 +0.0 +0.1 0.7 0.4 0.3 +00 0.1 +0.1 0.2 +0.3 04 0.3 0.7 +0.6 +0.2 0.7 0.3 +0.7 +0.1 0.7 +0.4 +0.6 0.2 -0.8 + 0.0 15 +0.1 2.0 1.1 1.1 +0.6 21 1.6 1.2 2.2 1.0 1.4 1.2 2.2 2.7 23 0.6 -2.9 3.5 1.7 15 0.0 0.2 0.0 1.0 2.0 -2.0 3.1 + 1.0 +2.1 + 1.4 0.7 +0.2 +0.2 +1.9 -0.8 0.3 + 0.1 0.9 +0.3 0.1 +0.1 -0.9 1.4 1.0 +0.7 1.6 2.2 0.4 02 + 1.3 + 1.1 + 1 3 +0.3 0.7 0.7 1.8 +2.3 +3.4 +0.6 0.3 +0.1 +0.1 +0.8 0.4 0.1 +0.0 -0.4 +0.1 +0.0 +0.1 0.4 -0.6 0.4 +0 3 -0.7 1.0 -0.2 0.1 +06 +0.5 +0.6 1+0 1 -0.3 -0.3 0.8 + 1 + 1.5 16 17 18 19 20 21 ... 22 23 24 25 27 .... 28 29 30 31 June 1 3 4 5 6 7 25 26 26 27 27 27 28 Mar. 22 to Ma Mar. 28 to Ap Apr. 2 to Ap May 14 to Ma May 19 to Ma May 24 to Ma May 30 to Jui Juue 5 to Jui June 26 to Jui 7! 58 8.62 7.92 18.32 i 7.74 8.0C +CK45 0.59 +0.11 02fl I+0.2H 1+0.03 +0.20 0.26 +0.05 01: +O.lb +0.01 1. 02 +0.24+0. ii 1.30J 0.04 0.01 1.70044-0.19 2.20 0.94'- 041 0.541+0.72 +0.32 0.80+0. 46i+ 0.20 MEANS -15.61 =6.87 /* 8.03 = 3.53/u 1.26 = O.oo// 34 COMPARISON OF METERS C. S., At and at 16. 67. AND P. & W 2 Date. r 91 fl P? I QQ d sTo 1* *3 O A A 0) a <3 Pk OQ d M 08 ^d ft cd<1 d A A 1883. o div. div. div. ( div. div. div. f* Mar. 22 1.93 350.4 -317.9 0.3 0.1 56.9 55.4 + 2.2 + 10 23 1.30 337.2 315.3 + 2.3 + 1.0 54.9 53.9 + 3.7 + 1.6 25 0.25 323.4 319.2 1.6 0.7 54.3 _54.2 + 3.4 + 15 25 + 2.27 288.0 326.2 8.6 -8.8 58.5 60.2 2.6 1.1 26 + 0.92 308.0 323.51 5.9 2.6 58.7 59.4 1.8 0.8 98 + 6.40 204.7 312.5 + 5.1 +2.2 48.3 53.1 + 4.5 + 2.0 29 + 1.05 302.2 319.9 2.3 1.0 57.7 58.5 0.9 0.4 30 0.38 3246 318.2 0.6 0.3 5(5.7 56.3 + 1.3 + 0.6 30 + 1.25 - 290.7 311.8 + 5.8 + 3.8 54.3 55.2 + 2.4 + 1.0 Apr. 1 + 0.07! 311.3 312.5 + 5.1 + 2.2 58.3 58.4 0.8 0.4 2 0.14 323.9 321.6 4.0 1.8 65.0 _64.9 7.3 3.2 3 + 4.51 243.21 319.2 1.6 0.7 56.6 60.0 2.4 1.1 8 + 12.58 106.1 318.1 0.3 0.1 48.6 58.2 0.6 0.3 9 + 10.34 140.4 314.6 + 3.0 + 1.3 50.4 58.2 0.6 0.3 10 + 6.98 195.6! 313.2 + 4.4 + 1.9 52.9 58.1 0.5 0.2 At 16.67 At 16*67 May 14 + 14.68 71.9 38.4 6.3 2.8 38.2 36.7 f 5.9 + 2.6 15 + 14.58 66.5 31.3 + 0.8 + 0.4 _45 2 43.6 1.0 0.4 16 + 15 02i 53.4 25.6 + 6.5 + 2.9 33. bj 32.4 +10.2 + 4.5 17 + 14.75! 62.3 29.9 + 2.2 + 1.0 44.5 ! 43.01 0.4 02 18 + 14.46 57.1 19.9 + 12.2 + 5.4 44.4 42.8 0.2| 0.1 19 + 1454 70.4 34.5 2.41.1 42.5 40. 9 ! + 1.7 + 0.7 20 + 14.43 68.3 30.6 + 1.5 + 0.7 40.3 38.7 + 3.9 + 1.7 21 -t- 14.66 66.6 32.7 0.6 0.3 43.5 42.0 + O.G + 0.3 22 + 14.84 63.2 32.4 0.3 0.1 41.9 40.5 + 2.1 + 0.9 23 + 14.58 67.5 32.3 0.2 0.1 38.1 36.5 + 6.1 + 2.7 24 + 14.49 75.3 38.6 6.5 2.9 46.3 44.7 2.1 0.9 25 + 14.27 73.1 32.7 0.6 0.3 43.3 41.5 + 1.1 + 0.5 27 + 14.41 72.0 33.9 1.8 0.8 41.8 40.1 -f 2.5 + 1.1 28 + 14.64 70.7 36.5 4.4 1.9 45.3 43.8 1.2 0.5 29 + 14.76 68.5 36.3 4.2 1.8 _44.9 _42.6 0.3 0.1 30 + 14.79 63.9 32.3 0.2 0.1 41.6 40.2 + 2.4 + 1.1 31 + 14.80; 67.4 359 3.8 1.7 42.4 41.0 + 1.6 + 0.7 June I + 14 99 60.8i 32.5 0.4 0.2 41.9 40.7 + 1.9 + 0.7 3 + 19.18 + 11.8 30.5 + 1.6 + 0.7 40.7 42.6 + 0.0 + 0.0 4 + 17.59 19.0 34.5 2.4 1.1 37.7 38.4 + 4.2 + 1.8 5 + 17.07 22.9 29.6 + 25 + 1.1 37.7 38.0 +46 + 2.0 6 + 17.07| 20.2 26.9 + 5.2 +2.3 42.7 _43.0 _ 0.4 0.2 7 + 17.231 19.2 28.7 + 3.4 +1.5 _ 4i.6i 42.1 + 0.5 + 0.2 25 + 17 80 15.8 35.8 3.7 1.6 45.0 45.8: 3.2 1.4 26 + 17.89 10.2 30.4 + 1.7 +0.7144.3 44.1 1.5 0.7 26 + 18.04 11. Oj 34.2 2.1 0.9 43.6 50.9! 8.3 3.7 27 27 27 + 17.87 + 17.97 + 18.10 ll.fc 8.0 4.8 31.6 30.0 29.5 + 0.5 + 2.1 + 2.6 + 0.2 + 0.9 4-1.1 42.5 44.7 41.6 48.9! 63 51.7 9.1 49.5 69 28 40 31 28 + is.oa 11.1 34.0 1.9 0.8 ! 43.4 50.61 8.0 04 35 COMPARISON OF METERS Rj AND R 2 , AND OF YARDS R AND R 2 . At and at 16. 67. Meters. Yards. Si * OS 91 Date. T 1 fe A A | $? A A- PH' P-I PLJ PH i 1 HIM i 51 I II Ml| V I I i II a to b graduated in 16ths, 8ths, and 4ths, the latter being bands of 3 lines each. b to c " inches only, bands of 3 lines each. d to e " lOths and 20ths, each quarter-inch being a band of 3 lines. betof " to represent diameter at root of thread, U. S. Standard Thread Gauges, inch to 2 inches inclusive, 2 lines each, one line light and one heavy. Initial line at b e, reading towards a d. I to f " to represent diameter as above for 2 inches to 4 inches in- clusive, single line each. Initial line at I, reading ing towards a d. g to k Band of lines ^ of an inch long, ruled 2 inches, 2,500 per inch. Investigation of the Working Standard P. & W. 5 The first set of comparisons between the 4 inches of P. & ~W. 5 and the first 4 inches of P. & W. 2 a s made with the Universal Comparator in April, 1881, gave the relation : p. & W. 5 0.000012 in. =J Y In September, 1881, a more complete set was made with the new comparator. The following are the results obtained : 44 Second Series. Early Morning Observations. Mid- Afternoon Observations. Therm. P.&W. 5 Therm. -P.&W. 6 1881. o at 62. Fahr. 1881. o at 62. Fahr Sept. 11 67 1.04 div. Sept. 11 67.9 + 0.55 div. 12 67.0 0.80 13 81.3 1.75 13 81.3 2.15 13 79.8 + 2.24 13 79.8 + 0.13 15 64.6 + 1.33 15 66.6 + 0.11 18 61.4 1.99 15 64.3 + 1.67 19 62.4 0.68 15 64.3 + 1.63 20 63.4 + 2.63 18 57.0 2.74 21 63.6 + 2.76 19 62.0 0.20 22 61.1 0.75 20 63.0 + 0.94 20 63.1 0.93 Mean +0.48 21 63.6 + 0.50 22 59.4 + 0.28 23 61.8 + 0.66 Mean 0.10 For the mean value we have : P. & W.. +0.2 div. - 1 P. & W -a But Whence, & W. 2 2 0.1 P. & W. P. & W. + 0.1 + 0.000002 = Y . = Y Third Series. With Comparator No. 1. Comparison of P. & W. 6 with the first 4 inches of P.&W., Therm. -P.&W.s Therm. P. & W. B 1881. At 62. 1881. At 62. Oct. 6 36.8 + 4. 9 div. Oct. 11 59.0 + 1.3 div. 7 50.3 + 2.6 11 58.4 1.9 7 51.8 1.3 18 84.4 + 2.1 9 57.6 6.1 18 84.4 + 1.7 9 58.3 1.0 18 84.4 + 3.6 10 59.6 0.6 19 86.8 + 0.4 10 59.8 2.2 , 19 86.8 .+ 2.8 20 80.3 + 2.3 Whence, P. & W. fi + 0.6 div.=J P. & W. 2 And P. & W. 6 + 0.000009 in.:= J Y 45 Fourth Series. With Comparator No. 1. Comparison of P.&W. 6 with the first 4 inches of Therm. ^Ri-P.&W.g Therm. &RI P.&W. 1881. At 62.0 1881. At 62. Oct. 6 36.8 + 33. 2 div. Oct. 11 58.4 + 35. 9 div. 7 50.3 + 33.5 18 84.4 + 37.0 7 51.8 + 30.5 18 84.4 + 34.7 9 57.6 + 30.5 18 84.4 + 33.7 9 58.3 + 39.9 18 86.8 + 30.0 10 59.6 + 31.4 19 86.8 + 30.3 10 59.8 + 35.9 19 88.3 + 26.2 11 59.0 + 32.2 20 88.3 + 30.6 Whence, P. & W. 5 + 32. 8 div. = iRi But R, -33. 8 =i Y Whence, p. & W. 5 - 1. = i Y p. & W. 5 - 0. 000020 in.= Y Fifth Series. Comparison of P. & W. 5 with the first four inches of a steel half-yard designated \ Y. In March of the present year I requested that you would return to me P. & W. 5 in order that I might compare this stand- ard with the sub-divisions of a new standard half-yard whose relation to J P. & W. 2 a 2 has been determined with the greatest care from observations extending over several months. This half-yard has no sensible correction for total length. The cor- rections for errors of sub-division are as follows : A plus sign indicates that the indicated space is too short; a minus sign that it is too long. Space. Correction. 1 0.000006 inch. 2 +0.000024 3 +0.000000 4 +0.000000 5 0.000024 6 +0000005 Space. Correction. 7 +0.000005 inch. 8 0.000004 9 0.000012 10 0.000042 11 0.000026 12 +0.000036 Space. Correction. 13 +0.000000 inch. 14 +0.000020 15 0.000016 16 +0.000014 17 +0.000016 18 +0.000010 A comparison with the first four inches of this bar gave the result : P.& W. 6 0.000005 in.= Y. 46 Collecting results, we have : From Series I. P. & W. 5 0.000012 in. = Y Series II. P. & W. 5 f 0.000002 Y Series TIL P. & W. 6 + 0.000009 J Y Series IV. P. & W. 8 0.000020 - i Y Series V. P. & W. e - 0.000005 =Y Whence: P. & W. 5 0.000005 in. J Y Or: P. & W. 5 is 5 millionths of an inch too long at 62.0 Fahr. Investigation of the Errors of the Line and End-Measure Yard and Meter P. & W. 4 For the end-measure meter, I find for C. : p. & W. 4 O.G/i = A Or: End-meter P. & W. 4 is 0.6 mikrons too long at C. For the yard, I find : P. & W. 4 0.000112 in. = Y at 62.0. Or: Yard P. & W. 4 is 112 millionths of an inch too long at 62. 0. The report upon the line graduations of P. & W. 4 will be delayed until the completion of a series of observations now in progress for the purpose of ascertaining the effect of drift in thermometers upon the summer and winter comparisons of standards which have widely different coefficients of expansion. Corrections for Errors of Sub -divisions. SUB-DIVISIONS OF P. & W. 2 *2 July 17. July 18. div. div. I. _ 1.9 1.8 II. 4. 6.8 + 6.4 III. 4.8 5.4 (i div. = .504 /j) , FEET. Mean of all previous Adopted Mean. Observations. Corrections. div. div. div. inch. 1.6 - 0.9 - 1.2 = - 0.000024 + 6.6 + 4.2 + 5.4 = + 0.000108 -5.1 -3.3 4.2 = -f 0.000084 47 THREE-INCH SPACES OF THE FIRST FOOT. July 15. div. July 15. div. July 17. div. July 18. div. July 19. div. I. - 6.6 5.4 3.2 -2.8 3.6 II. + 2.9 + i.o 1.3 + 0.3 1.0 III. 3.0 - 2.3 1.5 3.6 -2.1 IV. -f 6.8 + 8.6 + 6.0 + 6.4 + 6.7 July 20. div. July 81. div. Means, div. inc I. -4.3 4.1 4.3 000 II. f 0.9 -j- 0.9 + 0.2 + 0.00' nr. - 3.4 2.2 2.6 0.00' IV. -f 5.7 + 5.5 + 6.8 + 0.00' INCHES OF THE FIRST THREE-INCH SPACE. July 17. div. July 18. div. July 19. div. Mean, div. I. - 0.9 0.5 + 0.0 0.5 II. + 1.6 + 0.8 + 0.8 + 1.1 III. - 0.7 - 0.3 - 0.8 0.6 inch. 0.000010 + 0.000022 0.000012 SIX-INCH SPACES OF THE FIRST FOOT. Inch. I. - 0.000089 II. _ 0.000084 1. IT. III. IV. V. FOUR-INCH SPACES OF THE FIRST FOOT. Inch. I. 0.000003 II. 0.000112 III. +0.000115 INCH SPACES OF THE FIRST Six INCHES. Inch. I. _ 0.000028 II. - 0.000064 III. + 0.000008 IV. 0.000020 V. 0.000028 VI. + 0.000004 SUBDIVISIONS OF P.&W., 3 Decimeters of P.&W. 3 a 2 Counted from the center towards the end. CORRECTIONS. Series I. Series II. + 1.7/1 +1.2/ 1.3 0.6 + 0.2 0.8 0.7 + 0.8 + 0.2 0.7 Mean. + 1.4 1.0 + 0.1 + 0.2 0.7 48 6 inch spaces of P.&W g . a 2 Corrections. I. + 0.000002 inch. II. -0.000076 j III. + 0.000074 6-inch spaces of P.&\V 3 . b i2f* Corrections. I. + 0.000010 inch. II. 0.000031 III. + 0.000021 First six -inch spaces of P. &W. 3 a 2 Fii st six-inch spaces of P.&W. 3 b -Ugi* I. + 0.000026 inch. I. -f 0.000020 inch. II. -0.000040 II. +0.000002 III. -0.000016 III. -0.000048 IV. -0.000028 IV. -0.000010 V. -f 0.000064 V. + 0.000016 VI. 0.000006 VI. +0.000020 SUBDIVISIONS OF P.&W. I. II. 111. IV. Inch spaces. Corrections. 0.000009 inch. + 0.000037 0.000025 0.000003 I. II. III. IV. V. VI. VII. VIII. J-inch spaces. Corrections. 0.000002 inch. + 0.000004 + 0.000006 0.000005 + 0.000005 + 0.000004 0.000012 + 0.000004 It is to be noted that all the corrections given above are relative corrections, since no account has been taken of the absolute errors of the entire space sub-divided. These values are therefore to be corrected by the proportional part of the errors for total length. It is my intention to present, at some future time, a supple- mentary report upon the standards P.&W. 2 and P.&W. 4 when the observations now in progress are completed. In conclusion, allow me to express my appreciation of your kindness in offering the facilities which you have, with great liberality, placed at my disposal for this investigation. I remain, gentlemen, Your obedient servant, WM. A. ROGERS. CAMBRIDGE, MASS., July 7, 1886. 49 THE OBSERVATORY OF YALE COLLEGE. THERMOMETRIC BUREAU. Examination of the Mercurial Thermometer, No. , Made by (Used by The Pratt & Whitney Co. for determination of reduction to Standard temperature.) THERMOMETER READING. CORRECTION. o 32 F. + C .4F. 52 62 + 0.2 + 0.1 72 82 + 0.1 0.0 92 0.1 Graduated from 5 to + 280 C. 25 to + 235 F. 1. This thermometer has been examined in a vertical position with the metallic scale and tube immersed in water having the temperature of the bulb. 2. When the correction is + it must be added to the thermometer read- ing, and when it must be subtracted. For example, suppose the thermome- ter to register 81. and the respective tabular corrections at 72 and 92 to be 0.5 and 0.7, then the corrected reading of the thermometer would be 81.0 0.6 = 80.4. The theoretical mercurial standard thermometer to which this instrument has been referred, is graduated by equal volumes upon a glass stem of the same dimensions and chemical constitution as the Kew standards 578 and 584. The permanent freezing point is determined by an exposure of not less than 48 hours to melting ice, supposing the temperature of the standard has not been greater than 25 C. =77 F. during the preceding six months. The boiling point is determined from the temperature of the steam of pure water at a barometric pressure of 760 mm. = 29.922 in. (reduced to C.) at the level of the sea and in the latitude of 45. This standard coincides with the perfect gas thermometer within 0.l F. for temperatures between zero and 212 F. LEONARD WALDO, Astronomer in Charge. NEW HAVEN, CONN., June 10, 1882. 4 50 AMERICAN SOCIETY OF MECHANICAL ENGINEERS. SECRETARY'S OFFICE, No. 239 Broadway, NEW YORK, Dec. 15, 1882. THE PRATT & WHITNEY Co., Hartford, Conn. Gentlemen, By action of this Society, I am directed to transmit to you a certified copy of the Report of the Committee on Standards and Gauges. I have the pleasure of forwarding it herewith. Respectfully yours, THOS. W. RAE, Secretary. EEPOET OF COMMITTEE ON STANDARDS AND GAUGES, PRESENTED AT THE ANNUAL MEETING OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, HELD IN NEW YORK, NOVEMBER, 1882. Your Committee on Standards and Gauges have to report that they have examined the Rogers-Bond Comparator in use by The Pratt & Whitney Company at Hartford, Conn., together with gauges for end-measure produced by this machine. This apparatus is used, first, to compare line-measures of length with attested copies of the standard bars of England and the United States; second, to sub-divide these line-measures into their aliquot parts, and to investigate and determine the errors, if any, of these subdivisions; and third, to reduce these line- measures to end-measures for practical use in the shops. A paper read by Professor W. A. Rogers, before the American Academy of Arts and Sciences, April 14, 1880, on " The Present State of the Question of Standards of Length," and a paper read by Mr. George M. Bond before this society at its regular meeting in Hartford, in 1881,* will give all needed information on the subject of standards of line-measure. The comparator is provided with two microscopes, their mag- nifying power being about 150 diameters, each having a micro- meter eye-piece, the divisions of which represent about Fu.iinr Trans. Am. Soc. Mech. Eng., Vol. II, p. 80. 51 of an inch, and in reading, these divisions are usually subdivided by the eye into tenths. In every case at least three readings are taken, and the mean of the three is used in calculating the result, The microscopes are mounted upon a carriage which slides freely upon two cylindrical guides, which are heavy tubes of hard tool steel, carefully ground true and cylindrical. These are supported at their ends in bearings formed in the heavy cast- iron base of the machine. Counter-weight levers are applied under these tubes at about one-quarter the total length from each end, to overcome the flexure arising from their own weight and that of the carriage and stops. These stops are arranged so as to be clamped firmly to the guides at any desired distance apart, and serve to limit the motion of the microscope plate or carriage when brought in contact with either stop. The carriage is moved up against the stops by a rack and pinion which is pro- vided for the purpose, the rack being secured to the bed of the comparator between and independent of the guide bars. The abutting surfaces of the carriage and stops are hardened steel, those on the carriage being spherical, while those on the stops are flat, and each stop is provided with an electro-magnet which serves to hold the carriage firmly against the stop, so as to prevent its settling back during an observation. On one side of the comparator is a table provided with rapid vertical and lateral adjustments and with a traverse parallel with the motion of the microscope plate of about forty-five inches ; on top of this table is an adjustable plate on which the standard bars are laid to be compared. This plate is provided w r ith fine adjustments for parallelism, focus and position, and several line- measure standards may thus be compared at once under the microscope without handling the bars. This is an important feature, as it will be evident that errors due to variations of tem- perature resulting from handling or from any other cause, must be carefully guarded against. On the opposite side of the com- parator is a fixed table or projecting ledge forming part of the base on which this adjustable plate may be placed, so that stand- ard bars may be investigated on either side of the machine. For regular work, this place is occupied by the caliper for. reducing from line to end-measure. The microscopes are mounted upon the carriage in such a manner that they may ba used both on one 52 side, or one on each side of the carriage, at variable distances apart, according to the character of the work to be examined. The comparator is firmly supported on solid brick piers, capped with stone, and the movable table having a traverse of about forty-five inches, referred to above, is on an entirely separate foundation, to avoid all disturbance of the microscopes 'that might arise from moving the table.* Subdivisions of a standard bar may be compared by placing the microscopes say twelve inches apart, if the subdivisions under investigation are one-third of the yard, the variation being measured or read by means of the micrometer eye-piece ; the standard is then moved under the fixed microscope, so as to compare each separate twelve inches successively, their relation being thus determined. .Another method is to fix the stops so that the microscope carriage will have a movement of as near the length of the sub- divisions to be examined as may be convenient. In this case only one microscope is used, the carriage moving a fixed distance between the two stops and the subdivisions of the standard ; being thus compared with a constant quantity, their relation is con- sequently determined. Line-measure standards may be compared on this machine : (a) By referring the standards to a fixed distance between two stops. (b) By bringing the defining lines under two fixed microscopes placed a distance apart nearly equal to the length of the stand- ards to be compared. (c) By placing two standards to be compared side by side, arid placing one microscope over each bar, the carriage being then moved the length of the bars, the relative length of the standards is readily determined. (a) By placing one standard on one side of the line of motion of the microscope carriage and one on the opposite side, using one microscope for each bar ; by reversing the position of the bars the mean difference may be found. (e) By comparing standards by the use of two microscopes placed horizontally and at a fixed distance apart, so that stand- * For general view of the Comparator see Frontispiece. 53 ards may be compared in the same position and under the same conditions that comparisons are made at the United States Coast Survey Department at Washington.* The microscope carriage should move in an absolutely straight line, and the cylindrical guides give perhaps the closest approxi- mation to this condition. Errors, however, will exist, and the correction for possible horizontal curvature of the guide-bars is found by comparing a standard with a fixed distance between the stops, first on the left hand side of microscope carriage, and afterwards on the right-hand side, under the same conditions in both cases, of temperature, points of support of the standard, and of focus. The face of the bar must in both cases be main- tained in the same horizontal plane, to avoid errors due to verti- cal flexure of the guides ; the difference of the two comparisons with the fixed or constant distance furnishing data for calculating the radius of curvature and the position of the center that is, on which side it is located and hence determining the sign ot the proper correction, whether it be plus or minus, should the amount be appreciable. The vertical curvature, or flexure, may be determined in the same way, using the standard bar placed at varying heights and comparing it with the constant distance moved by the microscope carriage, the microscope and bar being kept always in the same vertical plane, to eliminate errors of horizontal curvature. In transferring from line to end-measure, as the two micro- scopes do not move in the same vertical plane, correction for horizontal curvature, if of an appreciable amount, must be applied with the proper sign, as remarked above, as in such case one microscope evidently would move a distance differing from that of the other by the difference of the lengths of the sub- tended chords. Errors due to vertical curvature or deflection of the guide-bars may be practically eliminated by taking care to keep the sur- faces, on which the lines to be observed by the microscope are ruled, in precisely the same horizontal plane. The caliper attachment to the comparator provides means for reducing line-measure to the practical form of end-measure, and consists of a fixed stop and a movable plunger, cylindrical in * See page 8, Prof. Rogers 1 Report. 54 form, sliding in well fitted bearings, and having a traverse of about six inches. The abutting faces of the plunger and fixed stop are of hardened steel, three-eighths of an inch in diameter, and are ground to true plane surfaces which are perpendicular to the line of motion of the plunger. The plunger is pressed against the fixed stop and also against anything hfld between the surfaces of the plunger and the fixed stop, by a rod which compresses a spiral spring within the plunger. This rod is clamped to place so as to hold the pressure of the spring constant while an observation is being made, the amount of compression of the spring being made approximately equal in each case. This simple contrivance dispenses with the need of the gravity piece used by Whitworth. No great care need be taken as to the amount of the compres- sion of the spring, as no perceptible difference is shown under the microscope when the spring is compressed an amount varying from a quarter of an inch to two and one-half inches. The line upon the plate on the plunger being about FTSYOQ-O f an mcn in width, and the line of the micrometer eye-piece being in exact coincidence with the ruled line upon the plate, no change of relative position was perceptible during a continued observa- tion using a microscope magnifying about 150 diameters, while the spring was subjected to varying compression within the above limits. The error due to flexure of the end-measures is not appreciable in pieces up to six inches in length, but standard bars of twelve inches and longer require supports, and great care must then be taken to have the bar to be measured, parallel to the line of motion of the plunger and the microscope carriage. This caliper is used with two microscopes, one of which is over a finely ruled standard bar, and the other over a finely ruled plate which is attached to the plunger, care being taken to have this plate, throughout its entire line of motion, in the same horizontal plane as is the surface of the standard ruled bar. The faces of the caliper are brought in contact by the rod and spiral spring, and the microscope adjusted until it bisects the line upon the plate attached to the plunger. The other microscope is set so as to bisect the initial line on the standard ruled bar, both microscopes being firmly attached to the carriage ; the plunger 55 is now drawn back, the piece to be tested put between the faces of the caliper, and the plunger forced up until the spiral spring is compressed about the same amount as before. The carriage is now moved until the line on the plate is again bisected by its microscope, and the microscope over the standard bar by the aid of the micrometer determines the exact length of the piece in terms of the subdivisions of the ruled standard. This, operation can be performed very rapidly and with uniform results. One accustomed to the use of the micrometer will readily measure within one division. A test to determine the accuracy of setting to a single line on the ruled bar, made by six members of this Committee most of whom were quite inexperienced in the use of the microscope showed between the highest and lowest of eighteen readings, a difference of 5.5 divisions, a quantity less than Tovroo- ^ an ^ ncn > while the average of the eighteen read- ings differed from the average readings of Mr. Bond by four- tenths of one division, or about T^OYOO-TT of an inch. The end-measure pieces which your Committee were shown at the works of The Pratt & Whitney Company, were stated to be correct within 5-57000- of an inch, and perhaps the severest practical test was made by laying a number of these pieces in a groove planed in a massive block of cast-iron, one piece being clamped down to form an end stop, and when the pieces laid down reached the length of twelve inches, another piece was clamped down. A quarter-inch end-measure was used as a try piece, and was held by a strip of wood inserted in a small hole passing through the piece ; the end stops were adjusted until this try piece would just move easily, almost by its own weight. These pieces were then removed, and others which had been laid on the cast-iron block so they might all have the same tempera- ture, were substituted, care being taken not to disturb the end stops"; some twelve different sets were tried in this way, the same quarter-inch piece being used as a gauge, and these twelve sets were practically uniform in length, with one exception. In this case the quarter-inch piece was quite loose, and accordingly the end-measure pieces composing this set were all carefully measured on the comparator, as well as a set that had stood the test. The difference in length between the two sets, one com- posed of nine pieces and the other of seven, was found to be less 56 than TTr,&f a Stated Hating of the Franklin Institute of the State of Pennsylvania for the Promotion of the Mechanic Arts, held December 15, 1864. " The Special Committee appointed by the Franklin Institute, April 21, 1864, to investigate the question of the proper system of Screw Threads, Bolt-heads, and Nuts, to be recommended by the Institute for general adoption by American Engineers, REPORT, "That in the course of their investigations they have become more deeply impressed with the necessity of some acknowledged standard, the varieties of threads in use being much greater than they had supposed possible; in fact, the difficulty of obtaining the exact pitch of a thread not a multiple or sub-multiple of the inch measure is sometimes a matter of extreme embarrassment. " Such a state of things must evidently be prejudicial to the best interests of the whole country, a great and unnecessary waste is its certain consequence ; for not only must the various parts of new machinery be adjusted to each other in place of being interchangeable, but no adequate provision can be made for repairs, and a costly variety of screwing apparatus becomes a necessity. It may reasonably be hoped that should a uniformity of practice result from the efforts and investigations now under- taken, the advantages flowing from it will be so manifest as to induce reform in other particulars of scarcely less importance. " Your committee have held numerous meetings for the purpose of considering the various conditions required in any system which they could recommend for adoption. Strength, durability, with reference to wear from constant use and ease of construc- tion, would seem to be the principal requisites in any general system ; for although in many cases, as, for instance, when a square thread is used, the strength of the thread and bolt are both sacrificed for the sake of securing some other advantage, yet all such have been considered as special cases, not affecting the general inquiry. With this in view, your Committee decided that threads having their sides at an angle to each other must necessarily more nearly fulfill the first condition than any other form ; but what this angle should be must be governed by a vari- 79 ety of considerations, for it is clear that if the two sides start from the same point at the top, the greater the angle contained between them the greater will be the strength of the bolt ; on the other hand, the greater this angle, supposing the apex of the thread to be over the center of its base, the greater will be the tendency to burst the nut, and the greater the friction between the nnt and the bolt, so that if carried to excess the bolt would be broken by torsion al strain rather than by a strain in the direc- tion of its length. If, however, we should make one side of the thread perpendicular to the axis of the bolt, and the other at an angle to the first, we should obtain the greatest amount of strength, together with the least frictional resistance ; but we should have a thread only suitable for supporting strains in one direction, and constant care would be requisite to cut the thread in the nut in the proper direction to correspond with the bolt. We have consequently classed this form as exceptional, and decided that the two sides should be at an angle to each other and form equal angles with the base. " The general form of the thread having been determined upon the above considerations, the angle which the sides should bear to each other has been fixed at 60, not only because this seems to fulfill the conditions of least frictional resistance, combined with the greatest strength, but because it is an angle more readily obtained than any other, and it is also in more general use. As this form is in common use almost to the exclusion of any other, your Committee have carefully weighed its ad vantages and disad- vantages before deciding to recommend any modification of it. It cannot be doubted that the sharp thread offers us the simplest form, and that its general adoption would require no special tools for its construction, but its liability to accident, always great, becomes a serious matter upon large bolts, whilst the small amount of strength at the sharp top is a strong inducement to sacrifice some of it for the sake of better protection to the remain- der ; when this conclusion is reached, it is at once evident a cor- responding space may be filled up in the bottom of the thread, and thus give an increased strength to the bolt, which may com- pensate for the reduction in strength and wearing surface upon the thread. It is also clear that such a modification, by avoiding the fine points and angles in the tools of construction, will 80 increase their durability ; all of which being admitted, the ques- tion comes up, What form shall be given to the top and bottom of the thread? for it is evident one should be the converse of the other. It being admitted that the sharp thread can be made interchangeable more readily than any other, it is clear that this advantage would not be impaired if we should stop cutting out the space before we had made the thread full or sharp, but to give the same shape at the bottom of the thread would require that a similar quantity should be taken off the point of the cutting tool, thus necessitating the use of some instrument capable of measur- ing the required amount; but when this is done the thread, hav- ing a flat top and bottom, can be quite as readily formed as if it were sharp. A very slight examination sufficed to satisfy us that, in point of construction, the rounded top and bottom pre- sents much greater difficulties ; in fact, all taps and screws that are chased or cut in a lathe required to be finished or rounded by a second process. As the radius of the curve to form this must vary for every thread, it will be impossible to make one guage to answer for all sizes, and very difficult, in fact impossible, without special tools, to shape it correctly for one. " Your Committee are of opinion that the introduction of a uniform system would be greatly facilitated by the adoption of such a form of thread as would enable any intelligent mechanic to construct it without any special tools, or, if any are necessary, that they shall be as few and as simple as possible, so that although the round top and bottom presents some advantages when it is perfectly made, as increased strength to the thread and the best form to the cutting tools, yet we have considered that these are more than compensated by ease of construction, the certainty of fit and increased wearing surface offered by the flat top and bottom, and, therefore, recommend its adoption. The amount of flat to be taken off should be as small as possible, and only sufficient to protect the thread ; for this purpose one-eighth of the pitch would seem to be ample, and this will leave three- fourths of the pitch for bearing surface. The considerations gov- erning the pitch are so various that their discussion has consumed much time. " As in every instance the threads now in use are stronger than their bolts, it became a question whether a finer scale would not 81 be an advantage. It is possible that if the use of the screw- thread was confined to wrought-iron or brass, such a conclusion might have been reached ; but as cast-iron enters so largely into all engineering work, it was believed finer threads than those in general use might not be found an improvement, particularly when it was considered that, so far as the vertical height of thread and strength of bolt are concerned, the adoption of a flat top and bottom thread was equivalent to decreasing the pitch of a sharp thread 25 per cent., or, what is the same thing, increasing the number of threads per inch 33 per cent. If finer threads were adopted they would require also greater exactitude than at pres- ent exists in the machinery of construction, to avoid the liability of over-riding, and the wearing surface would be diminished ; moreover, we are of opinion that the average practice of the mechanical world would probably be found better adapted to the general want than any proportions founded upon theory alone. " We have taken some pains to ascertain what the proportions in use are, and submit the following, as being in our judgment a fair average, viz : Diameter of Bolt, No. threads per in Diameter of Bolt, No. threads per in, # 5-16 20 18 I *%\4X 16 7-16 14 y* 13 9-16 % 12 11 3% 10 2% 6 4%\ 5 5* 2% 2% " The proportions for bolt-heads and nuts, as given in most of our books of reference, are believed to be larger than necessary, and all are tabulated, necessitating constant reference. A simple formula would be more convenient, and would probably induce a uniform practice ; but as most of the sizes in common use are made by machinery, and also by hand, it is believed the bolt-head and nut for finished work should be made somewhat smaller than for rough, to avoid the confusion that would ensue, if the neces- sary allowance for dressing should be made upon work intended for finishing. " In conclusion, therefore, your Committee offer the following : " Resolved, That the Franklin Institute of the State of Penn- sylvania recommend, for general adoption by American engi- neers, the following forms and proportions for screw-threads,. bolt- heads, and nuts, viz. : 82 " That screw-threads shall be formed with straight sides at an angle to each other of 60, having a flat surface at the top and bottom equal to one-eighth of the pitch. The pitches shall be as follows, viz. : Diameter of Bolt, No. threads per in Diameter of Bolt, No. threads per in 5-16 % 20 i 18 | 16 ^__^_ 4 7-16 14 13 zy, 9-16 18 11 10 8* 3 1 ojT 4 |4M 4% 2% 6 I 6 5 ;5^ 2% 5 | 5 2% " The distance between the parallel sides of a bolt-head and nut, for a rough bolt, shall be equal to one and a half diameters of the bolt, plus one-eighth of an inch. The thickness of the heads, for a rough bolt, shall be equal to one-half the distance between its parallel sides. The thickness of the nut shall be equal to the diameter of the bolt. The thickness of the head, for a finished bolt, shall be equal to the thickness of the nut. The distance between the parallel sides of a bolt-head and nut, and the thickness of the nut, shall be one-sixteenth of an inch less for finished work than for rough. " Resolved, That a copy of these resolutions be forwarded to the Quartermaster-General, Chief of the Bureau of Steam Engi- neering of the Navy, and the Chiefs of Ordnance for the Army and Navy, and Chiefs of the Engineer and Military R. R. Corps, and the Superintendent and M. M. of R. R. Companies, request- ing them to use their influence to promote the adoption of a uni- form system of screw-threads, bolt-heads, and nuts, by requiring all builders under any new contracts to conform to the propor- tions recommended. " Resolved, That a copy of these resolutions be also sent to all Mechanical and Engineering Associations or Institutes, and the principal machine and engine shops in the country, with a request that they will use their influence in the proposed system. ^ Kesolued, That this Committee be now discharged." "WM. B. BEMENT, Firm of Bemenl Dougherty. C. T. PARRY, Supt. Baldwin's Locomotive Works. J. YAUGHAN MERRICK, Firm of Merrick & /Sons. ^JoHN H. TOWNE, Firm of I. P. Morris, Towne & Co. COLEMAN SELLERS, Eng. Wm. Sellers & Co. H. BARTOL, Supt. Southwark Foundry. EDWARD LONGSTRETH, Foreman Baldwin's Locomotive Works. JAMES MOORE, Firm of Matthews & Moore. WM. SELLERS, Firm of Wm. Sellers & Co. ALGERNON HOBERTS, Of the Pencoyd Iron Works" [REPRINTED FROM THE R. R. GAZETTE, JULY 20, 1883.] A SCREW-THREAD PRIMER. Notwithstanding all the discussion of this subject, and all that has been written about it, there are still many persons whose duties require that they should know all about the standard system of screw-threads, but who are nevertheless in almost com- plete ignorance of what has been done, or of what may be called the present status of the question. It must be admitted that the information which such people should have is not very readily accessible. It is contained in various articles and reports, of the existence of which a person needing information would probably be ignorant. Tims, the proceedings of the sixteenth annual con- vention of the Master Car-Builders' Association contains a report* of a special committee on this subject which gives a history of what has been done in relation to a standard system of screw- threads. The report, however, is a long one, and probably those who want to learn only the essential principles and practice which should control the construction of standard screw-threads would not have the time or patience to read it. One of the diffi- culties in the way of the general introduction of the standard system of screw-threads is that there are so many persons belong- ing to the class described who do not know what the standard is which has been recommended for general adoption. It is pro- posed in this article to describe its essential features in as simple and clear a way as possible. There will be nothing, or very little, that will be new in what is said, and which may not be found in other publications. All that is aimed at, is to present the essential points of what has heretofore been stated, in as clear and simple a way as possible. It will not be necessary to say to the persons for whom we are writing, that in order that bolts and nuts may be interchange- able, it is essential that they should have the same number of Seepage 59, Ante. 84 threads to the inch, as obviously a f nut with nine threads to an inch will not screw on a bolt with twelve without injuring or destroying the threads of one or both. Therefore, in order to make bolts and nuts interchangeable, the first thing which had to be done was to adopt a standard number of threads to an inch for each diameter of screws. Before giving the number of threads per inch which is now the standard in this country, it should be explained that " in 1864 the inconvenience and confusion resulting from the diversity in the screw-threads used in a machine and other construction was brought up for consideration before the Franklin Institute of Philadelphia. A committee was then appointed to investigate and report on the subject. That committee recommended the system designed by Mr. William Sellers, and the Institute after- wards adopted their recommendation." * In 1868 the system was authorized for the naval service by the Secretary of the Navy, and soon after the Master Mechanics' Association, and in 1871 the Master Car-Builders' Association recommended it for use in the construction of locomotives and cars. The following are the numbers of threads to an inch which are specified for the different sizes of screws : Diameter of screw. % inch, . A y* No. of threads per inch. 20 18 16 . 14 13 12 11 10 9 8 7 7 Unfortunately, when the two associations named recommended the Sellers system of screw-threads for use on railroads, the mem- bers did not seem to understand fully what the system was, and the impression was very general among the members that it con- sisted merely of the specified number of threads to an inch. The * Page 78, Reprinted Report. 85 consequence was that the forms of the threads of screws made at different places varied, and consequently the bolts and nuts were often not interchangeable. It was also found that it was a com- mon practice among iron manufacturers to roll iron over-size, that is, iron that was nominally f in. in diameter was found to be ^ or ^ larger. If the taps and dies used in cutting the screws for such iron were of the exact size, it of course was nec- essary to cut away the excess of material, which injured the dies and took more time. To avoid this it was a very common prac- tice to have taps and dies made over-size ; that is, taps, instead of being of that diameter, were made ^ or ^V? <> r possibly T V in. larger in diameter than that size. This of course made it impos- sible to interchange bolts and nuts which were of the right size with those which were larger, and as there was no common prac- tice in the matter of over-size, those who made taps and dies fa large could not interchange with those who increased the size T V It was also found that even where different manufacturers aimed to make taps and dies of the same nominal diameters, they varied from these sizes, from the fact that they had no common standards of measurement of sufficient precision to insure inter- changeability. Investigation showed, too, that a very high degree of precision is required in the manufacture of taps and dies, in order to make bolts and nuts interchangeable, and that a differ- ence of 0.002 of an inch in the diameter of a |-in. bolt and nut will make them fit each other loosely. The attention of those interested in the matter was therefore directed to the means of attaining the required degree of precision. The efforts of those who took the matter up were seconded by The Pratt & Whitney Company of Hartford, Conn., which Company devoted much time and money to investigating the subject, and to perfecting the machinery required to make gauges of the required accuracy to insure interchangeability. As it would take too much space to recount the successive steps which it was necessary to take to accomplish the end aimed at, the results only will be described here.* Before doing so, it should be fully explained that the Sellers system of screw-threads consists not alone in the number of threads to an inch, but the diameters of the screws and the form I * See Report of Committee, page 59, ante. 86 of the threads are also distinctly and exactly specified. The angle between the sides of the thread is 60, and the point of the thread and the space between it is .flattened. The amount taken off the point and that filled in at the root are equal to one-eighth of the pitch. Now it should be observed that all these dimensions and proportions are definitely specified. For example, the out- side diameters of Sellers screws are , T V J, T 7 ff , &, ^, f, f, J, 1, li, 1J in. and upward. There are no sizes between those given. There is no such thing as a screw ff 1 or ^ in. larger or smaller than the sizes given in the Sellers system. If mechanics wish to adopt the Sellers Standard, they must therefore adopt these sizes and no others. In making taps and dies to conform to the Sellers standard, it is therefore important that the diameter, outside and at the root of the thread, should be determined with sufficient precision to insure interchangeability. For this, and other similar purposes, what are called cylindrical size-gauges, figs. 7 and 8, are provided. The first is a hardened steel cylindrical plug, ground and lapped FIG. 7. FIG. 8. perfectly round and straight, and warranted not to vary more than sTJviinr of an inch from the true size. Fig. 8 is a ring which fits the cylindrical plug. Suitable caliper gauges, for use in the shop, are made and maintained to the correct size from the cyl- indrical gauges. In the manufacture of taps, cylindrical gauges are made for their outside diameters, and also for the diameters at the root of the threads. In this way the required amount of precision in these dimensions can be maintained. It will be impossible to explain, in an article like this, the ingenious methods which have been devised for making chasing tools which will cut threads whose sides will have an inclination of exactly 60 to each other, and which will leave just the right amount of material at the root of the threads. All this work must be done with the utmost precision to insure the interchange- ability of bolts and nuts. 87 The question then naturally arises, whether this degree of pre- cision can be maintained if the work of manufacturing taps and dies is done in ordinary shops. Any one acquainted with the processes and appliances needed to maintain the required degree of precision must, it is thought, inevitably conclude that if inter- changeability of bolts and nuts is ever brought about, it will be through the manufacture of taps and dies b} 7 firms who make a specialty of the business, and in shops supplied with all the appliances required to maintain a very high degree of precision. The objection to having them made by one firm or company is that it would inevitably result in the creation of a monopoly, and deprive the users of taps and dies of the wholesome influ- ence of competition. Therefore, when the question of abandon- ing the manufacture of these tools is proposed to either private firms or railroad companies, they are apt to object to placing themselves in a position in which they would not have the privi- lege of buying such tools in the open market. What they require is some means of learning whether a given lot of taps and dies conform near enough to the standard dimensions and proportions to insure the interchangeability of the bolts and nuts made with them. To meet this requirement, The Pratt & Whitney Company make what is called " internal and exter- nal standard thread gauges," represented by figs. 9 and 10. FIG. 9. FIG. 10. The internal gauge (fig. 9) consists of a threaded cylinder, made to exact standard size, and the external gauge has a corresponding screw-thread, which is adjustable to the internal gauge. With a set of these gauges, the nuts and bolts cut by any taps or dies can be tested at once, and it can be known whether they conform to the standard sizes. With such a set of gauges in the tool-room of a railroad or other shop, the person in charge can at once know whether taps and dies bought of any firm are of the right size. This leaves the purchaser free to buy in the open market, and at the same time maintains the standard at the required degree of precision. 88 In adopting the Sellers, or Franklin Institute, or United States standard, as it is variously called, a difficulty arose from the fact that it is the habit of iron manufacturers to make iron over-size, and as there are no over-size screws in the Sellers system, if iron is too large it is necessary to cut it away with the dies. So great is this difficulty, that, as already explained, the practice of mak- ing taps and dies over-size has become very general. If the Sellers system is adopted, it is essential that iron should be obtained of the correct size, or very nearly so. Of course no high degree of precision is possible in rolling iron, and when exact sizes were demanded, the question arose how much allowa- ble variation there should be from the true size. The matter was discussed at a meeting of the Master Car-Builders' Club during the past winter (Dec. 21, 1882), and after consultation with different iron-makers it was concluded that there might be a variation of about 0.01 in. in the smallest sizes, 0.015 in. in J--in. and 0.02 in 1 in. iron. It was suggested, too, that limit gauges should be made for inspecting iron. It was proposed to make these of caliper form, with two openings, one larger and the other smaller than the standard size, and then specify that the iron should enter the large end and not enter the small one. After further discussion it was agreed to make the difference in the size of the large and the small end of the gauge for -in. iron 0.01 in., and increase the difference by 0.001 in. for the sizes above that. The following table of dimensions for the limit gauges was therefore drawn up, and was recommended by the Master Car-Builders' Association : Size of iron. Size of large end of gauge. Size of small end of gauge. Difference in size of large and of small end of iron. 2550 2450 0010 JL 8180 3070 Oil 4 3810 3690 012 ? 4440 04310 0013 * . 5070 4930 014 A 5700 5550 015 p.. '":: : 6330 06170 016 i . . . . 7585 7415 017 ^ 08840 08660 018 i 1 0095 0.9905 0.019 1 1350 1 1150 0020 H. u 1 2G05 1 2395 0.021 The Pratt & Whitney Company took the matter up, and at the Chicago Exposition of Railway Appliances exhibited a com- plete set of such gauges, one of which is represented by Fig. 11 . FIG. 11. It is obvious, though, that if used in inspecting iron, such gauges would soon wear so as not to be sufficiently accurate for the purpose for which they are intended. To provide for this the company has also made " standard reference gauges," Fig. 12, FIG. 12. consisting of a series of cylindrical gauges, arranged like steps, those at one end being of the sizes of the small end of the cali- per-gauges, and those at the other end the sizes of the large end. Whenever it is suspected that the caliper-gauges have been injuri- ousty worn, they can be tested with the reference gauge and the required correction made. In this way their accuracy can be maintained. The question is often asked by master mechanics, car-builders, and others, "What must we do to adopt the Sellers, Franklin Institute, or United States standard system of screw-threads?" From what has been said it will be seen that, in taking these steps, what is required is : 1. Abandon the manufacture of taps and dies altogether. 90 2. Get a set of screw-gauges for testing the accuracy of the taps and dies that are bought. 3. Get a set of limit gauges for round iron, and require man- ufacturers to make iron to the size of those gauges, and then have every lot received inspected. 4. Abandon entirely the use of over-size screws for new work. STANDARD LIMIT GAUGES FOR EOUND IRON. In accordance with a resolution of the Master Car-Builders' Association and its constitution, a circular was mailed last November * by Mr. M. BT. Forney, the Secretary, to the several members, containing the following : " In introducing the Sellers or Franklin Institute standard sys- tem of screw-threads a serious difficulty has been encountered, owing to the fact that round-bar iron has heretofore been very generally rolled over-size that is, it has been made a small fraction of an inch larger, and in some cases smaller, than its nominal diameter. In order to have standard screws of the cor- rect diameter it is therefore necessary to cut down the iron with the screw-cutting dies, which causes them to wear rapidly ; and, inasmuch as the screw, if it is of the same or less diameter than the bolt, is the weakest part, there is a great waste of material when the bolt is of larger diameter than the screw. It is there- fore desirable that round iron should be made of the right size, so that, in cutting standard screws, there will be as little waste as possible. But, as it is impracticable to roll iron to exact sizes, some variation in diameter must be allowed. Therefore, in specifying the size, all that can be required is that the iron shall not be larger than a certain dimension, nor smaller than another. "To make it easy to determine whether the size of iron is within given limitations, it has been proposed to use a limit gauge, like that represented by fig. 11, consisting of double fixed calipers, one end of which is a fraction of an inch larger than the standard size, and the other a fraction of an inch smaller, * See Report of the Proceedings of the 17th Annual Convention of the Master Car-Builders' Association, held in Chicago, Jane, 1883. 91 and then require that all iron of the nominal size of the gauge shall be so large as not to enter its small end, and so small that it will enter the large end. Before such limit gauges could be made or their use adopted, it was essential to establish a standard for the difference in size of the large or -f end and the small or one. With this end in view the following resolution was pre- sented at the last annual Convention of the Master Car-Builders' Association : "Resolved, That the following sizes for limit gauges for round iron for the Sellers standard threads are hereby established by the Master Car-Builders' Association as the standard sizes for such gauges, and it is recommended that round iron of the nominal standard sizes be made of such diameter that each one will enter the larger or + end of the gauge intended for it, in any way, and will not enter the small or end in any way" Diameter. Inches. Large size, -fend. Inches. Small size, end. Inches. Total variation. Inches. i 2550 2450 010 A . 3180 3070 Oil 4 . 3810 3690 012 .4440 4310 013 -i 5070 4930 014 A 5700 5550 015 1. . 6330 6170 016 1 . 7585 7415 017 ' I 8840 8660 018 \ 1 0095 9905 019 11. . 1 1350 1 1150 020 li. . 1 2605 1 2395 021 In accordance with the constitution, blank ballots were sent out to the members by the Secretary, asking a vote on the adop- tion of the above resolution. Sixty days after sending these ballots, as the constitution requires, the ballots received were counted, and the Secretary announces that 81 ballots were cast, aggregating 301 votes, of which 291 were in favor of the resolu- tion. More than two-thirds having voted for the standard, it was adopted." 92 [Reprinted from the Journal of the Franklin Institute, April, 1887 THE SELLERS OR FRAJSTKLIN INSTITUTE SYSTEM OF SCREW-THREADS. The following correspondence has grown out of an inquiry addressed to the INSTITUTE by the Society of German Engineers of Berlin, and is self-explanatory. W. H. W. BERLIN W., den 22. October, 1886, Wichmannstrassee 14. An das FRANKLIN INSTITUTE, Philadelphia (V. St. A.) 15 Smith Seventh Street. Fur die in unserm Yereine noch immer im Gange befindliche Agitation zur Aufstellung eines einheitlichen Schraubengewinde- systems auf Grundlage des Metermaasses wfirde es uns von hohem Werthe sein, die Yerhandlungen und Beschlusse eines verehrlichen FRANKLIN INSTITUTE fiber diese Frage kennen zu lernen ; insbe- sondere wurde es uns interessiren, zu erfahren, ob in den Yer. Staaten ein Standard -Gewinde aufgestellt ist, und zwar welches, und welche Geltung es bisher erlangt hat. In der Zeitschrift Engineering, vom 10. September d. J., ist ein Aufsatz, welcher unter Anderem die Behauptung enthalt, dass das von Sellers vorgeschlagene Gewinde, mit geraden Flachen statt der Whitworth'schen Abrundungen, als nicht bewahrt befunden und wieder aufgegeben worden sei ; auch hieruber waren uns Mitthei- lungen sehr erwfinscht. Mit Freuden bereit, auch Ihnen vorkommenden Falles zu Diensten zu sein, zeichnen wir Hochachtungsvoll, DER YEREIN DEUTSCHER INGENIEURE. Th. Peters. [Translation. ~\ BERLIN W., October 22, 1886. To the FRANKLIN INSTITUTE, Philadelphia (U. S. A.) 15 South Seventh Street. In connection with the subject of establishing a uniform system of screw-threads based on the metrical system which for a long 93 time lias been agitated by this society it would be of the greatest value to us to be advised respecting any proceedings taken and conclusions reached by the FKANKLIN INSTITUTE upon this subject. It would especially interest us to learn if any standard has been adopted in the United States, and if so, what standard, and to what extent it has, up to the present time, received acceptance. In Engineering, of September 10, 1886, there appears an article on this subject, in which the assertion is made, that the system of threads, proposed by Sellers having straight surfaces instead of the rounded ones of Whitworth had not been found to fully meet the requirements of practice, and had been abandoned. On this point, also, any information would be very acceptable. With the expression of our willingness to serve you, should the occasion offer itself, we subscribe ourselves, With high regard, THE SOCIETY OF GERMAN ENGINEERS. Th. Peters. The article in (London) Engineering, herein referred to, is given below, viz. : In the year 1857, many of the leading engineers in England began to recognize the evil and the very great inconvenience which arose from various quarters through individual machine and engine makers using a separate system of screw-threads. So important did Sir Joseph Whitworth consider the matter, that he undertook to establish and introduce a uniform system of standard pitches and form of thread for use throughout the country. His first table was published in the same year, viz., 1857, and a second one in 1861, in which he gave fuller particulars, and proposed a few minor improvements. The main points to be considered in arranging such a system were, briefly : (I.) The best and most suitable pitches or number of threads per inch of length for given diameters of bolts, the main object being to reduce the strength of the bolt as little as possible, and at the same time to make the threads of sufficient depth to prevent liability to " cross-threading " taking place, and to get a convenient thickness of nut which would stand at least as much longitudinal tensile stress as the bolt at the bottom of the thread. After very careful consideration on the part of Sir Joseph Whitworth, he decided upon a set of pitches 94 which were published in tabular form, copies of which are found in all engineering text-books. The following formula, taken from Un win's Machine Design, page 117, gives a very close approximation: Let d = the original diameter of the bolt. p = the pitch of the threads. Then p = 0.08 d+ 004, and the diameter at the bottom of the thread, d' 0.9 d 0.05. (2.) The form or cross-section of the thread best suited for practi- cal purposes, which involved the consideration of ease of manufacture and reproduction, combined with security against damage by the com- paratively rough treatment bolts and screws are subjected to. The form of cross-section Whitworth adopted for ordinary purposes was that of a triangle, whose height was 0.96 pitch and the angle at the bottom of the threads 55 (see Unwin's Machine Dexign, page 117); one-sixth of these triangular sections was rounded off at the top and bottom.* This system has been very widely and almost universally used for the last thirty years, the chief and only important exception to their universality being in the United States, where Sellers's threads are very much used; they are of a slightly different pitch and form of cross-section, being an equilateral triangle with one-eighth of the depth cut off square, both top and bottom; the pitch is nearly p = 0.1 d -f 0.025, and the diameter at the bottom of thread d l = 0.87 d 0.03. (See Unwin's Machine Design, page 119.) The relative values of these two systems lie chiefly in the merits of round or sharp corners. We shall return presently to consider both systems in detail, but it is well to note here that the latter system is being discarded for one very similar to the Whitworth. This is briefly how the screw-thread question stands at the present time. However, in Germany and on the continent of Europe generally, the English system of measurement in feet and inches is not in common use, but the metrical system is almost universal, viz., of meters with decimal subdivisions. Hence, a small body of German engineers have been for some time urging for a universal metrical standard of screw-threads, and consequently seek to overthrow the Whitworth system. In 1874,f the Miinchen District Society of German Engineers took up the matter, when they not only procured the opinions of the Ger- man district societies, but communicated with various well-known Con- * See page 60, Ante. t Vide a paper " On the Thread Question, 1 ' by J. H. Mehrtons, engineer, of Berlin. 95 tmental engineering societies, and at the same time sent out 2,000 cir- culars to owners of works to obtain their views upon the practicability of introducing a metrical system in the place of Whitworth's, maintain- ing that this system was not in general use; but the result of this inquiry was in favor of retaining the Whitwortb system. Out of the 2,000 circulars sent out, only 365 were returned, 316 of which were from makers who used the Whitworth system exclusively, and the remaining forty-nine retained the pitch, but used different diameters of bolts. Of the twenty district societies which were con- sulted, only six decided in favor of the metrical system. The practi- cal effect of this inquiry was to set the Whitworth system on a firmer basis than ever. In spite of this, however, the Karlsruhe District Society brought forward motions in favor of the metrical system at the principal meeting of the Society of German Engineers in 1877, but they were at once dismissed by them. Again, in 1885, the same society brought up the matter under a rather different aspect, viz., not whether it was desirous to introduce a metrical system of screw-threads, but what metrical system shall be introduced, implying that the former was a settled matter, and the only matter requiring consideration was the details of the system. The directorate thought it desirable to appoint a special commission to inquire into it. The main objections brought against the Whit- worth system by the commission and the Karlsruhe Society, were briefly: (1.) The Whitworth system is not universally used in Germany, and consequently great disorder prevails. (2.) The Whitworth system being measured in inches, it is incon- venient for metrical measurements. (3.) The cross-section of the Whitworth thread is difficult of manu- facture. The first objection has been dealt with above in the remarks on the action taken by the Karlsruhe and Miinchen District Societies, and, again, the Whitworth system is universally used by the German rail- ways and dockyards, and unless a general desire is shown for a metri- cal system of threads, it is evidently quite useless for a handful of o-bscure scientific men to attempt a radical change in such an import- ant matter. The second objection, on the surface, appears slightly more justifia- ble, but even that is extremely insignificant when more closely exam- ined and viewed from a different standpoint. This matter does not stand upon the same ground that it did ten years ago, when the whole 96 of the bolts and screws in use were constructed in small quantities as they were required at the various machine and engine works; to-day the case is totally different, as only a very small percentage are con- structed in this way ; they are almost entirely bought from special screw-makers, who turn out better and cheaper work than is possible fcr individual machine shops. Thus the imaginary difficulty lies entirely in the screw-makers' hands. They do not complain; why, then, should those whom it does not affect to any appreciable extent ? If a new universal system of screw-threads must be adopted, then it should not be tied down to any special system of measurement, but should rather be designed on a system of standard gauges of various grades, similar to our Birmingham wire-gauge system. Some of the German engineers complain that a considerable number of Whitworth bolts and nuts purchased from one firm of screw makeis, will not fit those purchased from another firm, and lay the blame to the system ; but this is decidedly unjust, for it is evident to any practical engineer that the fault lies not in the system itself, but with the manufacturers for not using standard screw-gauges, as Sir Joseph Whitworth advo- cated in his original report on the subject. None can say but what the proposed new system would be quite as faulty, perhaps even worse in this respect, as it has never been practically put to the test. If German engineers persist in their course, and carry out this proposed scheme in the machinery they manufacture, they only will be the suf- ferers by ruining their foreign trade, for no foreigners will think of purchasing machinery which cannot readily be repaired by local engi- neers without sending to Germany for special bolts and nuts. The third objection is totally unjustifiable, for thirty years of prac tice have most unmistakably proved the Whitworth form of cross-sec- tion to be the best. The square-tipped thread, on the other hand, as advocated by the metrical system, has proved unsuccessful. It has been thoroughly tried by Sellers in the United States, where it has been found practically impossible to produce a good thread by screw- ing apparatus; the sharp corners on the taps and dies rapidly break away, when a very imperfect thread must naturally follow. The present state of affairs in America conclusively shows the system to have been a failure, and all the leading machine tool-makers there are supplying nothing but the V-thread, very similar to Whitworth's. Again, the strength of the bolt is reduced more by the square-cor- nered than by the rounded thread, although the sectional areas of the bolts at the bottom of the threads are the same; for example, it is always found to be absolutely necessary in the preparation of test 97 specimens for tensile tests to have the corners well rounded oft'; if not. the specimen almost invariably breaks short off at the square corner. With good tools and good men to use them, there is no diffi- culty whatever in producing the Whitworth cross section of thread. The round at the bottom of the thread is easily pi oduced by a rounded point to the screw-cutting tool, a gauge for which is carried by every, turner in his waistcoat pocket. The round at the top of the thread is produced by the chaser, which is itself cut by a standard hob, and consequently reproduces the correct form of cross-section on whatever work it is used. Engineering, Sept. 10, 1886. SECRETARY'S OFFICE, HALL OF THE FRANKLIN INSTITUTE, PHILADELPHIA, Jan. 31, 188T. The Society of German Engineers: GENTLEMEN: In response to your letter of October 22d ult., asking to be informed respecting any proceedings taken and con- clusions reached by this INSTITUTE upon the subject of establish- ing a uniform system of screw-threads, whether any standard has been adopted in the United States, and if so, what standard, and to what extent it has, up to the present time, received accept- ance, also referring to an article in Engineering of September 10,. 1886, with quotation therefrom, I have the honor to report: The proceedings taken by the FRANKLIN INSTITUTE with refer- ence to a uniform system of screw-threads w T ere inaugurated by. a paper upon this subject by Mr.. William Sellers, read by him, before the INSTITUTE at its regular monthly meeting, held April, 21, 1864 (see copy of the Journal for April of that year, forwarded,, with other papers hereinafter referred to, by book-post, on tlm 31st inst.). This was followed by the appointment of a commit- tee to investigate and report. The report of this committee will, be found in the number of the Journal for January, 1865,* for- warded as above, and this ended the proceedings so far as the FRANKL.IN INSTITUTE was concerned. Early in 1868, the Secre- tary of the Navy of the United States appointed a board of engi- neers to investigate and report upon a system of screw-threads which might with advantage be adopted by that department of the government, and this board reported May 9, 1868, recom- mending the system advocated by Sellers and approved by this * See copy of this report, page 78. 7 98 INSTITUTE (see copy of report forwarded as above). This report was approved by the Secretary of the Navy, and thenceforth it has been the standard of the United States Government, not only for the Navy Department, but for all other departments, except- ing for small arms and other specific requirements, where a much finer thread is necessitated. This action by the government was followed by its general adoption in the large private establish- ments all over the country engaged in constructing the heavier classes of machinery. In April, 1869, the Pennsylvania Railroad Company ordered a set of gauges to the new form of thread, and adopted the system upon all of its lines, and this was followed by various other rail- roads throughout the country, until, in 1872, the Master Car Builders' Association recommended the Sellers or FRANKLIN IN- STITUTE system of screw-threads and bolts as a standard. The progress thereafter in this direction is shown by the Report of the Proceedings for 1885, forwarded as above, and similar action was taken by the Master Mechanics' Association. To answer your inquiry, " to what extent it has, up to the present time, received acceptance," and also the " article in Engineering" before referred to, the secretary of the INSTITUTE addressed the following letter to the proper officers of the princi- pal railroads in the United States, and to several individual manufacturers : PHILADELPHIA, December, 1886. To the Superintendent of Railroad Company: DEAR SIR: The Society of German Engineers of Berlin has made certain inquiries of the FRANKLIN INSTITUTE concerning the Standard Screw-Thread recommended for general adoption by the FRANKLIN INSTITUTE in 1864, and adopted by the Navy Department of the United Stales in 1868, among which inquiries the durability of the straight surfaces, as compared with the rounded ones of Whitworth, is ques- tioned. It is probable that the straight surfaces of the standard thread would show a modification of form to the eye which would not be observable upon the curved surface of the Whitworth thread ; but, as some contribution to this inquiry, it would be of interest to know whether the standard thread has been adopted upon your road, and whether you have experienced any difficulty in practically maintaining the form of the thread, or at least sufficiently so as to make the nuts 99 interchangeable. If you find that the straight surfaces are more diffi- cult to maintain than the curved ones of the Whitwortli thread, would this be counterbalanced by the greater facility for making the straight thread with a single tool overthat of the curved thread, which requires two (2) tools, and which form of thread can most easily be constructed and tested, for accurate conformity with a standard of its form? Any information you can give me in connection with this subject will be highly appreciated by, etc., Yours truly, WM. H. WAHL, Secretary. In response to this letter, lie has received replies from the fol- lowing railroad companies : Pennsylvania Railroad Company, operating and controlling 7,346 miles of railroad. Chicago, Milwaukee & St. Paul Railway Co., 4,921 miles. New York Central & Hudson River Railroad Co., 993 miles. Chicago, Rock Island & Pacific Railroad Co., 1,383 miles. Delaware, Lackawanna & Western Railroad Co., 889 miles. Louisville & Nashville Railroad Co., 3,727 miles. Chicago, Burlington & Quincy Railroad Co., 3,646 miles. New York, Lake Erie & Western Railway Co., 1,601 miles. He has also a reply from one of our largest manufacturers of bolts and nuts, and one from our most important manufacturers of taps and dies. The article in the Railroad Gazette, of September 24, 1886, referred to by the latter is forwarded by book-post with the other paper hereinbefore referred to. THE LETTERS received in response to the Secretary's inquiry are as follows : Louisville & Nashville Raikoad Company, Office of Superintendent Machinery. LOUISVILLE, KY., December 6, 1886. WM. H. WAHL, ESQ., Secretary FEANKLIN INSTITUTE, Philadelphia, Pa. DEAR SIR: Yours of December 14th is at hand and noted. We adopted the United States Standard Thread, sometimes called the FRANKLIN INSTITUTE Thread, about five (5) years ago, in all the shops of our lines, and have used it ever since. We have found no difficulty whatever from the wearing of the taps and dies as long as they are not used beyond a proper length of time. Of course, as taps and dies wear away, it will make a slight difference in the form of the thread; 100 but I do not believe that that change is any greater or can give any more trouble than in the case of the Whit worth thread referred to. We have experienced no difficulty in the interchange of nuts and bolts on account of the slight change that occurs in the form of the thread in the wearing of the taps and dies. Of course, any form of thread will change slightly from the wearing of the taps and dies, and it is impossible to avoid that by any form of thread uc-ed. A straight side to a thread is easier to make than a rounding side, and therefore more likely to be perfect. A straight side to a thread, it seems to me, will change as little, perhaps less, than a rounding side. The proper way to keep threads as near the original as possible is to throw away the taps and dies before they are worn to such an extent as will make any practical difference in the shape of the thread. This is a matter that is sometimes overlooked. The expense of taps and dies is not great, and only perfect taps and dies should be used; and as soon as the wear amounts to enough to make an appreciable difference in the form of the thread, they should be thrown away and renewed. We have made it a rule to purchase from reliable manufacturers nearly all of our taps and hobs for cutting dies, and we have been particular to throw away taps as soon as they are worn to any considerable extent, and use new ones. The same in regard to dies; as soon as to amount to anything, we re-cut them, dress them up, and then they are as good as new. It seems to me a flat-top form of thread will change as little as a thread that runs to a point. It will change less in diameter from out to out of the thread. With a sharp-top thread, when the sides wear away slightly, it reduces the height of the thread. With a flat- top thread the wear of the sides will not reduce the diameter from out to out of the thread, but will simply make the thread a little thinner at the point, etc. Yours truly, R. WELLS, Superintendent Machinery. Delaware, Lackawanna & Western Railroad Company^ Office of Machine Shops. SCRANTON, PA , December 8, 1886. MR, WM. H. WAHL, Secretary FRANKLIN INSTITUTE, Philadelphia, Pa. DEAR SIR: Replying to yours of the 4th inst., in regard to the Standard Screw-Thread, would say, the United States Standard has been adopted on this road and gives entire satisfaction. It is much easier to make, and the tools to make it less expensive to keep up, Yours truly, CHAS. GRAHAM, Master Mechanic. 101 Chicago, Milwaukee & St. Paul Railway, Office of General Master Mechanic. WEST MILWAUKEE, Wis., December 11, 1886. WM. H. WAHL, ESQ., Secretary FRANKLIN INSTITUTE of Pennsylvania, Philadelphia, Pa. DEAR SIR: I make the object of this, to reply to your favors of the 4th inst Jn 1871, the locomotive department of this company adopted what is known as the United States, or FRANKLIN INSTITUTE Standard, for Diameters and Threads, and have continued to use it up to the present time. We have experienced no particular difficulty in the interchanging of nuls. Should there be any difficulty in maintain- ing the straight surfaces of the threads more than those of the Whit- worth type, it would in our opinion be more than counterbalanced in costing less to maintain the straight surfaces than the curved. We are of opinion, however, that the Whitworth thread is the strongest, i. e.j less liable to fracture the bolt. I am, yours truly, I. M. LOWRY, General Master Mechanic. Chicago, Rock Island & Pacific Railway, Master Mechanic's Office. CHICAGO, December 15, 1886. WM. H. WAHL, ESQ., Secretary FRANKLIN INSTITUTE, Philadelphia, Pa. DEAR SIR: About three years ago we adopted the United States Standard Thread for Bolts and Nuts, and have so far experienced no difficulty whatever in practically maintaining the form of the thread. I have not yet seen a case where a bolt had worn so that nuts were not interchangeable. I have had very little experience with the Whitworth thread, but feel certain that any slight advantage in durability or strength which it may have. over the United States standard, is far outweighed by the inconvenience in its construction. Regretting that I cannot give you more scientific and interesting data, I am, Yours truly, THOS. B. TWOMBLY, General Master Mechanic. 102 Chicago, Burlington & Quincy Railroad Company, Office Superintendent Motive Power. AURORA, ILL., January 5, 1887. FRANKLIN INSTITUTE of Pennsylvania, WM. H. WAHL, Secretary, Philadelphia, Pa. DEAR SIR: Yours of the 4th duly received, asking whether this road has adopted the United States Standard thread, and. whether we have experienced any difficulty in maintaining the form of the thread. The United States Standard or FRANKLIN INSTITUTE thread was adopted in the car department of the Chicago, Burlington & Quincy, in 1883, and since then has been gradually introduced into the loco- motive and track departments. For two years past we have used this thread for all purposes. We have had no difficulty whatever in main- taining the form of the thread, that is to say, we can forward to any point on our line new nuts, which can be used satisfactorily on old bolts. Our foremen all speak highly of the United States Standard, owing to the facility of maintaining a uniform shape. One of our foremen at Burlington, Mr. Scholey, who has used the Whit worth thread in the old country, and the United States Standard in this country, says the latter is much more easily maintained. We enclose you some correspondence from our master mechanics on this matter. J. West, M. M., Burlington Shop. L. E. Johnson, M. M., Aurora. C. F. Geyer, General Foreman Aurora Shop. Yours truly, G. W. RHODES, Supt. M. P. Chicago, Burlington & Quincy Railroad Company, Locomotive and Car Department. WEST BURLINGTON, December 16, 1886. G. W. RHODES. ESQ., Superintendent Motive-Power, DEAR SIR: Referring to attached letters in regard to screw-threads, I fully agree with Messrs. Johnson and Geyer in the matter of threads. I have talked this matter over with our general foreman, Mr. Scholey, and he says that with our American or United States Standard, it is much easier to keep up taps and dies than with the Whitworth thread with rounded edges and angles, which he used in the old country, and a good 'fit is easier to make. Yours, J. WEST. Nuts. United States Standard vs. Whitworth Thread. 103 Chicago, Burlington & Qaincy Railroad Company, Master Mechanic's Office. AURORA, ILL., December 11, 1886. G. W. RHODES, ESQ., Superintendent M. P., Aurora. DEAR SIR: Returning your communication from the FRANKLIN INSTITUTE, and, in reply to the same, would respectfully state that the United States Standard thread has been in use in the car department since 1883. During that time, we have experienced no difficulty what- ever in practically maintaining the form of the thread ; that is to say, that we can forward to any point a supply of new nuts, which can be used on bolts that have been in service since that time. Foremen of other shops substantiate Mr. Geyer's statement, that it is much more difficult to maintain the curved surface of the Whitworth thread than the straight, or United States Standard. We have no absolute data on this subject, other than practical experience for the past three years. We are gradually changing the thread of bolts in all departments to the straight, or United States Standard. In doing this, we experience no difficulty or annoyance, as the men in each de- partment keep a small quantity of old nuts with the old thread, so as to avoid throwing away bolts. We undoubtedly shall eventually have nothing but the United States Standard thread in use in all departments. I enclose you copy of Mr. Geyer's report. Yours respectfully, L. E. JOHNSON. AURORA, ILL., December 9, 1836. L. E. JOHNSON, ESQ., Div. M. M., Aurora. DEAR SIR : In regard to the enclosed, it is my opinion that the Whitworth Standard tap is very impracticable, as it is a hard matter to make them twice alike, therefore, much more expensive. It is true, if a nut and bolt is in constant use, it will wear about the shape of the Whitworth Standard, and it may be more durable. We have never, as yet, experienced any trouble with the United States Standard thread. A new nut can always be substituted where an old one of the same size is taken off. It will cost at least double to maintain the tools of the round or Whitworth thread, and, it is my opinion, it is not any better or' stronger than the straight or United States Standard thread. Respectfully yours, [Sgd.] C. F. GEYER. 104 SUBJECT STANDARD SCREW-THREADS. The Pennsylvania Railroad Company, Office of General Superintendent of Motive Power. ALTOOXA, PA., December 20, 1886. WILLIAM H. WAHL, ESQ., Secretary FRANKLIN INSTITUTE, Philadel- phia. Pa. DEAR SIR : In reply to your letter of December 3d, would say, that in our experience we have had no trouble at all in maintaining the form of thread of the United States Standard, and the nuts we tap are perfectly interchangeable. We think the straight surfaces are much more easily maintained than the curved ones of the Whitworth thread would be, for the rea- son that it is easier to discover irregularities in straight than in curved lines, and it is quite easy to grind a thread cutting-tool to the straight lines of the standard thread. Yours truly, THEO. N. ELY, General Superintendent Motive Power. Tke New York Central & Hudson River Railroad Company. Office Superintendent Motive Power and Rolling Stock. Room IJf, Giand Central Station. WM. BUCHANAN, Superintendent. NEW YORK, December 20, 1886. WM. H. WAHL, ESQ., Secretary FRANKLIN INSTITUTE. Philadelphia, Pa. DEAR SIR : In answer to your inquiry of 4th inst., we adopted the United States Standard form of thread three (3) years ago, and have never experienced any difficulty in maintaining the form of the threads or in making nuts interchangeable. For durability, think the Whitworth thread is the best, but for ordi- nary work, think this feature is offset by the difficulty in reproducing it. The facility with which the straight threads can be produced by an ordinary workman with tools that can be readily made and main- tained, so as to conform to the standard guages, is a recommendation sufficient in itself. Yours truly, WM. BUCHANAN. 105 2?ew York, Lake Erie & Western Railroad Company, Office Superin- tendent of Motive Power. BUFFALO, N. Y., February 8, 1887. WILLIAM H. WAHL, ESQ., Secretary FRANKLIN INSTITUTE, Philadel- phia, Pa. DEAR SIR : In answer to yours of December 4th, ult., making inquiry in regard to the Standard Screw-Thread recommended for general adoption by FRANKLIN INSTITUTE in 1861. in comparison with the Whit worth thread, would say that we have made careful inquiry in regard to this matter from all our master mechanics and foremen of car-repair, and the general opinion is about as follows : There is little question about the practical superiority of the Sellers, or United States Standard Thread. The principal differences between the two are in the angle of the thread and the form at top and root of thread. The angle of the Sellers thread is more easily maintained than the other, because a templet can be accurately made without the use of special tools, as it is easy to construct the angle geometrically. It is also simpler and cheaper to cut the Sellers thread in a lathe. It is a difficult matter to make the nut fit closely on the curved portion of the Whitworth thread, and practically the bearing surface will probably be limited to the straight parts, making it considerably less than in the Sellers system, consequently more liable to be distorted as far as this element goes. We have no trouble arising from the wear of the United States Standard tap sufficient to prevent the nuts from being interchangeable. Yours truly, RICHARD H. SOULE, Superintendent Motive Power. T. The Pratt & Whitney Company, Manufacturers of Machinists'' Tools. HARTFORD, CONN., U. S. A., December 29, 1886. DR. WM. H. WAHL, Secretary FRANKLIN INSTITUTE, Philadelphia, Pa. DEAR SIR : Your favor of the 28th inst., is to-day received. We trust you will pardon us for the delay in complying with your esteemed request of the 4th inst., mainly due to absence of the writer to whom the matter was referred, and the subsequent unusual demands upon his time. Regarding our experience as manufacturers of taps and dies, espe- cially those covering the application of the Sellers System of Screw-. 106 Threads, now known as the FRANKLIN INSTITUTE or United States Standard, we can say, as stated in our letter to the Railroad Gazette, and published in their issue of September 24, 1886, included in article on " Screw-Threads," that the orders we have received for taps and dies from railroad companies, bolt manufacturers, bridge builders, and man- ufacturers generally, in the United States, are largely for the United States Standard thread. Fully ninety per cent, are strictly so, and many of the others not United States Standard both in form of thread and pitch, are so in shape of the thread, i. e., flat at top and bottom one- eighth of the pitch, and having a greater number of threads per inch. This is necessary for special cases, such as tool work and small diame- ter taps and bolts. The form of the Sellers, FRANKLIN INSTITUTE or United States Standard thread, is such as to make it the most practicable for dupli- cation to guage, and by making the outside diameter slightly larger (not, however, larger in the angle of the thread), the life of the tap or before it wears below guage size, is greatly lengthened. The claim that the form of the Sellers thread cannot be maintained in use, seems in our experience inadmissible, for although the corners may wear slightly, this wear is unimportant if the taps are properly used, and especially so, if made as recommended slightly larger in the outside diameter. Our position in the matter is stated more fully in the article pub- lished in the Railroad Gazette, referred to, and should you desire further information, we shall be glad to be of service to you if in our power. Regretting the delay, we are, Tours respectfully, THE PRATT & WHITNEY COMPANY, GEO. M. BOND, Manager Gauge Department. [Following is the article from the Railroad Gazette, September 24, 1886, referred to in Mr. Bond's letter.] SCREW-THREADS. The last issue of Engineering publishes an article on " Screw- Threads," chiefly dealing with a movement, in Germany, to abandon the Whitworth Standard for a new one based on metric measures, in which some very large-sized and strangely erroneous statements are 107 made in reference to what has now become the American Standard _ The Sellers thread. It says : " The form of cross-section Whit worth adopted for ordinary pur- poses, was that of a triangle, whose height was 0.96 of the pitch and the angle at the bottom of the threads 55 ; one-sixth of these triangular sections was rounded off at the top and bottom. This system has been very widely and almost universally used for the last thirty years, the chief and only important exception to their universality being in the United States, where Sellers threads are very much used : they are of a slightly different pitch and form of cross-section, being an equilat- eral triangle with one eighth of the depth cut off square, both top and bottom. "The objection (to the form of the Whitworth thread) is totally unjustifiable, for thirty years of practice have most unmistakably proved the Whitworth form of cross-section to be the best ; the square- tipped thread, on the other hand, as advocated by the metrical sys- tem, has proved unsuccessful. It has been thoroughly tried by Sellers in the United States, where it has been found practically im- possible to produce a good thread by screwing apparatus, the sharp corners on the taps and dies rapidly break away, when a very imper- fect thread must naturally follow. The present state of affairs in America conclusively shows the system to be a failure, and all the leading machine tool-makers there are supplying nothing but the V-shaped thread very similar to Whitworth's." The Sellers threads are, indeed, " very much used," as they are the standards of the United States army and navy, and of the Master Mechanics' and Master Car-Builders' Associations, and of most of the large railroad shops at least. That "all" the leading tool-makers are supplying " nothing " but the V-thread " very similar to Whit- worth's," is a fabrication, by some one, out of the whole cloth. The facts of the case are, that from eighty to ninety per cent, of the taps and dies sold by various dealers are already of the Sellers Standard, and the remainder of a plain V-thread, the latter having been form- erly universal, and being still quite largely used, taking the whole United States together. That the Sellers Standard is, in any sense of the word, going out and still less that it has practically gone out, as Engineering explicitly asserts is utterly untrue. On the con- trary, it is coming in. There is little room for doubt that its use is becoming more general every day, and it would now be hard to find a railroad anywhere on which it would not be asserted, at least, that the Sellers (or "M. C. B.," or "United States," as it is variously 108 known) Standard was in use. Many more will assert that they use it than actually do use it, but that is natural. The comparative merits of the Whitworth and Sellers Standards we are not discussing. This, however, we may say, that records, as respects durability and adherence to standard, are being made every day with taps aijd dies of the Sellers Standard, which certainly have not been, and probably cannot be, surpassed or even approached. The " sharp" angles (120) do not, so far as we have ever heard, or can learn, give any difficulty from breaking off, while they do enable the standard to be exactly reproduced and readily maintained, so that complete interchangeability is assured. As it now appears quite cer- tain that it will come into practically universal use in America, and as there is no prospect that any other standard will, anything calculated td impede its so far continuous progress to that end is greatly to be regretted. Fortunately, Engineering's assertions are so exaggerated, and to anyone familiar with American practice palpably false, that they are calculated to disprove themselves. To make assurance doubly sure in this matter, we addrersed an inquiry to The Pratt & Whitney Company of Hartford, Conn , famous throughout this continent, and, we should imagine, throughout the world, not only for the magnitude and excellence of their products, but for their exertions and success in turning out minutely exact standards of various kinds, and especially for screw-threads. We risk little in saying that no house in the world is better qualified by experience to form correct conclusions in such a matter. The follow- ing is their reply: " Referring to Engineering's comments on the second objection brought up by the commission and the Karlsruhe Society against the Whitworth thread, viz.: " ' (2.) The Whitworth system being measured in inches, it is incon- venient for metrical measurements,' and the reply by the author of the. article in Engineering referred to, which is as follows : " ' If a new universal system of screw-threads must be adopted, then it should not be tied down to any special system of measurement, but should rather be designed on a system of standard gauges of various grades, similar to our Birmingham wire-gauge system,' " We would say that if the writer had been aware of the fact that the British Board of Trade had established in decimal sizes all Bir- mingham gauge dimensions in effect on and after March 1, 1884 he would not have made the assertion there given. " In regard to the disposal by Engineering of the third objection to 109 the Whitworth thread raised by the Karlsruhe Society, viz. (that it is difficult of manufacture), a method of disposal which has justly aroused your indignation and our own, we can also say that the Sellers or FRANKLIN INSTITUTE thread, now generally known as the United States Standard, is in every respect a more practical form of thread to maintain to gauge than the old V -thread, or even the Whitworth, and is a much more simple thread to produce by machinery or the ordinary work-shop tools than the latter form. " As to the Sellers thread being a 'failure,' we will only refer to the fact that in our large and increasing production of taps and dies for the market in this country, ninety per cent, are United States Standard, while many not strictly United States Standard in number of threads per inch, are so in form of thread, i. e., one-eighth of the pitch flat, top and bottom. " V-threads and over-size threads are not used to the extent they once were, thanks to the untiring devotion of the Master Car-Builders' Association, through their committee having this matter in charge; for it is now an accomplished fact that bolts and nuts are interchange- able throughout the United States, which was not possible under the old system of V and over-size threads. "Furthermore, a United States Standard tap made in the proper manner will cut ten times as many nuts as wiJl one with the simple V-thread, without appreciable change of size as compared with a stand- ard gauge. " The United States Standard form of thread embodies a condition which makes this great lengthening of the life of a tap possible, and this is not nearly so easily accomplished in the Whitworth thread. At all events, it is impracticable in the latter form to carry out the conditions referred to, and an impossibility in the V-thread. "As to the objection regarding relative strength of the bolt cut with the United States Standard or the Whitworth thread, we can refer to the United States Navy Board report of May 9, 1868, which certainly .shows this objection to be unfounded. "THE PRATT & WHITNEY COMPANY. ("GEO. M. BOND, Manager Gauge Department") This is not the first time that facts and figures as to American prac- tice have been "evolved from the inner consciousness" of writers across the water, to suit the occasion, but it is not often that such a complete perversion and reversal of the facts is given currency in a 110 journal of standing. In addition to the railroad shops, the Baldwin Locomotive Works, and nearly, if not quite, all the other large loco- motive shops, are using the Sellers system, as are also most of the car shops. Hoopes & Townsend of Philadelphia, the largest single manu- facturers of track bolts, are also using it. The prospects are excellent that the system will come into universal use, as it is now in large and rapidly increasing use. A correction would, therefore, seem to be in order. Railroad Gazette, Sept. 2Jk 1886. I have taken this method of replying to your inquiry as best cal- culated to answer such allegations as are made in (London) Engi- neering, of September 10, 1886, and have only to add, that, from the letters and publications above referred to, it must be evident that the Sellers or FRANKLIN INSTITUTE Standard for pitches and form of thread is accepted and used throughout the United States, to the exclusion of any other ; that is to say, while there are still some parties who have not adopted any standard, there are none who have adopted any other standard than the Sellers. Hoping you may find the information herewith forwarded to be a satisfactory answer to your inquiries, I have the honor to remain, Yours respectfully, WM. H. WAHL, Secretary. [Reprinted from the JOURNAL OF THE FRANKLIN INSTITUTE, April, 1884, with Revision by the Author, June, 1887.] STANDARDS OF LENGTH AND THEIR SUBDIVISION. BY GEORGE M. BOND, Hartford, Conn. [A lecture delivered before the FRANKLIN INSTITUTE, February 21, 1884.] We are all, no doubt, familiar with the old table of English measures of length beginning " three barleycorns make one inch." I, for one, can remember having vague ideas in regard to barley- corns in general, and their exact size in particular, though I imagined'! knew exactly what constituted an inch. Later in life I began to doubt my knowledge in this respect, having had con- siderable difficulty in reconciling the differences between two separate inches not exactly alike, one of which evidently was not 3^ part of a standard yard. It may be of interest to glance over the history of the gradual development of the modern science of minute measurement, to notice how such crude standards as the human foot or arm, and standards called cubits, fathoms, or the foot made up of " thirty- six barleycorns, round and dry, placed end to end," in the course of time grew into the more exact determinations of scientific research, as shown in the results of the labors of men like Kater, Baily, Bessel, Sheepshanks, Shuckburgh, and Sir George Airy in the great problem of establishing a standard of length from a natural unit. They gave us so closely the relation of the length of a pendulum beating seconds of time to the length of a yard, that it was thought they had determined, beyond further doubt, the means for restoring a lost standard should it become neces- sary to do so from any cause. However good these crude standards, such as a barleycorn, a human arm or foot, may have been for practical purposes at the time they were adopted, they certainly are in our times com- 112 pletely out of the question and useless for precise determina- tions. As all measures derived from them were purely arbi- trary and sanctioned by law, no reference made to any of these sources could be presumed to restore a lost original standard, even such as a common yard-stick, except within a very liberal margin of error; we need not be surprised to find that there happened such a wide range of value for a foot as that of the Pythic of 9f inches to that of Geneva of 19 inches. The adoption of an invariable unit as a standard of length, while seemingly only applicable to the refined methods of science, really becomes a necessity in our ordinary workshop practice, as we shall see later on in our presentation of this subject. The arm of King Henry the First, or the barleycorn, though possibly furnishing a standard good enough at that time, would hardly satisfy the requirements of our modern mechanics or tool- makers, who work very often within the limit of a thousandth of an inch, and even one-tenth of this apparently minute quantity, with surprising unconcern and no less accuracy. To the celebrated philosopher and scientist Huyghens is due the honor of having demonstrated the principle, that the times of the vibrations of pendulums depend entirely upon their length. About the year 1670 his inventive genius conceived the plan of using this fact to establish the length of a standard which should be the unit for measures of length. This he divided into three equal parts, each of about thirteen inches, calling this third part the " horary foot." Picard, in 1671, also proposed using the length of a pendulum beating seconds of mean time, which should be adopted as the unit of length, thus endorsing the plan of Huyghens. It was Picard who first measured the arc of the meridian from Paris to Amiens, in 1669, deducing from it the value of a degree to be 68.945 miles. Picard was the first to suggest that the diurnal revolution of the earth necessarily affected the times of oscilla- tion of a seconds pendulum, and that it ought to vibrate more rapidly at the poles than at the equator. His experiments at different latitudes, howevor, failed to confirm this theory, probably owing to the lack of sufficiently accurate apparatus for his work, and it was left to Richer, in the same year, (1671,) to prove that, at the equator, or 4 56' north, where the observations were 113 made, the difference of the length of a seconds pendulum at that place, as compared with the length at Paris, or 48 50' north, was about a line and a quarter, or over one-tenth of an inch. Cassini, in 1718, proposed a unit which should be ^00- P ai> t of a minute of a degree of a great circle of the earth, and which would be nearly equal to a third part of our yard.* M. de la Condirnine, who had measured a degree at the equa- tor in Peru, in a Memoir read before the Academy of Sciences at Paris, advocated the use of a pendulum as the unit of length, proposing that it should beat seconds at the equator, a place least likely to cause prejudice that might follow national jeal- ousy, were the latitude of any particular place selected. Talleyrand, in 1790, proposed to the Assembly of France that a commission be appointed to consult with a similar commission from the English government, to consider the subject of a uni- form international system of metrology. He favored the length of a pendulum as compared with the unit obtained by the subdi- vision of a quadrant of the earth's meridian ; but after a careful consideration of the three plans proposed, the pendulum, a quarter of the equator, and a quadrant of the earth's meridian, they concluded to recommend the latter method. In 1790, one year before the International Commission had: adopted the ten-millionth part of the quadrant, as settling the question of a natural unit for a standard measurement of length, and before any steps had been taken by them in the matter,.. Thomas Jefferson, then Secretary of State, in obedience to a reso- fution of Congress calling upon the Secretary to propose a plan, for establishing a uniformity in the currency, weights, and meas- ures for the United States, recommended, in his report, a deci- mal system of metrology, and that the unit be derived from a. natural and invariable standard of length. Jefferson considered that though the globe or its great circles- might be invariable, the means to be employed to obtain an, accurate subdivision of a quadrant from previous trials had showed their unreliability and promised too great a degree of uncertainty ; he therefore objected to the ordinary form of the * Report on Weights and Measures, by Dr. Alfred B. Taylor, Eighth Annual Session, Phar. maceutical Association, Boston, September 15, 1859. 8 114 pendulum, as " not without its uncertainties," the length not being possible to be accurately determined, owing to variations in the clock-work mechanism and to barometric and thermo- metric variations. He recommended the latitude of 45 and a mean temperature of the year at that location. Instead of using the ordinary pendulum of thirty-nine inches, he advised the use of a seconds rod of five feet, known as Leslie's pendulum rod. This was a simple straight bar, without a disc or bob, sus- pended at' one end, and free to swing at that point, its center of oscillation being at a distance of two thirds of its length from the point of suspension. It would be one-half longer than the ordinary loaded pendulum. A rod of this kind, vibrating seconds, is 58.72 inches long. He proposed that this rod be made of iron, of such a length that at a level of the sea, at a latitude of 45, and with a con- stant temperature, it should beat seconds of mean time ; its length, given exactly, would be 58.72368 inches. Jefferson then proposed dividing this length into five equal parts, calling each part a foot, which would give 11.74473 inches as the length of the new foot. He then divided the foot into ten equal parts, affording a decimal subdivision to correspond with the decimal character of the coinage of the country. The French Commission, after carefully determining the length of a quadrant of the earth's meridian, and dividing it into ten million equal parts, presented science and the world with the meter as a universal standard to which posterity might ever afterward refer. Its length, as they computed it, is very nearly the length of the seconds pendulum, or 39.370788 inches, or nearly 3f inches longer than the yard. This meter, which is an end-measure standard, was made of an alloy of platinum and iridium, ninety parts of the former to ten of the latter. It is called the "Metre des Archives," and is kept in the buildings of the International Bureau, at Breteuil, between Paris and Versailles. Having thus briefly touched upon the history of individual and national efforts to secure a unit for a standard of length, .covering a period of about two hundred years preceding the .legal adoption of our standard yard, it may be interesting to 115 know that just five hundred years after the statute of 17th, Edward II, A. D. 1324, which enacted that " three barleycorns, round and dry," make an inch, and twelve inches make one foot, it was, by act of 5th, George IV, Cap. 74 (1824), that a legal definition of the yard was made, and by it was declared that the yard-bar, made by Bird in 1760, should be the standard beyond any question or doubt.* It may be in place to quote here an abstract of the Act of June 17, 1824, legalizing this standard, and which reads as follows: SECTION I. Be it enacted .... that from and after the first day of May, one thousand eight hundred and twenty-five, the Straight Line or Distance between the Centers of the Two Points in the Gold Studs in the Straight Brass Rod, now in the Custody of the Clerk of the House of Commons, whereon the Words and Figures " Standard Yard, 1760, " are engraved, shall be and the same is hereby declared to be the Extension called a Yard ; and that the same Straight Line or Distance between the Centers of the said Two Points in the said Gold Studs in the said Brass Rod, the Brass being at the temperature of Sixty-two Degrees by Fahrenheit's Thermometer, shall be and is hereby denominated the " Imperial Standard Yard." SECTION III. And whereas it is expedient that the said Stand- ard Yard, if lost, destroyed, defaced, or otherwise injured, should be restored to the same Length by reference to some invariable natural Standard ; And whereas it has been ascertained by the Commissioners appointed by His Majesty to inquire into the subject of Weights and Measures, that the Yard hereby declared to be the Imperial Standard Yard, when compared with a Pen- dulum vibrating Seconds of Mean Time in the Latitude of Lon- O don in a Vacuum at the Level of the Sea, is in the proportion of Thirty-six Inches to Thirty-nine Inches and one thousand three hundred and ninety three ten-thousandth Parts of an Inch; Be * This Act was introduced into the House of Commons in 1822, but failed to pass the House of Lords. It was again introduced, with modifications, in 1823, but was not passed until June 17, 1824, to go into effect, as stated, May 1, 1825. This was, however, postponed to January 1, 1826. [" Weights and Measures," by Prof. F. A. P. Barnard, Johnson's New Cyclopaedia, p. 1737, Appendix. See, also, Encyclopaedia Brittanica, 8th Edition, Vol. xxi., pp. 803 and 807.] 116 it therefore enacted and declared, That if at any Time hereafter the said Imperial Standard Yard shall be lost or shall be in any Manner destroyed, defaced, or otherwise injured, it shall and may be restored by making a new Standard Yard, bearing the same proportion to such Pendulum as aforesaid, as the said Imperial Standard Yard bears to such Pendulum. Just ten years afterward, Oct. 16, 1834, occurred the calamity for which the carefully worded text of Section III was intended to provide, a contingency certainly most wisely considered. This was the destruction of the Standard Yard by fire, when both houses of Parliament were burned. The bar was recovered, but in a damaged condition, and all hopes of restoring its usefulness were abandoned when it was found that one of the gold plugs had been melted out. The provisions of the Act now came into service, in order to repro- duce the lost Standard, and it became necessary to decide whether it could be restored by the use of the method so carefully prescribed. It has been proved conclusively since the passage of the Act that there were errors in the determination of the specific grav- ity of the pendulum employed; the reduction to the sea-level had been shown by Dr. Young to have been doubtful ; the reduc- tion for the weight of air was also proved erroneous, and Kater showed that sensible errors had been introduced in comparing the length of the pendulum with Shuckburgh's scale, this bar having been compared with Bird's " Standard, 1760," and found to agree closely. Shuckburgh's scale, marked (0 36 in ), was made by Troughton in 1798, and had been compared with the pendulum and with the meter. It may be interesting to know, that previous to Shuck- burgh, all transfers of the yard were made by the use of beam compasses, and comparisons were also made in the same way. It was not until 1798 that optical instruments were used for this purpose, and Troughton must be credited with having intro- duced this wonderfully improved manner of dealing with minute measurements, and which afterward, no doubt, led to the discov- ery of the errors found to have crept in when the relation of the yard to the length of the pendulum was originally established. 117 All attempts, therefore, to use the pendulum for the purpose of reproducing the lost standard were abandoned. The next step was to approximate this result by the use of standards then in existence, which had been compared with the original yard. The bars used for this purpose were : (a) Shuckburgh's Scale (0 36 in ). (b) Shuckburgh's Scale, with Kater's authority. (c) The Yard of the Royal Society, constructed by Kater. (d) Two Iron Bars, marked A 1 and J 2 , belonging to the Ord- nance Department, and kept in the Office of the Trigonometrical Survey. To Sir Francis Baily was intrusted the work of the restoration of the yard. His death, unfortunately, occurred in 1844, before the work was completed. He had then only completed the pro- visional or preliminary investigations necessary for this most important undertaking. .He had, however, made a great many experiments to deter- mine the proper material for the new standard, and finally decided upon the alloy of which Bronze No. 1 was afterwards made. It is still known as Baily's metal. Its composition is copper 16, tin 2J, and zinc 1. The work was now entrusted to the Rev. R. Sheepshanks. He constructed first, a brass bar as a " working standard." This bar was compared with all the standards considered by him nec- essary for the purpose, and which were those just mentioned. Taking the average of all the values of each, compared with the brass bar No. 2, as the working standard was designated, and reducing to an assumed value of the original standard yard, he found for the relation of the new yard, brass bar No. 2 = 36.00025 inches of the lost Imperial standard, taken at 62 Fahr. The brass tubular scale of the Astronomical Society did not appear in the list of bars used as references (see Phil. Trans. 1857, p. 661), and the statement that this was the principal authority for the new standard is therefore incorrect. Bronze 19, as the new yard was designated, or now known as No. 1, was graduated according to this value, in terms of the lost Imperial standard, found from the'comparison of these five stand- ards, and is made, as just stated, of Baily's metal, the dimensions are: length 38 inches, depth 1 inch, width 1 inch. The gradua- 118 tions are upon gold pings inserted in wells of sncli a depth as to bring the polished surfaces of the plugs at a distance from the top equal to one-half the depth of the bar, the plugs being 36 inches apart. The bar which is here exhibited, is a copy in every respect, except that it has the subdivision of feet besides ; but we have the same material, the same dimensions, and the same conditions in the graduations, while more than all, the distance between the two defining lines as compared with Bronze No. 1, varies less than one hundred-thousandth of an inch at 62 Fahr. This bar was constructed by Professor W. A. Rogers, of Har- vard College Observatory, Cambridge, for The Pratt & Whitney Company of Hartford, Conn., for their use as a final reference standard. It has been compared directly with Bronze 11, at the office of the Coast Survey, by Professor J. E. Ililgard and Pro- fessor Rogers, and allowing for the known relation between Bronze 11 and Bronze No. 1, its value was found to be within this minute limit, in terms of the Imperial Yard.* The reason assigned for placing the lines at the center of the depth of the bar, was to neutralize errors arising from flexure which were liable to occur; that is, by the bending of the bar, the distance between the lines would become less. Having the graduations at the center was thought would neutralize this effect. We all know that if a beam is supported at the ends and loaded in the middle, the beam is compressed at the top, and stretched or extended at the bottom, and if we were to measure between finely drawn lines, before and after the load was applied, we would find that the lines were nearer together when the beam was under strain than when free, measuring, of course, in a straight line; hence it was thought that having the lines midway between the top and bottom of the standard bar, this error would be reduced. Captain Kater was the first to discover the variations due to the flexure of standard bars upon which graduations were traced, and he first proposed a " neutral plane," which would have the effect, within certain limits, of reducing this error to zero. He first located this plane in the center of the bar, as was done in the * See Report of Professor Ililgard, U. S. Coast and Geodetic Survey, reprinted, pp. 24-27. 119 case of the Imperial Yard, but after further investigation, he concluded that it was not quite one-third the thickness of the bar below the graduated surface. He found that the errors from the effect of flexure depended upon the thickness of the bars as compared with each other, and when resting upon a surface which is not plane (Phil. Trans. 1830.) He also found that this error far exceeds that which would arise from the difference of the length of the arc and its chord under the same circumstances ; so much so, that in a bar an inch thick, with the versed sine, that is, the distance at the center of the bar from the horizontal plane joining the two ends to the curved surface, equal to one hundredth of an inch, the sum of the errors would be nearly one thousandth of an inch in the length of a standard yard. To overcome the objection of a variable result at every position of a standard bar, the number of supports for it has been carefully determined, and in the case of- the Imperial Bronze 1, the number of these supports is eight, and having been decided by Mr. Baily to be necessary, this was adopted for the national standards. The distance between the supports is about 4 inches. Sir George Airy gave a formula for determining the distance between the supports for any standard bar, in order to neutralize the effect of flexure. It is Length of the bar, " n " being the number of supports. In the bar we now have before us, the condition under which it was transferred, and also when investigated, was when resting upon two supports, and using the formula just given, the distance between them is about 22 inches, the total length being 38 inches. You will notice it places the supports a little Jess than one quarter the length of the bar, measured from each end. This gives the surface a certain permanence or equilibrium of position when resting upon any level surface, whether a true plane or not, and if used thus under the same conditions of support and tem- perature, the distance between the defining lines remains the same. If we move the supports each nearer the ends, say an inch and a half, the surface changes slightly, and the result 120 is to bring the lines at each end nearer together, as we have just mentioned. According to the Report of Professor J. E. Hilgard, Chief U. S. Coast and Geodetic Survey, in charge of Verification of Standards, 1880, Bronze No. 1 is kept at a very uniform tem- perature within the walls of the Houses of Parliament, while Bronze No. 6, which is the accessible national standard, is pre- served in the Strong Room of the Old Treasury, now No. 7, Old Palace Yard. There is not now any perceptible difference in the lengths of these two Standards. The Imperial Yard is in charge of Dr. H. J. Chancy, his official position being Warden of the Standards. In order to secure, as far as possible, accurate duplicates of the new standard, four Parliamentary copies were constructed^ one of which is kept in the Royal Mint, one is in charge of the Royal Society, one is preserved in the new Westminster Palace, and the other is kept at the Royal Observatory at Greenwich. There were also 40 copies made of Baily's metal for distribu- tion among the different governments. Only two of these 40 bars are exactly standard at 62 Fahr., these are, Bronze 19, and Bronze 28. Both are kept at the Royal Observatory for refer- ence, as representing the national 'standards. All the other copies have a certain relation to Bronze 1, and instead of giving this relation, the temperature at which they are standard is established for each. The standards prepared by Mr. Sheepshanks were legalized by Act of Parliament, June 30, 1855, and in 1856 Bronze 11, one of the 40 copies made of Baily's metal, was presented to the United States Government by the British Board of Trade, and was then standard at 61. 79 Fahr. This bar is deposited in the office of the United States Coast Survey at Washington. It has since been found that Bronze No. 11 is shorter than Bronze No. 1 by 0.000088 of an inch at 62 Fahr. from comparisons made by Professor J. E. Hilgard, who, in 1878, compared it directly with the Imperial Yard at the Standards Office in London. Conse- quently, to be standard, it must be considered so at 62. 25 Fahr.* Previous to 1856, the distance between the 27th and 63d line * See Methods and Remits, American Standards of Length,, U. S. Coast and Geodetic Survey, Appendix No. 12 Report for 1877, pages 33 and 35. 121 of the brass scale of 82 inches, made by Trotighton,* was taken as standard, though never having been legalized by Act of Con- gress it had an indirect authority, as it was adopted by the Treas- ury Department in 1832, on the recommendation of Mr. Hassler (Weights and Measures Eeport, Washington, 1857), and copies of it were made for distribution among the different States, under the charge of Mr. Joseph Saxton. The fact is noticeable that all the copies of the Imperial Yard are made of the same material as that of the original Bronze 1. This is no doubt owing to the greater uniformity obtained in the coefficient of expansion for each standard bar, admitting of com- parisons at any temperature. Comparisons otherwise would not be possible, except for bars of other metals whose coefficient or rate of change for each degree of temperature was definitely known, and even with this knowledge it would present an exceed- ingly nice problem. To illustrate this in a few words. If a steel bar or a platinum standard be compared with one made of brass or Baily's metal, and each were standard only at 62, if we should compare them at 72 we would find them not alike in length, because brass expands more for each degree of rise of temperature than does the steel or the platinum ; the difference would be greater in the comparison of platinum with the brass standard, as steel and brass have a coefficient more nearly alike. Let us now briefly refer to what has been done to fix perma- nently the metric standard of length. The metric system is represented in Great Britain by two bars made of platinum, one being a line-measure, and the other an end-measure standard. These bars are of the following dimensions : ( Length, 41.000 inches. Line Meter, . . 1 Breadth, 1.000 " ( Thickness, 0.211 " Length, 39.37-1- " End Meter, . . J Breadth, 1.000 " ( Thickness, 0.287 " The defining lines nearly traverse the face of the bar for the line meter, and arrows arbitrarily placed, indicate the position on the lines where measurements are to be made. *See House Doc. No. 299, XXII Congress, first session, and also Am. Phil. Society Trans., vol. 2, new series. 122 The line meter lias the words " Royal Society, 45 " engraved on the under side. The end meter, being made of so soft a material as platinum, is not at present in a condition to use as a standard for very accurate work, the edges of the end surface being indented and other signs of change in the surface being visible. The end meter has the words, " Metre a Bouts " engraved on one side, and " Fortin a Paris, Royal Society, 44," on the other. These bars, together with the original standard prepared by Hassler in 1832, are the only recognized standards which have been compared directly with - the "Metre des Arch- ives," as the French standard is called. The Meter of the Archives, as already stated, is made of plati- num and iridium, the dimensions being about the same as the metric standard in London, and this bar was made a legalized standard after all attempts to make it conform to a natural unit were abandoned. It is standard only at Centigrade, or 32 Fahrenheit. Thus we see, that after all, the actual use of a natural unit for creating and reproducing a standard of length was not realized ; and standards, made standard by law, were really the final result. It has been said that " a mystery is a truth hid behind some other truth, and about which the latter throws a veil," and it would seem as if this definition might apply to the great difficul- ties met with in the attempts to obtain a standard of length from natural laws and natural conditions, using the grand truths which are known and accepted, but which seem to throw just enough uncertainty around the truth sought as to make the results doubtful for the purposes for which they are intended. Truth is exacting, it allows for no " errors of observation " or of <; personal equation," and in no other kind of investigation does this requirement seem more difficult to be fulfilled, as so many " variables " to use a mathematical term enter into the problem ; variations of temperature, internal strain due to posi- tion of the bar; errors of curvature; errors of observation in using optical instruments ; differences in material or of density, thus affecting the rate of expansion or contraction, and a score of other variables, all tending to make the problem a complicated one. We cannot fail to realize at least partially the won- derful skill and patience necessary to conduct the experiments 123 which gave us, as English speaking people, the Standard Imperial Yard, which 50 years ago were engaging the attention of some of the greatest minds the world has ever known. o There is still another natural unit which has been proposed as a standard of length. This is the length of a wave of monochro- matic or single color light. We have all seen the beautiful colors so wonderfully arranged in the thin film of a soap bubble. These colors are caused by what is termed " interference." To briefly explain this kind of interference, we should know that light is made up of seven dis- tinct colored rays, which blended together produce clear color- less light. Each of these separate rays has an undulatory or wave motion through space, and the length of a wave, or the distance from the crest of one wave to the top of the next, is dif- ferent for each as compared with one of unlike color, but con- stant for its own ; that of the green ray, for instance, being com- puted as being about 3-ovro o of an inch from crest to crest. When light is reflected from the two surfaces of the thin film of a soap bubble to the eye, a portion of it must evidently travel a distance twice the thickness of the thin film of the bubble, as part is reflected from the outer and part from the inner surface of the film. The particular ray which must thus travel farther, loses a half of a wave length in the reflection, so that when these two portions of the reflected light come into the same path again, there is more or less interference, and if the retardation lias been such that the wave crest of one falls into the trough of the other, they completely neutralize each other, and the corre- sponding color rays are destroyed. Without attempting the mathematical discussion of this subject, we know that when this relation happens more or less coincident, the rays are either deadened or are so blended that they form the beautiful rings or bands so often noticed. As the film of the bubble changes in thickness, these colors are rearranged, as different sets of color rays or waves are deadened and as different colors disappear from the reflected light. The adoption of this unit, no doubt, could be relied upon to produce a standard within certain small limits, but the addition or multiplication of such minute units for the purpose of obtain- ing a practical standard of length might introduce errors in the 124 total, greater than would be likely to result from either of the methods already mentioned. The use made of this unit seems to confirm the theories in regard to the limit of divisibility of matter, and these same soap bubbles which are such a delight to children and we might include some of the older people as well have shown a way in which to estimate, in a purely scientific discussion, the dimen- sions, approximately, of a molecule, a form of matter so minute that the smallest object visible under the most powerful micro- scope is made up of countless numbers of them. It has been demonstrated that the mechanical energy required to pull apart the molecules of water in forming steam, is no greater, according to the theory of capillary action, than is required to reduce the thickness of a film of water to the 3Tro-,woYoiro of an inch ; a force quite large when compared with the small amount of water which we are considering. The measurement of this minute thickness is based upon the varying colors exhibited in the soap bubble, using the length of any given wave. Probably before this extreme tenuity could be attained, there would remain only a single layer of molecules held together by their mutual attraction, giving as the estimated average diame- ter of a molecule the ^oyoio^orir ^ atl i ncn > a dimension so in- finitely minute as to be quite beyond our ability to realize. Sir William Thomson, from a comparison of these phenomena, has estimated the limits of range or size of these minute mole- cules to be between ^S^TTOOYO o o" an d s\Tnru,i?F?r,-nly 4.33 cents. This represents a saving of about $675,000 a year. This was after the system had been adopted by the railroad company of making parts of locomotives in dupli- cate, using gauges and templates for this purpose. Had the rate of cost of 1871 prevailed in 1881, the expenses of locomotive maintenance would have been $790.492 greater than they were. The conclusion must not be formed, however, that all the above savings, or even a major part of them, have resulted alone from the system above mentioned. Much of the economy is doubtless due to other reforms introduced by the management of the road about the same time ; but a considerable part is certainly due to 142 the adoption of rigid standards and of interchangeable parts. Moreover, a very considerable number of the old engines still remain, with all their imperfections, so that further benefits may be expected to result from the system as it becomes extended in the future." In the system upon which are based the gauges produced by The Pratt & Whitney Company for the purpose of establishing and main- taining this interchangeability, the sizes are all constructed from ac- curate subdivisions of the British yard, fftade so carefully that end- measure pieces, representing any subdivision of a foot, and taking any of these sizes from a quarter of an inch to four inches, varying by sixteenths, the sum or combination of them, taken at random and in numbers sufficient to constitute the length of a foot, will be found to produce in the total addition, exactly the same result. When we consider that in the experiment just mentioned, the variation of only one thirty-thousandth of an inch in each, if all one way, either plus or minus, would amount to an error, in some cases, of over half a thousandth of an inch, and particularly in the case of one combination where fifteen or sixteen sizes were added, it will be seen that the error would be very perceptible in the test which they would thus be compelled to undergo. This severe practical test was applied by the Committee on Gauges, of the American Society of Mechanical Engineers, in their investigation of this system of making standard gauges, a set of these end-measure pieces being found to be within the limit of accuracy necessary to fulfill this condition.* In the production of these end-measures, it is necessary that the end surfaces be perfectly parallel. This is a matter which is a simple operation as done by The Pratt & Whitney Company. FIG. 17. Two sides of a hardened end-measure standard, such as the one we have now before us (Fig. 17), are made as nearly perfect planes as *See Trans. Am. Society Mechanical Engineers, 1882, Vol. iv, Report of Committee on Standards and Ganges, page 26. (Reprinted, page 50, ante.) 143 is possible, and at right angles to each other. The ends are then made perpendicular to these two surfaces, by means of a simple fixture which holds the end-measure vertically and clamps it in the angle of a movable block of cast iron which slides freely over the plane surface of another block also made of cast iron. In the center of this latter block is a copper matrix having diamond dust or washed emery imbedded in its upper surface. The end-measure is passed rapidly over this surface, and being held perpendicularly, its- highest points are ground away, and eventually this surface becomes a polished plane. The bar is reversed and the same conditions are applied to the other end ; both ends being perpendicular to the same planes, are conse- quently parallel to each other. These parallel surfaces being true planes, are, when brought together, capable of sustaining the weight of either one or the other, or in the case of the two which we have before us, they may be held horizontally and still not separate. In a lecture be- fore the Royal Institution, June 4, 1875, Dr. Tyndall states that experiments by Robert Boyle, with plane surfaces placed in con- tact, show this clinging tendency even in a vacuum ; and that with the surface plates he used, made by Whitworth, the force necessary to pull them apart was thirty times greater than that due to gravity, showing a mutual attraction or actual cohesion of the two surfaces. This is evidently the case, for we know that if the particles or atoms of a piece of steel are closely enough associated, they form a solid mass. By making their condition, artificially, as nearly like this as is possible, the atoms are brought comparatively near each other, and more or less of this cohesive force evidently results. Of course, in the present case we have apparently the weight of the atmosphere to produce this result, but if we consider how small the surface is on which this pressure is acting, we must admit that part of this clinging tendency must result from a cohesive force, for in the case before us, the surfaces in contact of one of these end-measure pieces are each less than a quarter of an inch square, and the weight of a column of air, even if there was a perfect vacuum between the two surfaces, would be scarcely enough to sustain this weight, even were the surfaces perfect planes. Perhaps the most marked example of interchangeable work 144 resulting from a standard gauge system is that shown in the thread gauges which represent the Sellers or Franklin Institute system. This form, proposed by Mr. William Sellers in 1864,* has, on account of being adopted by the Government, been called the United States Standard thread. In order to produce these standard gauges and to be able to guarantee them as being standard, it was necessary first to establish a standard inch. This standard inch must be one thirty-sixth part of the British Impe- rial yard, no more, no less. Then having obtained this standard inch, the subdivisions of it were to be obtained. So much for the size. Then in order to establish an angle of sixty degrees for the angle of the thread, it was necessary to produce this in a practical way, in order to furnish a gauge by which tools could be made that would insure absolute practical accuracy. This " master triangle," designed by Mr. J. W. Heyer, furnishes the means of originating a triangle which shall be equi-angular, and consequently possessing angles of sixty degrees. In order to obtain accurately the width of the flat, which is one-eighth of the pitch, for top and bottom of the United States Standard thread, it was necessary to establish a model triangle as a starting point, in connection with this master triangle. This model was, when finished, two inches long on each side. The method used for obtaining a triangle having sides known to be exactly two inches long, without the necessity of their being actually measured, is as follows : f An eight-inch triangle (Fig. 27), was so constructed that its center was definitely located by making it of parallel pieces of steel, J inch thick and If inch wide, accurately scraped and fitted together. Within this triangle, its inner sides tangent to the circumference, was fitted a cylindrical plug or center. This plug having been turned upon a true mandrel, the condition of the hole passing through it exactly in the center, naturally took care of itself. A second cylindrical plug, hardened and ground, was next fitted to the center plug. This hardened cylinder was ground to size exactly equal to the diameter of the largest circle which can be in- scribed in an equilateral triangle, the sides of which are two inches. Its diameter is, therefore, f -/3, or 1.1547 inches. * See page 97, ante. t See aleo page 161 for further description of the construction of this master triangle. 145 By securely holding a triangular piece of hardened steel ^ in. thick (Fig. 18), upon the stud passing through the center plug, and having its faces or sides reversed in position as regards the sides of the large triangle, the sides are each ground parallel to the opposite sides of the master triangle, and also ground until a sharp-edged corrected square, held against the side of the large triangle, determines the tangency of the sides to the inscribed circle 1.1517 inches in diameter. FIG. 18. As the large triangle is carefully tested for equality of angles,., this inscribed circle furnishes the remaining data for producing., a triangular model whose sides are known to be each two inches- long, without the necessity of their being actually measured. In fact it would be impossible to measure them in any other- known way within the limit which this method makes entirely practicable, and which at the same time " fortifies " each step in* the process, by employing fundamental principles, and keeping, the limit of error within what is claimed, which is TO^O f an ' inch. Imagine any one measuring the sides of such a two-inch triangle by actual contact with the almost infinitely sharp edges^ where the sides must, theoretically, meet ; I venture to say no- two readings would agree, and it is certainly safe to assume that each succeeding measurement would become less and less, as these fine edges were destroyed by this unavoidable contact. In the method described, using the inscribed circle, it is not necessary to have any edge whatever, as we may feel certain that the length of the sides would be two inches if prolonged to meet, each other. For the purpose intended, it does not matter if these edges are blunt or even more or less trun.cat.ed, as it is the position,. 10 146 and not the actual length of the sides, which it is necessary to establish. In order to have the flat of the thread correct for such a pitch, in this case taking two inches as a base from which to start, the flat of which would be one-quarter of an inch or one-eighth of two inches, the method adopted is as follows : The altitude of the frustum of this triangle was obtained after having removed the smaller triangle at the top, the sides of which are one-quarter of an inch, by subtracting the altitude of this small triangle from the total altitude of the equi-angular two-inch model, which gave the distance from the base to the top of this truncated triangle. By having this measured exactly, the top and bottom planes being parallel to each other, this distance came naturally, and evidently must be one-quarter of an inch without the neces- sity of its being measured. The actual measurement of this quarter-inch flat would evidently be very difficult, because we are dealing with the edges formed by obtuse angles, and the accuracy obtainable would certainly not be within the limit FIG. 19. which is required. After this triangle was established, a microm- eter was made, which we have before us (Fig. 19), in which the model two-inch triangle is used to determine the extreme limit through which the micrometer jaw shall move ; establishing a " zero," if it may be so called, for a starting point, the jaw of the caliper moving towards the smallest possible flat that might be measured, or that would be required for the finest pitches. This ;inicrometer is, as its name implies, a divided circle and a screw, .measuring very small advances of the jaw. In order to verify 147 these subdivisions, lines were ruled by Professor Rogers, four hundred to the inch, with a diamond, upon the polished, hard- ened surface of the center of the bar. There being 250 divisions graduated upon the index circle, and the pitch of the screw being ? V of an inch, each division represents T ff!oir of an inch. Each of the lines ruled 400 to the inch upon the sliding bar serves to check or correct the readings of every 25th division of the graduated circle, and thus to provide corrections for possible errors in the screw. By the use of this micrometer one can accurately measure the flats of the tools which are used to cut the United States Standard or Franklin Institute thread of any number of threads per inch. In order to show the adaptation of this form of thread to interchangeable work, and also to demonstrate its extreme sim- plicity as a basis for an interchangeable system of screw thread gauges, we have (Fig. 20) a drawing showing how, should this thread be even larger in diameter on the outside, but with the diameter correct in the angle of the thread, the variation of this outside diameter from that of a standard cylindrical size has no effect upon the fit of the nut which may be screwed upon the standard or upon a bolt representing this standard size. The only difference which we would notice is that the top of the thread would 'be narrower, and consequently the top would be higher, in the space cut away by the tap. Plence, taps that are FIG. 20. made for tapping nuts with the United States Standard thread, if made exactly right in the angle of the thread, that is, having the angle sixty degrees, and the diameter measured in this angle of the thread, correct, the outside diameter has no effect, within 148 certain limits, to change its size, merely cutting away within the nut more metal outside of the limit of one-eighth the pitch. In the case of the bolt which fits this nut, the outside diameter should be kept standard, the space between the bottom of the thread of the nut and the top of the thread of the bolt allowing particles of dirt to lodge, without affecting the fit of the screw. This condition is often applied in the manufacture of taps, and has been found to lengthen the life of the tap in a very marked degree. In the case of one company I have in mind, and who make small bolts and nuts, the taps they use being about three-six- teenths of an inch in diameter, they were formerly satisfied to have a tap cut fifteen or sixteen thousand nuts before perceptible wear occurred, they have found that in having them made under the conditions just mentioned, instead of stopping at sixteen thousand, they now cut a hundred and twenty thousand without practical variation in the size of the nut as compared with the standard gauge. As an instance of the " eternal fitness of things," allow me to quote from Mr. Forney's Report* at the convention of Master Car-Builders, held in this city (Philadelphia), in June, 1882: " It is worthy of note that a remedy for the evil complained of by master car-builders, that nuts made by some firms, or at some shops, would not screw on bolts made at others, at first baffled the ability of the most prominent manufacturers of tools in the country, and to provide an adequate remedy it was necessary to secure the assistance of the highest scientific ability in the coun- try, which was supplied through the co-operation of the Professor of Astronomy of the oldest and most noted institution of learning in the land. " The man of science turned his attention from the planets, and the measurement of distances counted by millions of miles, to listen to the imprecation, perhaps, of the humble car- repairer, lying on his back, and swearing because a f-inch nut 'a leetle small' will not screw on a bolt a ' trifle large.'" In the system so wonderfully developed by Sir Joseph Whit- * Report of the Committee of the Master Car-Builders' Association, appointed "to investigate and report on the present construction of screws and nuts used in cars ; and the amount of accuracy that is desirable to secure, and the best means of maintaining it, in the standard adopted by the Association, in Richmond, Va., June 15, 1871," etc. Submitted at the annual Convention, in June, 1882. (For complete Report, reprinted, see page 59, ante.) 149 worth for the manufacture of machinery by the use of inter- changeable gauges, he obtained the subdivision of the yard by making three foot pieces as nearly alike as was possible, and working these foot pieces down until each was equal to the others, and placing them end to end in his millionth measuring machine ; the total length of the three foot pieces was then com- pared with a standard end measure yard. These three foot pieces were ground until they were exactly equal to each other, and the three added together equal to the standard yard. The subdivision of the foot into inch pieces was made in the same way. This method required the exercise of extreme care, and also the expenditure of an enormous amount of time, while in the system which has been adopted by The Pratt & Whitney Com- pany, the sizes are not constructed in this way, but ruled lines, which represent the subdivision of the British yard, are first investigated, their accuracy determined, and corrections, if neces- sary, applied, before a single gauge or any end-measure is made. This method of investigation you will remember was partially described in our previous lecture. One can readily understand what an unsatisfactory task it would be to attempt to subdivide a yard, or even a foot, into end- measure pieces varying by sixteenths of an inch, say from a quarter of an inch to four inches, sixty-one in all, each of which to fulfill the condition of being exactly an aliquot part of the standard yard, which they each should represent. We can imag- ine the difficulties to be overcome by any one attempting this work by the subdivision of a standard foot, using the method adopted by Whitworth as early as 1834. Without having a line measure to which to refer, this standard foot providing it was standard at the start would necessarily be duplicated and this copy subdivided into two parts, each representing six inches, equal to each other of course, and together equal to the foot. Constant reference would have to be made to the original standard foot piece, which would obviously result in more or less wear of the end surfaces. Then the six inches would need to be halved, and so on until the inch was obtained. Then, in order to prove that the inch was one-twelfth of the foot, it would be necessary to make twelve of these inches, or six inches equal to the six-inch piece, and the sum of all to be equal 150 to twelve inches, or the original foot. We can all of us realize that more or less wear has resulted, reducing the length of the standard foot in the course of this constant reference to it as the original standard. Providing, even, that all these subdivisions were carefully made, and that no wear perceptible had occurred to the original standard, we are still not below an inch. Subdivisions into quarters and sixteenths would still further complicate the matter, and should the tentative subdivision be complete, providing the operator's patience or even life held out, he would then not be positive that he had even the inch a stand- ard, having by this time worn appreciably his Original standard foot during the long and tedious process of comparison and refer- ence necessary. Hence a definite line-measure is really the only reliable means of preserving a constant and standard size, and it is this princi- ple, which, practically carried out, has been the means of produc- ing results which so far seem to fulfill all the requirements nec- essary for an accurate system of interchangeable gauges. In order to help out the matter, in the method of subdivision by trial, recourse must be had, for further subdivision, to the use of a screw and a divided micrometer index circle. Just here we introduce the use of what has long been considered one of the impossibilities to be obtained by mechanical skill a perfect screw. It was upon this that Whitworth was obliged to depend in obtaining his subdivisions by sixteenths. We have before us upon the screen* a perspective view of the celebrated Whitworth millionth measuring machine, designed and used by Sir Joseph Whitworth to measure minute differences of inch standards. This machine, as you will see, combines the use of a screw for obtaining slight advances of the measuring faces of the instru- ment, a divided micrometer circle, and also a worm wheel to still farther magnify slight variations of position of the measuring faces of this carefully constructed micrometer. We have here a sectional view of this machine, showing the method of providing against back lash of the nut and screw, which is secured by a double nut, as shown (Fig. 21) in the repro- duction of the drawing before us.f You will notice that the * (Not here illustrated; see Fig. 21.) t See The Whitworth Measuring Machine, by Goodeve and Shelley. London, 1877. 151 machine is very massive,' and the accuracy with which it was constructed is designed to indicate with extreme delicacy differ- ences between any two standard inch pieces, so called. Between FIG. 21. the end or face of the rectangular bar which advances by means of the screw and nut, and the standard end-measure piece, is a small polished piece of steel, having parallel faces, called a " feel- ing piece." The difference in length of two end-measure stand- ards is detected by the variation in the reading of the divided wheel, and the uniformity of contact is indicated by means of this feeling piece. The tightness of an end-measure inch which is only one mil- lionth of an inch longer than one to which the machine had pre- viously been adjusted, will, it is claimed, prevent this feeling piece from dropping when placed between the caliper jaw and the standard. In order to make gauges for shop use, and to make them ot such a shape as to be practicable and not readily worn through constant reference, Whitworth proposed a form of cylindrical gauges represented by plugs and rings. These standard plugs he measures in his machine, duplicating his end-measure sizes in this more serviceable form. In using his measuring machine, he has not claimed it to be an instrument for originating sizes, but merely for comparison of minute differences. Hence, in order to maintain a constant stand- ard, reference must be had to end-measures which are certainly liable to sustain some slight change from wear or oxidation. 152 As already stated, the method adopted by The Pratt & Whit- ney Company, and which was proposed originally by Professor Rogers, is that of making gauges to correspond to line-measures which are accurate subdivisions of the imperial yard, thus obvi- ating this liability to wear. The gauges are made by referring each separate standard to a line-measure ruled upon hardened steel which has a rate of expansion, due to variations of temperature, the same as that of the hardened steel gauges with which it is compared. In mak- ing any number of gauges of the same size, this method will ensure the last gauge being exactly the same as the first, without reference to each other or to any other perishable standard. This has actually been done in the work so carefully gone through by the company, and it is possible and entirely practicable to pro- duce gauges so nearly alike, by this means, that a variation between any two of even one forty or one fifty-thousandth of an inch is eliminated. We have found from our own experience that tool-makers are very critical. They w r ork closer than they themselves imagine, and in duplicating parts of any machine or FIG. 22. any work requiring this exactness, they work often w T ithin a limit of a fifty-thousandth of an inch without being aware of the fact ; so that, in making a number of gauges of the same size, it is certainly necessary that they should be made within this limit. Nothing could throw more gloom over the spirits of a manufac- turer of gauges than the discovery that a tool-maker is able to prove conclusively that two of his gauges, when new, and both marked alike, are unlike in size. In the illustration before us (Fig. 22), we have a form of a 153 simple bench micrometer or measuring machine, in which the screw and subdivided index circle form the main features.* In order to obtain practically the same result, in duplicating sizes from a standard for ordinary gauge work, auxiliary faces or caliper jaws are used, and are shown at the left of the measuring faces. These auxiliary jaws serve to hold a small cylindrical plug, so that in adjusting the machine or caliper to any given size, the pressure between the caliper jaws in which this standard is placed can be determined by the tightness or position of this small cylindrical plug. By taking the reading on the micrometer and bringing a second gauge in contact in place of the original, the same conditions of pressure upon this second gauge may be readily determined, by noting the behavior of this little " feeling piece," as Whitworth might call it. The varia- tion may then be read in the ordinary way by the subdivisions upon the divided index circle. As an instrument for originating a size, even with a screw of the utmost precision, it could not be expected to be infallible, the limit of error being about -s^irs of an inch ordinarily ; but to copy or duplicate sizes it has been found to be very serviceable. A variation as minute as one hundred-thousandth of an inch has been shown to be appreciable in cases which have come under my own observation. In order to make standard gauges within the limit of accuracy necessary for interchangeability, and to fulfill the requirements of modern work-shop practice, it may be unqualifiedly stated that line measure, adapted for use as an ultimate practical reference standard, is the best for this purpose. The strong reason for this statement is that the ever present element of wear from constant use is entirely eliminated. The standard line-measure bar we now have before us (Fig. 23), is one which has certainly shown this to be not only a strong reason, but a valid one. The lines, which represent aliquot sub- divisions of the Imperial yard, were ruled upon a dividing engine constructed by Professor Rogers, the work being done at the factory of the American Watch Company, at Waltham, Mass. The total length, represented by the defining lines, is exactly one-ninth of the length of the Imperial Yard, or four inches, hav- ing no correction at 62 F. In other words, it is within a limit *See also, page 205, Illustrated Catalogue, January 1886, The Pratt & Whitney Company. 154 of ToAiro f an inch.* "The subdivisions are inches, half inches, quarters, eighths, and sixteenths along one edge, and a band of lines, 2,500 per inch, extending two inches from one end. Next is ruled a series of lines representing the exact bottom diameters or " tap sizes " of all United States standard thread gauges from i in. to 4 inches inclusive. 51 I 1 1 1 I II FIG. 23. Along the edge opposite the series of sixteenths, are traced lines representing tenths and twentieths of an inch, also covering a space of two inches. This bar is made of steel, hardened and ground perfectly plane on its upper surface and highly polished. The graduated lines were transferred to this surface using a metric screw, the pitch of this screw being one-half a millimeter. The ruling was done with a diamond. So carefully was the relation be- tween the value of the pitch of this metric screw and the length of the yard determined by Professor Rogers, that upon investigation, using the method of the " stops," mentioned in our previous lec- ture (page 137), the greatest error in any ruled subdivision was found to be within a limit of ^oifo of an inch for the particular subdivision of the Imperial yard which each should represent. When we realize that the transfer of each separate line, except the band of 2,500 per inch (this band being carefully checked during the operation of ruling), was an actual computed setting of the diamond before the line was traced, some idea may be obtained of the wonderful precision of the mechanism of the dividing engine, as well as the correctness, and pains taken, in the mathematical calculations involved. Being hardened steel, the measurement of hardened steel gauges, by being referred to it, becomes entirely practicable at any convenient temperature, providing, of course, that an equal temperature for both standard bar and gauge is maintained. As the lines are less than -^-s^w of an inch in width, all comparisons must be made using a microscope of a ordinarily high power. The practicability of " calipering " under a microscope has long been urged by Professor Rogers as being the only exact method *See Prof. Rogers 1 Report, page 46, ante. 155 of inspecting standard gauges. The results obtained by the use of this method, combining, as it does, science and practice, have demonstrated beyond any question, the simplicity, as well as the accuracy of the method. To give some idea of its value for the purposes of originating standard sizes, an instance in mind may be stated. A number of cylindrical size gauges, external and internal, commonly called plugs and rings, a representation of which is FIG. 24. shown in Fig. 24, were made. They w r ere finished to agree with the subdivisions upon this little hardened steel line-measure standard. Nearly eighteen months afterward, a new lot of the same sizes were made, and upon trial it was shown that any ring of the first lot fitted perfectly any plug of the second. Both lots had been made without reference to any intermediate standard set of plugs, except to " rough them out," as it is called, within about T oto~o f an inch, all finishing after this having been done from data determined by calipering under the microscope. * A good gauge fit is not that the ring shall slide freely over the plug without perceptible " shake," but one such that the ring, when well lubricated with sperm or other good oil, shall move easily after having it fairly on the plug, showing no tendency to " grip " the plug while the ring is kept in motion. Let the ring, however, stop moving even for a few seconds, and this condition of an apparently easy fit is suddenly changed to & driving fit, often causing serious damage to the plug or ring in separating them. In order to show this condition of perfect fit to best advantage, the temperature, of course, must be the same for both. The surfaces of the plug and ring must be as hard as steel can be made, and polished as carefully as the state of the art will admit. A good way of testing the* accuracy of any set or pair of cylin- drical gauges in reference to their being aliquot parts of any adopted standard, is to place within a ring which fits a standard plug, two smaller size-gauges tangent to each other, and if their * See Fig. 15, page 133. 156 sum is equal to the diameter of the larger single gauge they will be tangent to the ring also. If exactly right, they will be found to hold together tightly, as the elements of the cylinders which are in contact must either occupy the same space or be compressed enough to allow this practical tangency to be made. Care must be taken not to force the second gauge in too far, as this would evidently tend to injure them. In the gauges before us, which are 2i, li, and 1 inch, we may see how nicely this test is met. If we now use a gauge which is J^VTJ- of an inch smaller than one inch in diameter, in the addi- tion to 2J inches, the tangency is incomplete, for this gauge drops through, hardly touching. A thousandth of an inch, you may say, is almost not worth considering, but here we have a standard plug and ring, the ring fitting perfectly, as you see. We now insert the plug which is FIG. 25. of an inch too small ; it can be literally thrown on or off, one might even say that it " fairly rattles," the difference seems so great as compared with the fit of the standard. We have here a f -inch plug which is only I^-^-Q of an inch smal- ler than standard, the plug and ring representing which we also have. You will notice it is not so loose as was the inch plug which is roVo- of an inch small, but still less than one-third of this 157 minute difference is perceptible, and shows plainly that it does not perfectly fit the ring. In our experience in the manufacture of standard gauges, even this test is not a delicate nor an entirely satisfactory one. It is not equal to that obtained by the use of a fixed caliper gauge of drop forged steel, having polished parallel jaws, a specimen gauge of this form being represented in Fig. 25. For the purpose of testing the larger sizes, this latter form of gauge is the best, as the friction between the two surfaces of cyl- indrical gauges is decidedly a variable quantity, depending upon the degree of hardness and polish of the fitting surfaces of plug and ring. It is also possible that the cohesive force which we have already mentioned may act in this close-fitting relation, explain- ing why the ring should suddenly be so tightly " gripped," when allowed to remain together. With a two-inch gauge, a variation of -g^fa-is of an inch is im- perceptible when a ring is used to determine this small differ- ence, while with a caliper gauge made as just described, having polished parallel jaws, this minute difference may be readily detected, if the caliper be first carefully adjusted to a standard two-inch cylindrical gauge. To convey some idea of the minute variation which may thus be detected, I may state that a fragment of gold leaf, so thin that a mere touch of the fingers caused its total disappearance, on being carefully measured under the microscope, showed that its average thickness was 7Tr j ririr of an inch. This same gold leaf would actually float in the air like a spider's web, and yet this extreme " thinness," if it may be so termed, is actually twice the amount of the limit of error within which it is possible to duplicate hardened standard plug gauges, by " lapping," or grinding, referring them to a line-measure under the microscope. To convey some idea of the minuteness of the lines and the spaces between them, of the lines ruled upon this standard line- measure bar in the space covered by the first two inches, 2,500 per inch, they would, if placed one inch apart, the lines being magnified in proportion, be represented by furrows or marks one- tenth of an inch wide, and would extend over a length of 416 feet 8 inches, or nearly one-twelfth of a mile. Before concluding, it might be well to refer to work requiring only an ordinary degree of accuracy, though none the less impor- 158 tant in its way. The measurement of the diameter of drawn wire has long been a matter of confusion, owing to the use of numbers to designate arbitrary sizes, which in many cases do not correspond with each other for the same numbers used in differ- ent standards or styles of fixed wire gauges. Even wire gauges of the same standard do not agree with each other, due perhaps to wear, if not from actual variation of the gauges when new. To overcome this serious difficulty, the use of the micrometer, indicating thousandths of an inch for wire and sheet metal measurement, was adopted by the Association of Master-Mechan- ics, in Convention at Niagara Falls, June, 1882. Since this date, in England, the Standards Department, Board of Trade, has issued a table of wire gauge sizes to be the legal standard on and after March 1st, 1884. In the table just men- tioned, and herex given, the numbers are retained, but each num- ber must represent exactly a certain diameter in thousandths of an inch. The table is also extended to include the metric system by placing opposite each size, in thousandths of an inch, its value in millimeters, carried out decimally to tenths of a millimeter. IMPERIAL STANDARD WIRE GAUGE. [In effect, March 1, 1884.] BIRMINGHAM BIRMINGHAM DI WIRE GAUGE NO. IN. 7/0 0.500 6/0 .464 5/0 .432 4/0 .400 3/0 .372 2/0 .348 .324 1 .300 2 .276 3 .252 4 .232 5 .212 6 .192 7 .176 8 .160 9 .144 10 .128 11 .116 12 .104 13 .092 14 .080 15 .072 16 .064 17 .056 18 .048 19 OA .040 flQA () 21 .Oo6 .032 22 .028 DIAMETER. MM. WIRE G> 12.70 23 11.78 24 10.97 25 10.16 26 9.45 27 8.84 28 8.23 29 7.62 30 7.01 31 6.40 32 5.89 33 5.38 34 4.88 35 4.47 36 4.06 37 3.66 38 3.26 39 2.95 40 2.64 41 2.34 42 2.03 43 1.83 44 1.63 45 1.42 46 1.22 47 1.01 48 0.91 49 0.81 50 0.71 DIAMETER. IN. MM. 0.024 0.61 .022 0.56 .020 0.51 .018 0.45 .0164 0.42 .0148 0.38 .0136 0.35 .0124 0.31 .0116 0.29 .0108 0.27 .0100 0.25 .0092 0.23 .0084 0.21 .0076 0.19 .0068 0.17 .0060 0.15 .0052 0.13 .0048 0.12 .0044 0.11 .0040 0.10 .0036 0.09 .0032 0.08 .0028 0.07 .0024 0.06 .0020 0.05 .0016 0.04 .0012 0.03 .0010 0.025 159 Tins table, for instance, begins with No. 7/0, which is .500 of an inch in diameter, or 12.7 millimeters. No. 1 is .300 of an inch, and No. 50, the smallest in the list of sizes, is .001 of an inch. The range, therefore, is from one-thousandth of an inch to one- half of an inch. The variations are irregular, not advancing by equal amounts for each succeeding larger size. This is no doubt due to the effort to retain, as nearly as possible, a general average of the old wire-gauge sizes. In every case, however, the exact size is stated in thousandths of an inch, or the decimal parts of the meter. The feeling in regard to the great lack of a uniformity in wire- gauge sizes, under the old notched gauge system, may be best expressed by a remark recently made by the master mechanic of one of our best Eastern railroads. He said that any one would be as likely to go to a lumber-yard and order a plank ten feet long, twelve inches wide, and as " thick as a notch cut in a fence post made by Tom Jones," as to think of ordering sheet metal, specifying that it should be simply " No. 13 wire gauge," as has often been done, not even stating what particular u standard " gauge it is so called. The application of Standards of Length to ordinary workshop practice has so wide a range that it would be impossible, in the time at our disposal this evening, to attempt an enumeration of the many forms of gauges and templates necessary to secure the three important elements we have already mentioned, "cheap- ness, serviceableness, and quantitative accuracy," even in a sin- gle department of work requiring interchangeability of parts, as, for instance, the manufacture of sewing-machines, or the results obtained by the use of standard gauges in the manufac- ture of firearms. It must not, however, be understood that all work produced by the use of a system of standard interchangeability is as perfectly in duplicate as are the gauges to which they are referred. The gauges are the means provided for keeping within certain definite bounds in the production of thousands of pieces of the same size or shape, in which oftentimes a certain amount of vari- ation is allowed, both plus and minus. Standard gauges prevent the gradual slipping away from the original size and serve to bring back within the necessary limit, 160 variations of size which would cause endless trouble, and no small loss in the final assembling of these intended interchange- able parts. This accurate fitting is really only necessary in gauge work, for if bearings or other parts of machinery were as closely made, they would not move, or if bj r applying power enough they should be started, the absence of oil and the effect of the cohe- sion, if we may be allowed to say it, would quickly ruin the sur- faces in contact; hence a certain amount of freedom must be allowed. By making the journals and the bearings in which they are to run to certain definite sizes for each, the journal as many thousandths or ten-thousandths of an inch smaller, as the size or length of bearing may require, referring each to some par- ticular gauge as a standard, no fear need be entertained that other than a satisfactory fit will be the practicable result. Before concluding, brief mention should be made of the neces- FIG. 26. sity of definite action to secure uniformity in gauge dimensions for steam and gas pipe thread and fittings ; a standard for which is now claiming the serious attention of manufacturers and users of pipe and pipe fittings in this country, and also in England.* Pipe ^thread dimensions, when permanently established in the form of standard gauges (Fig. 26), made so by referring them to accurate subdivisions of the Imperial yard, though seeming to *Since authoritatively settled by the legislation of the Association of Wronght-Iron Pipe Manufacturers, October 27, 1886, and the Manufacturers' Association of Brass and Cast Iron Fit- tings, December 8, 1886, in adopting the Briggs Standard. See Report of Committee on Standard Pipe and Pipe Threads, Am. Soc. Mech. Engineer?, Vol. VIII. Transactions. 161 be an unnecessary refinement for so ordinary a class of work, really furnishes the true means of placing upon a sound basis, and of extending the already well-developed and recognized prin- ciple of modern manufactures, which is "cheapness, serviceable- ness, and quantitative accuracy." The following is a description of the method employed by The Pratt & Whitney Company in establishing the angle and width of flat of the top and bottom of the thread of gauges represent- ing the United States Standard system, reprinted in extract, with some revision, from an article by Mr. J. "W. Heyer, published in Mechanics, Jan. 13, 1883: The correct conditions to be established mechanically were first, the angle, which is 60 degrees; second, the width of the flat on the top and bottom of the thread, which is one-eighth of the pitch; and third, the number of threads per inch, which is determined by means of a formula,* and must be, in a correct gauge, as nearly a perfect screw as can be obtained by machine methods. A method of obtaining the first condition, or of making by machined work an equilateral triangle closely to mathematical lines, was designed by the writer, and was used also for the purpose of estab- lishing a "zero" or positive starting point from which to measure the flats on the tools used to cut the various United States Standard pitches, so that if a gauge is made having the correct outside diameter, the thread cut to the proper depth and the correct number of threads per inch, the angle of the thread exactly 60 degrees, and the lead of the screw of accurate pitch, a tool having the requisite amount of flat on the point will leave the flat on the top of the thread exactly the same width as that of the flat at the bottom of the thread. Fig. 27 shows two views of an equilateral triangle obtained by machined work, and which was originated as follows: Three bars of steel, each 8 inches long, were made, having their sides parallel, and equal in every respect to each other. The holes in the ends- of the bars were placed the same distance apart and at an equal distance from either edge of the bars by means of templets and fixtures shown in Fig. 28, in which S represents a lathe spindle, and c a lathe center fitting the spindle, the center being turned so as to accurately fit a bush, d, made of steel. A rectangular block, e, was then made, having a slot fitting the bush, d; the bars, A, A, A, also accurately fitted this slot. * See page 167, (a). 11 162 The rectangular block was then firmly fastened to the face-plate of a lathe, as shown in the figure, and a hole bored in it exactly the same E I 1 1 D i i | 1 3 yy , 1 Mill 1 IkJJ ' | 1 !; ji ^ r i i --, v_^ ! 1 1 i 1 1 i 1 FIG. 27. size as that in the bush, thus locating the hole in the center of the slot, and at right angles to its base. This rectangular block was then placed 163 on the lathe center, as shown in Fig. 28, and each bar placed in this slot and firmly bolted to the face-plate and a hole then bored in one end. A parallel piece, /, equal in thickness to the base of the block, e, was then firmly fastened to the face-plate, as shown in the cut. This piece was used to bore the first hole in the bars used for the sides of this "master triangle." In boring the second hole in these bars, a pin was inserted in a hole, g, in the parallel piece, /, and the first hole in each of the bars fitted this pin. The bars A, A, A, Fig. 27, after being halved at the ends and dow- eled together, formed an equilateral triangle, mechanically or practi- FIG. 28. cally perfect, and represented a triangle machined approximately to mathematical lines. In Fig. 27, B is a bush having a flange, and is fitted to the inside of the triangle, being screwed and doweled to the bars, A, A, A, securing the conditions of a cylindrical hole accurately located in the center of our master triangle. The bush, B, has on the outside of the flange a. projection. D, a hardened steel cylinder, ground to the diameter of an inscribed circle of a triangle having sides of two inches, this diameter- being 1.1547 inches. A small triangular piece of steel having a hole in its center, of the same diameter as that in the bush, B, which fits the inner sides of the large triangle, was then bolted to the projecting part of the flange, D, 164 as shown in Fig. 27, the bolt nicely fitting both holes. The master triangle was then placed on a planer and strapped to a right-angled "knee" and each side of the small triangle planed to the dimensions represented by the projecting cylinder, which, as stated, is 1.1547 inches diameter. To obtain the width of the flat at the top, one-eighth of the altitude of the small triangle was planed off parallel to the base, leaving a flat which is exactly one-quarter of an inch long. (See page 146.) The flat of this small triangle or test piece thus represents the width of the flat of the thread of a gauge of two inches pitch, and is used in a micrometer made for the purpose of measuring the width of flat of the tools used to cut threads of any number per inch, from the small- est possible to make up to the largest diameter and coarsest pitch. Fig. 29 represents this micrometer, which has a screw 40 threads per inch, and an index circle divided into 250 parts, one division TTT.Vinr of au inch - FIG. 29. In determining the "zero" on this micrometer, the test-piece trian- gle is placed between the jaws; and when light is shut out from the three bearing edges, the index line is then adjusted so as to coincide with the zero of the graduated circle. We now have two sides of an equilateral triangle under conditions such that they can be moved parallel to their original position, varying them at will for the width of the space at the beam of the micrometer to represent the correct width of flat, and gauging, within a limit of Tov&inr f an mcn ? the amount to be ground off the point of the tool for any United States Standard pitch of thread. We thus establish a starting-point at one-quarter inch, and by moving the jaws towards each other, never necessarily touching the fine edges of the jaws, for the flat of any diameter of screw, however 165 small, must have some appreciable width, an accurate adjustable gauge is available to measure within the closest possible practical limit the proper width of flat as well as the angle of the tools used to cut the entire range of United States Standard pitches. This limit is one so close that if the space cut by any one of these tools be applied to the thread produced by the operation, the coincidence is so complete that the light is shut out at the top, bottom, and sides of the thread. This may be safely considered as exact as machined work can be produced at the present time, and certainly within limits which are practicable. The third point to be covered that of producing an accurate lead of the thread, the number of threads per inch being determined by the Sellers formula was obtained by the use of a standard leading screw, carefully cut and tested, so that it is now entirely possible and practicable to originate thread gauges, applying the principles of a standard system of measurement such as has been previously described, and, having every step known to be within the limits of accuracy necessary, the various operations described for the production of thread gauges become comparatively simple, and the results are con- clusive evidence that this accuracy has been attained. From what has already been stated, it is evident that in order to produce gauges which shall accurately represent the United States Standard or Franklin Institute thread, the following con- ditions must be secured in the various stages of their manufac- ture, each condition being important in its relation to each of the others, as shown in the test which is applied when the gauges are finished, to which reference has been made and which is described later on ; a variation from the limit of accuracy re- quired, even in only one particular, making it impossible to meet the requirements imposed by this test. The points to be considered are six in number : 1. Correct outside diameter. 2. Correct diameter at the bottom or root of the thread. 3. Correct lead or pitch of the thread. 4. Correct angle (60 degrees) of the thread in the plane of the axis. 5. Correct position of the tool in cutting, which must be exactly at right angles to the axis of the gauge. 166 6. Correct width of the flat of the thread, top and bottom (one- eighth of the pitch). The test above referred to is that of applying to the thread of the finished gauge, at the top and sides, a thin templet of sheet steel which has been formed by the same tool used to cut the thread of the gauge, the thin templet having been planed between two blocks of cast iron for the purpose of preserving the edges intact. This templet or impression, being an exact copy of the thread space, together with the width of the bottom flat, should agree perfectly with the top and sides of the thread proper of the gana'e. Any variation which may appear, will evidently be double the amount which actually exists, owing to the peculiar conditions presented by this form of thread. . To explain more fully, it might be well to draw attention to the fact that, while the outside diameter may be correct, the diameter at the bottom or root of the thread may not be so; hence the width of the flat at the top of the thread resulting from these conditions will be greater than one-eighth of the pitch, providing, of course, that the tool has the proper width at the edge or point in cutting the thread. Reversing the conditions, the opposite will be the result. Or, if the width of the flat is not one-eighth of the pitch, the diameters being both correct in this case, the error in the test is made doubly apparent as in the other cases noted above, for in applying the templet the amount taken from one is evidently added to the other, hence the real error is increased twice the amount, making the test a decisive one. If the angle is not sixty degrees, or if the cutting tool has not been placed at right angles to the axis of the gauge, this error is also doubled in the test thus made; therefore, if at the end of all the different operations required for the production of standard gauges for this form of thread, this simple test be found to be successfully met, the real error will certainly be within a limit necessary for interchangeable gauge work. In other words, the impression taken of the bottom and sides of the thread being an exact copy of the thread space, the actual variation is doubled, so that if each be incorrect ^iroiro of an inch, this apparent error will be indicated by a difference of TITOOU of an inch, which is plainly perceptible to the eye, by the use of the inspection templet mentioned. 167 The requirements of this test determine the correctness of every one of the six conditions referred to, and even the wear of the threading tool itself has to be allowed for in the operation of cutting, in order that the width of the flat at the point may be within the necessary limit at the final moment to make it possible to meet this test successfully; so that some idea may be formed of the care which was necessary in all the operations carried through to produce the model set of unhardened steel thread-gauges made for final reference by The Pratt & Whitney Company, in order that every set of gauges made thereafter might be not only duplicates, but standard in every respect within the closest possible limit. In order to definitely fix the proper number of threads per inch for any required diameter of screw or bolt, Mr. William Sellers constructed the following empirical formula, which serves to determine independently of tables or other aids, the correct pitches for any diameter of bolt, and is in which d = the number of sixteenths in the diameter of the bolt + 10; a = 2.909; c = 16.64; and p= pitch of the thread. A simpler and more convenient form of this equation, and one which is readily deduced from it, is ^ = 0.241/^+0.625-0.175, (a) in which D represents the diameter of the bolt or screw in inches. Quoting exactly from the " Report of the Board to Recom- mend A Standard Gauge for Bolts, Nuts, and Screw Threads for the United States Navy," May, 1868 : " To illustrate the use of this formula, we take, for example, a two- inch bolt and let it be required to determine the pitch of the thread, and the number of threads per inch. Making the proper substitution, the formula becomes ff = 0.24^2 + 0. 625 0.175 = 0.24^/2.625-0.175 = 0.24x1.62-0.175 = 0.2138 of an inch. "The reciprocal of this, or ^1^4.68, gives the proper number of threads per inch. u For the purpose of avoiding the use of troublesome fractions, the nearest convenient aliquot, or 4, is taken. This will be found to cor- respond with the number of threads given in the table." 168 This latter provision is designed to avoid the necessity for com- plicated screw cutting gear, by preventing, as far as possible, the use of fractional threads. The proper number of threads per inch for all sizes of bolts or screws, from one-quarter to six inches, inclusive, varying by six- teenths of an inch, as found by the application of the foregoing formula, is given complete in the table appended : DIAMETER OF SCREW. THREADS PER INCH. DIAMETER OF SCREW. THREADS PER INCH. DIAMETER OF SCREW. THREADS PER INCH. lin. . 20 2A in. 4A 44 in 21 A in 18 21 in 41 4 ^ in 2i 4 in . 16 35 i n 4 *T 1JJ> 41 in 21 -TTf in 14 24 in . 4 4 ^ n 24 & in 18 2 T V in 4. 71 1 ff " 44 in 24 T 9 F in- 4 in . 12 11 ^Tff A "' 2i in 2A- in 4 4 4 T V in. 4| in 2f 24 44 in 10 24 in. 4 4 T 9 7r in 24 16 4 in. . 10 2Uin 4 44 in 24 44 in 9 24 in 4 444 in 24 16 l m. 9 244 in 'Sir 4f in 24 ft in. g . ~16 "* 21 in. . 3i 444 in 24 ^ iu. 1 m 8 244 in. 3.1 . ^TT 1U - 4it in. . 24 IT* in- 7 3 in 34- 444 in. 2i Hin . 7 3 T Sr in 31 ^y^ i, 5 in 24- 1A in 7 34 in . 3i 5 T V in 24- A Tfr 1U - 11 in. . 7 3A in. sl 54 in. . 2i 1A in 6 31 in 31 5A in 24- If in 6 35 in 8l 51 in 21 1A in 6 34 in. . 8 5A in- 2i 14- in 6 37 in 3! 5|in 24 1A in 54- 31 in 3i 5 T V in 21 14 in . 54 3A in 8 51 in 2| 144 in 51 3| in 31 5 A in. 2| If in 5 344 in 3 5f in 24 144 in 5 3fin. 3 5H in 2 11 in . 5 3J4 in 3 5 in. . 2| 144 in. 5 31 in; 3 5f| in. 21 2 in 44- 344 in 3 &j in 21 2A in 4! Ojy 111. 4 in 3 5fl in. 21 2i in 44- 4A- in 24 6 in 21 ^T 1U< [Bolts and screws }-J, jf , and f| inch diameter have been, and are now often made, having 11, 10, and 9 threads per inch respectively, and called United States Standard, but under the formula the correct number of threads per inch is as given in the table.] The formula from which is derived the correct diameter of United States Standard bolts at the bottom of the thread, or 169 what would be the exact diameter of the " tap drill ", with no allowance for clearance,* is as follows : d = v __ 1.2990381 _ No. of threads per inch In which d = the diameter at the root of the thread, and D the diameter of the outside of the thread of bolt or screw. The width of flat for any number of threads per inch is one-eighth the pitch, or W= -( 1 \ (c} 8 \No. of threads per inch/ v ' A table giving the root or bottom diameters and widths of flat for each diameter of bolt from to 6 inches inclusive, in sizes ordinarily used, is here appended : DIAMETER. NUMBER THREADS DIAMETER AT WIDTH OF FLAT, INCH. PER INCH. ROOT OF THREAD. TOP AND BOTTOM. * 20 0.1850 0.0063 T\ 18 0.2403 0.0069 16 0.2938 0.0078 & 14 0.3447 0.0089 1 I'd 0.4001 0.0096 T 9 12 0.4542 0.0104 { 11 0.5069 0.0114 t 10 6201 0.0125 9 0.7307 0.0139 1 8 0.8376 0.0156 H 7 0.9394 0.0179 i 7 1.0644 0.0179 if 6 1.1585 0.0208 4 6 1.2835 0.0208 H 5| 1.3888 0.0227 if 5 1.4902 0.0250 i* 5 1.6152 0.0250 2 4| 1.7113 0.0278 2i 4i 1.9613 0.0278 2i 4 2.1752 0.0313 2 4 2.4252 0.0313 3 3| 2.6288 0.0357 3i 8| 2.8788 0.0357 3i 3 3.1003 0.0385 8* 3 3.3170 0.0417 4 3 3.5670 0.0417 4i 3i 3.7982 0.0435 4i 2| 4.0276 0.0455 4f 2f 4.2551 0.0476 5 2i 4.4804 0.0500 5i 2| 4.7304 0.0500 5i 2| 4.9530 0.0526 5f 2| 5.2030 0.0526 6 2i 5.4226 0.0556 [The usual allowance above exact bottom diameter is from 0.004 for i in., to 0.010 for 2 in. taps.] 170 A modification of formula (a), which has met with general acceptance, changing the coefficient from 0.24 to 0.23, or p = 0.23 V ' D + 0.625 0.175, (d) as proposed by the writer in 1882, makes it applicable to screw threads which are smaller in diameter than one-quarter of an inch, and increases the number of threads per inch more rapidly as the diameter decreases than is found to result from the use of the original formula (a). This formula might be applied to the pitches of small screws when finer threads are desirable, and with the Sellers or United States form of thread it gives for sizes below one-quarter of an inch a good ratio of diameter to the pitch, as will be seen by reference to the following table : 1 DIAMETER. INCH. NUMBER OF THREADS DIAMETER AT WIDTH OF FLAT, PER INCH. ROOT OF THREAD. TOP AND BOTTOM. f 64 50 0.0422 0.0678 0.0020 0.0026 i 40 0.0925 0.0031 36 0.1202 0.0035 A 32 0.1469 0.0039 A 28 0.1724 0.0045 171 F The following table of Briggs Standard Pipe Thread sizes is taken from the report of the Committee on Standard Pipe and Pipe Threads, American Society Mechanical Engineers, Yol. VIII, Proceedings of the New York Meeting, November 29 to December 3, 1886. STANDARD DIMENSIONS OF WKOUGHT-!EON WELDED TUBES. DIAMETER OP TUBE. SCREWED ENDS. Nominal Inside. Actual Inside. Actual Outside. THICKNESS OF MH.TAL. Number of Threads per Inch. Length of Perfect Screw. Inches. Inches. Inches. Inch. No. Inch. i 0.270 0.405 0.068 27 0.19 0.364 0.540 0.088 18 0.29 i 0.494 0.675 0.091 18 0.30 i 0.623 0.840 0.109 14 0.39 i 0.824 1.050 0.113 14 0.40 i 1.048 1.315 0.134 1H 0.51 i 1.380 1.660 0.140 11* 0.54 H 1.610 1.900 0.145 1H 0.55 2 2.067 2.375 0.154 Hi 0.58 2* 2.468 2.875 0.204 8 0.89 3 3.067 3.500 0.217 8 0.95 a* 3.548 4.000 0.226 8 1.00 4 4.026 4.500 0.237 8 1.05 4* 4.508 5.000 0.246 8 1.10 5 5.045 5.563 0.259 8 1.16 6 6.065 6.625 0.280 8 1.26 7 7.023 7.625 0.301 8 1.36 8 7.982 8.625 0.322 8 1.46 9 9.000 9.688 0.344 8 1.57 10 10.019 10.750 0.366 8 1.68 Taper of conical tube ends, 1 in 32 to axis of tube, (f inch per foot taper in diameter.) The length of thread complete, which is represented by standard pipe thread-gauges made for this purpose, is determined by adding to the figures in the last column the length of two threads for each pitch of thread, as for instance, in the case of 8 threads per inch, the length of a 2| inch gauge would be 0.89 + 0.25, or 1.14; or, more strictly stating it, 1.138 inches. 172 In conclusion, it might not be out of place to mention here one of the latest important standards adopted by the American Rail- way Master Mechanics' Association, which is designed to bring about uniformity in the diameter of driving wheel centers and tires for locomotives, by reducing the number of sizes to six and requiring that these be of definite and standard diameter. The amount of allowance for shrinkage for each diameter of wheel center, or the amount less than the actual diameter of each size wheel center, to which tires must be bored, in order to en- sure the proper degree of strain within the elastic limit when the tire is "set," has also been definitely established, so that it is now possible and practicable to keep locomotive tires ready bored in stock, thus materially reducing both first cost and the time re- quired for renewals or repairs. As stated in the circular issued by the Association, dated Sep- tember 15, 1886, this standard was unanimously adopted at their meeting held in Boston, June, 1886. The diameters of driving wheel centers as proposed by the Committee and adopted at that time are as follows: 38 in., 44 in., 50 in., 56 in., 62 in., and 66 in. Gauges representing these sizes, and also those representing the diameter of tire with shrinkage allowance for each, have been made by The Pratt & Whitney Company under arrangement with the Committee, as stated in the circular, and are for reference only, the gauges for wheel centers being end-measure standards made of weldless cold drawn steel tube, with hardened steel ends ground to standard size, and hence are called " reference stand- ards " for the diameters of wheel centers adopted by the Associa- tion. The gauges for the diameter of tire are calipers or " snap " gauges, with hardened jaws, and are made entirely of tool steel. Each of the latter gauges represents the diameter of a tire bored to standard size having the proper shrinkage allowance as given in the table appended, which is taken from the circular referred to : 38 in. less 0.040 in., 37.960 in. 44 50 56 62 66 0.047 " 43.953 0.053 " 49.947 0.060 " 55.940 0.066 " 61.934 0.070 " . ..65.930 ADDENDA. At a general meeting of the Society of German Engineers, held in Leipzig, August 15, 16, and 17, 1887, the report of the Karls- ruhe District Society, recommending a metric screw thread sys- tem, was submitted, in which was proposed for adoption a thread having the Sellers form for top and bottom of the thread, or flat one-eighth of the pitch, but recommending for the angle of the thread 53 8', instead of 60 degrees, the angle proposed by Mr. Sellers and recommended by the Franklin Institute. A commission is to be appointed to test the practicability of the system advocated by the Karlsruhe Society, with a view to its general introduction throughout Germany. THE JOHN SCOTT LEGACY MEDAL. (Engraving one-half size.) GENERAL INDEX. Airy, Sir George : Page. Formula for neutralizing effect of flexure, . . . . 6, 119 Baily, Sir Francis : Baily's metal, composition of,' 117 Chancy, H. J., Warden of British Standards, 2, 120 Chanute, O. : Investigations relating to size of round iron for U. S. Standard bolts 64 Investigations in relation to screw threads, .... 65, 72 Paper by, "Uniformity in Railway Rolling Stock," . . 141 Coefficient of Expansion : Determination of, by means of ice water, . . . . 18 Example of ratio for different materials, . . . . 13 General law as to rate of change, 14 No correction necessary in use of steel standard P. & W. 5 , 57 Table of results in determination of meters used, ... 20 Comparator : Description of, . . . . . . . . . 5, 131 Method of testing accuracy of, 135 Rogers-Bond Universal, description of, . ... . .50, 130 Saxton's Reflecting, 126, 129 Curvature : Errors of, 53 Correction of, ... 135 Engineering, London : Article reprinted from, on standard screw threads, . . 93 Flexure : Determination of, using mercury surface, .... 7 Formula for neutralizing, ....... 6 Forney, M. K : Chairman Committee, 77 Report, extract from, 148 Franklin Institute : Or United States Standard thread, 144 Special committee report, 78 Froment, M. : Steel end-measure meter, record of, 4 176 Gauges: Page Briggs Standard, pipe thread, 160 Briggs Standard, table of dimensions, to 10 inches, . . 171 Drop-forged caliper, 157 Illustrations of " good and bad fit, " 71,155 Limit, adoption by Master Car-Builders' Association, . . 91 Limit for round iron for United States Standard bolts, . . 88 Standard cylindrical size, 86, 155 Test of end-measure, 55, 142 Thread, " hardened and not ground," 75,87 Thread, method of making, 73 Thread, method of grinding hardened, .... 75 Wire standard, 158 German Engineers, Society of : Form of thread recommended by Karlsruhe Society, Leipzig meeting, 1887, 173 Letter to Franklin Institute, 92 Herschell, Sir John : Uniformity of manufactured articles compared, . . . 139 Huyghens : Principle of vibrations of pendulum, . . . . . 112 Imperial Yard : Act legalizing, 115 Destruction of, 116 Restoration of, 117 Where kept, 120 Interchangeability : Application of, ......... 159 International Bureau of Weights and Measures, .... 3 Kater, Captain: Position of neutral plane in standard bars, . . . . 118 Yard of the Royal Society, . . . . ... 117 Master Car-Builders' Association : Committee report, ......... 59 Recommendation of the United States Standard or Franklin Institute thread, 63 Reference set standard thread gauges and 24-inch line and end-measure bar, .* 77 Master Mechanics' Association : Recommendation of United States Standard thread, . . 63 Reference set standard thread gauges, 76 Wire gauge, adoption of micrometer as a standard for reference, 158 Wheel center and tire standards and gauges, . . . 172 Molecule : Diameter of, 124 177 Measuring Machine : Page. Description of calipering attachment, Universal Comparator, 53 Improved 12-inch bench caliper, ...... 152 Whitworth, .... . ... 151 Microscope : Error of focal distance, . . . . . . . 17 Limit of error in setting eye-piece micrometer, ... 55 Magnifying power, . . . . . . . 54 Personal error in reading, ....... 57 Micrometer : For measuring flat of United States Standard thread tools, . 146 For wire gauge standard, ....... 158 Pendulum : Use as a unit of length, . . . . . . . 112 Leslie's, . . . . . 114 Pennsylvania Railroad : Adoption of the Franklin Institute thread in 1869, . . 98 Railroad Gazette: Article "A Screw Thread Primer," 83 Editorial, September 24, 1886, 106 Report : American Society Mechanical Engineers, committee of, on standards and gauges, 50 to Chief of Bureau of Steam Engineering, extracts from, . 62, 167 Franklin Institute, special committee on screw threads, . 78 Hilgard, Prof. J. E., United States Coast and Geodetic Sur- vey, 24 Master Car-Builders' Association, committee on screw threads, 59 Rogers, Prof. W. A., to The Pratt & Whitney Co., . 1 Waldo, Dr. Leonard, on thermometer used by the P. & W. Co. , 49 Sellers or Franklin Institute thread, 144 Sellers, William: Reasons stated for variation in original thread gauges, . . 66 Screw Thread : Sharp "V," Sellers or United States Standard, and Whitworth, 60 Primer, from Railroad Gazette, . . . . . . 83 Sheepshanks, Rev. R. : In charge of restoration of imperial standards, . . . 117 Work legalized by Parliament, ...... 120 Standards : Baily's metal, 117, 125 Bird's " Standard Yard 1760," ... . 115 Bronze No. 11: Comparisons at Washington, . . . . . 10 Direct standard of reference, 1 12 178 Standards, Bronze No. 11 (continued) : p age . Investigations in relation to imperial yard, ... 2 Presented to the United States, 120 Standard at 61. 79 Fahr., 2 Coast Survey yard and meter, 19 Comparisons by Drs. Chaney and Benoit, ... 28 Comparisons by Prof. W. A. Rogers, . . . . 30 Construction of, 8 Description of bars made for the P. & W. Co., ... 5 Description of line-measure bar P. & W. 5 , .... 43, 154 End-measure grinding, ....... 9, 56, 142 End-measure pieces, test of, 55, 142 Different values for length of the foot, . . . . . 112 Flexure of, 2, 6, 119 Graduation of 4-inch line-measure bar (P. & W. 5 ), . . 70, 154 Imperial Yard, composition of, . . . 1> 69, 117 Investigation of : Yard and meter P. & W. 3 , 40 Line and end-measure yard and meter P. & W. 4 , . 46 Steel line-measure P. & W. 5 (4 inch), .... 45 Of length and their subdivision, Lecture I, . . . . Ill Of length as applied to gauge dimensions, Lecture II, . . 139 Materials available for, . 125 Materials necessary for practical purposes, . . . . 2, 125 Methods of comparison on Universal Comparator, . . 52, 13(5 Methods of subdivision and investigation, .... 137 Metre des Archives, .... ... 3 Meter of the. Conservatoire des Arts et Metiers, . . 4, 114 Metric, limited use, practically, in this country, ... 3 P. & W. Co. bronze bar, No. 1, . . 24, 118 P. & W. Co. bronze bar, No. 2, description of, . . 25 Relation of Imperial yard to P. & W.j and P. & W. 2 , . . 27 Relation between P. & W. 6 and ^ yard, 46 Relation of yard and meter at same temperature, . Russian iron bar, for geodetic surveys, . . 125 Shuckburgh's scale (0-36 in.), . 116 Stevens Institute line and end-measure bars and Whitwort li steel yard used, .3 Tresca copper meter, . . . 12, 125, 126 Troughton 82-in. brass scale, . 69, 121 Value of line-measure for oriyiimtiity and prescrriiKj ttanda/rd sizes, .';' 56, 5S, 15:5 Whitworth's method of subdivision of the yard, . I ill Yard of the Royal Society, construction of , . . . 117 179 Taps, U. S. Standard : Pa ge . Endurance or life of, 72, 148 Exact " tap drill " size, 169 Temperature : Necessary precautions to be taken, . . . . . 16 Thermometer : Indications of, ......... 15 Investigation of, in use by the P. & W. Co., ... 49 Thomson, Sir William : Graphic illustration of an infinitesimal dimension by, . . 124 Thread Gauges, U. S. Standard : Conditions necessary to secure accuracy, . . . . 165 Method of establishing angle and width of flat, . . 144, 161 Necessity, of reference to an accepted standard as a basis, . 72 Necessity for and practical use of, ..... 87 Tolles, R. B. : Objective illumination, 134 Tresca, M. and G. : Transfer of meter by, ........ 4 Troughton : 82-in. brass scale, value of, and legal authority, . . . 69, 121 Tyndall, Dr. : Extract from lecture, ........ 143 U. S. Standard Thread: Adaptation to interchangeability, ...... 147 Angle of the thread tool, ...... 74 Correspondence relating to, 92 from C., B. & Q. R. R. Co., . 102 M. & St. P. Ry. Co., . ,. . 101 R-I. & P. Ry. Co., . 101 D. L. & W. R. R. Co., 100 L. & N. R. R. Co., .... 99 N. Y. C. & H. R. R. R. Co., . . 104 N. Y., L. E. & W. R. R. Co., . 105 P. R. R. Co., 104 Society German Engineers, . . . 92 The Pratt & Whitney Co., . . . 105 Wahl, Dr. Wm. H., Sec'y Franklin Institute, 99 Formula for.bottom diameter, 169 Formula for number of threads per inch, . 167, 170 Formula for width of flat, ... . . 169 Strength of, ........ $2 Table of diameters at root of thread and width of flat, . . 169 Table of sizes and threads per inch, 168 Table of sizes below ^ in., . . 170 180 Unit of Length : Page. Leslie's pendulum, . . . . . . . 114 Metre des Archives, . 114, 122 Seconds pendulum, ....... 112, 115 Ten-millionth of the earth's quadrant, 114 Wave of monochromatic light, 128 Watts, James: Difficulties under which his work was accomplished, . . 141 Wheel Center and Tire gauges, . .172 Whitney, Eli: First to introduce iuterchangeability in manufacture of arms, 141 Whitworth, Sir Joseph: Development by, of system of interchangeable gauges, . 148, 149 Measuring machine, 150, 151 Method of subdivision of the yard, .... 149 Steel yard bar, ......... 3 Surface plates, ... 143 Wire Gauge, Imperial Standard, . . 158 Zentmayer, Joseph : Eye-piece micrometer, . . . . . . . . 134 to desk from which borrowed. on the last date stamped below. SENT ON ILL 4 ?.006 .C. BERKELEY REC'DLD JUN22'64-4PM NOV 6 1978 LD2 l-100m-U,'49(B7146sl6)476 M323716