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Complete Calibration —The simple method of Gay-Lussac does Calibration of a Mercury Thermometer.—To facilitate description, "vve will take the case of a fine - bore tube, such as that very well for short intervals when the number ot steps is not of a thermometer, to be calibrated with a thread of mercury. excessive, but it would not be satisfactory for a laige range owing The bore of such a tube will generally vary considerably even in to the accumulation of small errors of estimation, and the variation the best standard instruments, the tubes of which have been of the personal equation. The observer might, for instance consistover-estimate the length of the thread m one half of the tube, specially drawn and selected. The correction for inequality of ently bore may amount to a quarter or half a degree, and is seldom less and under-estimate it in the other. The errors near the middle of the range would probably be large. It is evident that the correction than a tenth. In ordinary chemical thermometers it is usual to the middle point of the interval could be much more accurately make allowance for variations of bore in graduating the scale, at determined by using a thread equal to half the length of the but such instruments present discontinuities of division, and interval To minimize the effect of these errors of estimation, it cannot be used for accurate work, in which a finely-divided scale of equal parts is essential. The calibration of a mercury thermo- is usual’to employ threads of different lengths in calibrating the same interval, and to divide up the fundamental interval ot the meter intended for work of precision is best effected after it has thermometer into a number of subsidiary sections for the purpose been sealed. A thread of mercury of the desired length is separcalibration, each of these sections being treated as a step in the ated from the column. The exact adjustment of the length of of calibration of the fundamental interval. The most symmetrical the thread requires a little manipulation. The thermometer is method of calibrating a section, called by Guillaume a Complete inverted and tapped to make the mercury run down to the top of Calibration,” is to use threads of all possible lengths which are the tube, thus collecting a trace of residual gas at the end of the integral multiples of the calibration step. In the example already bulb. By quickly reversing the thermometer the bubble passes given nine different threads were used, and the length ol each to the neck of the bulb. If the instrument is again inverted and was observed in as many positions as possible. Proceeding in tapped, the thread will probably break off at the neck of the manner the following numbers were obtained for the excessbulb, which should be previously cooled or warmed so as to this of each thread in thousandths of a degree in different obtain in this manner, if possible, a thread of the desired length. length If the thread so obtained is too long or not accurate enough, it is positions, starting in each case with the beginning of the thread removed to the other end of the tube, and the bulb further at 0°, and moving it on by steps of 1°. warmed till the mercury reaches some easily recognized division. Table ll.—Complete Calibration of Interval o/10° in 10 Steps. At this point the broken thread is rejoined to the mercury column from the bulb, and a microscopic bubble of gas is condensed which Lengths of Threads. generally suffices to determine the subsequent breaking of the mercury column at the same point of the tube. The bulb is then -48 - 2 - 8 • CO ~ <X> -28 -32 - 67 -62 -11 -15 allowed to cool till the length of the thread above the point ot - 8 -22 +21 +24 -33 -21 -47 -28 +14 s'SiSi +23 +26 + 6 +58 separation is equal to the desired length, when a slight tap 8 + 1 +2 ° <SM 3° -17 +36 +28 - 9 +26 + 5 - 3 +41 suffices to separate the thread. This method is difficult to woik § 60“ +45 I +49 — 7 + 4 P-.S 4° + 6 +31 with short threads owing to deficient inertia, especially if the - 6 +43 o ^'S.S n 5°(i - 3 + 5 -15 0 tube is very perfectly evacuated. A thread can always be separated + 7 -16 + 2 g ® 2 'S' •' -20 +10 +23 1 by local heating with a small flame, but this is dangerous to the thermometer, it is difficult to adjust the thread exactly to the J05Ci ^0, d£ P-i<» 8', - 4 +29 required length, and the mercury does not run easily past a point 01.5555 9‘ + 5 of the tube which has been locally heated in this manner. in the first column are the excess-lengths of the Having separated a thread of the required length, the thermo- The observations of 1° already given in illustration of the method ot Gaymeter is mounted in a horizontal position on a suitable support, thread The other columns give the corresponding observations preferably with a screw adjustment in the direction of its length. Lussac. with the longer threads. The simplest and most symmetrical By tilting or tapping the instrument the thread is brought into method of solving these observations, so as to find the errors ot position corresponding to the steps ot the calibration successively, step in terms of the whole interval, is to obtain the ditlei and its length in each position is carefully observed with a pair ot each of the steps in pairs by subtracting each observation Irom reading microscopes fixed at a suitable distance apart. Assuming ences one above it. This method eliminates the unknown lengths that the temperature remains constant, the variations of length the the threads, and gives each observation approximately its due of the thread are inversely as the variations of cross - section of Subtracting the observations in the second line irom of the tube. If the length of the thread is very nearly equal to weight. in the first, we obtain a series of numbers, entered m one step, and if the tube is nearly uniform, the average ot the those 1 of the next table, representing the excess ol step (1) observed lengths of the thread, taking all the steps throughout column each of the other steps. The sum of these differences is ten the interval, is equal to the length which the thread should ha e over the error of the first step, since by hypothesis the sum ot occupied in each position had the bore been uniform throughout times errors of all the steps is zero in terms of the whole interval and all the divisions equal. The error of each step is thereiore the The numbers in the second column of Table III. are similarly found by subtracting the average length from the observed length by subtracting the third line from the second in in each position. Assuming tliat the ends of the interval itself obtained II., each difference being inserted in its appropriate place are correct, the correction to be applied at any point of calibration Table the table. Proceeding in this way we find the excess of each to reduce the readings to a uniform tube and scale, is found >y in over those which follow it. The table is completed by a taking the sum of the errors of the steps up to the point con- interval diagonal row of zeros representing the difference of each step Iron sidered with the sign reversed. . . , by repeating the numbers already found in symme n ‘ In the following example of the method an interval ot ten itself, andwith their signs changed, since the excess of any step, degrees is taken, divided into ten steps of 1° each. The distances positions say 6 over 3, is evidently equal to that of 3 over 6 with the s gn of °tlie ends of the thread from the nearest degree divisions are changed. The errors of each step having been found by adding estimated by the aid of micrometers to the thousandth of a degree. the columns, dividing by 10, the corrections at each point ol The error of any one of these readings probably does not exceed the calibrationand are deduced as before. half a thousandth, but they are given to the nearest^thousandth Table HI.—Solution of Complete Calibration. only. The excess length of the thread in each position over the corresponding degree is obtained by subtracting the second reading Step from the first. Taking the average of the numbers in this line, No. the mean excess-length is — 10*4 thousandths. The enor of each +32 step is found by subtracting this mean from each of the numbers +34 +25 + 7 +26 ++ 23 0 — o + 11 +20 1 +29 +12 +31 28 +22 in the previous line. Finally, the corrections at each degree are 0 +16 +23 +39 2 +5 + 15 +13 +13 - 4 3 -11 -16 - 80 + 80 +24 obtained by adding up the errors of the steps and changing the + 7 + 4 + 13 4 -20 -23 -24 15 +150 +- 59 -12 sign. The errors and corrections are given in thousandths ot 1 . -26 - 8 -10 5 -34 -39 -17 0 + 2 - 1 +8 6 -25 -29 -13 + 125 ++269 +17 0 + 19 + 16 +26 Table l.—Calibration by Method of Gay-Lussac. -12 + 4 7 -19 2 8 -26 -31 -15 -- 74 ++108 + 1 -16 + 03 - 30 ++ 96 9 -23 -28 -13 No. of 0 - 9 -26 10 -32 -37 -22 -13 + 2 Step. -008 Error of Ends f +-010] - '016 --020 --031 +-016 + •008 + •013 +-017 ++ •004!+1-9 + 16-7+7-1 -10-1 +8-9 | +6-1 +15-1 step. of 1 +-038, +-017 - ‘003 - •022 +‘010 + •005 + -033S + -018 -013j--003 thread J + •005 - -028 - •033 -■017 -•009 +-006 -•003 - -020 - '001 ExcessCorrec- + 17-3 +39-3 +45-7S+43-8 +27T +20-0 +30T +21-2'+15T length. tions. +15-4 +6-4 +9-4 Error of -17-6 -22'6 -6'6 j-r-1'4 |+16‘4 +7-4 -9'6 1 step. 0 + 5 4 The advantages of this method are the simplicity and symmetry +17-6 +40-2 +4o-8 +45-4 4-29-0 +21-6 +31-2 +21-8 Correcof the work of reduction, and the accuracy of the result, whi tion.