1843.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



271 



A NEW AND SIMPLE METHOD TO FIND 

 THE PERPENDICULAR HEIGHT OF MOUNTAINS, HEAD- 

 LANDS, &c. ABOVE ANY GIVEN DATUM, FROM 

 BAROMETRICAL AND THERMOMETRICAL 

 OBSERVATIONS. 



By Oliver Byrne, Mathematician, Author of " The Doctrine of 

 Proportion," &c. 



Rule. — Add the allowance found in Table I for the difference of 

 temperature taken by the attached thermometer, to the logarithm of 

 that height of the barometer which corresponds to the least degree of 

 the thermometer. Then to the logarithm of the difference of the 

 logarithms of the heights of the barometer observed at the higher and 

 lower stations, thus corrected, add the logarithm of the allowance 

 found in Table II, for the mean temperature of the detached thermo- 

 meter when increased by the constant number -92 102 ; this sum will 

 be the logarithm of the required height in fathoms. Observe : the 

 first four figures of the logarithms of the heights of the barometer, 

 together with the indices, are to be counted whole numbers, and the 

 numbers taken from Tables I and II must always have five places of 

 decimals, though they need not always be used. Tables I and II may 

 be dispensed with, as -456789 answers to a degree of the attached 

 thermometer in Table I, and -0024080 to a degree of the detached, in 

 Table II. 



Previous to M. De Luc commencing his experiments on the baro- 

 meter, it was considered that a mean between the two temperatures 

 shown by the thermometer attached and the height of the mercury in 

 the barometer at two different stations, was sufficient to determine the 

 perpendicular distance of those stations. But De Luc found, by re- 

 peated experiments, that an additional or detached thermometer was 

 likewise necessary, which has since been confirmed by General Roy, 

 Sir G. Shuckburgh, and others. 



However, before making further remarks, we shall illustrate the 

 rule just given by practical examples. 



Table I. | Table LI. 



Of the allowance for the differenceOf the allowances for the mean 

 of the temperatures of the at-! temperatures of the detached 

 tached thermometer. thermometer. 



|Tens 



lUnits 

 ITenthll 



4 567 

 9 135 

 3 703 



8 271 

 2 839 

 7 407 

 1975|2 



1543 1 



i inn 



[Hundreds 



|Units 

 |Tenths 



<>0 



00 



OO 

 00 

 OiOil 



ooii 



21 6 



49 3 



74J0 

 987 

 •J 3 1 

 480 



00 1 727 

 00 1974 

 0!2'22ll 



Examples. 



1. The heights of the barometer at the bottom and top of a hill are 

 29-862 and 26-137 inches; the attached thermometer at the bottom 

 and top indicates 68° and 63° ; also, the detached thermometer at 

 these stations gives 7T and 55° respectively. It is required to find 

 •the perpendicular height of the mountain. 



Thermometer attached. 



Lower station . . 68° 



Higher " ..63 



Ditterence 5 



Thermometer detached. 

 Lower station .. 71° 



Higher 



2) 126 

 63 



Barometer at summit, where attached 1 a a iot i nira -a 



thermometer indicates least degree / 2b ' 137 ' ]o & = 14172,; > 57 

 From Table I for 5 units we have 2-28394 



Log. corrected 14174-84094 



Barometer at base=^29-862, log. 14751-189 



Take 14174-84094 



Log. 576-34806 = 



Then, from Table II, for 6 tens -14808 



For 3 units (making in all 63°) -0O74O 

 Constant 



2-7606848 



Log. 



•92102 

 1-07650 = 0-0320140 



Height in fathoms = 620-4385, corresponding to log. 2-7926988 



II. Wishing to know the perpendicular height of the mountain 

 Chraughaun, in the county Wicklow, and having two barometers and 

 detached thermometers which for months before agreed with each 

 other in different states of the air, leaving an assistant on a level with 

 the sea near Arklow, with directions to make accurate observations 

 every fifteen minutes from 3 to 4 o'clock (our watches being pre- 

 viously regulated) I proceeded to the top of the mountain, and at the 

 appointed hour commenced observations. The mean result of the five 

 were as follows : — the barometer stood at the summit 28-635, and at 

 the base 30-609 inches; attached thermometer, 61° and 65-5,° and de- 

 tached thermometer 54-5° and 70°, respectively. It is required from 

 these data to find the height of the eminence. 



Thermometer attached. 



Lower station . . 65*5° 

 Upper " .. 61-0 



Difference 4-5 



Thermometer dttachid. 



Lower station 

 Upper " 



Mean 



7o° 

 54-5 



2 ) 124-5 



62-25 



Barometer at summit, where attached \ . 



thermometer is least 

 For 4 units, from Table I, we have 

 For 5 tenths 



28-635, log. 14568-972 



1-82715 



•22839 



Log. corrected for temperature 



Barometer at summit, where the 

 attached thermometer is least 

 Subtract 



From Table II we have, 

 For 6 tens = 



For 2 units = 



For 2 tenths = 

 For 5 hundredths^ 

 Constant = 



Log. of 



Log. of 



1 1858-491 

 14571-02754 



287-46346 



14571-02754 



2-4585880 



•14808 ^ 



•00494 1 , . cooo . 



•00049 ( lnakl »S "P b 2 -25 



•000 12 J 



•92102 



1-07465 



= 0-0312671 



Hence the height in fathoms = 308-923, log. = 2-4S98551 



It may be observed, that this experiment was repeated at different 

 times, and consequently in various atmospheres, yet the result never 

 varied two feet. We may, therefore, conclude that the highest sum- 

 mit of the Wicklow mountains is very nearly 1S53 feet above the 

 level of the sea. 



This rule will be found to give results more accurate than either 

 that of General Roy or of Sir G. Shuckburgh, and can be applied 

 with greater ease. 



General Roy makes the height in fathoms = (10000 I ~T -168 d)X 

 (l+[/— 32°] -00245). 



Sir G. Shuckburgh makes it, 

 (10000 / If. -440 d) X (1 + [/— 32°] -00243) fathoms; where I = 

 the difference of the logs, of the heights of the barometer at the two 



37 



