1865.] and Temperature in Barometric Hypsometry, fyc. 281 



be correct, the total method makes the interval v w greater than the gra- 

 dual by no less than 610 feet, owing to its distributing the warm tempera- 

 tures over so large an interval of extreme cold. If we then omit the inter- 

 val vw, we find 359 feet for the sum of all the cases in which the total 

 method was in excess of the gradual, and 20 1 feet for the cases of defect, 

 leaving a total excess of 158 feet in 26450 or 26292 feet, which is thus 

 shown to be a very inadequate measure of the degree of uncertainty due to 

 the total method. 



In Table IV. the results to c, or even d, substantially agree ; but at d the 

 temperature decreases very slowly, and soon becomes absolutely stationary. 

 Great differences immediately appear. From I to r the temperature in- 

 creases, and the total method gains greatly on the gradual till at r it is 

 541 feet in advance. At stations s, t the total method indicates a de- 

 scent with a falling barometer, whereas the gradual method gives a very 

 slow ascent. Mr. Glaisher's observations show that for the same baro- 

 metric pressure of 14'637 inches, as at r, the temperature varied succes- 

 sively through 36-l, 38'2, 38'l, 42'2 Fahr., which on the total method 

 indicate different heights, whereas the gradual methods cannot admit any 

 variation of height without a variation of pressure. The rapid fall of the 

 thermometer from u to w causes the total method to give very much smaller 

 intervals than the gradual, but the nearly stationary temperatures of*, y, z 

 turn the balance the other way. On the whole, the total method gives 

 686 feet in excess, and 335 feet in defect of the gradual method, remaining 

 351 feet in excess. The temperature varied so abnormally in this ascent 

 that little confidence can be reposed in either result after station h, when 

 the total method is only 32 feet out of 941 1 or 9379 in advance of the gra- 

 dual, which is still a large amount. 



It may be objected to the gradual method that, by multiplying stations, 

 it multiplies errors of observation. But even when the stations are so un- 

 necessarily multiplied as in Tables III. and IV. (in which nearly every re- 

 corded case of a simultaneous observation of barometer and thermometer 

 has been admitted), the error is not likely to approach that arising from the 

 total method. We may, however, calculate the ascent of Table III. as far 

 as r, beyond which, as already remarked, the variation of temperatures 

 renders the results uncertain, in six instead of sixteen stations, as follows. 



Abridged Gradual Method. 



