AT KEW OBSERVATORY AND THEIR DISCUSSION. 



489 



This gives sum of differences descending less ascending = k(4:'2m + 91 '9 45'5Z). 



44. As A; is a common multiplier; all quantities such as ratios of differences of 

 ascending and descending readings to the mean difference, or ratios of sums of such 

 differences for different ranges, depend on only two constants, I and m. When these 

 are known, k may be found for any given aneroid from the observed sum of the 

 differences of its descending and ascending readings over any given range. 



For the old Kew observations, summarised in Table I., I found by trial 



I = 0-83, 

 m 1-3, 



employing these values for all the ranges. 



To test the theory severely, it seemed expedient to compare with it the observed 

 results for the law of variation of the ratios of the differences of the descending and 

 ascending readings to the mean difference over the several ranges. For this com- 

 parison I have utilised the figures resulting directly from the observations at each 

 inch of pressure, and not the data in Table II., as the latter arise from a combination 

 of actual observations at adjacent points of the scale. This should obviate the 

 suspicion that naturally arises when data compared with theory have been subjected 

 to any kind of manipulation. 



The observed, "0," and the calculated, " C," values appear side by side in 

 Table XLII. To adequately appreciate the agreement, the reader should remember 

 that unity in the table answers to the mean difference between the descending 

 and ascending readings. It thus answers to only about '34 inch even in the range 

 30-15 inches. In the range 30-26 inches it represents only a tenth of this. 



VOL. cxci. A 



