12 Probability of Error in Experimental Research. January, 



weight of iooo grains will displace 0*1462 grain of air; an 

 equivalent platinum weight 0*058271 grain of air. The 

 1000 grains of glass and water displace 1*9736 grains of air, 

 so that their absolute weight is 1001*9736 grains. Now the 

 glass and water balanced by the brass weight would give, 

 less the air displaced by the weight, 1001*8274 grains as the 

 true value of the water and glass; while 1001*9736 grains, 

 less 0*058271 grain, give 1001*915329 grains as the value to 

 be ascertained. So, supposing the barometrical pressure to 

 remain constantly at 760 m.m., we have an error of 1*8276 

 grains per 1000 in weighing with brass weights uncorrected 

 in air, and 1*915329 grains per 1000 with platinum weights 

 at the same barometric pressure. But we know that the 

 barometer does not always record the same pressure. What, 

 then, will be the result of its variation ? — the variation, of 

 course, of the weight of air displaced. Now a litre of dry 

 air (at Greenwich), at 760 m.m. pressure and o c C, weighs 

 1*293561 grms., and its weight will be proportionately lower 

 at lower pressures. At 740 m.m. the weight of air displaced 

 by water and apparatus will be 1*9216 grains, and at 

 715 m.m. 1*8890 grains. The weight of air displaced by 

 the fcfrass and by the platinum weight also decreases propor- 

 tionately. So that, weighing with the brass weight, we 

 have, at 740 m.m., an error of 1*7792 grains on the 1000, 

 and at 715 m.m. an error of 1*7505 grains. With platinum 

 Weights we have, at 740 m.m., 1*864863 grains error, and 

 1*834334 grains at 715 m.m. These discrepancies are too 

 important to be disregarded. For suppose our weighings to 

 have taken place on different days, at different pressures 

 which were not noted, we should have serious error ; and 

 the error would be increased with a specifically lighter fluid 

 than water. 



Chemists are aware how greatly an error of similar 

 character would influence the determination of the amount 

 of carbonic acid and of- water yielded by an organic 

 body under combustion. Suppose the potash bulbs em- 

 ployed in the analysis to weigh 600 grains, there would 

 be displaced 0*366 of a grain of air at 760 m.m. pressure, 

 0*327 grain at 740 m.m., and 0*316 grain at 715 m.m. Thus 

 if weighings were made at 715 m.m. and at 760 m.m., there 

 would be an increase of weight of 0*02 grain ; and this, if 

 3*5 grains of the organic compound were under analysis, 

 would give an error of o*6 per cent. Similarly with a 

 chloride of calcium tube, weighing, with its contents, 350 

 grains, there would be an error which — with the error in the 

 estimation of the carbonic acid — would give a total error of 



