Mr. Herapath on the Iitfluence of Humidity, S^c, 419 



units, the value of the series is 0; the value of the series thea 

 always lies between and 1. m^: 



We observe then that whatever may be the number of units in 

 the denominator, if that number be less than infinite, the form 

 of the series is still the same. It would appear from the preced- 

 ing investigation, however, that the value of the series diminishes 

 continually from 1 to 0, and that the value of the series 1 — 1 -f- 

 1 — 1 + &c. to infinity varies from 1 to 0. 



It is well known that a neutral series is the limit between a 

 diverging and a converging series ; may we not then from this 

 circumstance, and what is shown above, conclude that such a 

 series has no determinate value ; at least that it has no value 

 that can be determined from the series itself by a direct investi'^ 



gation. If the series 1— • 1 + 1—1+ &c be said to 



have a determinate value, or limit, we may naturally ask, which 

 of its values is meant? Or if 1 should chance to meet with the 

 above series in any calculations, what vulgar fraction ought. I 

 to substitute as its value ; for it has been proved above to be 

 equal to i, ^, 4-, 8cc. to infinity ; or to f, f, -f-, &c. to infinity, 

 beside a great many others. We may conclude then that -i-, 

 instead of being universally the value of the series 1 — 1 + 1 — 1 + 

 Scc . to infinity, is only one particular value out of an infinite 

 number, u 



Article VII. 



Remarks on Dr. Thomson's Paper " On the Influence of Humi- 

 dity in modifying the Specific Gravity of Gases" By Johji 

 Herapath, Esq. 



(To the Editor of the Annals of Philosophy,) 



DEAR SIR, Cranfordy London, April W^ 1822. 



Dr. Thomson having, for the expressed purpose of " calling 

 the attention of chemists " to the subject, pubhshed in the 

 Annals for April some views on vapour and latent heat, I am 

 induced, as a branch of science to which I have paid a little at- 

 tention, to offer some remarks in the Doctor's ideas. 



" Whatever he the temperature of steam from 212° upwards" 

 says Dr. Thomson, " if we take the sajne weight of it, and con- 

 dense it hy water, the temperature of the water will always be 

 elevated the same number of degrees.''^ " It follows from this 

 general law that the latent and sensible heats of steam (reckon- 

 ing from 32*^) added together always form a constant quantity, 

 whatever be the temperature of the steam." From these prin- 

 ciples, the Doctor has calculated a table exhibiting the *' latent 

 and sensible heats " of steam to about every 50°, from 32° to 



2 e2 



