210 PHILOSOPHICAL TRANSACTIONS. [aNNO J 777. 



Feel. 



And lastly, -^ of an inch of quicksilver, when the barometer stands at 29/^7 inches (viz. 

 from 29.2'2 inches to 29.32 inches) witli the temperature 53°, is equal to a column of tlie 



atmosphere of , g i. 7 



This quantity, according to my barometrical observations, is t)3.83 



But according to Mr. De Luc's rules C) i .66' 



We see here then that the statical experiment agrees with the result of my 

 barometrical ones to within about 1 1 inches in 100 feet, and I am not sure that it 

 is not still capable of much further precision; and though perhaps alone it might 

 carry with it, to some persons, a less conclusive testimony, who reluctantly 

 reason from the little to the great, yet, in conjunction with what has been 

 before shown, I think it has considerable weight; and I am the less inclined to 

 reject such an indirect method of proof, as I have the great authorities of Hailey 

 and Newton on my side. 



I have thus endeavoured to show that the error of the theory is — , ° g g ^, 

 when the temperature of the air is 6l°.4. It remains therefore finally, that we 

 deduce a rule, the error of which shall be nothing, viz. to find the temperature 

 in which the difference of the logarithms of the height of the barometer, taken 

 to 4 places of figures, will give the true difference of elevation in English 

 fathoms. Previous to this investigation, with which I intend to conclude this 

 paper, it will be necessary to remark, that by repeated experiments with the 

 manometer, I find a small difference in the equation for the expansion of air by 

 a change of temperature, and even in that of quicksilver from the same cause, 

 from what Mr. De Luc's observations have given it. I shall not here trouble the 

 reader with the experiments at large, too simple in themselves to deserve such a 

 detail, unless a future occasion should render that necessary, as the methods here 

 used may be met with among Hawkesbee's or Mr. Boyle's experiments; and 

 content myself with relating only the result of the different trials. 



1000 parts of air of the temperature of freezing, and pressure of 30^ inches, 

 increased in volume by an addition of l degree of heat on Fahrenheit's ther- 

 mometer as follows: by a mean of 8 experiments with one manometer 2.44; 

 and by a mean of 5 with a second 2.42. The mean of these two sorts of 

 observations made with different instruments, is 2.43, viz. 1000 parts of the 

 air at freezing become by expansion from l^of heat equal to 1002.43 parts, or 

 1002.385 parts with the standard temperature 39°.7. Mr. De Luc's experiments 

 reduced give this quantity equal to 1002.23.* 



* 



* It has generally been supposed, tliat air expands -j^ with each degree of the tliermometerj 

 commencing from tlie mean temperature 55°; and, in consequence of tliis, astronomers have com- 

 puted tables for correcting their mean refractions ; but, on reducing the result of my observations to 

 the temperature 55°, we shall have the correction of 1" = -.1^-^^ or ;j^. Now according to 

 Mr. De Luc this equation is ^otAt = tet which would produce a difference of about +" in the 

 corrected refraction, on an altitude of 5°, with tiie temperature 35°. If my numbers may be 8up- 



