520 PHILOSOPHICAL TRANSACTIONS. [aNNO 1774. 



On the whole, I humbly conceive, that Dr. Pemberton's meaning, in the 

 former passage, might have been better expressed in Latin, as follows: " Saepiiis 

 eos reprehendebat, qui res mere geometricas algebraicis rationibus tractavissent ; 

 et libro suo de algebr^ Arithineticae Universalis titulum ponebat, asserens Carte- 

 siurn suum de re e^dem volumen inscite dixisse Geometriam, in quo ostendit, 

 quomodo hae computationes subsidia esse possunt geometris ad inveniendum." 

 Which of these translations does most justly express the sense of the original, 

 may, I suppose, be safely left to the judgment of every person that understands 

 both the languages, I would only add, that this mistake of Castillione must 

 have been owing, either to inadvertence, or to his not being perfectly acquainted 

 with the English language; as he elsewhere appears to have had the highest vene- 

 ration for Sir Isaac Newton. This mistake may, to some, appear trivial; but, 

 in my apprehension, every circumstance relative to so illustrious a character as 

 that of Sir Isaac Newton, derives importance from it, and ought to be marked 

 with great exactness. 



XX. M. De Lues Rule for Measuring Heights by the Barometer, reduced to 

 the English Measure of Length, and adapted to Fahrenheit's Thermometer, 

 and other Scales of Heat, and reduced to a more Convenient Expression. By 

 the Astronomer Royal. \_Mr. Mashelyne.^ p. 158. 



M. De Luc, F. R. s,, in his Treatise on the Barometer and Thermometer, 

 has given a rule for the measurement of heights by the barometer, deduced from 

 his experiments, and far more accurate than any published before; since it 

 appears that he could determine heights by it generally to 10 or 15 feet, and that 

 the error seldom, if ever, amounted to double that quantity. This valuable 

 degree of exactness he has obtained principally by detecting the faults of the 

 common barometer, and improving its construction; and by introducing the use 

 of the mercurial thermometer, to accompany that of the barometer. The prin- 

 cipal faults, which he found in the common barometers, arose from the repulsion 

 of the quicksilver by the glass tube, from air and moisture admitted into the tube, 

 and from the variations of the density of quicksilver by he.it and cold; another very 

 considerable error arose, in calculating heights from the barometer, by not allowing 

 for the changes in the density of the air, whose gravity affords us this measure of 

 heights, owing to heat and cold. The first cause of error, that of the repulsion of the 

 tubes, he remedied, by substituting a syphon barometer instead of the simple 

 upright tube, the repulsion of the two legs of the syphon counteracting itself 

 The error arising from air and moisture in the tube, he cured by boiling 

 the quicksilver after it was put into the tube, and other precautions. The 

 errors, in the estimation of the heights arising from the changes in the 

 density of the quicksilver, and density of the air by heat and cold, he shows 

 how to correct by allowances depending on two thermometers, one attached to 



