Central Theorem for cifcerlaining Specific Gravities. 1 15 



fluid; c the weight which placed with the folid in the upper bafon immerfes the inllrument to 

 the mark; d the additional weight to produce the fame effeft when the body is in the lower 

 bafon; 11 the fpecific gravity of diftilled water, at the temperature of 12.5 degrees of the 

 decimal thermometer, and the prefTure of 7577 millimeters = 1 ; IT the fpecific gravity 

 .of the water made ufe of. 



The following formula gives the folutlon * : x — — — 



The value of 11' is firft to be found, which is greater than unity when tlic water made 

 ufe of is heavier than diftilled water, and in the contrary cafe is a fraftion. 



Let P reprefent the weight of the gravinieter without any additional weight t; V the con- 

 ftant volume of the immerfed part ; a the additional conllant weight in the upper bafon, 

 or that which immerfes it to the mark in diftilled water 11; and we fhall have P +« = Vfl; 



whence V = — = — 



Again l> reprefents the weight more or lefs than n, which muft be fubftltuted to produce 



the fame imraerfion in another liquor different from diftilled water. 



P + i P + i 

 t We fhall therefore have n = -vt- = n— : — • 



* V r + a 



The value of 11' being found, every thing elfe is known ; nothing more being necefTary 

 than to fubftitute this value in the formula. 



I am perfuaded that philofophers will immediately perceive the advantages of this method. 

 Diftilled water was wanting ; but this praxis renders it unneceflary. Even if diftilled 

 water were at hand, it would feldom happen that the times of the ftandard temperature 

 and prefTure would agree with thofe of the experiment ; and when an artificial temperature 

 is produced, it is fubjefl to vary during the courfe of the experiment. All thefe difficulties 

 are removed; and even when diftilled water is at hand, I prefer, more efpecially in fummer, 

 water containing a fmall portion of neutral fait. Two motives juftify this preference : 



ininaiion. I am not prepared to ftate the meihod of applying this correftion ; and (hall onlv remark, in this 

 place, that the mere change of dim£nfions from temperature in a piece of fteel (independent of the greater change 

 in the whole inftrumcnt) will alter the fourth figure at every third degree of Fahrenheit. For pyrometrical 

 Jata. fee Philof. Journal, I. 58. N. 



• For the fake of thcfc who are unacquainted with fymbols, I (hall here give the rule in words at length: 

 From the weight in tlie upper difh, when the inftrument is properly immerfed in the unknown fluid, take the 

 weight which is placed with the body in the fame fcale at the like adjuftmcnt. The remainder is the abfolutc 

 weight of the folid. Multiply this by the fpecific gravity of the fluid, and refcrve the produfl. From the ad- 

 ditional weight when the body is placed in the lower bafon, take the additional weight when it was placed in 

 the upper. The remainder will be the lofs of weight by immerfion. Divide the rcferved produft by the lofs 

 by immerfion, and the quotient will be the fpecific gravity of the folid with regard to diftilled water at the 

 ftandard temperature and prelTure. N. 



t In the upper difli. For as the lower additional piece aSs only by its refidual weight, and this reuft vary 

 with th« Suid, it is clear that it muft be confldcred as part of the inflrument, and enter into (he value of P 

 ^tfhalcver it is ufed. In fa£t, the gravimetcr with this piece is an inftrument perfeftly diftinft from that in 

 >»bich k itnot ufed, and the adiuflment may then be made as well (and perhaps more ealily) by a conftant 

 fmall wcigbi io the upper difli, as by tlic very delicate prucefs of i\\e author. N. 



♦ Or in words; To the weight of the gravimetcr add the vKciijht required in the upper bafon to fink it in 

 the unknown fluid. Agjin, to the weight of the graviitietcr add the weight required in the fame manner to 

 fmk it in diftilled water. Divide the firft fum by the latter, and the quotient will be the fpecific grjrity of the 

 flyid in c^ucftion. N. 



Qji I. U 



