Mr Mcikle onjindinff the Derv-Po'mt, ^c. 99 



hyperbolas would answer so well for the purpose as I shall now 

 shew they do. 



In this scheme, of which I shall at present only give an out- 

 line on a small scale, the Fahrenheit temperature is estimated 

 nearly in the same way as latitude is reckoned from the equator ; 

 that is, by the perpendicular distance from a straight line ZO 

 parallel to AG, the transverse axis of the two hyperbolas PAZ, 

 EGO. Thus the distance of a point P, in the hyperbola PAZ, 

 from ZO, which is at the zero of the scale, denotes the tempera- 

 ture of the air; while the distance of a point D, in the asymp- 

 tote CD, from the same line ZO, represents the temperature of 

 the moist thermometer ; and if a straight line, representing the 

 ruler above mentioned, be applied to P and D, so as to cut the 

 hyperbola EGO in any point E, the distance of E from ZO de- 

 notes the temperature of deposition, or the dew-point. 



Through D draw DH parallel to AG, and upon DH let fall 

 the perpendiculars PH, CF, EI ; produce CA and PH to meet 

 in N. Through the centre C draw Cp parallel to DP, and 

 meeting the hyperbola AP in ^ ; on CN let fall the perpendicu- 

 lar pn. Then it is a known property of the hyperbola, that the 

 semidiameter Cp is a mean proportional between the segments 

 PD and DE ; and, therefore, because the three triangles PHD, 

 DIE, pnC, are obviously similar, pn is a mean proportional be- 

 tween PH and EI. By means of these properties we may find an 

 expression for EI in terms of PH, and other known or constant 

 quantities. It is evident that PH represents the depression of the 

 wet thermometer below the temperature of the air, and that EI 

 denotes the farther depression of the dew-point below that again. 



Put a = AC the semitrans verse axis, and 

 b for the seraiconjugate ; then, from the 



A' 

 known properties of ^the curve, PN* = — 



(CN' — o2), and CN' = ^ PN« -I- a»; also DF 



=^ ICF and DH = DF + CN = ^ CF + 

 6 



n/ 



^ PN' + a«. Again, pn' 



n 



b^ 



5(Cn«-«t), 



and Cn' = ^ j- x pn'^ + «* ; «nd because the 

 triangles PHD, pnC, are similar, we have 



