OF ARTS AND SCIENCES. 



135 



exclude any form in which both positive and negative terms enter, as 

 also forms where the exponents of the powers of r are both positive 

 and negative. 



Three simple equations satisfy these conditions : — 



(1.) T,r, = c. (2.) L + - = c.- (3.) r,Jrr, = c 



(3) represents the ellipse; and all forms r^"' -|- r.^ = c are of 

 equally little use to us. 



The isothermal points for 1 = c are approximately: — 



488 — 627 

 495 — 620 

 500 —615^ 

 502^ — 612 

 505 _ 608^ 

 507^ — 605 

 510 — 602| 

 1 



515_595x 

 517 — 593 

 520 — 590 

 525 — 585-^ 

 527 — 583i 

 530 — 580 

 535 — 575 



The isothermal curves for — - -I ; = c are much nearer circles, and 



the isothermal points more nearly equidistant from the pole. This 

 approximation to a series of circles increases with the degree of the 

 equation. There remains to be considered only Z r/" + '■ r.^ ~'z^ c. 

 The physical conditions require thkt the two loops of the isothermal 



curves shall be approximately equal. But, whenever the ratio 



in the equation r.^'^'r^'' ■=. c differs much from 1, the loops are very 

 unequal ; and any term in which a ratio of this sort is found introduces 

 into the equation I! r^'^' r^-' = c an inequality unbalanced by the 

 other terms- 

 Assuming now rj?'^2 = '^1 ^^ the equation of our experimental curve, 

 the values of jo, corresponding to the isothermal points in the " Mean " 

 column, are as follows : — 



average 1.059 



