218 Lord Rayleigh on General Theorems relating to 



§ 75. Nitrate of Sodium. — The temperature at which this 

 cryohydrate is formed was found by experiment to be — 17°*5 ; 

 but, for reasons partly considered in § 69, I believe this tem- 

 perature to be too low, and that, when supersaturation does not 

 intervene, the temperature is — 16 0, 5. Here, however, I assign 

 to it the temperature got by direct observation. Of the last 

 portion to solidify, 5*4210 grms. gave 2-2140 of NaN0 3 , or 

 408 per cent., which indicates the composition 

 NaN0 3 + 813H 2 0. 



Of the previous crop of crystals, 6*9820 grms. gave 2*8850 of 

 NaN0 3 . 



§ 76. Nitrate of Potassium. — This was examined in § 24. 

 The cryohydrate solidifies at — 2°*6, and contains 1T2 per cent, 

 of nitre. The water- worth is expressed by the relation 



KN0 3 +44-6H 2 0. 

 § 77. The nitrates of the alakalies therefore arrange them- 

 selves as follows : — 



Temperature of 

 solidification of 

 cryohydrate. Water- worth. 



NH 4 N0 3 . . -17-2 5-72 



NaN0 3 . . . -17-5 (16-5) 8*13 



KN0 3 ... ~ 2-6 446 



I believe that here again the water-worth really falls with 



the temperature of solidification. But the order of the salts 



in regard to their water-worths is again different from the order 



observed with the sulphate, as well as from that of the chlorides 



of the same metals. 



[To be continued.] 



XXV. General Theorems relating to Equilibrium and Initial and 

 Steady Motions. By Lord Rayleigh, M.A., F.R.S.* 



JF a material system start from rest under the action of given 

 impulses, the energy of the actual motion exceeds that of 

 any other which the system might have been guided to take by 

 the operation of mere constraints ; and the difference is equal to 

 the energy of the motion which must be compounded with either 

 to produce the other (Bertrand). A proof of this interesting 

 theorem is given in Thomson and Tait's 'Natural Philosophy/ 

 §311 — by a slight modification of which a more general result 

 may be arrived at, giving rise to important corollaries. 



Let P, Q, it denote the components of impulse on the par- 

 ticle m, and x> y, z the component velocities assumed. Then, if 



* Communicated by the Author. 



