136 Remarks on Dr. 'EnjleWs Institutes 



and the resolution was accordingly made. But in doing it,. 

 two things were confounded which are widel}^ different : the 

 sum of the iiroducts, arid the product of the sums. — It would 

 have been better if the compiler had not attempted to de- 

 viate from Rutherfortb. Supposing only one power, and 

 only one resisting force which balance each other through 

 the intervention of a series of mechanical powers, — the 

 power will be to the weight simply as the velocity of the 

 weight is to the velocity of the povrer.* 



Prop. 60. Schol. The method here given of finding 

 the initial velocity of a projectile, gives only that part of it 

 .which is in a direction perpendicular to the horizon. To 

 obtain the whole velocity, this result ought to have been in- 

 creased in the ratio of radius to the cosecant of the angle of 

 elevation. But it would have been altogether preferable to 

 omit noticing a naethod so entirely useless and even de- 

 ceptive in practice, and to have substituted for it that by the 

 ballistic pendulum. 



Prop. 68. In the last edition, several palpable errors 

 which formerly perplexed the demonstration have been cor- 

 rected ; but the reasoning is still far from being demonstra- 

 tive. The erroneous figure of former editions is also retain- 

 ed. The circle GNV, instead of GML, should have had 

 T for its centre, and GML should have been an ellipse hav- 

 ing T for its farther focus. 



" D-sf. 16. Schol. It is improperly asserted in this scho- 

 lium, that " the projectile and the centrifugal forces differ 

 from each other as the whole from the part." These forces 

 are dissimilar in kind, and are incapable of comparison. 

 They stand to one another in the same relation as pressive 

 and percussive foices. If the tangent which measures the 

 projectile, and the subtense which measures the centrifu- 

 gal force, be diminished indefinitely, as they must be before 

 we can properly make the attempt to compare them, the 

 latter becomes evanescent in respect to the former. The 

 centrifugal is rather a consequence of the projectile force, 

 than Q part of it. 



Prop. 70. " When bodies revolve in a circular orbit 

 about a centre, the centripetal and centrifugal forces arc 

 equal." This proposition imphes that in other orbits these 



- SeaRulherfoi-th's System, Vol. I. Art. 72/ 



