152 Remarks on Dr. Enfield's Tnstituiea 



among those which compose the chapter, is borrowed from 

 Rutherforth. 



Prop 168. Schol. This method of finding the directiorj 

 of gravity includes only the effect of the centrifugal force. 

 Including the joint effect of rotation and of figure, the di- 

 rection is manifestly that of a perpendicular to the tangent 

 plane of the earth's surface, or of a normal to the elliptical 

 curve of the meridian passing through the given place. 



Prop. 173. In the concluding paragraph of the demon- 

 stration, the relative forces of the sun and moon to raise 

 tides are erroneously stated. The real forces are directly 

 as the masses, and inversely as the cubes of the distances. 



The concluding scholium of the Astronomy consists of 

 extracts from a paper of Dr. Herschel's in the Philos. 

 Trans, for 1795. These extracts are so unskilfull}^ made, 

 and are presented in so disjointed a form, as to afford scarce- 

 ly any idea of the train of argument pursued in the origi- 

 nal. But in the original itself, high as is the estimation in 

 which the author is justly held as an observer, we must be 

 permitted to think that there are several statements which 

 cannot be defended. With the view of multiplying the 

 points of analogy between the sun and the planets, and 

 thus increasing the presumption that the former is inhabit- 

 ed, he endeavours to shew that both primaries and seconda- 

 ries shine in some measure by iheir own light. The partial 

 illumination of the moon, for example, during a total eclipse.- 

 cannot be entirely ascribed to the light which may reach it 

 from the earth's atmosphere;^ — " because, in some cases, 

 the focus of the sun's rays refracted by the earth's atmos- 

 phere must be many thousand miles beyond the moon.'' 

 Dr. Herschel assumes as the basis of this calculation that 

 the rays of the sun are bent by the atmosphere at only an 

 angle of 31'. He seems to have inadvertendy neglected 

 the circumstance that the rays undergo a second equal re- 

 fraction in passing out of the atmosphere. In consequence 

 of this, the real inflection is 62', (or rather 66', taking 33' 

 as the mean horizontal refraction,) so that the focus of the 

 sun's rays as refracted by the earth's atmosphere can never 

 in fact be so distant as the moon. An observer stationed at 

 the moon, even during a central echpse of the sun, would 

 see a luminous ring encircling the earth. The light thus 

 thrown upon the moon's disc is amply sufficient to explain 



