Mr. J. Utting on Planetary Motion. 119 



it might be found in many other places ; certainly it must have 

 been formed in the old Franklin furnace, in Sussex county 

 New-Jersey, where so many fruitless attempts were made to 

 work the Franklinite. 



Before I conclude these repiarks, I must observe, that it 

 does not appear that the presence of zinc affects the properties 

 of iron. In Belgium the iron is of good quality; and it is an 

 interesting fact, that the bar-ii-on of Ancram is in great de- 

 mand at g 120 per ton, a higher price than is at present paid 

 for any unported iron. The castings from the Ancram fur- 

 nace are in such a repute, that no other pigs are used at the 

 West Point Foundry for the heavy gims ( j2 and 42 pounders) 

 now casting for the United States' navy. 



The Ancram furnace equals, in beauty of workmanship, and 

 economy of means, any that we have seen ; and we entertain 

 no doubt, that all works carried on with such admirable per- 

 fection, must and will alwa3'S prove equally honourable and 

 profitable to their owners and directors. 



XXIV. On a Planetary Analogy ; or a Laxso of Motion 

 pervading and connecting cdl the Planetary Orbits. By 

 Mr. J. Utting. 



To the Editors of the Philosophical Magazine and Journal. 



Lynn Regis, June 21, 1823. 

 npHE following beautiful analogy which obtains in the mo- 

 -*• tions of the jilanetary orbs has, I believe, never been de- 

 scribed by any astronomical writer, or is not generally known, 

 viz. If the mean orbicular motion of each planet in its orbit, 

 be multiplied by the square root of its mean distance from the 

 sun, a product will be obtained commoir to all the planets : 

 for instance, if the orbicular motion in miles of each planet in 

 one sidereal day, be multiplied by the square root of its mean 

 distance from die sun, the jn-oduct will be 15.634'.588.170 miles, 

 a constant quantity lor all the planets, as the mean velocity of 

 the planets, multiplied by the square root of their respective 

 mean distance, is always a constant quantity. 



Tlie same analogy obtains in each respective system of sa- 

 telhtes; for, if the velocity of a satellite be multiplied by the 

 square root of its mean distance from its primary, a constant 

 product will also be produced in each respective system of 

 satelHtcs; and if this constant product be multiplied by the 

 square root of the recij)rocal t)f the sun's attractive power, and 

 that of their respective primaries, the same result will be pro- 

 duced as tliat which obtains in the planetary motions, as above. 

 Thus a constant product, or quantity, obtains in tlie motions 



of 



