•' • [Ocl i 



0.08 

 evidenl that each division will be equal to ,. —0.0053. Tins fraction 



1.) 



is, therefore, the litre oi tliis scale. Dissolving 5 mgr. of a mineral con- 

 taining manganese aud nothing that could interfere, we find the point of 

 extinction at 17, then we have percentage p of Mn.o 



(O.OOoB X 17) X 100 

 P=- g -=1.802. 



In a subsequent paper I shall give tables ami determinations for a num- 

 ber of important minerals and ores. As the determinations will have to 

 be made, tin- the most of them, in the humid way, the labor will be exten 

 sive and time consuming. I should esteem it a great favor if my co-labor- 

 ers in mineral chemistry would furnish me with such small samples of 

 minerals and ores analyzed by them and coming within the limits of this 

 method. In so much as each worker multiplies himself, so to speak, by 

 lessening the time consumed in determinations, I cannot but consider this 

 chromometric method as of the greatest importance, and again ask foractive 

 co-operation in its further development. Thus far I have proved the 

 method thoroughly only for manganese, iron and chromium. The former 

 offers no difficulty and gives equally accurate results with the most ap- 

 proved gravimetric methods. I shall next extend it to copper ores. 



Crucial Harmonies. By Pliny Earle Chase, LL.D., Professor of Phi- 

 losophy in lliin rj'iird College. 



(Bead before the American Philosophical Society, October Wi, 1878.) 



Ts'o surer test of any hypothesis has ever been suggested than its furnish- 

 ing a successful anticipation, or prediction, of facts or phenomena that 

 were previously unknown. 



The harmonic progression, which starts from Jupiter's centre of linear 

 oscillation as a fundamental unit and which has 4 for its denominator-dif- 

 ference, was taken as the ground for such a prediction, in the communica- 

 tion which I read to the American Philosophical Society on the 2d of May, 

 1ST;;.* Kirkwood had, a short time before, computed a probable orbit for 

 "Vulcan," which satisfactorily represented the second interior term of 

 the series, and this accordance was one of the principal sources of the con- 

 fidence with which I ventured upon a publication of the prediction. 



Forty-one days afterwards, on the 19th of June, De la Rue, Stewart 

 and Loewy communicated to the Royal Society certain conclusions, based 

 upon three sets of sun-spot observations, taken in three different years, 

 and extending over periods, respectively, of 145, 123 and 139 days. Those 

 observations indicated some source of solar disturbance at .267 of Earth's 

 mean radius-vector, which represented the first interior term of my series 

 and gave the first conclusive verification of my prediction. In announcing 



* Proc. Soc. Phil. Amer., xiii, 



