1878.]

[Chase.

The constancy of wave-velocity requires that h and t should vary inversely as g. The law of conservation of areas demands the same ratios of variability in the rotation of any contracting or expanding nebular nucleus; for, the velocity of rotation varying inversely as radius, and the distance traversed varying as radius, the time of rotation (or t, the time of semirotation) varies as the square of radius; but g varies inversely as the square 1 of radius, .. gt x r2, and is constant for all possible stages of nebular condensation. The record of rotation is, therefore, invariable, representing the undulatory velocity of the ethereal medium, as well as the constant limiting velocity of gravitating tendency for which Faraday sought.

The value of g being a maximum, in our system, at Sun's surface, there is where the limiting value of gt is to be found. If we estimate Sun's semi diameter* at 16' 2', Earth's mean radius vector is 214.41 solar radii. Laugier's mean estimate of t (the time of Sun's semi-rotation) is 12.67 days, or 1093872 seconds; V ́gr (214.41% × 2r) → (365.256 × 86400).. gr÷2559500. and gt =r2.340. But the velocity of light, according to Struve's constant of aberration, is 214.41 r 497.825 1÷ 2.322. This investigation, therefore, leads to the same result as those which I have before undertaken, and gives the velocity of light as the limiting constant of gravitation.

Stated Meeting, November 1, 1878.

Present, 20 members.

Vice-President, MR. FRALEY, in the Chair.

Mr. J. B. Knight, Prof. L. Haupt, and Dr. Morris Longstreth, newly elected members, were introduced to the presiding officer and took their seats.

Letters accepting membership were received from Dr. Albert H. Smith, dated 1419 Walnut St., Phila., Oct. 20, 1878; Rev. Edward A. Foggo, D. D., 717 Locust St., Phila., Oct. 28, 1878; Rev. Samuel Longfellow, Germantown, Oct. 24; and Dr. A. S. Packard, Jr., Brown University, Providence, R. I., Oct. 18, 1878.

Letters of acknowledgment were received from the Observatory at Prag, Nov. 6, 1877 (99,100, List); the Royal Danish Academy, Sept. 30, 1878 (100, List); the Royal

Amer. Nautical Almanac.

+ This is equivalent to Faye's value of gt for lat. 16° 59′, or Carrington's for lat. 11 16'.

Institution, London, Oct. 15, (101, Cat. III); the Royal Astronomical Society, Oct. 18, (101, Cat. III); the Society of Antiquaries, London, Oct. 14, (101, Cat. III); and the Boston Public Library, Oct. 17, (Cat. I, II, III).

Letters of envoy were received from Sir Lewis Mallet, India Office, Oct. 11, 1878; Physical Society of Bordeaux, Oct. 15 (acknowledging also the receipt of Proc. 95, 96, 98, 99); Meteorological Office, London, Oct., 1878; and Mr. E. Steiger, 25 Park Place, New York, Oct. 23, 1878.

Donations for the Library were received from the Academies at St. Petersburg, Copenhagen, and Brussels; the Société Vaudoise; Geographical Society, School of Mines, and Revue Politique, Paris; -Commercial Geographical Society at Bordeaux; Observatory at Sau Fernando; Harvard College Library, and Museum of Comparative Zoology, Cambridge; E. Steiger; Entomological Society of Brooklyn; Engineers Club, and Historical Society, Phila.; Museum of Wesleyan University, Middletown, Conn.; Public School Library, St. Louis; and the Argentine Society of Sciences at Buenos Ayres.

Prof. Chase read a "Note on the density of the Kinetic Ether."

Prof. Sadtler read a paper "On the Electrolytic Estimation of Cadmium, by Edgar F. Smith, Ph.D." as a contribution from the Laboratory of the University of Pennsylvania.

Prof. Sadtler presented to the Society a chemical preparation obtained by a new and interesting reaction from Pennsylvania petroleum.

The presence of Olefines or unsaturated hydrocarbons in Petroleum has been proved by Prof. Schorlemmer, who obtained bromides of these hydrocarbons by the action of bromine upon the several fractions of petroleum. This reaction has only proved the presence of the lower boiling members of the series however. I had given to me by Dr. C. M. Cresson a thick viscid liquid said to be mainly made up of higher olefines. Now the following reactions have been carried out with Ethene C, H,

I endeavored to apply these reactions to the mixture of higher olefines

1878.j

and succeeded perfectly. In oxydising I used the "chromic acid” mixture, and after obtaining the chlorine-substitution acids I saponified them with caustic soda. The preparation shown is, therefore, a mixture of soda salts of these chlorine-substitution compounds of the higher fatty acids As these compounds cannot be made by such reaction from the higher "paraffins," their formation proves conclusively the presence of the higher "olefines."

Prof. Houston read a joint paper entitled "On the circumstances influencing the efficiency of Dynamo-electric machines, by Prof. Houston and Prof. Thompson.

Prof. Haupt read a paper entitled "On the scales of Maps" with tables.

Pending nomination No. 871 was read.

Prof. Houston's resolutions, offered October 4, were called up for consideration, and after a discussion of the subject by Prof. Barker, Prof. Houston, Prof. Thompson, Dr. König, and other members present, it was

Resolved, That the fourth and fifth paragraphs of page 728 of No. 101 of the Proceedings, being portions of the minutes of the meeting of June 21st, 1878, be corrected to read as follows:

"Prof. Houston exhibited a microphone relay invented and made by himself and Prof. Thompson of the Philadelphia High School, to be applied to the articulating telephone."

"Prof. Barker exhibited a suite of Mr. Edison's instruments invented and made by him during the last year or two, and stated that, in his opinion, in their inventions so far as they involve similarity of principle, Mr. Edison had priority over Mr. Hughes."

It was then, on motion of Dr. LeConte, resolved that the Index on page 730 be corrected accordingly.

Prof. Sadtler referred to the reading of a letter from Prof. Morton to the Secretaries, at the last meeting, and said that he had already himself made due acknowledgment to Prof. Morton before the Society at the meeting of August 16th, 1878, as the minutes show.

And the meeting was adjourned.

Contributions from the Laboratory of the University of Pennsylvania, No. XVI.-On the Electrolytic Estimation of Cadmium.

BY EDGAR F. SMITH, PH. D.

(Read at the meeting of the American Philosophical Society, Nov. 1, 1878.)

In a recent article published in the American Journal of Science and Arts (Vol. XVI., Sept., 1878), Prof. F. W. Clarke calls attention to the estimation of cadmium by electrolysis, which, however, proved unsuccessful-the cadmium being indeed thrown out of the solution but in such a form as to enclose impurities; yielding consequently unsatisfactory results.

Out of curiosity, to see what might be effected by substituting some other salt for the chloride, I employed an acetate solution and met with success, as the following experiments will show :

I. .1450 grms. cadmium oxide were dissolved in acetic acid, the excess of the latter expelled upon a water bath and the platinum crucible then about half filled with water, and placed upon a copper ring connected with the negative pole of a two-cell Bunsen battery, while joined to the wire leading from the positive pole was a strip of platinum foil extending into the acetate solution. The deposition of the cadmium upon the sides of the platinum crucible was regular and in a perfectly crystalline grayish white layer. In about three hours the separation was complete. The cadmium was first washed with distilled water, then with alcohol and finally with ether. It was dried over sulphuric acid. The metallic cadmium weighed .1270 grms. corresponding to 87.58 % Cd. The calculated percentage of metal in the oxide is 87.50.

II. 2046 grms. cadmium oxide placed in a small broad platinum crucible were dissolved in acetic acid and after evaporating the excess of the latter water was added-the solution, however, remaining rather concentrated. The platinum vessel was connected with the negative pole of a bichromate battery. To the copper wire of the positive pole was attached a platinum wire from which was suspended a small platinum crucible, which dipped into the solution in the larger vessel. The space between the walls of the two crucibles was not more than the eighth of an inch. Only two cells of the battery were employed. The deposit of cadmium here as in the first experiment was perfectly crystalline and metallic in appearance. Not the slightest trace of spongy metal was visible. The separation of the metal was finished in about the same time as in (I), and it was then washed and dried as above. Found .1790 grms. metal-corresponding to 87.48 % Cd.

From the various experiments made I have discovered that to obtain good results the following should be observed: 1st. Work with rather concentrated solutions of the acetate. 2d. Employ a sufficient number of cells of either battery to produce a rapid and rather energetic current.

October 31, 1879.

Nov. 1, 1878.]

[Haupt.

On the Scales of Maps. By L. M. Haupt, Prof. of Civil Engineering Towne Scientific School,

(Read before the American Philosophical Society, Nov. 1, 1878.)

The object of this paper is to attempt if possible the removal of the ambiguities existing in regard to the use of ratios as expressing the scales of maps and degrees of slopes.

Mathematical authorities are by no means agreed concerning the definition of the term ratio. They all maintain that it is an expression for the relation existing between two quantities, but differ in the manner of determining the value of this relation; some, as Peck, Davies, Robinson and others, divide the second quantity or consequent by the first or antecedent; some, as Hutton, Alsop, Ray and others, divide the first by the second quantity, and still a third class, as Chauvenet and others, define it as being the quotient obtained by dividing one quantity by another. It may therefore be either or, 2,000,000, or 2555000.

The same confusion is found to exist in designating the scales of maps and drawings. Some publishers and engineers giving it as so many miles, or other denomination, to the inch; others, as so many inches to the mile. Again in expressing slopes many authorities use the tang. of the angle made with the horizon, that is the height divided by the base () while others use the co-tang. or.

b

Now if we consider the manner of obtaining the value of the ratio in a Geometrical Series or progression where no ambiguity exists, we find that as each subsequent term is obtained from its predecessor by multiplying by a constant factor called the ratio, so to obtain this factor or ratio we must necessarily divide any term by the preceding one, and as this is the only way in which its value can be determined, it establishes a rule which should be made to apply to all other cases.

We should then define a ratio as being the expression for the value of the relation existing between two quantities, and as obtained by dividing the SECOND by the FIRST.

The query then arises as to which quantity should be considered the first and which the second, and we answer that the given material object to be represented by the map or drawing is the Unit or measure with which the other is to be compared. The map or drawing may be made of any convenient size, but the object to be represented is already fixed or constant in its dimensions, and hence, as the unit or standard of comparison, should be made the dicisor, or denominator of the quantity expressing the ratio; it is consequently the antecedent or first quantity. To illustrate, let it be required to determine the ratio between a map and its original in nature.

The tract to be delineated in miniature is the fixed object, invariable in size, which is to be compared with the plot representing it, and which may be made larger or smaller according to circumstances, hence it become the unit of comparison, and is the antecedent or first quantity, and as such the denominator of the fraction expressing the ratio. The formula will then be: