Stationary Storms.

When a storm center has crossed the United States and passed to Nova Scotia or Newfoundland, we often find on the United States Weather Maps for two or three subsequent days the word low on the northeast corner of the maps, seeming to indicate that the center of the storm remained during that period nearly stationary. The Danish maps (from Dec., 1873, to Aug., 1874,) show us that storms do sometimes remain nearly stationary for several days.

Case L. From the 5th to the 8th of March, 1874, a violent storm moved from New Mexico to the St. Lawrence valley. On the 9th the center of this storm was a little north of Halifax; on the 10th it was still near the same place; on the 11th it had moved northeast nearly 400 miles; on the 12th it had moved south about 200 miles; on the 13th it had moved north about 200 miles; on the 14th it had moved south about 200 miles; and on the 15th it moved northeast about 700 miles. Thus during five days (March 9-14) the center of the storm had advanced less than 350 miles, being an average motion of less than three miles an hour, and during the first four days the barometric depression was greater than it was on the 8th.

Case II. From April 26th to 30th, 1874, a storm moved across the United States from Colorado to the St. Lawrence valley. During the next day (May 1st) the storm was stationary; on the 2d it moved a little to the southeast; on the 3d it moved a little to the east; and on the 4th it reached St. Johns, Newfoundland. Thus in four days the center moved 775 miles, being an average rate of about eight miles an hour; and during the first half of this time the average movement scarcely exceeded four miles an hour.

In preparing the materials for this article, I have been assisted by Mr. Edward S. Cowles, a graduate of Yale College of the class of 1873.

ART. II-Studies on Magnetic Distribution; by HENRY A. ROWLAND, of the Johns Hopkins University, Baltimore.

(Continued from page 458 of the last volume.)

V.

LET us now consider the case of that portion of the bar which is covered by the helix. First of all, when the helix is symmetrically placed on the rod, equations (5) and (6) will apply. As Q" is the quantity which is usually taken to represent

AM. JOUR. SCI.-THIRD SERIES, VOL. XI, No. 61.-JAN., 1876.

the distribution of magnetism, being nearly proportional to the "surface-density" of magnetism, I shall principally discuss it.

In the first place, then, this equation shows that the distribution of magnetism in a very elongated electro-magnet, and indeed of a steel magnet, does not change when pieces of soft iron bars of the same diameter as the magnet are placed against the poles, provided that equal pieces are applied to both ends; otherwise there is a change. This result would be modified by taking into account the variation of the permeability, &c.

Let us first consider the case where the rod projects out of the end of the helix, as in Tables V, VI and VII. By giving proper values to the constants we obtain the results given in the last columns of the table. The agreement with observation is in most cases very perfect. We also see the same variation of r that we before noticed in the rest of the curves, and we see that it is in just the direction theory would indicate from the change of μ.

In these tables we come to a very important subject, and one to which I called attention some years back, namely, the change in the distribution when the magnetizing-force varies, and which is due to change of permeability. The following tables and figures show this extremely well, and are from very long rods with a helix a foot long at their center, as in the last three tables. The bar in both these tables was 19 inch in diameter and 5 feet long. The zero-point was at the center of the bar and of the helix. The tables give values of Q' for the magnetizing-forces which appear at the head of each column, and which are the tangents of the angles of deflection of the needles of a tangent-galvanometer. Table VIII. only gives the part covered by the helix. Both tables are from the mean of both ends of the bar.

These experiments show in the most positive manner the effect we are considering, and we are impressed by them with the great complication introduced into magnetic distribution by the variable character of magnetic permeability.

1

In fig. 3 I have represented the distribution on half the bar as given in Table IX, the other half being of course similar. Here the greatest change is observed in the part covered by the helix, though there is also a great change in the other part.

Plot of Table IX, showing surface-density for different values of the magnetizing

force.

These tables show that, as the magnetization of the bar increases, at least beyond a certain point, the curves on the part covered by the helix increase in steepness; and the figure even shows that near the middle of the helix an increase of magnetizing-force may cause the surface-density to decrease; and Table VIII. shows this even better. Should we calculate Q", however, we should always find it to increase with the magnetizingforce in all cases. These effects can be shown also in the case where the bar does not extend beyond the helix, but not nearly so well as in this case, seeing that here Q" can obtain a greater value.

Assuming that u is variable, the formula indicates the same change that we observe; for as Q" increases from zero upward, u will first increase and then decrease; so that as we increase the magnetizing-force from zero upward, the curve should first decrease in steepness and then increase indefinitely in steepness.

In these tables the decrease of steepness is not very apparent, because the magnetization is always too great, and indeed on this account it is difficult to show it; but in Tables V, VI and VII. this action is shown to some extent by the values of r in the formulæ. The change of distribution with the helix arranged in this way at the center of the bar is greater than in almost every other case, because the magnetism of the bar Q" can change greatly throughout the whole length of the helix, and thus the value of r be changed, and so the distribution become different.

The next case of distribution which I shall consider is that of a very long rod having a helix wound closely around it for some distance at one end.

Table X. is from a bar 9 feet long with a helix wound for one foot along one end. The bar was 25 inch in diameter. All except the first column is the sum of two results with the current in opposite directions, and after letting the bar stand for some time, as indeed was done in nearly every case. The first column contains twice the quantities observed, so as to compare with the others. The zero-point was at the end of the bar covered by the helix.

The value of Q", between 0 and 1 includes the lines of force passing out at the end of the bar, and is therefore too large.

4.

D

C

B

20

Plot of Table X.

In fig. 4 we have a plot of the results found for this bar. The curves are such as we should expect from our theory except for the variations introduced by the causes which we have hitherto considered. Thus the sharp rise in the curve when near the end of the bar has already been explained in connection with Table III. A small portion of it, however, is due to those lines of induction which pass out through the end section of the bar, and in future experiments these should be. estimated and allowed for. When considering surface-density we should also allow for the direct action of the helix, though this is always found too small except in very accurate experiments.

To estimate the shape of the curve theoretically in this case, let us take equation (4) once more, and in it make s'∞ and s=RR' which will make it apply to this. We shall then have A'=-1, and A"=∞.

Whence for the positive part of Q", we have

And if x is reckoned from the end of the rod, we have

(2 — 2εb);

(10)