 We can calculate the gradient by using the methods described in the lesson. Let's pick a point in Pennsylvania about here and then we'll calculate the gradient for that point. We will first look at the gradient in the x direction, which goes along in this parallel with the north and south boundaries of Pennsylvania. And we'll use the method of center differences that's described. So we'll look at this contour here, this isotherm, and this one over here on the other side. And we note that this distance here is very, very similar to the distance of Pennsylvania between the parallel borders, which is 135 nautical miles. And so each one of these contours is 4 degrees Fahrenheit, so we have two of them. So 8 divided by 135 nautical miles gives us a gradient in the x direction of 0.059 degrees Fahrenheit per nautical mile. Now we can do the y direction, so we pick two points here, one here and one about here to be on the gradients. And we note that this is a little bit more than half the height of Pennsylvania, it's actually about 80 nautical miles. But also note that as y goes more positive, the temperature becomes more negative. And therefore we have to use minus 8 over 80 and we get, for the gradients in the y direction, minus 0.1 degrees Fahrenheit per nautical mile. When we put these in to get the magnitude, it's the square root of the squares, we see that we end up with 0.12 degrees Fahrenheit per nautical mile with a magnitude of the gradient. To find the direction of the gradient, we see that mu, the angle with respect to the x-axis, so this is a math angle, is equal to the arc tangent of the gradient in y divided by the gradient in x. And so that would be the arc tangent of minus 0.1 over 0.059, which is minus 59 degrees. And that is of course measured from the x-axis here, so that is measured from this direction here like this. And so that's minus of 59, and it's the same as if we went all the way around and we would get 301 for alpha if we're looking at the math angle. Now we can look and get an idea about gradients in other places really quickly. So let's just take this point in central Oregon. So now x is going like this over here, and so we see that the gradient in the east-west direction, or x direction, is, there's a, to go to another contour you have to go very, very far. And so that would be 8 degrees, and so it's so far that really the gradient is essentially 0. Whereas if we go in the north-south direction, that is in the wide direction here, we see that there's quite a substantial distance here. And so since this is 8 degrees, just like this is 8 degrees over here, then what that means is the gradient is going to be quite a bit smaller in this direction than it is in Pennsylvania here, where the isotherms are much, much closer together. So we would expect a gradient that's a fourth or a fifth of the gradient that we got for Pennsylvania. And so it'll be very weak. So this, it'll point toward the hotter air, and it'll look something like this.